Logo for College of DuPage Digital Press

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

7 Module 7: Thinking, Reasoning, and Problem-Solving

This module is about how a solid working knowledge of psychological principles can help you to think more effectively, so you can succeed in school and life. You might be inclined to believe that—because you have been thinking for as long as you can remember, because you are able to figure out the solution to many problems, because you feel capable of using logic to argue a point, because you can evaluate whether the things you read and hear make sense—you do not need any special training in thinking. But this, of course, is one of the key barriers to helping people think better. If you do not believe that there is anything wrong, why try to fix it?

The human brain is indeed a remarkable thinking machine, capable of amazing, complex, creative, logical thoughts. Why, then, are we telling you that you need to learn how to think? Mainly because one major lesson from cognitive psychology is that these capabilities of the human brain are relatively infrequently realized. Many psychologists believe that people are essentially “cognitive misers.” It is not that we are lazy, but that we have a tendency to expend the least amount of mental effort necessary. Although you may not realize it, it actually takes a great deal of energy to think. Careful, deliberative reasoning and critical thinking are very difficult. Because we seem to be successful without going to the trouble of using these skills well, it feels unnecessary to develop them. As you shall see, however, there are many pitfalls in the cognitive processes described in this module. When people do not devote extra effort to learning and improving reasoning, problem solving, and critical thinking skills, they make many errors.

As is true for memory, if you develop the cognitive skills presented in this module, you will be more successful in school. It is important that you realize, however, that these skills will help you far beyond school, even more so than a good memory will. Although it is somewhat useful to have a good memory, ten years from now no potential employer will care how many questions you got right on multiple choice exams during college. All of them will, however, recognize whether you are a logical, analytical, critical thinker. With these thinking skills, you will be an effective, persuasive communicator and an excellent problem solver.

The module begins by describing different kinds of thought and knowledge, especially conceptual knowledge and critical thinking. An understanding of these differences will be valuable as you progress through school and encounter different assignments that require you to tap into different kinds of knowledge. The second section covers deductive and inductive reasoning, which are processes we use to construct and evaluate strong arguments. They are essential skills to have whenever you are trying to persuade someone (including yourself) of some point, or to respond to someone’s efforts to persuade you. The module ends with a section about problem solving. A solid understanding of the key processes involved in problem solving will help you to handle many daily challenges.

7.1. Different kinds of thought

7.2. Reasoning and Judgment

7.3. Problem Solving

READING WITH PURPOSE

Remember and understand.

By reading and studying Module 7, you should be able to remember and describe:

  • Concepts and inferences (7.1)
  • Procedural knowledge (7.1)
  • Metacognition (7.1)
  • Characteristics of critical thinking:  skepticism; identify biases, distortions, omissions, and assumptions; reasoning and problem solving skills  (7.1)
  • Reasoning:  deductive reasoning, deductively valid argument, inductive reasoning, inductively strong argument, availability heuristic, representativeness heuristic  (7.2)
  • Fixation:  functional fixedness, mental set  (7.3)
  • Algorithms, heuristics, and the role of confirmation bias (7.3)
  • Effective problem solving sequence (7.3)

By reading and thinking about how the concepts in Module 6 apply to real life, you should be able to:

  • Identify which type of knowledge a piece of information is (7.1)
  • Recognize examples of deductive and inductive reasoning (7.2)
  • Recognize judgments that have probably been influenced by the availability heuristic (7.2)
  • Recognize examples of problem solving heuristics and algorithms (7.3)

Analyze, Evaluate, and Create

By reading and thinking about Module 6, participating in classroom activities, and completing out-of-class assignments, you should be able to:

  • Use the principles of critical thinking to evaluate information (7.1)
  • Explain whether examples of reasoning arguments are deductively valid or inductively strong (7.2)
  • Outline how you could try to solve a problem from your life using the effective problem solving sequence (7.3)

7.1. Different kinds of thought and knowledge

  • Take a few minutes to write down everything that you know about dogs.
  • Do you believe that:
  • Psychic ability exists?
  • Hypnosis is an altered state of consciousness?
  • Magnet therapy is effective for relieving pain?
  • Aerobic exercise is an effective treatment for depression?
  • UFO’s from outer space have visited earth?

On what do you base your belief or disbelief for the questions above?

Of course, we all know what is meant by the words  think  and  knowledge . You probably also realize that they are not unitary concepts; there are different kinds of thought and knowledge. In this section, let us look at some of these differences. If you are familiar with these different kinds of thought and pay attention to them in your classes, it will help you to focus on the right goals, learn more effectively, and succeed in school. Different assignments and requirements in school call on you to use different kinds of knowledge or thought, so it will be very helpful for you to learn to recognize them (Anderson, et al. 2001).

Factual and conceptual knowledge

Module 5 introduced the idea of declarative memory, which is composed of facts and episodes. If you have ever played a trivia game or watched Jeopardy on TV, you realize that the human brain is able to hold an extraordinary number of facts. Likewise, you realize that each of us has an enormous store of episodes, essentially facts about events that happened in our own lives. It may be difficult to keep that in mind when we are struggling to retrieve one of those facts while taking an exam, however. Part of the problem is that, in contradiction to the advice from Module 5, many students continue to try to memorize course material as a series of unrelated facts (picture a history student simply trying to memorize history as a set of unrelated dates without any coherent story tying them together). Facts in the real world are not random and unorganized, however. It is the way that they are organized that constitutes a second key kind of knowledge, conceptual.

Concepts are nothing more than our mental representations of categories of things in the world. For example, think about dogs. When you do this, you might remember specific facts about dogs, such as they have fur and they bark. You may also recall dogs that you have encountered and picture them in your mind. All of this information (and more) makes up your concept of dog. You can have concepts of simple categories (e.g., triangle), complex categories (e.g., small dogs that sleep all day, eat out of the garbage, and bark at leaves), kinds of people (e.g., psychology professors), events (e.g., birthday parties), and abstract ideas (e.g., justice). Gregory Murphy (2002) refers to concepts as the “glue that holds our mental life together” (p. 1). Very simply, summarizing the world by using concepts is one of the most important cognitive tasks that we do. Our conceptual knowledge  is  our knowledge about the world. Individual concepts are related to each other to form a rich interconnected network of knowledge. For example, think about how the following concepts might be related to each other: dog, pet, play, Frisbee, chew toy, shoe. Or, of more obvious use to you now, how these concepts are related: working memory, long-term memory, declarative memory, procedural memory, and rehearsal? Because our minds have a natural tendency to organize information conceptually, when students try to remember course material as isolated facts, they are working against their strengths.

One last important point about concepts is that they allow you to instantly know a great deal of information about something. For example, if someone hands you a small red object and says, “here is an apple,” they do not have to tell you, “it is something you can eat.” You already know that you can eat it because it is true by virtue of the fact that the object is an apple; this is called drawing an  inference , assuming that something is true on the basis of your previous knowledge (for example, of category membership or of how the world works) or logical reasoning.

Procedural knowledge

Physical skills, such as tying your shoes, doing a cartwheel, and driving a car (or doing all three at the same time, but don’t try this at home) are certainly a kind of knowledge. They are procedural knowledge, the same idea as procedural memory that you saw in Module 5. Mental skills, such as reading, debating, and planning a psychology experiment, are procedural knowledge, as well. In short, procedural knowledge is the knowledge how to do something (Cohen & Eichenbaum, 1993).

Metacognitive knowledge

Floyd used to think that he had a great memory. Now, he has a better memory. Why? Because he finally realized that his memory was not as great as he once thought it was. Because Floyd eventually learned that he often forgets where he put things, he finally developed the habit of putting things in the same place. (Unfortunately, he did not learn this lesson before losing at least 5 watches and a wedding ring.) Because he finally realized that he often forgets to do things, he finally started using the To Do list app on his phone. And so on. Floyd’s insights about the real limitations of his memory have allowed him to remember things that he used to forget.

All of us have knowledge about the way our own minds work. You may know that you have a good memory for people’s names and a poor memory for math formulas. Someone else might realize that they have difficulty remembering to do things, like stopping at the store on the way home. Others still know that they tend to overlook details. This knowledge about our own thinking is actually quite important; it is called metacognitive knowledge, or  metacognition . Like other kinds of thinking skills, it is subject to error. For example, in unpublished research, one of the authors surveyed about 120 General Psychology students on the first day of the term. Among other questions, the students were asked them to predict their grade in the class and report their current Grade Point Average. Two-thirds of the students predicted that their grade in the course would be higher than their GPA. (The reality is that at our college, students tend to earn lower grades in psychology than their overall GPA.) Another example: Students routinely report that they thought they had done well on an exam, only to discover, to their dismay, that they were wrong (more on that important problem in a moment). Both errors reveal a breakdown in metacognition.

The Dunning-Kruger Effect

In general, most college students probably do not study enough. For example, using data from the National Survey of Student Engagement, Fosnacht, McCormack, and Lerma (2018) reported that first-year students at 4-year colleges in the U.S. averaged less than 14 hours per week preparing for classes. The typical suggestion is that you should spend two hours outside of class for every hour in class, or 24 – 30 hours per week for a full-time student. Clearly, students in general are nowhere near that recommended mark. Many observers, including some faculty, believe that this shortfall is a result of students being too busy or lazy. Now, it may be true that many students are too busy, with work and family obligations, for example. Others, are not particularly motivated in school, and therefore might correctly be labeled lazy. A third possible explanation, however, is that some students might not think they need to spend this much time. And this is a matter of metacognition. Consider the scenario that we mentioned above, students thinking they had done well on an exam only to discover that they did not. Justin Kruger and David Dunning examined scenarios very much like this in 1999. Kruger and Dunning gave research participants tests measuring humor, logic, and grammar. Then, they asked the participants to assess their own abilities and test performance in these areas. They found that participants in general tended to overestimate their abilities, already a problem with metacognition. Importantly, the participants who scored the lowest overestimated their abilities the most. Specifically, students who scored in the bottom quarter (averaging in the 12th percentile) thought they had scored in the 62nd percentile. This has become known as the  Dunning-Kruger effect . Many individual faculty members have replicated these results with their own student on their course exams, including the authors of this book. Think about it. Some students who just took an exam and performed poorly believe that they did well before seeing their score. It seems very likely that these are the very same students who stopped studying the night before because they thought they were “done.” Quite simply, it is not just that they did not know the material. They did not know that they did not know the material. That is poor metacognition.

In order to develop good metacognitive skills, you should continually monitor your thinking and seek frequent feedback on the accuracy of your thinking (Medina, Castleberry, & Persky 2017). For example, in classes get in the habit of predicting your exam grades. As soon as possible after taking an exam, try to find out which questions you missed and try to figure out why. If you do this soon enough, you may be able to recall the way it felt when you originally answered the question. Did you feel confident that you had answered the question correctly? Then you have just discovered an opportunity to improve your metacognition. Be on the lookout for that feeling and respond with caution.

concept :  a mental representation of a category of things in the world

Dunning-Kruger effect : individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

inference : an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

metacognition :  knowledge about one’s own cognitive processes; thinking about your thinking

Critical thinking

One particular kind of knowledge or thinking skill that is related to metacognition is  critical thinking (Chew, 2020). You may have noticed that critical thinking is an objective in many college courses, and thus it could be a legitimate topic to cover in nearly any college course. It is particularly appropriate in psychology, however. As the science of (behavior and) mental processes, psychology is obviously well suited to be the discipline through which you should be introduced to this important way of thinking.

More importantly, there is a particular need to use critical thinking in psychology. We are all, in a way, experts in human behavior and mental processes, having engaged in them literally since birth. Thus, perhaps more than in any other class, students typically approach psychology with very clear ideas and opinions about its subject matter. That is, students already “know” a lot about psychology. The problem is, “it ain’t so much the things we don’t know that get us into trouble. It’s the things we know that just ain’t so” (Ward, quoted in Gilovich 1991). Indeed, many of students’ preconceptions about psychology are just plain wrong. Randolph Smith (2002) wrote a book about critical thinking in psychology called  Challenging Your Preconceptions,  highlighting this fact. On the other hand, many of students’ preconceptions about psychology are just plain right! But wait, how do you know which of your preconceptions are right and which are wrong? And when you come across a research finding or theory in this class that contradicts your preconceptions, what will you do? Will you stick to your original idea, discounting the information from the class? Will you immediately change your mind? Critical thinking can help us sort through this confusing mess.

But what is critical thinking? The goal of critical thinking is simple to state (but extraordinarily difficult to achieve): it is to be right, to draw the correct conclusions, to believe in things that are true and to disbelieve things that are false. We will provide two definitions of critical thinking (or, if you like, one large definition with two distinct parts). First, a more conceptual one: Critical thinking is thinking like a scientist in your everyday life (Schmaltz, Jansen, & Wenckowski, 2017).  Our second definition is more operational; it is simply a list of skills that are essential to be a critical thinker. Critical thinking entails solid reasoning and problem solving skills; skepticism; and an ability to identify biases, distortions, omissions, and assumptions. Excellent deductive and inductive reasoning, and problem solving skills contribute to critical thinking. So, you can consider the subject matter of sections 7.2 and 7.3 to be part of critical thinking. Because we will be devoting considerable time to these concepts in the rest of the module, let us begin with a discussion about the other aspects of critical thinking.

Let’s address that first part of the definition. Scientists form hypotheses, or predictions about some possible future observations. Then, they collect data, or information (think of this as making those future observations). They do their best to make unbiased observations using reliable techniques that have been verified by others. Then, and only then, they draw a conclusion about what those observations mean. Oh, and do not forget the most important part. “Conclusion” is probably not the most appropriate word because this conclusion is only tentative. A scientist is always prepared that someone else might come along and produce new observations that would require a new conclusion be drawn. Wow! If you like to be right, you could do a lot worse than using a process like this.

A Critical Thinker’s Toolkit 

Now for the second part of the definition. Good critical thinkers (and scientists) rely on a variety of tools to evaluate information. Perhaps the most recognizable tool for critical thinking is  skepticism (and this term provides the clearest link to the thinking like a scientist definition, as you are about to see). Some people intend it as an insult when they call someone a skeptic. But if someone calls you a skeptic, if they are using the term correctly, you should consider it a great compliment. Simply put, skepticism is a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided. People from Missouri should recognize this principle, as Missouri is known as the Show-Me State. As a skeptic, you are not inclined to believe something just because someone said so, because someone else believes it, or because it sounds reasonable. You must be persuaded by high quality evidence.

Of course, if that evidence is produced, you have a responsibility as a skeptic to change your belief. Failure to change a belief in the face of good evidence is not skepticism; skepticism has open mindedness at its core. M. Neil Browne and Stuart Keeley (2018) use the term weak sense critical thinking to describe critical thinking behaviors that are used only to strengthen a prior belief. Strong sense critical thinking, on the other hand, has as its goal reaching the best conclusion. Sometimes that means strengthening your prior belief, but sometimes it means changing your belief to accommodate the better evidence.

Many times, a failure to think critically or weak sense critical thinking is related to a  bias , an inclination, tendency, leaning, or prejudice. Everybody has biases, but many people are unaware of them. Awareness of your own biases gives you the opportunity to control or counteract them. Unfortunately, however, many people are happy to let their biases creep into their attempts to persuade others; indeed, it is a key part of their persuasive strategy. To see how these biases influence messages, just look at the different descriptions and explanations of the same events given by people of different ages or income brackets, or conservative versus liberal commentators, or by commentators from different parts of the world. Of course, to be successful, these people who are consciously using their biases must disguise them. Even undisguised biases can be difficult to identify, so disguised ones can be nearly impossible.

Here are some common sources of biases:

  • Personal values and beliefs.  Some people believe that human beings are basically driven to seek power and that they are typically in competition with one another over scarce resources. These beliefs are similar to the world-view that political scientists call “realism.” Other people believe that human beings prefer to cooperate and that, given the chance, they will do so. These beliefs are similar to the world-view known as “idealism.” For many people, these deeply held beliefs can influence, or bias, their interpretations of such wide ranging situations as the behavior of nations and their leaders or the behavior of the driver in the car ahead of you. For example, if your worldview is that people are typically in competition and someone cuts you off on the highway, you may assume that the driver did it purposely to get ahead of you. Other types of beliefs about the way the world is or the way the world should be, for example, political beliefs, can similarly become a significant source of bias.
  • Racism, sexism, ageism and other forms of prejudice and bigotry.  These are, sadly, a common source of bias in many people. They are essentially a special kind of “belief about the way the world is.” These beliefs—for example, that women do not make effective leaders—lead people to ignore contradictory evidence (examples of effective women leaders, or research that disputes the belief) and to interpret ambiguous evidence in a way consistent with the belief.
  • Self-interest.  When particular people benefit from things turning out a certain way, they can sometimes be very susceptible to letting that interest bias them. For example, a company that will earn a profit if they sell their product may have a bias in the way that they give information about their product. A union that will benefit if its members get a generous contract might have a bias in the way it presents information about salaries at competing organizations. (Note that our inclusion of examples describing both companies and unions is an explicit attempt to control for our own personal biases). Home buyers are often dismayed to discover that they purchased their dream house from someone whose self-interest led them to lie about flooding problems in the basement or back yard. This principle, the biasing power of self-interest, is likely what led to the famous phrase  Caveat Emptor  (let the buyer beware) .  

Knowing that these types of biases exist will help you evaluate evidence more critically. Do not forget, though, that people are not always keen to let you discover the sources of biases in their arguments. For example, companies or political organizations can sometimes disguise their support of a research study by contracting with a university professor, who comes complete with a seemingly unbiased institutional affiliation, to conduct the study.

People’s biases, conscious or unconscious, can lead them to make omissions, distortions, and assumptions that undermine our ability to correctly evaluate evidence. It is essential that you look for these elements. Always ask, what is missing, what is not as it appears, and what is being assumed here? For example, consider this (fictional) chart from an ad reporting customer satisfaction at 4 local health clubs.

what is problem solving why does it is always associated with the word reasoning

Clearly, from the results of the chart, one would be tempted to give Club C a try, as customer satisfaction is much higher than for the other 3 clubs.

There are so many distortions and omissions in this chart, however, that it is actually quite meaningless. First, how was satisfaction measured? Do the bars represent responses to a survey? If so, how were the questions asked? Most importantly, where is the missing scale for the chart? Although the differences look quite large, are they really?

Well, here is the same chart, with a different scale, this time labeled:

what is problem solving why does it is always associated with the word reasoning

Club C is not so impressive any more, is it? In fact, all of the health clubs have customer satisfaction ratings (whatever that means) between 85% and 88%. In the first chart, the entire scale of the graph included only the percentages between 83 and 89. This “judicious” choice of scale—some would call it a distortion—and omission of that scale from the chart make the tiny differences among the clubs seem important, however.

Also, in order to be a critical thinker, you need to learn to pay attention to the assumptions that underlie a message. Let us briefly illustrate the role of assumptions by touching on some people’s beliefs about the criminal justice system in the US. Some believe that a major problem with our judicial system is that many criminals go free because of legal technicalities. Others believe that a major problem is that many innocent people are convicted of crimes. The simple fact is, both types of errors occur. A person’s conclusion about which flaw in our judicial system is the greater tragedy is based on an assumption about which of these is the more serious error (letting the guilty go free or convicting the innocent). This type of assumption is called a value assumption (Browne and Keeley, 2018). It reflects the differences in values that people develop, differences that may lead us to disregard valid evidence that does not fit in with our particular values.

Oh, by the way, some students probably noticed this, but the seven tips for evaluating information that we shared in Module 1 are related to this. Actually, they are part of this section. The tips are, to a very large degree, set of ideas you can use to help you identify biases, distortions, omissions, and assumptions. If you do not remember this section, we strongly recommend you take a few minutes to review it.

skepticism :  a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

bias : an inclination, tendency, leaning, or prejudice

  • Which of your beliefs (or disbeliefs) from the Activate exercise for this section were derived from a process of critical thinking? If some of your beliefs were not based on critical thinking, are you willing to reassess these beliefs? If the answer is no, why do you think that is? If the answer is yes, what concrete steps will you take?

7.2 Reasoning and Judgment

  • What percentage of kidnappings are committed by strangers?
  • Which area of the house is riskiest: kitchen, bathroom, or stairs?
  • What is the most common cancer in the US?
  • What percentage of workplace homicides are committed by co-workers?

An essential set of procedural thinking skills is  reasoning , the ability to generate and evaluate solid conclusions from a set of statements or evidence. You should note that these conclusions (when they are generated instead of being evaluated) are one key type of inference that we described in Section 7.1. There are two main types of reasoning, deductive and inductive.

Deductive reasoning

Suppose your teacher tells you that if you get an A on the final exam in a course, you will get an A for the whole course. Then, you get an A on the final exam. What will your final course grade be? Most people can see instantly that you can conclude with certainty that you will get an A for the course. This is a type of reasoning called  deductive reasoning , which is defined as reasoning in which a conclusion is guaranteed to be true as long as the statements leading to it are true. The three statements can be listed as an  argument , with two beginning statements and a conclusion:

Statement 1: If you get an A on the final exam, you will get an A for the course

Statement 2: You get an A on the final exam

Conclusion: You will get an A for the course

This particular arrangement, in which true beginning statements lead to a guaranteed true conclusion, is known as a  deductively valid argument . Although deductive reasoning is often the subject of abstract, brain-teasing, puzzle-like word problems, it is actually an extremely important type of everyday reasoning. It is just hard to recognize sometimes. For example, imagine that you are looking for your car keys and you realize that they are either in the kitchen drawer or in your book bag. After looking in the kitchen drawer, you instantly know that they must be in your book bag. That conclusion results from a simple deductive reasoning argument. In addition, solid deductive reasoning skills are necessary for you to succeed in the sciences, philosophy, math, computer programming, and any endeavor involving the use of logic to persuade others to your point of view or to evaluate others’ arguments.

Cognitive psychologists, and before them philosophers, have been quite interested in deductive reasoning, not so much for its practical applications, but for the insights it can offer them about the ways that human beings think. One of the early ideas to emerge from the examination of deductive reasoning is that people learn (or develop) mental versions of rules that allow them to solve these types of reasoning problems (Braine, 1978; Braine, Reiser, & Rumain, 1984). The best way to see this point of view is to realize that there are different possible rules, and some of them are very simple. For example, consider this rule of logic:

therefore q

Logical rules are often presented abstractly, as letters, in order to imply that they can be used in very many specific situations. Here is a concrete version of the of the same rule:

I’ll either have pizza or a hamburger for dinner tonight (p or q)

I won’t have pizza (not p)

Therefore, I’ll have a hamburger (therefore q)

This kind of reasoning seems so natural, so easy, that it is quite plausible that we would use a version of this rule in our daily lives. At least, it seems more plausible than some of the alternative possibilities—for example, that we need to have experience with the specific situation (pizza or hamburger, in this case) in order to solve this type of problem easily. So perhaps there is a form of natural logic (Rips, 1990) that contains very simple versions of logical rules. When we are faced with a reasoning problem that maps onto one of these rules, we use the rule.

But be very careful; things are not always as easy as they seem. Even these simple rules are not so simple. For example, consider the following rule. Many people fail to realize that this rule is just as valid as the pizza or hamburger rule above.

if p, then q

therefore, not p

Concrete version:

If I eat dinner, then I will have dessert

I did not have dessert

Therefore, I did not eat dinner

The simple fact is, it can be very difficult for people to apply rules of deductive logic correctly; as a result, they make many errors when trying to do so. Is this a deductively valid argument or not?

Students who like school study a lot

Students who study a lot get good grades

Jane does not like school

Therefore, Jane does not get good grades

Many people are surprised to discover that this is not a logically valid argument; the conclusion is not guaranteed to be true from the beginning statements. Although the first statement says that students who like school study a lot, it does NOT say that students who do not like school do not study a lot. In other words, it may very well be possible to study a lot without liking school. Even people who sometimes get problems like this right might not be using the rules of deductive reasoning. Instead, they might just be making judgments for examples they know, in this case, remembering instances of people who get good grades despite not liking school.

Making deductive reasoning even more difficult is the fact that there are two important properties that an argument may have. One, it can be valid or invalid (meaning that the conclusion does or does not follow logically from the statements leading up to it). Two, an argument (or more correctly, its conclusion) can be true or false. Here is an example of an argument that is logically valid, but has a false conclusion (at least we think it is false).

Either you are eleven feet tall or the Grand Canyon was created by a spaceship crashing into the earth.

You are not eleven feet tall

Therefore the Grand Canyon was created by a spaceship crashing into the earth

This argument has the exact same form as the pizza or hamburger argument above, making it is deductively valid. The conclusion is so false, however, that it is absurd (of course, the reason the conclusion is false is that the first statement is false). When people are judging arguments, they tend to not observe the difference between deductive validity and the empirical truth of statements or conclusions. If the elements of an argument happen to be true, people are likely to judge the argument logically valid; if the elements are false, they will very likely judge it invalid (Markovits & Bouffard-Bouchard, 1992; Moshman & Franks, 1986). Thus, it seems a stretch to say that people are using these logical rules to judge the validity of arguments. Many psychologists believe that most people actually have very limited deductive reasoning skills (Johnson-Laird, 1999). They argue that when faced with a problem for which deductive logic is required, people resort to some simpler technique, such as matching terms that appear in the statements and the conclusion (Evans, 1982). This might not seem like a problem, but what if reasoners believe that the elements are true and they happen to be wrong; they will would believe that they are using a form of reasoning that guarantees they are correct and yet be wrong.

deductive reasoning :  a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

argument :  a set of statements in which the beginning statements lead to a conclusion

deductively valid argument :  an argument for which true beginning statements guarantee that the conclusion is true

Inductive reasoning and judgment

Every day, you make many judgments about the likelihood of one thing or another. Whether you realize it or not, you are practicing  inductive reasoning   on a daily basis. In inductive reasoning arguments, a conclusion is likely whenever the statements preceding it are true. The first thing to notice about inductive reasoning is that, by definition, you can never be sure about your conclusion; you can only estimate how likely the conclusion is. Inductive reasoning may lead you to focus on Memory Encoding and Recoding when you study for the exam, but it is possible the instructor will ask more questions about Memory Retrieval instead. Unlike deductive reasoning, the conclusions you reach through inductive reasoning are only probable, not certain. That is why scientists consider inductive reasoning weaker than deductive reasoning. But imagine how hard it would be for us to function if we could not act unless we were certain about the outcome.

Inductive reasoning can be represented as logical arguments consisting of statements and a conclusion, just as deductive reasoning can be. In an inductive argument, you are given some statements and a conclusion (or you are given some statements and must draw a conclusion). An argument is  inductively strong   if the conclusion would be very probable whenever the statements are true. So, for example, here is an inductively strong argument:

  • Statement #1: The forecaster on Channel 2 said it is going to rain today.
  • Statement #2: The forecaster on Channel 5 said it is going to rain today.
  • Statement #3: It is very cloudy and humid.
  • Statement #4: You just heard thunder.
  • Conclusion (or judgment): It is going to rain today.

Think of the statements as evidence, on the basis of which you will draw a conclusion. So, based on the evidence presented in the four statements, it is very likely that it will rain today. Will it definitely rain today? Certainly not. We can all think of times that the weather forecaster was wrong.

A true story: Some years ago psychology student was watching a baseball playoff game between the St. Louis Cardinals and the Los Angeles Dodgers. A graphic on the screen had just informed the audience that the Cardinal at bat, (Hall of Fame shortstop) Ozzie Smith, a switch hitter batting left-handed for this plate appearance, had never, in nearly 3000 career at-bats, hit a home run left-handed. The student, who had just learned about inductive reasoning in his psychology class, turned to his companion (a Cardinals fan) and smugly said, “It is an inductively strong argument that Ozzie Smith will not hit a home run.” He turned back to face the television just in time to watch the ball sail over the right field fence for a home run. Although the student felt foolish at the time, he was not wrong. It was an inductively strong argument; 3000 at-bats is an awful lot of evidence suggesting that the Wizard of Ozz (as he was known) would not be hitting one out of the park (think of each at-bat without a home run as a statement in an inductive argument). Sadly (for the die-hard Cubs fan and Cardinals-hating student), despite the strength of the argument, the conclusion was wrong.

Given the possibility that we might draw an incorrect conclusion even with an inductively strong argument, we really want to be sure that we do, in fact, make inductively strong arguments. If we judge something probable, it had better be probable. If we judge something nearly impossible, it had better not happen. Think of inductive reasoning, then, as making reasonably accurate judgments of the probability of some conclusion given a set of evidence.

We base many decisions in our lives on inductive reasoning. For example:

Statement #1: Psychology is not my best subject

Statement #2: My psychology instructor has a reputation for giving difficult exams

Statement #3: My first psychology exam was much harder than I expected

Judgment: The next exam will probably be very difficult.

Decision: I will study tonight instead of watching Netflix.

Some other examples of judgments that people commonly make in a school context include judgments of the likelihood that:

  • A particular class will be interesting/useful/difficult
  • You will be able to finish writing a paper by next week if you go out tonight
  • Your laptop’s battery will last through the next trip to the library
  • You will not miss anything important if you skip class tomorrow
  • Your instructor will not notice if you skip class tomorrow
  • You will be able to find a book that you will need for a paper
  • There will be an essay question about Memory Encoding on the next exam

Tversky and Kahneman (1983) recognized that there are two general ways that we might make these judgments; they termed them extensional (i.e., following the laws of probability) and intuitive (i.e., using shortcuts or heuristics, see below). We will use a similar distinction between Type 1 and Type 2 thinking, as described by Keith Stanovich and his colleagues (Evans and Stanovich, 2013; Stanovich and West, 2000). Type 1 thinking is fast, automatic, effortful, and emotional. In fact, it is hardly fair to call it reasoning at all, as judgments just seem to pop into one’s head. Type 2 thinking , on the other hand, is slow, effortful, and logical. So obviously, it is more likely to lead to a correct judgment, or an optimal decision. The problem is, we tend to over-rely on Type 1. Now, we are not saying that Type 2 is the right way to go for every decision or judgment we make. It seems a bit much, for example, to engage in a step-by-step logical reasoning procedure to decide whether we will have chicken or fish for dinner tonight.

Many bad decisions in some very important contexts, however, can be traced back to poor judgments of the likelihood of certain risks or outcomes that result from the use of Type 1 when a more logical reasoning process would have been more appropriate. For example:

Statement #1: It is late at night.

Statement #2: Albert has been drinking beer for the past five hours at a party.

Statement #3: Albert is not exactly sure where he is or how far away home is.

Judgment: Albert will have no difficulty walking home.

Decision: He walks home alone.

As you can see in this example, the three statements backing up the judgment do not really support it. In other words, this argument is not inductively strong because it is based on judgments that ignore the laws of probability. What are the chances that someone facing these conditions will be able to walk home alone easily? And one need not be drunk to make poor decisions based on judgments that just pop into our heads.

The truth is that many of our probability judgments do not come very close to what the laws of probability say they should be. Think about it. In order for us to reason in accordance with these laws, we would need to know the laws of probability, which would allow us to calculate the relationship between particular pieces of evidence and the probability of some outcome (i.e., how much likelihood should change given a piece of evidence), and we would have to do these heavy math calculations in our heads. After all, that is what Type 2 requires. Needless to say, even if we were motivated, we often do not even know how to apply Type 2 reasoning in many cases.

So what do we do when we don’t have the knowledge, skills, or time required to make the correct mathematical judgment? Do we hold off and wait until we can get better evidence? Do we read up on probability and fire up our calculator app so we can compute the correct probability? Of course not. We rely on Type 1 thinking. We “wing it.” That is, we come up with a likelihood estimate using some means at our disposal. Psychologists use the term heuristic to describe the type of “winging it” we are talking about. A  heuristic   is a shortcut strategy that we use to make some judgment or solve some problem (see Section 7.3). Heuristics are easy and quick, think of them as the basic procedures that are characteristic of Type 1.  They can absolutely lead to reasonably good judgments and decisions in some situations (like choosing between chicken and fish for dinner). They are, however, far from foolproof. There are, in fact, quite a lot of situations in which heuristics can lead us to make incorrect judgments, and in many cases the decisions based on those judgments can have serious consequences.

Let us return to the activity that begins this section. You were asked to judge the likelihood (or frequency) of certain events and risks. You were free to come up with your own evidence (or statements) to make these judgments. This is where a heuristic crops up. As a judgment shortcut, we tend to generate specific examples of those very events to help us decide their likelihood or frequency. For example, if we are asked to judge how common, frequent, or likely a particular type of cancer is, many of our statements would be examples of specific cancer cases:

Statement #1: Andy Kaufman (comedian) had lung cancer.

Statement #2: Colin Powell (US Secretary of State) had prostate cancer.

Statement #3: Bob Marley (musician) had skin and brain cancer

Statement #4: Sandra Day O’Connor (Supreme Court Justice) had breast cancer.

Statement #5: Fred Rogers (children’s entertainer) had stomach cancer.

Statement #6: Robin Roberts (news anchor) had breast cancer.

Statement #7: Bette Davis (actress) had breast cancer.

Judgment: Breast cancer is the most common type.

Your own experience or memory may also tell you that breast cancer is the most common type. But it is not (although it is common). Actually, skin cancer is the most common type in the US. We make the same types of misjudgments all the time because we do not generate the examples or evidence according to their actual frequencies or probabilities. Instead, we have a tendency (or bias) to search for the examples in memory; if they are easy to retrieve, we assume that they are common. To rephrase this in the language of the heuristic, events seem more likely to the extent that they are available to memory. This bias has been termed the  availability heuristic   (Kahneman and Tversky, 1974).

The fact that we use the availability heuristic does not automatically mean that our judgment is wrong. The reason we use heuristics in the first place is that they work fairly well in many cases (and, of course that they are easy to use). So, the easiest examples to think of sometimes are the most common ones. Is it more likely that a member of the U.S. Senate is a man or a woman? Most people have a much easier time generating examples of male senators. And as it turns out, the U.S. Senate has many more men than women (74 to 26 in 2020). In this case, then, the availability heuristic would lead you to make the correct judgment; it is far more likely that a senator would be a man.

In many other cases, however, the availability heuristic will lead us astray. This is because events can be memorable for many reasons other than their frequency. Section 5.2, Encoding Meaning, suggested that one good way to encode the meaning of some information is to form a mental image of it. Thus, information that has been pictured mentally will be more available to memory. Indeed, an event that is vivid and easily pictured will trick many people into supposing that type of event is more common than it actually is. Repetition of information will also make it more memorable. So, if the same event is described to you in a magazine, on the evening news, on a podcast that you listen to, and in your Facebook feed; it will be very available to memory. Again, the availability heuristic will cause you to misperceive the frequency of these types of events.

Most interestingly, information that is unusual is more memorable. Suppose we give you the following list of words to remember: box, flower, letter, platypus, oven, boat, newspaper, purse, drum, car. Very likely, the easiest word to remember would be platypus, the unusual one. The same thing occurs with memories of events. An event may be available to memory because it is unusual, yet the availability heuristic leads us to judge that the event is common. Did you catch that? In these cases, the availability heuristic makes us think the exact opposite of the true frequency. We end up thinking something is common because it is unusual (and therefore memorable). Yikes.

The misapplication of the availability heuristic sometimes has unfortunate results. For example, if you went to K-12 school in the US over the past 10 years, it is extremely likely that you have participated in lockdown and active shooter drills. Of course, everyone is trying to prevent the tragedy of another school shooting. And believe us, we are not trying to minimize how terrible the tragedy is. But the truth of the matter is, school shootings are extremely rare. Because the federal government does not keep a database of school shootings, the Washington Post has maintained their own running tally. Between 1999 and January 2020 (the date of the most recent school shooting with a death in the US at of the time this paragraph was written), the Post reported a total of 254 people died in school shootings in the US. Not 254 per year, 254 total. That is an average of 12 per year. Of course, that is 254 people who should not have died (particularly because many were children), but in a country with approximately 60,000,000 students and teachers, this is a very small risk.

But many students and teachers are terrified that they will be victims of school shootings because of the availability heuristic. It is so easy to think of examples (they are very available to memory) that people believe the event is very common. It is not. And there is a downside to this. We happen to believe that there is an enormous gun violence problem in the United States. According the the Centers for Disease Control and Prevention, there were 39,773 firearm deaths in the US in 2017. Fifteen of those deaths were in school shootings, according to the Post. 60% of those deaths were suicides. When people pay attention to the school shooting risk (low), they often fail to notice the much larger risk.

And examples like this are by no means unique. The authors of this book have been teaching psychology since the 1990’s. We have been able to make the exact same arguments about the misapplication of the availability heuristics and keep them current by simply swapping out for the “fear of the day.” In the 1990’s it was children being kidnapped by strangers (it was known as “stranger danger”) despite the facts that kidnappings accounted for only 2% of the violent crimes committed against children, and only 24% of kidnappings are committed by strangers (US Department of Justice, 2007). This fear overlapped with the fear of terrorism that gripped the country after the 2001 terrorist attacks on the World Trade Center and US Pentagon and still plagues the population of the US somewhat in 2020. After a well-publicized, sensational act of violence, people are extremely likely to increase their estimates of the chances that they, too, will be victims of terror. Think about the reality, however. In October of 2001, a terrorist mailed anthrax spores to members of the US government and a number of media companies. A total of five people died as a result of this attack. The nation was nearly paralyzed by the fear of dying from the attack; in reality the probability of an individual person dying was 0.00000002.

The availability heuristic can lead you to make incorrect judgments in a school setting as well. For example, suppose you are trying to decide if you should take a class from a particular math professor. You might try to make a judgment of how good a teacher she is by recalling instances of friends and acquaintances making comments about her teaching skill. You may have some examples that suggest that she is a poor teacher very available to memory, so on the basis of the availability heuristic you judge her a poor teacher and decide to take the class from someone else. What if, however, the instances you recalled were all from the same person, and this person happens to be a very colorful storyteller? The subsequent ease of remembering the instances might not indicate that the professor is a poor teacher after all.

Although the availability heuristic is obviously important, it is not the only judgment heuristic we use. Amos Tversky and Daniel Kahneman examined the role of heuristics in inductive reasoning in a long series of studies. Kahneman received a Nobel Prize in Economics for this research in 2002, and Tversky would have certainly received one as well if he had not died of melanoma at age 59 in 1996 (Nobel Prizes are not awarded posthumously). Kahneman and Tversky demonstrated repeatedly that people do not reason in ways that are consistent with the laws of probability. They identified several heuristic strategies that people use instead to make judgments about likelihood. The importance of this work for economics (and the reason that Kahneman was awarded the Nobel Prize) is that earlier economic theories had assumed that people do make judgments rationally, that is, in agreement with the laws of probability.

Another common heuristic that people use for making judgments is the  representativeness heuristic (Kahneman & Tversky 1973). Suppose we describe a person to you. He is quiet and shy, has an unassuming personality, and likes to work with numbers. Is this person more likely to be an accountant or an attorney? If you said accountant, you were probably using the representativeness heuristic. Our imaginary person is judged likely to be an accountant because he resembles, or is representative of the concept of, an accountant. When research participants are asked to make judgments such as these, the only thing that seems to matter is the representativeness of the description. For example, if told that the person described is in a room that contains 70 attorneys and 30 accountants, participants will still assume that he is an accountant.

inductive reasoning :  a type of reasoning in which we make judgments about likelihood from sets of evidence

inductively strong argument :  an inductive argument in which the beginning statements lead to a conclusion that is probably true

heuristic :  a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

availability heuristic :  judging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

representativeness heuristic:   judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

Type 1 thinking : fast, automatic, and emotional thinking.

Type 2 thinking : slow, effortful, and logical thinking.

  • What percentage of workplace homicides are co-worker violence?

Many people get these questions wrong. The answers are 10%; stairs; skin; 6%. How close were your answers? Explain how the availability heuristic might have led you to make the incorrect judgments.

  • Can you think of some other judgments that you have made (or beliefs that you have) that might have been influenced by the availability heuristic?

7.3 Problem Solving

  • Please take a few minutes to list a number of problems that you are facing right now.
  • Now write about a problem that you recently solved.
  • What is your definition of a problem?

Mary has a problem. Her daughter, ordinarily quite eager to please, appears to delight in being the last person to do anything. Whether getting ready for school, going to piano lessons or karate class, or even going out with her friends, she seems unwilling or unable to get ready on time. Other people have different kinds of problems. For example, many students work at jobs, have numerous family commitments, and are facing a course schedule full of difficult exams, assignments, papers, and speeches. How can they find enough time to devote to their studies and still fulfill their other obligations? Speaking of students and their problems: Show that a ball thrown vertically upward with initial velocity v0 takes twice as much time to return as to reach the highest point (from Spiegel, 1981).

These are three very different situations, but we have called them all problems. What makes them all the same, despite the differences? A psychologist might define a  problem   as a situation with an initial state, a goal state, and a set of possible intermediate states. Somewhat more meaningfully, we might consider a problem a situation in which you are in here one state (e.g., daughter is always late), you want to be there in another state (e.g., daughter is not always late), and with no obvious way to get from here to there. Defined this way, each of the three situations we outlined can now be seen as an example of the same general concept, a problem. At this point, you might begin to wonder what is not a problem, given such a general definition. It seems that nearly every non-routine task we engage in could qualify as a problem. As long as you realize that problems are not necessarily bad (it can be quite fun and satisfying to rise to the challenge and solve a problem), this may be a useful way to think about it.

Can we identify a set of problem-solving skills that would apply to these very different kinds of situations? That task, in a nutshell, is a major goal of this section. Let us try to begin to make sense of the wide variety of ways that problems can be solved with an important observation: the process of solving problems can be divided into two key parts. First, people have to notice, comprehend, and represent the problem properly in their minds (called  problem representation ). Second, they have to apply some kind of solution strategy to the problem. Psychologists have studied both of these key parts of the process in detail.

When you first think about the problem-solving process, you might guess that most of our difficulties would occur because we are failing in the second step, the application of strategies. Although this can be a significant difficulty much of the time, the more important source of difficulty is probably problem representation. In short, we often fail to solve a problem because we are looking at it, or thinking about it, the wrong way.

problem :  a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

problem representation :  noticing, comprehending and forming a mental conception of a problem

Defining and Mentally Representing Problems in Order to Solve Them

So, the main obstacle to solving a problem is that we do not clearly understand exactly what the problem is. Recall the problem with Mary’s daughter always being late. One way to represent, or to think about, this problem is that she is being defiant. She refuses to get ready in time. This type of representation or definition suggests a particular type of solution. Another way to think about the problem, however, is to consider the possibility that she is simply being sidetracked by interesting diversions. This different conception of what the problem is (i.e., different representation) suggests a very different solution strategy. For example, if Mary defines the problem as defiance, she may be tempted to solve the problem using some kind of coercive tactics, that is, to assert her authority as her mother and force her to listen. On the other hand, if Mary defines the problem as distraction, she may try to solve it by simply removing the distracting objects.

As you might guess, when a problem is represented one way, the solution may seem very difficult, or even impossible. Seen another way, the solution might be very easy. For example, consider the following problem (from Nasar, 1998):

Two bicyclists start 20 miles apart and head toward each other, each going at a steady rate of 10 miles per hour. At the same time, a fly that travels at a steady 15 miles per hour starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner until he is crushed between the two front wheels. Question: what total distance did the fly cover?

Please take a few minutes to try to solve this problem.

Most people represent this problem as a question about a fly because, well, that is how the question is asked. The solution, using this representation, is to figure out how far the fly travels on the first leg of its journey, then add this total to how far it travels on the second leg of its journey (when it turns around and returns to the first bicycle), then continue to add the smaller distance from each leg of the journey until you converge on the correct answer. You would have to be quite skilled at math to solve this problem, and you would probably need some time and pencil and paper to do it.

If you consider a different representation, however, you can solve this problem in your head. Instead of thinking about it as a question about a fly, think about it as a question about the bicycles. They are 20 miles apart, and each is traveling 10 miles per hour. How long will it take for the bicycles to reach each other? Right, one hour. The fly is traveling 15 miles per hour; therefore, it will travel a total of 15 miles back and forth in the hour before the bicycles meet. Represented one way (as a problem about a fly), the problem is quite difficult. Represented another way (as a problem about two bicycles), it is easy. Changing your representation of a problem is sometimes the best—sometimes the only—way to solve it.

Unfortunately, however, changing a problem’s representation is not the easiest thing in the world to do. Often, problem solvers get stuck looking at a problem one way. This is called  fixation . Most people who represent the preceding problem as a problem about a fly probably do not pause to reconsider, and consequently change, their representation. A parent who thinks her daughter is being defiant is unlikely to consider the possibility that her behavior is far less purposeful.

Problem-solving fixation was examined by a group of German psychologists called Gestalt psychologists during the 1930’s and 1940’s. Karl Dunker, for example, discovered an important type of failure to take a different perspective called  functional fixedness . Imagine being a participant in one of his experiments. You are asked to figure out how to mount two candles on a door and are given an assortment of odds and ends, including a small empty cardboard box and some thumbtacks. Perhaps you have already figured out a solution: tack the box to the door so it forms a platform, then put the candles on top of the box. Most people are able to arrive at this solution. Imagine a slight variation of the procedure, however. What if, instead of being empty, the box had matches in it? Most people given this version of the problem do not arrive at the solution given above. Why? Because it seems to people that when the box contains matches, it already has a function; it is a matchbox. People are unlikely to consider a new function for an object that already has a function. This is functional fixedness.

Mental set is a type of fixation in which the problem solver gets stuck using the same solution strategy that has been successful in the past, even though the solution may no longer be useful. It is commonly seen when students do math problems for homework. Often, several problems in a row require the reapplication of the same solution strategy. Then, without warning, the next problem in the set requires a new strategy. Many students attempt to apply the formerly successful strategy on the new problem and therefore cannot come up with a correct answer.

The thing to remember is that you cannot solve a problem unless you correctly identify what it is to begin with (initial state) and what you want the end result to be (goal state). That may mean looking at the problem from a different angle and representing it in a new way. The correct representation does not guarantee a successful solution, but it certainly puts you on the right track.

A bit more optimistically, the Gestalt psychologists discovered what may be considered the opposite of fixation, namely  insight . Sometimes the solution to a problem just seems to pop into your head. Wolfgang Kohler examined insight by posing many different problems to chimpanzees, principally problems pertaining to their acquisition of out-of-reach food. In one version, a banana was placed outside of a chimpanzee’s cage and a short stick inside the cage. The stick was too short to retrieve the banana, but was long enough to retrieve a longer stick also located outside of the cage. This second stick was long enough to retrieve the banana. After trying, and failing, to reach the banana with the shorter stick, the chimpanzee would try a couple of random-seeming attempts, react with some apparent frustration or anger, then suddenly rush to the longer stick, the correct solution fully realized at this point. This sudden appearance of the solution, observed many times with many different problems, was termed insight by Kohler.

Lest you think it pertains to chimpanzees only, Karl Dunker demonstrated that children also solve problems through insight in the 1930s. More importantly, you have probably experienced insight yourself. Think back to a time when you were trying to solve a difficult problem. After struggling for a while, you gave up. Hours later, the solution just popped into your head, perhaps when you were taking a walk, eating dinner, or lying in bed.

fixation :  when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

functional fixedness :  a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

mental set :  a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

insight :  a sudden realization of a solution to a problem

Solving Problems by Trial and Error

Correctly identifying the problem and your goal for a solution is a good start, but recall the psychologist’s definition of a problem: it includes a set of possible intermediate states. Viewed this way, a problem can be solved satisfactorily only if one can find a path through some of these intermediate states to the goal. Imagine a fairly routine problem, finding a new route to school when your ordinary route is blocked (by road construction, for example). At each intersection, you may turn left, turn right, or go straight. A satisfactory solution to the problem (of getting to school) is a sequence of selections at each intersection that allows you to wind up at school.

If you had all the time in the world to get to school, you might try choosing intermediate states randomly. At one corner you turn left, the next you go straight, then you go left again, then right, then right, then straight. Unfortunately, trial and error will not necessarily get you where you want to go, and even if it does, it is not the fastest way to get there. For example, when a friend of ours was in college, he got lost on the way to a concert and attempted to find the venue by choosing streets to turn onto randomly (this was long before the use of GPS). Amazingly enough, the strategy worked, although he did end up missing two out of the three bands who played that night.

Trial and error is not all bad, however. B.F. Skinner, a prominent behaviorist psychologist, suggested that people often behave randomly in order to see what effect the behavior has on the environment and what subsequent effect this environmental change has on them. This seems particularly true for the very young person. Picture a child filling a household’s fish tank with toilet paper, for example. To a child trying to develop a repertoire of creative problem-solving strategies, an odd and random behavior might be just the ticket. Eventually, the exasperated parent hopes, the child will discover that many of these random behaviors do not successfully solve problems; in fact, in many cases they create problems. Thus, one would expect a decrease in this random behavior as a child matures. You should realize, however, that the opposite extreme is equally counterproductive. If the children become too rigid, never trying something unexpected and new, their problem solving skills can become too limited.

Effective problem solving seems to call for a happy medium that strikes a balance between using well-founded old strategies and trying new ground and territory. The individual who recognizes a situation in which an old problem-solving strategy would work best, and who can also recognize a situation in which a new untested strategy is necessary is halfway to success.

Solving Problems with Algorithms and Heuristics

For many problems there is a possible strategy available that will guarantee a correct solution. For example, think about math problems. Math lessons often consist of step-by-step procedures that can be used to solve the problems. If you apply the strategy without error, you are guaranteed to arrive at the correct solution to the problem. This approach is called using an  algorithm , a term that denotes the step-by-step procedure that guarantees a correct solution. Because algorithms are sometimes available and come with a guarantee, you might think that most people use them frequently. Unfortunately, however, they do not. As the experience of many students who have struggled through math classes can attest, algorithms can be extremely difficult to use, even when the problem solver knows which algorithm is supposed to work in solving the problem. In problems outside of math class, we often do not even know if an algorithm is available. It is probably fair to say, then, that algorithms are rarely used when people try to solve problems.

Because algorithms are so difficult to use, people often pass up the opportunity to guarantee a correct solution in favor of a strategy that is much easier to use and yields a reasonable chance of coming up with a correct solution. These strategies are called  problem solving heuristics . Similar to what you saw in section 6.2 with reasoning heuristics, a problem solving heuristic is a shortcut strategy that people use when trying to solve problems. It usually works pretty well, but does not guarantee a correct solution to the problem. For example, one problem solving heuristic might be “always move toward the goal” (so when trying to get to school when your regular route is blocked, you would always turn in the direction you think the school is). A heuristic that people might use when doing math homework is “use the same solution strategy that you just used for the previous problem.”

By the way, we hope these last two paragraphs feel familiar to you. They seem to parallel a distinction that you recently learned. Indeed, algorithms and problem-solving heuristics are another example of the distinction between Type 1 thinking and Type 2 thinking.

Although it is probably not worth describing a large number of specific heuristics, two observations about heuristics are worth mentioning. First, heuristics can be very general or they can be very specific, pertaining to a particular type of problem only. For example, “always move toward the goal” is a general strategy that you can apply to countless problem situations. On the other hand, “when you are lost without a functioning gps, pick the most expensive car you can see and follow it” is specific to the problem of being lost. Second, all heuristics are not equally useful. One heuristic that many students know is “when in doubt, choose c for a question on a multiple-choice exam.” This is a dreadful strategy because many instructors intentionally randomize the order of answer choices. Another test-taking heuristic, somewhat more useful, is “look for the answer to one question somewhere else on the exam.”

You really should pay attention to the application of heuristics to test taking. Imagine that while reviewing your answers for a multiple-choice exam before turning it in, you come across a question for which you originally thought the answer was c. Upon reflection, you now think that the answer might be b. Should you change the answer to b, or should you stick with your first impression? Most people will apply the heuristic strategy to “stick with your first impression.” What they do not realize, of course, is that this is a very poor strategy (Lilienfeld et al, 2009). Most of the errors on exams come on questions that were answered wrong originally and were not changed (so they remain wrong). There are many fewer errors where we change a correct answer to an incorrect answer. And, of course, sometimes we change an incorrect answer to a correct answer. In fact, research has shown that it is more common to change a wrong answer to a right answer than vice versa (Bruno, 2001).

The belief in this poor test-taking strategy (stick with your first impression) is based on the  confirmation bias   (Nickerson, 1998; Wason, 1960). You first saw the confirmation bias in Module 1, but because it is so important, we will repeat the information here. People have a bias, or tendency, to notice information that confirms what they already believe. Somebody at one time told you to stick with your first impression, so when you look at the results of an exam you have taken, you will tend to notice the cases that are consistent with that belief. That is, you will notice the cases in which you originally had an answer correct and changed it to the wrong answer. You tend not to notice the other two important (and more common) cases, changing an answer from wrong to right, and leaving a wrong answer unchanged.

Because heuristics by definition do not guarantee a correct solution to a problem, mistakes are bound to occur when we employ them. A poor choice of a specific heuristic will lead to an even higher likelihood of making an error.

algorithm :  a step-by-step procedure that guarantees a correct solution to a problem

problem solving heuristic :  a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

confirmation bias :  people’s tendency to notice information that confirms what they already believe

An Effective Problem-Solving Sequence

You may be left with a big question: If algorithms are hard to use and heuristics often don’t work, how am I supposed to solve problems? Robert Sternberg (1996), as part of his theory of what makes people successfully intelligent (Module 8) described a problem-solving sequence that has been shown to work rather well:

  • Identify the existence of a problem.  In school, problem identification is often easy; problems that you encounter in math classes, for example, are conveniently labeled as problems for you. Outside of school, however, realizing that you have a problem is a key difficulty that you must get past in order to begin solving it. You must be very sensitive to the symptoms that indicate a problem.
  • Define the problem.  Suppose you realize that you have been having many headaches recently. Very likely, you would identify this as a problem. If you define the problem as “headaches,” the solution would probably be to take aspirin or ibuprofen or some other anti-inflammatory medication. If the headaches keep returning, however, you have not really solved the problem—likely because you have mistaken a symptom for the problem itself. Instead, you must find the root cause of the headaches. Stress might be the real problem. For you to successfully solve many problems it may be necessary for you to overcome your fixations and represent the problems differently. One specific strategy that you might find useful is to try to define the problem from someone else’s perspective. How would your parents, spouse, significant other, doctor, etc. define the problem? Somewhere in these different perspectives may lurk the key definition that will allow you to find an easier and permanent solution.
  • Formulate strategy.  Now it is time to begin planning exactly how the problem will be solved. Is there an algorithm or heuristic available for you to use? Remember, heuristics by their very nature guarantee that occasionally you will not be able to solve the problem. One point to keep in mind is that you should look for long-range solutions, which are more likely to address the root cause of a problem than short-range solutions.
  • Represent and organize information.  Similar to the way that the problem itself can be defined, or represented in multiple ways, information within the problem is open to different interpretations. Suppose you are studying for a big exam. You have chapters from a textbook and from a supplemental reader, along with lecture notes that all need to be studied. How should you (represent and) organize these materials? Should you separate them by type of material (text versus reader versus lecture notes), or should you separate them by topic? To solve problems effectively, you must learn to find the most useful representation and organization of information.
  • Allocate resources.  This is perhaps the simplest principle of the problem solving sequence, but it is extremely difficult for many people. First, you must decide whether time, money, skills, effort, goodwill, or some other resource would help to solve the problem Then, you must make the hard choice of deciding which resources to use, realizing that you cannot devote maximum resources to every problem. Very often, the solution to problem is simply to change how resources are allocated (for example, spending more time studying in order to improve grades).
  • Monitor and evaluate solutions.  Pay attention to the solution strategy while you are applying it. If it is not working, you may be able to select another strategy. Another fact you should realize about problem solving is that it never does end. Solving one problem frequently brings up new ones. Good monitoring and evaluation of your problem solutions can help you to anticipate and get a jump on solving the inevitable new problems that will arise.

Please note that this as  an  effective problem-solving sequence, not  the  effective problem solving sequence. Just as you can become fixated and end up representing the problem incorrectly or trying an inefficient solution, you can become stuck applying the problem-solving sequence in an inflexible way. Clearly there are problem situations that can be solved without using these skills in this order.

Additionally, many real-world problems may require that you go back and redefine a problem several times as the situation changes (Sternberg et al. 2000). For example, consider the problem with Mary’s daughter one last time. At first, Mary did represent the problem as one of defiance. When her early strategy of pleading and threatening punishment was unsuccessful, Mary began to observe her daughter more carefully. She noticed that, indeed, her daughter’s attention would be drawn by an irresistible distraction or book. Fresh with a re-representation of the problem, she began a new solution strategy. She began to remind her daughter every few minutes to stay on task and remind her that if she is ready before it is time to leave, she may return to the book or other distracting object at that time. Fortunately, this strategy was successful, so Mary did not have to go back and redefine the problem again.

Pick one or two of the problems that you listed when you first started studying this section and try to work out the steps of Sternberg’s problem solving sequence for each one.

a mental representation of a category of things in the world

an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

knowledge about one’s own cognitive processes; thinking about your thinking

individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

Thinking like a scientist in your everyday life for the purpose of drawing correct conclusions. It entails skepticism; an ability to identify biases, distortions, omissions, and assumptions; and excellent deductive and inductive reasoning, and problem solving skills.

a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

an inclination, tendency, leaning, or prejudice

a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

a set of statements in which the beginning statements lead to a conclusion

an argument for which true beginning statements guarantee that the conclusion is true

a type of reasoning in which we make judgments about likelihood from sets of evidence

an inductive argument in which the beginning statements lead to a conclusion that is probably true

fast, automatic, and emotional thinking

slow, effortful, and logical thinking

a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

udging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

noticing, comprehending and forming a mental conception of a problem

when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

a sudden realization of a solution to a problem

a step-by-step procedure that guarantees a correct solution to a problem

The tendency to notice and pay attention to information that confirms your prior beliefs and to ignore information that disconfirms them.

a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

Introduction to Psychology Copyright © 2020 by Ken Gray; Elizabeth Arnott-Hill; and Or'Shaundra Benson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Share This Book

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

Ch 8: Thinking and Language

Thinking and language.

Three side by side images are shown. On the left is a person lying in the grass with a book, looking off into the distance. In the middle is a sculpture of a person sitting on rock, with chin rested on hand, and the elbow of that hand rested on knee. The third is a drawing of a person sitting cross-legged with his head resting on his hand, elbow on knee.

Why is it so difficult to break habits—like reaching for your ringing phone even when you shouldn’t, such as when you’re driving? Why is it hard to pay attention to a conversation when typing out a text message? How does a person who has never seen or touched snow in real life develop an understanding of the concept of snow? How do young children acquire the ability to learn language with no formal instruction? Psychologists who study thinking explore questions like these.

As a part of this discussion, we will consider thinking, and briefly explore the development and use of language. We will also discuss problem solving and creativity. After finishing this chapter, you will have a greater appreciation of the higher-level cognitive processes that contribute to our distinctiveness as a species.

Learning Objectives

  • Understand why selective attention is important and how it can be studied.
  • Learn about different models of when and how selection can occur.
  • Understand how divided attention or multitasking is studied, and implications of multitasking in situations such as distracted driving.

Thinking and Problem-Solving

A man sitting down in "The Thinker" pose.

Imagine all of your thoughts as if they were physical entities, swirling rapidly inside your mind. How is it possible that the brain is able to move from one thought to the next in an organized, orderly fashion? The brain is endlessly perceiving, processing, planning, organizing, and remembering—it is always active. Yet, you don’t notice most of your brain’s activity as you move throughout your daily routine. This is only one facet of the complex processes involved in cognition. Simply put, cognition is thinking, and it encompasses the processes associated with perception, knowledge, problem solving, judgment, language, and memory. Scientists who study cognition are searching for ways to understand how we integrate, organize, and utilize our conscious cognitive experiences without being aware of all of the unconscious work that our brains are doing (for example, Kahneman, 2011).

  • Distinguish between concepts and prototypes
  • Explain the difference between natural and artificial concepts
  • Describe problem solving strategies, including algorithms and heuristics
  • Explain some common roadblocks to effective problem solving

What is Cognition?

Categories and concepts, concepts and prototypes.

The human nervous system is capable of handling endless streams of information. The senses serve as the interface between the mind and the external environment, receiving stimuli and translating it into nerve impulses that are transmitted to the brain. The brain then processes this information and uses the relevant pieces to create thoughts, which can then be expressed through language or stored in memory for future use. To make this process more complex, the brain does not gather information from external environments only. When thoughts are formed, the brain also pulls information from emotions and memories (Figure 9). Emotion and memory are powerful influences on both our thoughts and behaviors.

The outline of a human head is shown. There is a box containing “Information, sensations” in front of the head. An arrow from this box points to another box containing “Emotions, memories” located where the person’s brain would be. An arrow from this second box points to a third box containing “Thoughts” behind the head.

In order to organize this staggering amount of information, the brain has developed a file cabinet of sorts in the mind. The different files stored in the file cabinet are called concepts. Concepts  are categories or groupings of linguistic information, images, ideas, or memories, such as life experiences. Concepts are, in many ways, big ideas that are generated by observing details, and categorizing and combining these details into cognitive structures. You use concepts to see the relationships among the different elements of your experiences and to keep the information in your mind organized and accessible.

Concepts are informed by our semantic memory (you will learn more about this concept when you study memory) and are present in every aspect of our lives; however, one of the easiest places to notice concepts is inside a classroom, where they are discussed explicitly. When you study United States history, for example, you learn about more than just individual events that have happened in America’s past. You absorb a large quantity of information by listening to and participating in discussions, examining maps, and reading first-hand accounts of people’s lives. Your brain analyzes these details and develops an overall understanding of American history. In the process, your brain gathers details that inform and refine your understanding of related concepts like democracy, power, and freedom.

Concepts can be complex and abstract, like justice, or more concrete, like types of birds. In psychology, for example, Piaget’s stages of development are abstract concepts. Some concepts, like tolerance, are agreed upon by many people because they have been used in various ways over many years. Other concepts, like the characteristics of your ideal friend or your family’s birthday traditions, are personal and individualized. In this way, concepts touch every aspect of our lives, from our many daily routines to the guiding principles behind the way governments function.

Concepts are at the core of intelligent behavior. We expect people to be able to know what to do in new situations and when confronting new objects. If you go into a new classroom and see chairs, a blackboard, a projector, and a screen, you know what these things are and how they will be used. You’ll sit on one of the chairs and expect the instructor to write on the blackboard or project something onto the screen. You do this even if you have never seen any of these particular objects before , because you have concepts of classrooms, chairs, projectors, and so forth, that tell you what they are and what you’re supposed to do with them. Furthermore, if someone tells you a new fact about the projector—for example, that it has a halogen bulb—you are likely to extend this fact to other projectors you encounter. In short, concepts allow you to extend what you have learned about a limited number of objects to a potentially infinite set of entities.

A photograph of Mohandas Gandhi is shown. There are several people walking with him.

Another technique used by your brain to organize information is the identification of prototypes for the concepts you have developed. A prototype  is the best example or representation of a concept. For example, for the category of civil disobedience, your prototype could be Rosa Parks. Her peaceful resistance to segregation on a city bus in Montgomery, Alabama, is a recognizable example of civil disobedience. Or your prototype could be Mohandas Gandhi, sometimes called Mahatma Gandhi (“Mahatma” is an honorific title) (Figure 10).

Mohandas Gandhi served as a nonviolent force for independence for India while simultaneously demanding that Buddhist, Hindu, Muslim, and Christian leaders—both Indian and British—collaborate peacefully. Although he was not always successful in preventing violence around him, his life provides a steadfast example of the civil disobedience prototype (Constitutional Rights Foundation, 2013). Just as concepts can be abstract or concrete, we can make a distinction between concepts that are functions of our direct experience with the world and those that are more artificial in nature.

Link to Learning

Natural and artificial concepts.

In psychology, concepts can be divided into two categories, natural and artificial. Natural concepts  are created “naturally” through your experiences and can be developed from either direct or indirect experiences. For example, if you live in Essex Junction, Vermont, you have probably had a lot of direct experience with snow. You’ve watched it fall from the sky, you’ve seen lightly falling snow that barely covers the windshield of your car, and you’ve shoveled out 18 inches of fluffy white snow as you’ve thought, “This is perfect for skiing.” You’ve thrown snowballs at your best friend and gone sledding down the steepest hill in town. In short, you know snow. You know what it looks like, smells like, tastes like, and feels like. If, however, you’ve lived your whole life on the island of Saint Vincent in the Caribbean, you may never have actually seen snow, much less tasted, smelled, or touched it. You know snow from the indirect experience of seeing pictures of falling snow—or from watching films that feature snow as part of the setting. Either way, snow is a natural concept because you can construct an understanding of it through direct observations or experiences of snow (Figure 11).

Photograph A shows a snow covered landscape with the sun shining over it. Photograph B shows a sphere shaped object perched atop the corner of a cube shaped object. There is also a triangular object shown.

An artificial concept  on the other hand, is a concept that is defined by a specific set of characteristics. Various properties of geometric shapes, like squares and triangles, serve as useful examples of artificial concepts. A triangle always has three angles and three sides. A square always has four equal sides and four right angles. Mathematical formulas, like the equation for area (length × width) are artificial concepts defined by specific sets of characteristics that are always the same. Artificial concepts can enhance the understanding of a topic by building on one another. For example, before learning the concept of “area of a square” (and the formula to find it), you must understand what a square is. Once the concept of “area of a square” is understood, an understanding of area for other geometric shapes can be built upon the original understanding of area. The use of artificial concepts to define an idea is crucial to communicating with others and engaging in complex thought. According to Goldstone and Kersten (2003), concepts act as building blocks and can be connected in countless combinations to create complex thoughts.

A schema is a mental construct consisting of a cluster or collection of related concepts (Bartlett, 1932). There are many different types of schemata, and they all have one thing in common: schemata are a method of organizing information that allows the brain to work more efficiently. When a schema is activated, the brain makes immediate assumptions about the person or object being observed.

There are several types of schemata. A role schema makes assumptions about how individuals in certain roles will behave (Callero, 1994). For example, imagine you meet someone who introduces himself as a firefighter. When this happens, your brain automatically activates the “firefighter schema” and begins making assumptions that this person is brave, selfless, and community-oriented. Despite not knowing this person, already you have unknowingly made judgments about him. Schemata also help you fill in gaps in the information you receive from the world around you. While schemata allow for more efficient information processing, there can be problems with schemata, regardless of whether they are accurate: Perhaps this particular firefighter is not brave, he just works as a firefighter to pay the bills while studying to become a children’s librarian.

An event schema , also known as a cognitive script , is a set of behaviors that can feel like a routine. Think about what you do when you walk into an elevator (Figure 12). First, the doors open and you wait to let exiting passengers leave the elevator car. Then, you step into the elevator and turn around to face the doors, looking for the correct button to push. You never face the back of the elevator, do you? And when you’re riding in a crowded elevator and you can’t face the front, it feels uncomfortable, doesn’t it? Interestingly, event schemata can vary widely among different cultures and countries. For example, while it is quite common for people to greet one another with a handshake in the United States, in Tibet, you greet someone by sticking your tongue out at them, and in Belize, you bump fists (Cairns Regional Council, n.d.)

A crowded elevator is shown. There are many people standing close to one another.

Because event schemata are automatic, they can be difficult to change. Imagine that you are driving home from work or school. This event schema involves getting in the car, shutting the door, and buckling your seatbelt before putting the key in the ignition. You might perform this script two or three times each day. As you drive home, you hear your phone’s ring tone. Typically, the event schema that occurs when you hear your phone ringing involves locating the phone and answering it or responding to your latest text message. So without thinking, you reach for your phone, which could be in your pocket, in your bag, or on the passenger seat of the car. This powerful event schema is informed by your pattern of behavior and the pleasurable stimulation that a phone call or text message gives your brain. Because it is a schema, it is extremely challenging for us to stop reaching for the phone, even though we know that we endanger our own lives and the lives of others while we do it (Neyfakh, 2013) (Figure 13).

A person’s right hand is holding a cellular phone. The person is in the driver’s seat of an automobile while on the road.

Remember the elevator? It feels almost impossible to walk in and not face the door. Our powerful event schema dictates our behavior in the elevator, and it is no different with our phones. Current research suggests that it is the habit, or event schema, of checking our phones in many different situations that makes refraining from checking them while driving especially difficult (Bayer & Campbell, 2012). Because texting and driving has become a dangerous epidemic in recent years, psychologists are looking at ways to help people interrupt the “phone schema” while driving. Event schemata like these are the reason why many habits are difficult to break once they have been acquired. As we continue to examine thinking, keep in mind how powerful the forces of concepts and schemata are to our understanding of the world.

Watch this CrashCourse video to see more examples of concepts and prototypes. You’ll also get a preview on other key topics in cognition, including problem-solving strategies like algorithms and heuristics.

You can view the transcript for “Cognition – How Your Mind Can Amaze and Betray You: Crash Course Psychology #15” here (opens in new window) .

Think It Over

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

Problem-Solving Strategies

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them. For example, a well-known strategy is trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Another type of strategy is an algorithm. An algorithm  is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic  is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

  • When one is faced with too much information
  • When the time to make a decision is limited
  • When the decision to be made is unimportant
  • When there is access to very little information to use in making the decision
  • When an appropriate heuristic happens to come to mind in the same moment

Working backwards  is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

What problem-solving method could you use to solve Einstein’s famous riddle?

You can view the transcript for “Can you solve “Einstein’s Riddle”? – Dan Van der Vieren” here (opens in new window) .

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Everyday Connections: Solving Puzzles

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (Figure 14) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

A four column by four row Sudoku puzzle is shown. The top left cell contains the number 3. The top right cell contains the number 2. The bottom right cell contains the number 1. The bottom left cell contains the number 4. The cell at the intersection of the second row and the second column contains the number 4. The cell to the right of that contains the number 1. The cell below the cell containing the number 1 contains the number 2. The cell to the left of the cell containing the number 2 contains the number 3.

Here is another popular type of puzzle that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

A square shaped outline contains three rows and three columns of dots with equal space between them.

Take a look at the “Puzzling Scales” logic puzzle below (Figure 16). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

A puzzle involving a scale is shown. At the top of the figure it reads: “Sam Loyds Puzzling Scales.” The first row of the puzzle shows a balanced scale with 3 blocks and a top on the left and 12 marbles on the right. Below this row it reads: “Since the scales now balance.” The next row of the puzzle shows a balanced scale with just the top on the left, and 1 block and 8 marbles on the right. Below this row it reads: “And balance when arranged this way.” The third row shows an unbalanced scale with the top on the left side, which is much lower than the right side. The right side is empty. Below this row it reads: “Then how many marbles will it require to balance with that top?”

Were you able to determine how many marbles are needed to balance the scales in the Puzzling Scales? You need nine. Were you able to solve the other problems above? Here are the answers:

The first puzzle is a Sudoku grid of 16 squares (4 rows of 4 squares) is shown. Half of the numbers were supplied to start the puzzle and are colored blue, and half have been filled in as the puzzle’s solution and are colored red. The numbers in each row of the grid, left to right, are as follows. Row 1: blue 3, red 1, red 4, blue 2. Row 2: red 2, blue 4, blue 1, red 3. Row 3: red 1, blue 3, blue 2, red 4. Row 4: blue 4, red 2, red 3, blue 1.The second puzzle consists of 9 dots arranged in 3 rows of 3 inside of a square. The solution, four straight lines made without lifting the pencil, is shown in a red line with arrows indicating the direction of movement. In order to solve the puzzle, the lines must extend beyond the borders of the box. The four connecting lines are drawn as follows. Line 1 begins at the top left dot, proceeds through the middle and right dots of the top row, and extends to the right beyond the border of the square. Line 2 extends from the end of line 1, through the right dot of the horizontally centered row, through the middle dot of the bottom row, and beyond the square’s border ending in the space beneath the left dot of the bottom row. Line 3 extends from the end of line 2 upwards through the left dots of the bottom, middle, and top rows. Line 4 extends from the end of line 3 through the middle dot in the middle row and ends at the right dot of the bottom row.

Pitfalls to Problem Solving

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set  is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now. Functional fixedness   is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias  occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. This bias proves that first impressions do matter and that we tend to look for information to confirm our initial judgments of others.

Watch this video from the Big Think to learn more about the confirmation bias.

You can view the transcript for “Confirmation Bias: Your Brain is So Judgmental” here (opens in new window) .

Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias  describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . To use a common example, would you guess there are more murders or more suicides in America each year? When asked, most people would guess there are more murders. In truth, there are twice as many suicides as there are murders each year. However, murders seem more common because we hear a lot more about murders on an average day. Unless someone we know or someone famous takes their own life, it does not make the news. Murders, on the other hand, we see in the news every day. This leads to the erroneous assumption that the easier it is to think of instances of something, the more often that thing occurs.

Watch the following video for an example of the availability heuristic.

You can view the transcript for “Availability Heuristic: Are Planes More Dangerous Than Cars?” here (opens in new window) .

Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in Table 2 below.

Learn more about heuristics and common biases through the article, “ 8 Common Thinking Mistakes Our Brains Make Every Day and How to Prevent Them ” by Belle Beth Cooper.

You can also watch this clever music video explaining these and other cognitive biases.

Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

The word language written on the chalkboard with a silhouette of children in front of the chalkboard.

  • Understand how the use of language develops
  • Explain the relationship between language and thinking

Language Development

Language is a communication system that involves using words and systematic rules to organize those words to transmit information from one individual to another. While language is a form of communication, not all communication is language. Many species communicate with one another through their postures, movements, odors, or vocalizations. This communication is crucial for species that need to interact and develop social relationships with their conspecifics. However, many people have asserted that it is language that makes humans unique among all of the animal species (Corballis & Suddendorf, 2007; Tomasello & Rakoczy, 2003). This section will focus on what distinguishes language as a special form of communication, how the use of language develops, and how language affects the way we think.

Components of Language

Language , be it spoken, signed, or written, has specific components: a lexicon and grammar. Lexicon refers to the words of a given language. Thus, lexicon is a language’s vocabulary. Grammar  refers to the set of rules that are used to convey meaning through the use of the lexicon (Fernández & Cairns, 2011). For instance, English grammar dictates that most verbs receive an “-ed” at the end to indicate past tense.

Words are formed by combining the various phonemes that make up the language. A phoneme  (e.g., the sounds “ah” vs. “eh”) is a basic sound unit of a given language, and different languages have different sets of phonemes. Phonemes are combined to form morphemes , which are the smallest units of language that convey some type of meaning (e.g., “I” is both a phoneme and a morpheme).  Further, a morpheme is not the same as a word. The main difference is that a morpheme sometimes does not stand alone, but a word, by definition, always stands alone.

We use semantics and syntax to construct language. Semantics and syntax are part of a language’s grammar. Semantics refers to the process by which we derive meaning from morphemes and words. Syntax  refers to the way words are organized into sentences (Chomsky, 1965; Fernández & Cairns, 2011).

We apply the rules of grammar to organize the lexicon in novel and creative ways, which allow us to communicate information about both concrete and abstract concepts. We can talk about our immediate and observable surroundings as well as the surface of unseen planets. We can share our innermost thoughts, our plans for the future, and debate the value of a college education. We can provide detailed instructions for cooking a meal, fixing a car, or building a fire. The flexibility that language provides to relay vastly different types of information is a property that makes language so distinct as a mode of communication among humans.

Given the remarkable complexity of a language, one might expect that mastering a language would be an especially arduous task; indeed, for those of us trying to learn a second language as adults, this might seem to be true. However, young children master language very quickly with relative ease. B. F. Skinner (1957) proposed that language is learned through reinforcement. Noam Chomsky (1965) criticized this behaviorist approach, asserting instead that the mechanisms underlying language acquisition are biologically determined. The use of language develops in the absence of formal instruction and appears to follow a very similar pattern in children from vastly different cultures and backgrounds. It would seem, therefore, that we are born with a biological predisposition to acquire a language (Chomsky, 1965; Fernández & Cairns, 2011). Moreover, it appears that there is a critical period for language acquisition, such that this proficiency at acquiring language is maximal early in life; generally, as people age, the ease with which they acquire and master new languages diminishes (Johnson & Newport, 1989; Lenneberg, 1967; Singleton, 1995).

Children begin to learn about language from a very early age (Table 1). In fact, it appears that this is occurring even before we are born. Newborns show preference for their mother’s voice and appear to be able to discriminate between the language spoken by their mother and other languages. Babies are also attuned to the languages being used around them and show preferences for videos of faces that are moving in synchrony with the audio of spoken language versus videos that do not synchronize with the audio (Blossom & Morgan, 2006; Pickens, 1994; Spelke & Cortelyou, 1981).

Dig Deeper: The Case of Genie

In the fall of 1970, a social worker in the Los Angeles area found a 13-year-old girl who was being raised in extremely neglectful and abusive conditions. The girl, who came to be known as Genie, had lived most of her life tied to a potty chair or confined to a crib in a small room that was kept closed with the curtains drawn. For a little over a decade, Genie had virtually no social interaction and no access to the outside world. As a result of these conditions, Genie was unable to stand up, chew solid food, or speak (Fromkin, Krashen, Curtiss, Rigler, & Rigler, 1974; Rymer, 1993). The police took Genie into protective custody.

Genie’s abilities improved dramatically following her removal from her abusive environment, and early on, it appeared she was acquiring language—much later than would be predicted by critical period hypotheses that had been posited at the time (Fromkin et al., 1974). Genie managed to amass an impressive vocabulary in a relatively short amount of time. However, she never developed a mastery of the grammatical aspects of language (Curtiss, 1981). Perhaps being deprived of the opportunity to learn language during a critical period impeded Genie’s ability to fully acquire and use language.

You may recall that each language has its own set of phonemes that are used to generate morphemes, words, and so on. Babies can discriminate among the sounds that make up a language (for example, they can tell the difference between the “s” in vision and the “ss” in fission); early on, they can differentiate between the sounds of all human languages, even those that do not occur in the languages that are used in their environments. However, by the time that they are about 1 year old, they can only discriminate among those phonemes that are used in the language or languages in their environments (Jensen, 2011; Werker & Lalonde, 1988; Werker & Tees, 1984).

After the first few months of life, babies enter what is known as the babbling stage, during which time they tend to produce single syllables that are repeated over and over. As time passes, more variations appear in the syllables that they produce. During this time, it is unlikely that the babies are trying to communicate; they are just as likely to babble when they are alone as when they are with their caregivers (Fernández & Cairns, 2011). Interestingly, babies who are raised in environments in which sign language is used will also begin to show babbling in the gestures of their hands during this stage (Petitto, Holowka, Sergio, Levy, & Ostry, 2004).

Generally, a child’s first word is uttered sometime between the ages of 1 year to 18 months, and for the next few months, the child will remain in the “one word” stage of language development. During this time, children know a number of words, but they only produce one-word utterances. The child’s early vocabulary is limited to familiar objects or events, often nouns. Although children in this stage only make one-word utterances, these words often carry larger meaning (Fernández & Cairns, 2011). So, for example, a child saying “cookie” could be identifying a cookie or asking for a cookie.

As a child’s lexicon grows, she begins to utter simple sentences and to acquire new vocabulary at a very rapid pace. In addition, children begin to demonstrate a clear understanding of the specific rules that apply to their language(s). Even the mistakes that children sometimes make provide evidence of just how much they understand about those rules. This is sometimes seen in the form of overgeneralization . In this context, overgeneralization refers to an extension of a language rule to an exception to the rule. For example, in English, it is usually the case that an “s” is added to the end of a word to indicate plurality. For example, we speak of one dog versus two dogs. Young children will overgeneralize this rule to cases that are exceptions to the “add an s to the end of the word” rule and say things like “those two gooses” or “three mouses.” Clearly, the rules of the language are understood, even if the exceptions to the rules are still being learned (Moskowitz, 1978).

Language and Thinking

Think about it:  the meaning of language.

Think about what you know of other languages; perhaps you even speak multiple languages. Imagine for a moment that your closest friend fluently speaks more than one language. Do you think that friend thinks differently, depending on which language is being spoken? You may know a few words that are not translatable from their original language into English. For example, the Portuguese word saudade originated during the 15th century, when Portuguese sailors left home to explore the seas and travel to Africa or Asia. Those left behind described the emptiness and fondness they felt as saudade (Figure 20) . The word came to express many meanings, including loss, nostalgia, yearning, warm memories, and hope. There is no single word in English that includes all of those emotions in a single description. Do words such as saudade indicate that different languages produce different patterns of thought in people? What do you think??

Photograph A shows a painting of a person leaning against a ledge, slumped sideways over a box. Photograph B shows a painting of a person reading by a window.

Language may indeed influence the way that we think, an idea known as linguistic determinism. One recent demonstration of this phenomenon involved differences in the way that English and Mandarin Chinese speakers talk and think about time. English speakers tend to talk about time using terms that describe changes along a horizontal dimension, for example, saying something like “I’m running behind schedule” or “Don’t get ahead of yourself.” While Mandarin Chinese speakers also describe time in horizontal terms, it is not uncommon to also use terms associated with a vertical arrangement. For example, the past might be described as being “up” and the future as being “down.” It turns out that these differences in language translate into differences in performance on cognitive tests designed to measure how quickly an individual can recognize temporal relationships. Specifically, when given a series of tasks with vertical priming, Mandarin Chinese speakers were faster at recognizing temporal relationships between months. Indeed, Boroditsky (2001) sees these results as suggesting that “habits in language encourage habits in thought” (p. 12).

Language does not completely determine our thoughts—our thoughts are far too flexible for that—but habitual uses of language can influence our habit of thought and action. For instance, some linguistic practice seems to be associated even with cultural values and social institution. Pronoun drop is the case in point. Pronouns such as “I” and “you” are used to represent the speaker and listener of a speech in English. In an English sentence, these pronouns cannot be dropped if they are used as the subject of a sentence. So, for instance, “I went to the movie last night” is fine, but “Went to the movie last night” is not in standard English. However, in other languages such as Japanese, pronouns can be, and in fact often are, dropped from sentences. It turned out that people living in those countries where pronoun drop languages are spoken tend to have more collectivistic values (e.g., employees having greater loyalty toward their employers) than those who use non–pronoun drop languages such as English (Kashima & Kashima, 1998). It was argued that the explicit reference to “you” and “I” may remind speakers the distinction between the self and other, and the differentiation between individuals. Such a linguistic practice may act as a constant reminder of the cultural value, which, in turn, may encourage people to perform the linguistic practice.

One group of researchers who wanted to investigate how language influences thought compared how English speakers and the Dani people of Papua New Guinea think and speak about color. The Dani have two words for color: one word for light and one word for dark . In contrast, the English language has 11 color words. Researchers hypothesized that the number of color terms could limit the ways that the Dani people conceptualized color. However, the Dani were able to distinguish colors with the same ability as English speakers, despite having fewer words at their disposal (Berlin & Kay, 1969). A recent review of research aimed at determining how language might affect something like color perception suggests that language can influence perceptual phenomena, especially in the left hemisphere of the brain. You may recall from earlier chapters that the left hemisphere is associated with language for most people. However, the right (less linguistic hemisphere) of the brain is less affected by linguistic influences on perception (Regier & Kay, 2009)

Learn more about language, language acquisition, and especially the connection between language and thought in the following CrashCourse video:

You can view the transcript for “Language: Crash Course Psychology #16” here (opens in new window) .

In this chapter, you learned to

  • describe attention
  • describe cognition and problem-solving strategies
  • describe language acquisition and the role language plays in communication and thought

You learned about non-memory cognitive processes in this chapter. Because each of you reading this is using language in some shape or form, we will end with a quick summary and a video on this topic. Language is a communication system that has both a lexicon and a system of grammar. Language acquisition occurs naturally and effortlessly during the early stages of life, and this acquisition occurs in a predictable sequence for individuals around the world. Language has a strong influence on thought, and the concept of how language may influence cognition remains an area of study and debate in psychology.

In this TED talk, Lera Boroditsky summarizes unique ways that language and culture intersect with some basic cognitive processes. How was your language shaped your thinking?

Abler, W. (2013). Sapir, Harris, and Chomsky in the twentieth century. Cognitive Critique, 7, 29–48.

Aronson, E. (Ed.). (1995). Social cognition. In The social animal (p. 151). New York: W.H. Freeman and Company.

Bartlett, F. C. (1932). Remembering: A study in experimental and social psychology. Cambridge, England: Cambridge University Press.

Bayer, J. B., & Campbell, S. W. (2012). Texting while driving on automatic: Considering the frequency-independent side of habit. Computers in Human Behavior, 28, 2083–2090.

Beilock, S. L., & Carr, T. H. (2001). On the fragility of skilled performance: What governs choking under pressure?  Journal of Experimental Psychology: General, 130 , 701–725.

Berlin, B., & Kay, P. (1969). Basic color terms: Their universality and evolution. Berkley: University of California Press.

Blossom, M., & Morgan, J. L. (2006). Does the face say what the mouth says? A study of infants’ sensitivity to visual prosody. In the 30th annual Boston University Conference on Language Development, Somerville, MA.

Boroditsky, L. (2001). Does language shape thought? Mandarin and English speakers’ conceptions of time. Cognitive Psychology, 43, 1–22.

Boroditsky, L. (2011, February). How language shapes thought. Scientific American, 63–65.Chomsky, N. (1965). Aspects of the theory of syntax. Cambridge, MA: MIT Press

Broadbent, D. A. (1958).  Perception and communication . London, England: Pergamon Press.

Cairns Regional Council. (n.d.). Cultural greetings. Retrieved from http://www.cairns.qld.gov.au/__data/assets/pdf_file/0007/8953/CulturalGreetingExercise.pdf

Callero, P. L. (1994). From role-playing to role-using: Understanding role as resource. Social Psychology Quarterly, 57, 228–243.

Cherry, E. C. (1953). Experiments on the recognition of speech with one and two ears.  Journal of the Acoustical Society of America, 25 , 975–979.

Chomsky, N.(1965). Aspects of the theory of syntax. Cambridge, MA: MIT Press

Corballis, M. C., & Suddendorf, T. (2007). Memory, time, and language. In C. Pasternak (Ed.), What makes us human (pp. 17–36). Oxford, UK: Oneworld Publications.

Curtiss, S. (1981). Dissociations between language and cognition: Cases and implications. Journal of Autism and Developmental Disorders, 11(1), 15–30.

Cyclopedia of Puzzles. (n.d.) Retrieved from http://www.mathpuzzle.com/loyd/

Deutsch, J. A., & Deutsch, D. (1963). Attention: some theoretical considerations.  Psychological Review, 70 , 80–90.

Fernández, E. M., & Cairns, H. S. (2011). Fundamentals of psycholinguistics. West Sussex, UK: Wiley-Blackwell.

Fromkin, V., Krashen, S., Curtiss, S., Rigler, D., & Rigler, M. (1974). The development of language in Genie: A case of language acquisition beyond the critical period. Brain and Language, 1, 81–107.

German, T. P., & Barrett, H. C. (2005). Functional fixedness in a technologically sparse culture. Psychological Science, 16, 1–5.

Goldstone, R. L., & Kersten, A. (2003). Concepts and categorization. In A. F. Healy, R. W. Proctor, & I.B. Weiner (Eds.), Handbook of psychology (Volume IV, pp. 599–622). Hoboken, New Jersey: John Wiley & Sons, Inc.

Hirst, W. C., Neisser, U., & Spelke, E. S. (1978). Divided attention.  Human Nature, 1 , 54–61.

James, W. (1983).  The principles of psychology . Cambridge, MA: Harvard University Press. (Original work published 1890)

Jensen, J. (2011). Phoneme acquisition: Infants and second language learners. The Language Teacher, 35(6), 24–28.

Johnson, J. S., & Newport, E. L. (1989). Critical period effects in second language learning: The influence of maturational state on the acquisition of English as a second language. Cognitive Psychology, 21, 60–99.

Johnston, W. A., & Heinz, S. P. (1978). Flexibility and capacity demands of attention.  Journal of Experimental Psychology: General, 107 , 420–435.

Kahneman, D. (2011). Thinking, fast and slow. New York: Farrar, Straus, and Giroux.

Lenneberg, E. (1967). Biological foundations of language. New York: Wiley.

Monsell, S. (2003). Task switching.  Trends in Cognitive Science, 7 (3), 134–140.

Moray, N. (1959). Attention in dichotic listening: Affective cues and the influence of instructions.  Quarterly Journal of Experimental Psychology, 11 , 56–60.

Moskowitz, B. A. (1978). The acquisition of language. Scientific American, 239, 92–108. Petitto, L. A., Holowka, S., Sergio, L. E., Levy, B., & Ostry, D. J. (2004). Baby hands that move to the rhythm of language: Hearing babies acquiring sign languages babble silently on the hands. Cognition, 93, 43–73.

Neyfakh, L. (2013, October 7). “Why you can’t stop checking your phone.” Retrieved from http://www.bostonglobe.com/ideas/2013/10/06/why-you-can-stop-checking-your-phone/rrBJzyBGDAr1YlEH5JQDcM/story.html

Petitto, L. A., Holowka, S., Sergio, L. E., Levy, B., & Ostry, D. J. (2004). Baby hands that move to the rhythm of language: Hearing babies acquiring sign languages babble silently on the hands. Cognition, 93, 43–73.

Pickens, J. (1994). Full-term and preterm infants’ perception of face-voice synchrony. Infant Behavior and Development, 17, 447–455.

Pratkanis, A. (1989). The cognitive representation of attitudes. In A. R. Pratkanis, S. J. Breckler, & A. G. Greenwald (Eds.), Attitude structure and function (pp. 71–98). Hillsdale, NJ: Erlbaum.

Regier, T., & Kay, P. (2009). Language, thought, and color: Whorf was half right. Trends in Cognitive Sciences, 13(10), 439–446.

Rymer, R. (1993). Genie: A Scientific Tragedy. New York: Harper Collins.

Sapir, E. (1964). Culture, language, and personality. Berkley: University of California Press. (Original work published 1941)

Simons, D. J., & Chabris, C. F. (1999). Gorillas in our midst: Sustained inattentional blindness for dynamic events.  Perception, 28 , 1059–1074.

Skinner, B. F. (1957). Verbal behavior. Acton, MA: Copley Publishing Group.

Spelke, E. S., & Cortelyou, A. (1981). Perceptual aspects of social knowing: Looking and listening in infancy. In M.E. Lamb & L.R. Sherrod (Eds.), Infant social cognition: Empirical and theoretical considerations (pp. 61–83). Hillsdale, NJ: Erlbaum.

Spelke, E. S., Hirst, W. C., & Neisser, U. (1976). Skills of divided attention.  Cognition, 4 , 215–250.

Strayer, D. L., & Drews, F. A. (2007). Cell-phone induced inattention blindness.  Current Directions in Psychological Science, 16 , 128–131.

Strayer, D. L., & Johnston, W. A. (2001). Driven to distraction: Dual-task studies of simulated driving and conversing on a cellular telephone.  Psychological Science, 12 , 462–466.

Strayer, D. L., Watson, J. M., & Drews, F. A. (2011) Cognitive distraction while multitasking in the automobile. In Brian Ross (Ed.),  The Psychology of Learning and Motivation  (Vol. 54, pp. 29–58). Burlington, VT: Academic Press.

Tomasello, M., & Rakoczy, H. (2003). What makes human cognition unique? From individual to shared to collective intentionality. Mind & Language, 18(2), 121–147.

Treisman, A. (1960). Contextual cues in selective listening.  Quarterly Journal of Experimental Psychology, 12 , 242–248.

Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124–1131.

van Troyer, G. (1994). Linguistic determinism and mutability: The Sapir-Whorf “hypothesis” and intercultural communication. JALT Journal, 2, 163–178.

Watson, J. M., & Strayer, D. L. (2010). Supertaskers: Profiles in extraordinary multitasking ability.  Psychonomic Bulletin & Review, 17 , 479–485.

Werker, J. F., & Lalonde, C. E. (1988). Cross-language speech perception: Initial capabilities and developmental change. Developmental Psychology, 24, 672–683.

Werker, J. F., & Tees, R. C. (1984). Cross-language speech perception: Evidence for perceptual reorganization during the first year of life. Infant Behavior and Development, 7, 49–63.

Whorf, B. L. (1956). Language, thought and relativity. Cambridge, MA: MIT Press.

CC original content.

Attention, Thinking and Language.  Authored by:  Karenna Malavanti Provided by: PressBooks. License: CC BY-SA: Attribution-ShareAlike

CC licensed content, Shared previously

  • Why It Matters: Thinking and Intelligence.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/introduction-10/
  • Attention. Authored by: Frances Friedrich. Located at NOBA Psychology. License: CC-BY-NC-SA. Retrieved from: Retrieved from  http://noba.to/uv9x8df5
  • Introduction to Thinking and Intelligence. Authored by : OpenStax College. License : CC BY: Attribution . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction   Located at : https://openstax.org/books/psychology-2e/pages/7-introduction .
  • What Is Cognition?. Authored by : OpenStax College. License : CC BY: Attribution . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction   Located at : https://openstax.org/books/psychology-2e/pages/7-1-what-is-cognition .
  • A Thinking Man Image. Authored by : Wesley Nitsckie. License : CC BY-SA: Attribution-ShareAlike   Located at : https://www.flickr.com/photos/nitsckie/5507777269 .
  • What Is Cognition?.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/what-is-cognition/
  • Categories and Concepts. Authored by : Gregory Murphy. Provided by : New York University. Project : The Noba Project. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike   Located at : http://nobaproject.com/textbooks/wendy-king-introduction-to-psychology-the-full-noba-collection/modules/categories-and-concepts .
  • Solving Problems.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at : https://pressbooks.online.ucf.edu/lumenpsychology/chapter/problem-solving/
  • Problem-Solving. Authored by : OpenStax College. License : CC BY: Attribution . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction . Located at : https://openstax.org/books/psychology-2e/pages/7-3-problem-solving .
  • Pitfalls to Problem Solving.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/reading-pitfalls-to-problem/
  • Introduction to Language.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/outcome-language/
  • Language. Authored by : OpenStax College.  License : CC BY: Attribution . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction   Located at : https://openstax.org/books/psychology-2e/pages/7-2-language .
  • Language. Authored by : geralt. Provided by : Pixabay. License : CC0: No Rights Reserved   Located at : https://pixabay.com/en/school-board-languages-blackboard-1063556/ .
  • Language and Language Use.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/language-and-language-use/
  • Language and Language Use. Authored by : Yoshihisa Kashima. Project : The Noba Project. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike   Located at : http://nobaproject.com/textbooks/introduction-to-psychology-the-full-noba-collection/modules/language-and-language-use .
  • Language Development.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/language/
  • Morpheme. Provided by : Wikipedia. License : CC BY-SA: Attribution-ShareAlike   Located at : https://en.wikipedia.org/wiki/Morpheme .
  • Language and Thinking.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/reading-language-and-thought/
  • Summary. Authored by : OpenStax College. License : CC BY: Attribution . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction . Located at : https://openstax.org/books/psychology-2e/pages/7-summary .

All rights reserved content

  • Cognition: How Your Mind Can Amaze and Betray You – Crash Course Psychology #15. Provided by : CrashCourse. License : All Rights Reserved . License Terms : Standard YouTube License   Located at : https://www.youtube.com/watch?v=R-sVnmmw6WY&feature=youtu.be&list=PL8dPuuaLjXtOPRKzVLY0jJY-uHOH9KVU6 .
  • Can you solve Einsteinu2019s Riddle? . Authored by : Dan Van der Vieren. Provided by : Ted-Ed. License : Other . License Terms : Standard YouTube License .  Located at : https://www.youtube.com/watch?v=1rDVz_Fb6HQ&index=3&list=PLUmyCeox8XCwB8FrEfDQtQZmCc2qYMS5a .
  • Language: Crash Course Psychology #16. Authored by : CrashCourse. License : Other . License Terms : Standard YouTube License .  Located at : https://www.youtube.com/watch?v=s9shPouRWCs&feature=youtu.be&list=PL8dPuuaLjXtOPRKzVLY0jJY-uHOH9KVU6 .
  • How language shapes the way we think Authored by: Lera Boroditsky.  Provided by :  TED.  License : Other . License Terms : Standard YouTube License .  Located at :  https://youtu.be/RKK7wGAYP6k

thinking, including perception, learning, problem solving, judgment, and memory

field of psychology dedicated to studying every aspect of how people think

a set of objects that can be treated as equivalent in some way

category or grouping of linguistic information, objects, ideas, or life experiences

best representation of a concept

mental groupings that are created “naturally” through your experiences

concept that is defined by a very specific set of characteristics

(plural = schemata) mental construct consisting of a cluster or collection of related concepts

set of expectations that define the behaviors of a person occupying a particular role

set of behaviors that are performed the same way each time; also referred to as a cognitive script

set of behaviors that are performed the same way each time; also referred to as an event schema

method for solving problems

problem-solving strategy in which multiple solutions are attempted until the correct one is found

problem-solving strategy characterized by a specific set of instructions

mental shortcut that saves time when solving a problem

heuristic in which you begin to solve a problem by focusing on the end result

continually using an old solution to a problem without results

inability to see an object as useful for any other use other than the one for which it was intended

faulty heuristic in which you fixate on a single aspect of a problem to find a solution

belief that the event just experienced was predictable, even though it really wasn’t

subset of the population that accurately represents the general population

faulty heuristic in which you make a decision based on information readily available to you

communication system that involves using words to transmit information from one individual to another

Words and expressions.

set of rules that are used to convey meaning through the use of a lexicon

basic sound unit of a given language

smallest unit of language that conveys some type of meaning

process by which we derive meaning from morphemes and words

manner by which words are organized into sentences

extension of a rule that exists in a given language to an exception to the rule

Psychological Science: Understanding Human Behavior Copyright © by Karenna Malavanti is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Share This Book

  • Bipolar Disorder
  • Therapy Center
  • When To See a Therapist
  • Types of Therapy
  • Best Online Therapy
  • Best Couples Therapy
  • Best Family Therapy
  • Managing Stress
  • Sleep and Dreaming
  • Understanding Emotions
  • Self-Improvement
  • Healthy Relationships
  • Student Resources
  • Personality Types
  • Verywell Mind Insights
  • 2023 Verywell Mind 25
  • Mental Health in the Classroom
  • Editorial Process
  • Meet Our Review Board
  • Crisis Support

Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

what is problem solving why does it is always associated with the word reasoning

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

what is problem solving why does it is always associated with the word reasoning

  • Identify the Problem
  • Define the Problem
  • Form a Strategy
  • Organize Information
  • Allocate Resources
  • Monitor Progress
  • Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

  • Asking questions about the problem
  • Breaking the problem down into smaller pieces
  • Looking at the problem from different perspectives
  • Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

  • Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
  • Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

Follow Now : Apple Podcasts / Spotify / Google Podcasts

You can become a better problem solving by:

  • Practicing brainstorming and coming up with multiple potential solutions to problems
  • Being open-minded and considering all possible options before making a decision
  • Breaking down problems into smaller, more manageable pieces
  • Asking for help when needed
  • Researching different problem-solving techniques and trying out new ones
  • Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Logo for Drake University Pressbooks

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

7 Thinking, Language, and Problem Solving

Three different artistic portrayals of a person in thought are shown. From left to right, a painting of a woman with an open book, a sculpture of a man hunched over, head on chin, and a ink painting of a man sitting cross-legged holding his head.

What is the best way to solve a problem? How does a person who has never seen or touched snow in real life develop an understanding of the concept of snow? How do young children acquire the ability to learn language with no formal instruction? Psychologists who study thinking explore questions like these and are called cognitive psychologists.

In other chapters, we discussed the cognitive processes of perception, learning, and memory. In this chapter, we will focus on high-level cognitive processes. As a part of this discussion, we will consider thinking and briefly explore the development and use of language. We will also discuss problem solving and creativity. After finishing this chapter, you will have a greater appreciation of the higher-level cognitive processes that contribute to our distinctiveness as a species.

Table of Contents

7.1 What is Cognition? 7.2 Language 7.3 Problem Solving

7.1 What is Cognition?

Learning Objectives

By the end of this section, you will be able to:

  • Describe cognition
  • Distinguish concepts and prototypes
  • Explain the difference between natural and artificial concepts
  • Describe how schemata are organized and constructed

Imagine all of your thoughts as if they were physical entities, swirling rapidly inside your mind. How is it possible that the brain is able to move from one thought to the next in an organized, orderly fashion? The brain is endlessly perceiving, processing, planning, organizing, and remembering—it is always active. Yet, you don’t notice most of your brain’s activity as you move throughout your daily routine. This is only one facet of the complex processes involved in cognition . Simply put,  cognition  is thinking, and it encompasses the processes associated with perception, knowledge, problem solving, judgment, language, and memory. Scientists who study cognition are searching for ways to understand how we integrate, organize, and utilize our conscious cognitive experiences without being aware of all of the unconscious work that our brains are doing (for example, Kahneman, 2011).

Upon waking each morning, you begin thinking—contemplating the tasks that you must complete that day. In what order should you run your errands? Should you go to the bank, the cleaners, or the grocery store first? Can you get these things done before you head to class or will they need to wait until school is done? These thoughts are one example of cognition at work. Exceptionally complex, cognition is an essential feature of human consciousness, yet not all aspects of cognition are consciously experienced.

Cognitive psychology  is the field of psychology dedicated to examining how people think. It attempts to explain how and why we think the way we do by studying the interactions among human thinking, emotion, creativity, language, and problem solving, in addition to other cognitive processes. Cognitive psychologists strive to determine and measure different types of intelligence, why some people are better at problem solving than others, and how emotional intelligence affects success in the workplace, among countless other topics. They also sometimes focus on how we organize thoughts and information gathered from our environments into meaningful categories of thought, which will be discussed later.

Concepts and Prototypes

The human nervous system is capable of handling endless streams of information. The senses serve as the interface between the mind and the external environment, receiving stimuli and translating it into nervous impulses that are transmitted to the brain. The brain then processes this information and uses the relevant pieces to create thoughts, which can then be expressed through language or stored in memory for future use. To make this process more complex, the brain does not gather information from external environments only. When thoughts are formed, the mind synthesizes information from emotions and memories ( Figure 7.2 ). Emotion and memory are powerful influences on both our thoughts and behaviors.

A flow chart is overlaid on a drawing of a head with a ponytail. The flowchart reads: Information, sensations (arrow) emotions, memories (arrow) thoughts (arrow) behavior. Thoughts is also connected to Emotions, memories via a feedback arrow.

Concepts are informed by our semantic memory (you will learn more about semantic memory in a later chapter) and are present in every aspect of our lives; however, one of the easiest places to notice concepts is inside a classroom, where they are discussed explicitly. When you study United States history, for example, you learn about more than just individual events that have happened in America’s past. You absorb a large quantity of information by listening to and participating in discussions, examining maps, and reading first-hand accounts of people’s lives. Your brain analyzes these details and develops an overall understanding of American history. In the process, your brain gathers details that inform and refine your understanding of related concepts like democracy, power, and freedom.

Concepts can be complex and abstract, like justice, or more concrete, like types of birds. Some concepts, like tolerance, are agreed upon by many people, because they have been used in various ways over many years. Other concepts, like the characteristics of your ideal friend or your family’s birthday traditions, are personal and individualized. In this way, concepts touch every aspect of our lives, from our many daily routines to the guiding principles behind the way governments function.

Another technique used by your brain to organize information is the identification of prototypes for the concepts you have developed. A  prototype  is the best example or representation of a concept. For example, what comes to your mind when you think of a dog? Most likely your early experiences with dogs will shape what you imagine. If your first pet was a Golden Retriever, there is a good chance that this would be your prototype for the category of dogs.

Natural and Artificial Concepts

In psychology, concepts can be divided into two categories, natural and artificial. Natural concepts  are created “naturally” through your experiences and can be developed from either direct or indirect experiences. For example, if you live in Essex Junction, Vermont, you have probably had a lot of direct experience with snow. You’ve watched it fall from the sky, you’ve seen lightly falling snow that barely covers the windshield of your car, and you’ve shoveled out 18 inches of fluffy white snow as you’ve thought, “This is perfect for skiing.” You’ve thrown snowballs at your best friend and gone sledding down the steepest hill in town. In short, you know snow. You know what it looks like, smells like, tastes like, and feels like. If, however, you’ve lived your whole life on the island of Saint Vincent in the Caribbean, you may never have actually seen snow, much less tasted, smelled, or touched it. You know snow from the indirect experience of seeing pictures of falling snow—or from watching films that feature snow as part of the setting. Either way, snow is a natural concept because you can construct an understanding of it through direct observations, experiences with snow, or indirect knowledge (such as from films or books) ( Figure 7.3 ).

Two images labeled a and b. A depicts a snowy field on a sunny day. B depicts a sphere, rectangular prism, and triangular prism.

An  artificial concept , on the other hand, is a concept that is defined by a specific set of characteristics. Various properties of geometric shapes, like squares and triangles, serve as useful examples of artificial concepts. A triangle always has three angles and three sides. A square always has four equal sides and four right angles. Mathematical formulas, like the equation for area (length × width) are artificial concepts defined by specific sets of characteristics that are always the same. Artificial concepts can enhance the understanding of a topic by building on one another. For example, before learning the concept of “area of a square” (and the formula to find it), you must understand what a square is. Once the concept of “area of a square” is understood, an understanding of area for other geometric shapes can be built upon the original understanding of area. The use of artificial concepts to define an idea is crucial to communicating with others and engaging in complex thought. According to Goldstone and Kersten (2003), concepts act as building blocks and can be connected in countless combinations to create complex thoughts.

A  schema (plural: schemata)  is a mental construct consisting of a cluster or collection of related concepts (Bartlett, 1932). There are many different types of schemata, and they all have one thing in common: schemata are a method of organizing information that allows the brain to work more efficiently. When a schema is activated, the brain makes immediate assumptions about the person or object being observed.

There are several types of schemata. A  role schema  makes assumptions about how individuals in certain roles will behave (Callero, 1994). For example, imagine you meet someone who introduces himself as a firefighter. When this happens, your brain automatically activates the “firefighter schema” and begins making assumptions that this person is brave, selfless, and community-oriented. Despite not knowing this person, already you have unknowingly made judgments about him. Schemata also help you fill in gaps in the information you receive from the world around you. While schemata allow for more efficient information processing, there can be problems with schemata, regardless of whether they are accurate: Perhaps this particular firefighter is not brave, he just works as a firefighter to pay the bills while studying to become a children’s librarian.

An  event schema , also known as a  cognitive script , is a set of behaviors that can feel like a routine. Think about what you do when you walk into an elevator ( Figure 7.4 ). First, the doors open and you wait to let exiting passengers leave the elevator car. Then, you step into the elevator and turn around to face the doors, looking for the correct button to push. You never face the back of the elevator, do you? And when you’re riding in a crowded elevator and you can’t face the front, it feels uncomfortable, doesn’t it? Interestingly, event schemata can vary widely among different cultures and countries. For example, while it is quite common for people to greet one another with a handshake in the United States, in Tibet, you greet someone by sticking your tongue out at them, and in Belize, you bump fists (Cairns Regional Council, n.d.)

A crowded elevator.

Because event schemata are automatic, they can be difficult to change. Imagine that you are driving home from work or school. This event schema involves getting in the car, shutting the door, and buckling your seatbelt before putting the key in the ignition. You might perform this script two or three times each day. As you drive home, you hear your phone’s ring tone. Typically, the event schema that occurs when you hear your phone ringing involves locating the phone and answering it or responding to your latest text message. So without thinking, you reach for your phone, which could be in your pocket, in your bag, or on the passenger seat of the car. This powerful event schema is informed by your pattern of behavior and the pleasurable stimulation that a phone call or text message gives your brain. Because it is a schema, it is extremely challenging for us to stop reaching for the phone, even though we know that we endanger our own lives and the lives of others while we do it (Neyfakh, 2013) ( Figure 7.5 ).

A hand holds a cellphone in front of a steering wheel and front-shield window of a car. The car is on a road.

Remember the elevator? It feels almost impossible to walk in and  not  face the door. Our powerful event schema dictates our behavior in the elevator, and it is no different with our phones. Current research suggests that it is the habit, or event schema, of checking our phones in many different situations that makes refraining from checking them while driving especially difficult (Bayer & Campbell, 2012). Because texting and driving has become a dangerous epidemic in recent years, psychologists are looking at ways to help people interrupt the “phone schema” while driving. Event schemata like these are the reason why many habits are difficult to break once they have been acquired. As we continue to examine thinking, keep in mind how powerful the forces of concepts and schemata are to our understanding of the world.

7.2 LAnguage

  • Define language and demonstrate familiarity with the components of language
  • Understand the development of language
  • Explain the relationship between language and thinking

Language  is a communication system that involves using words and systematic rules to organize those words to transmit information from one individual to another. While language is a form of communication, not all communication is language. Many species communicate with one another through their postures, movements, odors, or vocalizations. This communication is crucial for species that need to interact and develop social relationships with their conspecifics. However, many people have asserted that it is language that makes humans unique among all of the animal species (Corballis & Suddendorf, 2007; Tomasello & Rakoczy, 2003). This section will focus on what distinguishes language as a special form of communication, how the use of language develops, and how language affects the way we think.

Components of Language

Language, be it spoken, signed, or written, has specific components: a lexicon and lexicon grammar .  Lexicon  refers to the words of a given language. Thus, lexicon is a language’s vocabulary.  Grammar  refers to the set of rules that are used to convey meaning through the use of the lexicon (Fernández & Cairns, 2011). For instance, English grammar dictates that most verbs receive an “-ed” at the end to indicate past tense.

Words are formed by combining the various phonemes that make up the language. A  phoneme  (e.g., the sounds “ah” vs. “eh”) is a basic sound unit of a given language, and different languages have different sets of phonemes. For example, the phoneme English speakers associate with the letter ‘L’ is not used in the Japanese language. Similarly, many Southern African languages use phonemes, sometimes referred to as ‘click consonants’ that are not used in English.

Phonemes are combined to form  morphemes , which are the smallest units of language that convey some type of meaning. Some words are morphemes, but not all morphemes are words.  For example, “-ed” is a morpheme used to convey the past-tense in English, but it is not a word. The word “review” contains two morphemes: re- (meaning to do something again) and view (to see). Finally, some words like “I” and “a” are both a phonemes and morphemes.

We use semantics and syntax to construct language. Semantics and syntax are part of a language’s grammar.  Semantics  refers to the process by which we derive meaning from morphemes and words by connecting those morphemes and words to stored concepts.  Syntax  refers to the way words are organized into sentences (Chomsky, 1965; Fernández & Cairns, 2011). For example, you would never say “the dog walked I today” to let someone know you took your dog for a walk–that sentence does not obey English syntax and is therefore difficult to make sense of.

We apply the rules of grammar to organize the lexicon in novel and creative ways, which allow us to communicate information about both concrete and abstract concepts. We can talk about our immediate and observable surroundings as well as the surface of unseen planets. We can share our innermost thoughts, our plans for the future, and debate the value of a college education. We can provide detailed instructions for cooking a meal, fixing a car, or building a fire. Through our use of words and language, we are able to form, organize, and express ideas, schema, and artificial concepts.

Language Development

Given the remarkable complexity of a language, one might expect that mastering a language would be an especially arduous task; indeed, for those of us trying to learn a second language as adults, this might seem to be true. However, young children master language very quickly with relative ease. B. F.  Skinner  (1957) proposed that language is learned through reinforcement. Noam  Chomsky  (1965) criticized this behaviorist approach, asserting instead that the mechanisms underlying language acquisition are biologically determined. The use of language develops in the absence of formal instruction and appears to follow a very similar pattern in children from vastly different cultures and backgrounds. It would seem, therefore, that we are born with a biological predisposition to acquire a language (Chomsky, 1965; Fernández & Cairns, 2011). Moreover, it appears that there is a critical period for language acquisition, such that this proficiency at acquiring language is maximal early in life; generally, as people age, the ease with which they acquire and master new languages diminishes (Johnson & Newport, 1989; Lenneberg, 1967; Singleton, 1995).

Children begin to learn about language from a very early age ( Table 7.1 ). In fact, it appears that this is occurring even before we are born. Newborns show preference for their mother’s voice and appear to be able to discriminate between the language spoken by their mother and other languages. Babies are also attuned to the languages being used around them and show preferences for videos of faces that are moving in synchrony with the audio of spoken language versus videos that do not synchronize with the audio (Blossom & Morgan, 2006; Pickens, 1994; Spelke & Cortelyou, 1981).

DIG DEEPER: The Case of Genie

In the fall of 1970, a social worker in the Los Angeles area found a 13-year-old girl who was being raised in extremely neglectful and abusive conditions. The girl, who came to be known as Genie, had lived most of her life tied to a potty chair or confined to a crib in a small room that was kept closed with the curtains drawn. For a little over a decade, Genie had virtually no social interaction and no access to the outside world. As a result of these conditions, Genie was unable to stand up, chew solid food, or speak (Fromkin, Krashen, Curtiss, Rigler, & Rigler, 1974; Rymer, 1993). The police took Genie into protective custody.

Genie’s abilities improved dramatically following her removal from her abusive environment, and early on, it appeared she was acquiring language—much later than would be predicted by critical period hypotheses that had been posited at the time (Fromkin et al., 1974). Genie managed to amass an impressive vocabulary in a relatively short amount of time. However, she never developed a mastery of the grammatical aspects of language (Curtiss, 1981). Perhaps being deprived of the opportunity to learn language during a critical period impeded Genie’s ability to fully acquire and use language.

You may recall that each language has its own set of phonemes that are used to generate morphemes, words, and so on. Babies can discriminate among the sounds that make up a language (for example, they can tell the difference between the “s” in vision and the “ss” in fission); early on, they can differentiate between the sounds of all human languages, even those that do not occur in the languages that are used in their environments. However, by the time that they are about 1 year old, they can only discriminate among those phonemes that are used in the language or languages in their environments (Jensen, 2011; Werker & Lalonde, 1988; Werker & Tees, 1984).

After the first few months of life, babies enter what is known as the babbling stage, during which time they tend to produce single syllables that are repeated over and over. As time passes, more variations appear in the syllables that they produce. During this time, it is unlikely that the babies are trying to communicate; they are just as likely to babble when they are alone as when they are with their caregivers (Fernández & Cairns, 2011). Interestingly, babies who are raised in environments in which sign language is used will also begin to show babbling in the gestures of their hands during this stage (Petitto, Holowka, Sergio, Levy, & Ostry, 2004).

Generally, a child’s first word is uttered sometime between the ages of 1 year to 18 months, and for the next few months, the child will remain in the “one word” stage of language development. During this time, children know a number of words, but they only produce one-word utterances. The child’s early vocabulary is limited to familiar objects or events, often nouns. Although children in this stage only make one-word utterances, these words often carry larger meaning (Fernández & Cairns, 2011). So, for example, a child saying “cookie” could be identifying a cookie or asking for a cookie.

As a child’s lexicon grows, she begins to utter simple sentences and to acquire new vocabulary at a very rapid pace. In addition, children begin to demonstrate a clear understanding of the specific rules that apply to their language(s). Even the mistakes that children sometimes make provide evidence of just how much they understand about those rules. This is sometimes seen in the form of  overgeneralization . In this context, overgeneralization refers to an extension of a language rule to an exception to the rule. For example, in English, it is usually the case that an “s” is added to the end of a word to indicate plurality. For example, we speak of one dog versus two dogs. Young children will overgeneralize this rule to cases that are exceptions to the “add an s to the end of the word” rule and say things like “those two gooses” or “three mouses.” Clearly, the rules of the language are understood, even if the exceptions to the rules are still being learned (Moskowitz, 1978).

Language and Thought

When we speak one language, we agree that words are representations of ideas, people, places, and events. The given language that children learn is connected to their culture and surroundings. But can words themselves shape the way we think about things? Psychologists have long investigated the question of whether language shapes thoughts and actions, or whether our thoughts and beliefs shape our language. Two researchers, Edward Sapir and Benjamin Lee Whorf, began this investigation in the 1940s. They wanted to understand how the language habits of a community encourage members of that community to interpret language in a particular manner (Sapir, 1941/1964). Sapir and Whorf proposed that language determines thought. For example, in some languages there are many different words for love. However, in English we use the word love for all types of love. Does this affect how we think about love depending on the language that we speak (Whorf, 1956)? Researchers have since identified this view as too absolute, pointing out a lack of empiricism behind what Sapir and Whorf proposed (Abler, 2013; Boroditsky, 2011; van Troyer, 1994). Today, psychologists continue to study and debate the relationship between language and thought.

WHAT DO YOU THINK? The Meaning of Language

Think about what you know of other languages; perhaps you even speak multiple languages. Imagine for a moment that your closest friend fluently speaks more than one language. Do you think that friend thinks differently, depending on which language is being spoken? You may know a few words that are not translatable from their original language into English. For example, the Portuguese word  saudade  originated during the 15th century, when Portuguese sailors left home to explore the seas and travel to Africa or Asia. Those left behind described the emptiness and fondness they felt as  saudade  ( Figure 7.6 ) .  The word came to express many meanings, including loss, nostalgia, yearning, warm memories, and hope. There is no single word in English that includes all of those emotions in a single description. Do words such as  saudade  indicate that different languages produce different patterns of thought in people? What do you think??

Two paintings are depicted in a and b. A depicts a young boy leaning on a trunk. He looks forlornly past the viewer. B depicts a woman wrapped in a black shawl standing near a window. She reads a letter while holding the shawl to her mouth.

One group of researchers who wanted to investigate how language influences thought compared how English speakers and the Dani people of Papua New Guinea think and speak about color. The Dani have two words for color: one word for  light  and one word for  dark . In contrast, the English language has 11 color words. Researchers hypothesized that the number of color terms could limit the ways that the Dani people conceptualized color. However, the Dani were able to distinguish colors with the same ability as English speakers, despite having fewer words at their disposal (Berlin & Kay, 1969). A recent review of research aimed at determining how language might affect something like color perception suggests that language can influence perceptual phenomena, especially in the left hemisphere of the brain. You may recall from earlier chapters that the left hemisphere is associated with language for most people. However, the right (less linguistic hemisphere) of the brain is less affected by linguistic influences on perception (Regier & Kay, 2009)

7.3 Problem Solving

  • Describe problem solving strategies
  • Define algorithm and heuristic
  • Explain some common roadblocks to effective problem solving and decision making

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

Problem-Solving Strategies

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A  problem-solving strategy  is a plan of action used to find a solution. Different strategies have different action plans associated with them ( Table 7.2 ). For example, a well-known strategy is  trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Another type of strategy is an algorithm. An  algorithm  is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a  heuristic  is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

  • When one is faced with too much information
  • When the time to make a decision is limited
  • When the decision to be made is unimportant
  • When there is access to very little information to use in making the decision
  • When an appropriate heuristic happens to come to mind in the same moment

Working backwards  is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

EVERYDAY CONNECTION: Solving Puzzles

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( Figure 7.7 ) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

A sudoku puzzle is pictured. The puzzle is a 4x4 square with each sub-square also divided into four. Inside the top left square, the numbers are 3, blank, blank, 4 from left-to-right and top-to-bottom. In the top right square, the numbers are blank, two, one, blank. In the bottom left square, the numbers are blank, 3, four, blank; and the bottom right square contains 2, blank, blank, 1.

Here is another popular type of puzzle ( Figure 7.8 ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Nine dots are arrayed in three rows of three.

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A  mental set  is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

The top figure shows a book of matches, a box of tacks, and a candle. The bottom figure shows the box tacked to the wall with the candle standing in the box.

Functional fixedness  is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. Duncker (1945) conducted foundational research on functional fixedness. He created an experiment in which participants were given a candle, a book of matches, and a box of thumbtacks. They were instructed to use those items to attach the candle to the wall so that it did not drip wax onto the table below. Participants had to use functional fixedness to solve the problem ( Figure 7.10 ). During the  Apollo 13  mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An  anchoring bias  occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The  confirmation bias  is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis.  Hindsight bias  leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did.  Representative bias  describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the  availability heuristic  is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision .  Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in  Table 7.3 .

Were you able to determine how many marbles are needed to balance the scales in  Figure 7.9 ? You need nine. Were you able to solve the problems in  Figure 7.7  and  Figure 7.8 ? Here are the answers ( Figure 7.11 ).

image

Chapter Summary

7.1 what is cognition.

In this section, you were introduced to cognitive psychology, which is the study of cognition, or the brain’s ability to think, perceive, plan, analyze, and remember. Concepts and their corresponding prototypes help us quickly organize our thinking by creating categories into which we can sort new information. We also develop schemata, which are clusters of related concepts. Some schemata involve routines of thought and behavior, and these help us function properly in various situations without having to “think twice” about them. Schemata show up in social situations and routines of daily behavior.

7.2 Language

Language is a communication system that has both a lexicon and a system of grammar. Language acquisition occurs naturally and effortlessly during the early stages of life, and this acquisition occurs in a predictable sequence for individuals around the world. Language has a strong influence on thought, and the concept of how language may influence cognition remains an area of study and debate in psychology.

Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

thinking; or, all of the processes associated with perception, knowledge, problem solving, judgement, language, and memory.

A modern school of psychological thought that empirically examines mental processes such as perception, memory, language, and judgement.

a category or grouping of linguistic information, images, ideas or memories, such as life experiences.

knowledge about words, concepts, and language-based knowledge and facts

the best example or representation of a concept, specific to an individual

concepts developed through direct or indirect experiences with the world

a concept defined by a specific set of characteristics.

a mental construct consisting of a cluster of related concepts

a set of ideas relating to how individuals in certain roles will behave.

also known as a cognitive script; a set of behaviors associated with a particular place or event

also known as an event schema; a set of behaviors associated with a particular place or event

a communication system that involves using words and systematic rules to organize those words to transmit information from one individual to another.

the words of a language

the rules of a language used to convey meaning through the use of the lexicon

the basic sounds that make up a language

the smallest unit of language that conveys meaning

the process by which we derive meaning from morphemes and words

the rules guiding the organization of morphemes into words and words into sentences.

Psychology 2e Copyright © 2020 by Openstax is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

Share This Book

National Academies Press: OpenBook

How People Learn II: Learners, Contexts, and Cultures (2018)

Chapter: 5 knowledge and reasoning, 5 knowledge and reasoning.

This chapter examines the development of knowledge as a primary outcome of learning and how learning is affected by accumulating knowledge and expertise. HPL I 1 emphasized these topics as well, but subsequent research has refined and extended understandings in a variety of learning domains. The first section of this chapter describes the problem of knowledge integration from the perspective of learning scientists and illustrates with research findings how people integrate their knowledge at different points in their development and in different learning situations. The second section describes what is known about the effects of accumulated knowledge and expertise on learning. The second half of the chapter discusses strategies for supporting learning. The committee has drawn on both laboratory- and classroom-based research for this chapter.

HPL I noted that the mind works actively to both store and recall information by imposing structure on new perceptions and experiences ( National Research Council, 2000 ). A central focus of HPL I was how experts structure their knowledge of a domain in ways that allow them to readily categorize new information and determine its relevance to what they already know. Because novices lack these frameworks, they have more difficulty assimilating and later recalling new information they encounter. This chapter expands on these themes from HPL I , citing relevant research reported since that study.

___________________

1 As noted in Chapter 1 , this report uses the abbreviation “ HPL I ” for How People Learn: Brain, Mind, Experience, and School: Expanded Edition ( National Research Council, 2000 ).

BUILDING A KNOWLEDGE BASE

Knowledge integration is a process through which learners put together different sorts of information and experiences, identifying and establishing relationships and expanding frameworks for connecting them. Learners must not only accumulate knowledge from individual episodes of experience but also integrate the knowledge they gain across time, location, circumstances, and the various formats in which knowledge appears ( Esposito and Bauer, 2017 ). How knowledge acquired in discrete episodes is integrated has been debated for decades ( Karmiloff-Smith, 1986 , 1990 ; Mandler, 1988 ; Nelson, 1974 ). Some researchers have suggested that infants are born with foundational knowledge that provides the elements necessary for learning and reasoning about their experiences ( Spelke, 2004 ; Spelke and Kinzler, 2007 ) or that infants can build from basic inborn reflexes to actively engage with the world and gradually build skills and knowledge ( Fischer and Bidell, 2006 ). Others have argued that all knowledge is generated through an individual’s direct experience with the world ( Greeno et al., 1996 ; Packer, 1985 ).

More recent work suggests that the integration of knowledge is a natural byproduct of the formation and consolidation of episodic memories ( Bauer, 2009 ; Bauer et al., 2012 ). As described in Chapter 4 , when a memory is consolidated, the learner associates representations of the elements of the experience (e.g., sights, sounds, tactile sensations) and these associations serve to help stabilize that memory. At the same time, these representations may also be linked with older memories from previous experiences that have already been stored in long-term memory ( Zola and Squire, 2000 ). The fact that old and new memory traces can be integrated shows that these traces are not fixed. Instead, elements common to the new and stored memory traces reactivate the old memory and, as the new memory is consolidated, the old memory may be reconstructed and undergo consolidation again ( Nader, 2003 ). When information from either learning episode is later retrieved, elements of both memory traces will be reactivated and will be simultaneously available for reintegration. As memory traces with common elements are simultaneously activated and linked, knowledge is expanded and memories are iteratively reworked. Figure 5-1 illustrates how this happens.

These linked traces may then be integrated with additional new information that comes to the learner later, and another new memory trace undergoes consolidation. Interestingly, it is exactly this process of integration of information from different episodes that may explain why people are sometimes unable to explain when and where they gained particular knowledge. Because the information generated by memory integration was not actually experienced as a single event, the information was not tagged with its origin ( Bauer and Jackson, 2015 ).

The studies of knowledge acquisition in children and college students presented in Box 5-1 illustrate the capacity to integrate unconnected infor-

Image

mation and retain this knowledge starting at a very young age. These studies underscore the active role of the learner; that is, even young children do not simply accrue knowledge from what they have experienced directly but build knowledge from the many things that they have figured out on their own, which, over time, they can do with less repetition and external support.

As discussed in Chapter 2 , adequate sleep is important for integration and learning. The brain continues the work of encoding and consolidation during sleep and facilitates generalizations across learning episodes ( Coutanche et al., 2013 ; Van Kesteren et al., 2010 ). Specifically, activation of the hippocampus (which plays a key role in memory integration) during sleep seems to allow connections between memory traces to be formed across the cortex. This process promotes the integration of new information into existing memory traces, allows for abstraction across episodes ( Lewis and Durant, 2011 ), and leads to the possibility of building novel connections, which may be both creative and insightful or may be bizarre ( Diekelmann and Born, 2010 ).

BOX 5-1 Examples of Developmental Differences in the Process of Knowledge Acquisition

Knowledge and expertise.

When people repeatedly engage with similar situations or topics, they develop mental representations that connect disparate facts and actions into more effective mental structures for acting in the world. For example, when people first move to a new neighborhood, they may learn a set of discrete routes for traveling between pairwise locations, such as from home to school and from home to the grocery store. Over time, people naturally develop a mental representation of spatial relationships, or mental map, that stitches these discrete routes together. Even if they have never traveled between the school and the grocery store, they can figure out the most efficient route by consulting their mental map ( Thorndyke and Hayes-Roth, 1982 ). The observation that experts in a domain have developed frameworks of information and understanding through long experiences in a particular area was a central focus of HPL I . In this section, we briefly describe some of the benefits of expert knowledge (a more detailed discussion of the benefits of expertise appears in HPL I ) and then discuss the knowledge-related biases that may come with expertise.

Benefits of Expertise

One of the most well-documented benefits of the acquisition of knowledge is an increase in the speed and accuracy with which people can complete recurrent tasks: remembering a solution is faster than problem solving. Another benefit is that people who develop expertise can handle increasingly complex problems. One way this occurs is that people master substeps, so that each substep becomes a chunk of knowledge that does not require attention (e.g., Gobet et al., 2001 ). People also learn to handle complexity by developing mental representations that make specific tasks easier to complete. When Hatano and Osawa (1983) studied abacus masters, they found that even without an abacus in front of them, the masters had prodigious memories for numbers and could carry out addition problems with very large numbers because they had developed a mental representation of an abacus, which they manipulated virtually. These abacus masters did not show similarly superior ability to remember or keep track of letters or fruits—tasks that were not aided by manipulating a virtual abacus.

A third benefit is an increase in the ability to extract relevant information from the environment. Experts not only have better-developed knowledge representations than novices have but also can perceive more information that is relevant to those representations. For example, radiologists are able to see telling patterns in an x-ray that appear merely as shadows to a novice ( Myles-Worsley et al., 1988 ). The ability to discern more precise information complements a more-differentiated mental representation of those phenomena.

An implication of this ability is that students need to learn to see the relevant information in the environment to help differentiate concepts, such as the difference between a positive and a negative curvilinear slope ( Kellman et al., 2010 ).

A fourth benefit of acquiring expert knowledge is that it helps people use their environment as a resource. Using what is known as distributed cognition, people can offload some of the cognitive demands of a task onto their environment or other people ( Hollan et al., 2000 ). For instance, a major goal of learning is to develop knowledge of where to look for resources and help, and this is still important in the digital age. Experts typically know which tools are available and who in their network has specialized expertise they can call upon.

Finally, acquiring knowledge helps people gain more knowledge by making it easier to learn new and related information. Although some cognitive abilities related to learning novel information decline, on average, with age, these declines are offset by increases in knowledge accumulated through the life span, which empowers new learning. For example, in a study of young adults and older adults (in their 70s) who listened to a broadcast of a baseball game, the older adults who knew a lot about baseball recalled more of the broadcast than the young adults who knew less about baseball. This occurred despite the fact that the younger adults had superior executive functioning ( Hambrick and Engle, 2002 ).

Bias as a Natural Side Effect of Knowledge

As people’s knowledge develops, their thinking also becomes biased. But the biases may be either useful or detrimental to learning. The word “bias” often has negative connotations, but bias as understood by psychologists is a natural side effect of knowledge acquisition. Learning biases are often implicit and unknown to the individuals who hold them. They appear relatively early in knowledge acquisition, as people begin to form schemas (conceptual frameworks) for how the world operates and their place within it. These schemas help individuals know what to expect and what to attend to in particular situations (e.g., in a doctor’s office versus at a friend’s party) and help them develop a sense of cultural fluency—that is, to know how things work “around here” ( Mourey et al., 2015 ).

Psychologists distinguish two types of bias: one is intrinsic to learning and primarily useful and empowering to the learner; the second occurs when prior experiences or beliefs undermine the acquisition of new knowledge and skills.

An aphorism from the context of medical diagnosis illustrates the two types of bias: “When you hear hoof-beats, think of horses not zebras.” In the United States, horses are much more common than zebras so one is much more likely to encounter the common “horses” than the rare “zebras.” Of course, one should modify assumptions in light of additional evidence: if the

large mammal from which the hoof-beats emanate has black and white stripes, it is much more likely to be a zebra than a horse. Thus, if one sees a striped animal in a zoo but insists that it is a horse and not a zebra, this resistance to new information is a strong form of the limiting effects of bias on learning. A person may fail even to notice the zebra at the zoo because he was so strongly expecting to see a horse instead and was attuned to notice only that kind of animal.

Making matters even more complicated, two people who have different prior levels of expertise, or different beliefs, might legitimately have different interpretations when initially presented with the same information. But if sufficient additional information suggests a particular interpretation, they should converge on an answer, especially if the higher level of expertise is brought to bear.

Beliefs about human-caused global climate change are a good example of the biases that blind individuals to new evidence. Despite nearly universal consensus among climate scientists that global climate change is taking place and that this change is induced by humans’ behavior, a considerable proportion of adults in the United States do not accept these interpretations of the evidence. One might expect that higher levels of science literacy would be associated with greater agreement with the scientific consensus. However, Kahan and colleagues (2012) found that it is among the individuals with the highest levels of science literacy that the most stark polarization is apparent. Those who only seek out and attend to information consistent with their prior beliefs will create an “echo-chamber” that further biases their learning. Often this echo-chamber effect is socially reinforced, as individuals prefer to discuss the topic in question with others whom they know hold beliefs similar to their own.

Stereotypes perpetuate themselves through learned bias, but not all learning biases are considered to have negative consequences. For example, some positive biases promote well-being and mental health ( Taylor and Brown, 1988 ), some may promote accuracy in perceptions of other people ( Funder, 1995 ), and others may be adaptive behaviors—for example, selective attention and action in situations in which errors have a high cost ( Haselton and Buss, 2000 ; Haselton and Funder, 2006 ). Hahn and Harris (2014) have written a useful historical overview of research on bias in human cognition.

Still other biases refine perception and serve to blur distinctions within categories that are not meaningful while highlighting subtle cross-category distinctions that may be important. For example, very young infants respond equally to phonological contrasts that matter in their language (e.g., “r” and “l” if the baby lives in an English-speaking context) and those that do not matter (e.g., “r” and “l” in a Japanese-speaking context). Over time, infants lose this discriminatory capability. This loss is actually a benefit, reflecting the baby’s increasing efficiency in processing his own language context, and is a mark of

learning ( Kuhl et al., 1992 ). In the other direction, dermatologists may learn from experience and formal training to distinguish subtle features of moles and skin growths that signal malignancy, features that to an untrained eye are indistinguishable from those of benign growths.

Biases affect the noncognitive aspects of learning as well. In a variable world, highly stable task environments are not guaranteed and so training to high efficiency may actually create a mindset that makes new learning more difficult, impeding motivation and interest in continuous growth and development. For instance, a person who has learned how to organize her schedule using a specific tool may be reluctant to learn a new tool because of the perception that it will take too much time to learn to use it, even though it may be more efficient in the long run. In this example, it is not that the person is unable to learn the new tool; rather, her beliefs about the amount of effort required affect her motivation and interest in learning. This kind of self-attribution, or prior knowledge of oneself, can have a large influence on how people approach future learning opportunities, which in turn influences what they will learn ( Blackwell et al., 2007 ).

KNOWLEDGE INTEGRATION AND REASONING

We have seen that building a knowledge base requires doing three things: accumulating information (in part by noticing what matters in a situation and is therefore worth attending to); tagging this information as relevant or not; and integrating it across separate episodes. These three activities can happen relatively quickly and automatically, or they can happen slowly through deliberate reflection. However, these processes alone are not sufficient for integrating and extending knowledge. Learners of all ages know many things that were not explicitly taught or directly experienced. They routinely generate their own novel understanding of the information they are accumulating and productively extend their knowledge.

Inferential Reasoning

Inferential reasoning refers to making logical connections between pieces of information in order to organize knowledge for understanding and to drawing conclusions through deductive reasoning, inductive reasoning, and abductive reasoning ( Seel, 2012 ). Inferential thinking is needed for such processes as generalizing, categorizing, and comprehending. The act of reading a text is a good example. To comprehend a text, readers are required to make inferences regarding information that is only implied in the text (see, e.g., Cain and Oakhill, 1999 ; Graesser et al., 1994 ; Paris and Upton, 1976 ). Some types of inferences help readers track the meaning of a text by integrating different information it supplies, for example by recognizing anaphoric

references (words in a text that require the reader to refer back to other ideas in the text for their meaning). Other types of inferences allow a reader to fill in gaps in the text by recruiting information from beyond it (i.e., background knowledge), in order to understand information within the text. Though these types of inferences are essential for understanding, they are thought to survive in working memory only long enough to aid comprehension ( McKoon and Ratcliff, 1992 ).

Other inferences that learners make survive beyond the bounds of working memory and become incorporated into their knowledge base. For example, a person who knows both that liquids expand with heat and that thermometers contain liquid may integrate these two pieces of information and infer that thermometers work because liquid expands as heat increases. In this way, the learner generates understanding through a productive extension of prior learning episodes.

Effective problem solving typically requires retrieved knowledge to be adapted and transformed to fit new situations; therefore, memory retrieval must be coordinated with other cognitive processes. One way to help people realize that something they have learned before is relevant to their current task is to explicitly give them a hint that it is relevant ( Gick and Holyoak, 1980 ). For example, such hints might be embedded in text, provided by a teacher, or incorporated into virtual learning platforms. Another strategy for helping people realize that they already know something useful is to ask people to compare related problems in order to highlight exactly what they have in common, increasing the likelihood that they will recall previously acquired knowledge with similar properties ( Alfieri et al., 2013 ; Gentner et al., 2009 ).

Kolodner et al. (2003) gives the example of an architect trying to build an office building with a naturally lit atrium. She realizes that a familiar library’s design, which includes an exterior wall of glass, could be reused for the office building, but would fit the building’s needs better if translucent glass bricks were used instead of a clear, glass pane. This kind of design-based reasoning is incorporated into problem-based learning ( Hmelo-Silver, 2004 ) activities. Problem-based learning emphasizes that memories are not simply stored to allow future reminiscing, but are formed so that they can be used, reshaped, and flexibly adapted to serve broad reasoning needs. The goal of problem-based learning is to instill in learners flexible knowledge use, effective problem-solving skills, self-directed learning, collaboration, and intrinsic motivation. These goals are in line with several of the goals identified in other contexts as important for success in life and work ( National Research Council, 2012b ).

Age-Related Changes in Knowledge and Reasoning

People’s learning benefits from a steady increase, over many decades, in the accumulation of world knowledge (e.g., Craik and Salthouse, 2008 ;

Hedden and Gabrieli, 2004 ). This accumulation makes it easier for older adults not only to retrieve vocabulary and facts about the world ( Cavanagh and Blanchard-Fields, 2002 ) but also to acquire new information in domains related to their expertise. For example, physicians acquire medical expertise, which enables them to comprehend and remember more information from medical texts than novices can ( Patel et al., 1986 ). It is also thought that older adults can compensate for declines in some abilities by using their extensive world knowledge. For instance, medical experts depend less on working memory because they can draw on their expertise to reconstruct only those facts from long-term memory that are relevant to a current need (e.g., Patel and Groen, 1991 ).

The knowledge learners accumulate throughout the life span is the growing product of the processes of both learning new information from direct experience and generating new information based on reasoning and imagining ( Salthouse, 2010 ). These two cognitive assets together—accumulated knowledge and reasoning ability—are particularly relevant to healthy aging. Reasoning and knowledge abilities tend to be correlated. That is, people who have comparatively higher reasoning capacity are likely to acquire correspondingly more knowledge over the life span than their peers ( Ackerman and Beier, 2006 ; Beier and Ackerman, 2005 ). Reasoning ability is a major determinant of learning throughout life, and it is through reasoning, especially in contexts that allow people to pursue their interests, that people develop knowledge throughout their life span ( Ackerman, 1996 ; Cattell, 1987 ).

On average, however, the trajectories of reasoning and knowledge acquisition are different across the life span. A number of research studies have described the general trajectories of age-related changes in ability, using a variety of measures and research designs (cross-sectional and longitudinal), and have shown a fairly consistent trend in which the development of knowledge remains steady as reasoning capacity (the ability to quickly and accurately manipulate multiple distinct pieces of factual information to make inferences) drops off ( Salthouse, 2010 ). However, there is considerable individual variability in the trajectories, which reflect individual health and other characteristics, as well as educational and experiential opportunities and even social engagement. Yet, even though there is an average decline in inferential reasoning capacity through adulthood, there is not a corresponding decline in the ability to make good decisions—a more colloquial use of the word “reasoning.” In other words, the research does not suggest that the average 14-year-old reasons better about what to do in a complex or emotional real-world situation than would an average 50-year-old. Instead, it describes the 14-year-old’s stronger ability to quickly manipulate multiple distinct pieces of factual information to make logical and combinatorial inferences.

The growth or decline of abilities can be expected to vary not only between individuals but also within the same person over time ( Hertzog et al.,

2008 ). Two 50-year-olds may have extremely different cognitive profiles, such that one may generally have the same ability profile as an average 30-year-old and the other may more closely resemble an average 70-year-old. Within the same person, abilities will decline or grow at varying rates as a function of that individual’s continuing use of some skills and intellectual development in particular domains; losses and declines are associated with disuse of other skills. (Factors that influence cognitive aging are discussed in Chapter 9 .) As mentioned, new learning depends on both reasoning ability and knowledge acquisition ( Ackerman and Beier, 2006 ; Beier and Ackerman, 2005 ). Even though reasoning abilities decline with age, knowledge accumulated throughout the life span facilitates new learning, as long as the information to be learned is aligned with existing domain knowledge. When people select environments for education, work, and hobbies that capitalize on their already-established knowledge and skills as they age, their selectivity allows them to capitalize on their repertoire of knowledge and expertise for learning new information ( Baltes and Baltes, 1990 ).

Cognitive abilities change throughout the life span in a variety of ways that may affect a person’s ability to learn new things (see Hartshorne and Germine, 2015 , for discussion). For instance, as people age, learning may rely more on knowledge and less on reasoning and quick manipulation of factual information. However, examining peoples’ cognitive abilities and learning becomes increasingly complex as people develop past the age of formal education. One reason is that the ways in which people learn become increasingly idiosyncratic outside of a standardized educational curriculum, and understanding this process requires assessing knowledge gained through a wide variety of adult experiences that different individuals amass over a lifetime ( Lubinski, 2000 ). The unique complexities of adult learning and development are discussed in Chapter 8 .

Effects of Culture on Reasoning

As described in Chapter 2 , learning is inherently cultural, given that a person’s experiences in a culture affect biological processes that support learning, perception, and cognition. In the area of reasoning, for example, researchers have explored fundamental differences in peoples’ reasoning about three basic domains of life: physical events (naïve physics), biological events (naïve biology), and social or psychological events (naïve psychology) (see e.g., Carey, 1985 , 2009 ; Goswami, 2002 ; Hirschfeld and Gelman, 1994 ; Spelke and Kinzler, 2007 ; also see Ojalehto and Medin, 2015c , for a review). These distinctions are compelling in the sense that each reflects a set of intuitive principles and inferences. That is, each domain is defined by entities having the same kind of causal properties. These might be marked, for example, by the way they move: physical entities are set into motion by external forces,

while biological entities may propel themselves. These domains are important for understanding cognition because researchers have suggested that whereas the perception of physical causality is universal, causal reasoning in the biological and psychological domains is culturally variable.

Two studies illustrate ways to examine these issues. Morris and Peng (1994) presented two types of animated displays to American and Chinese participants. One set of displays depicted physical interactions (of geometrical shapes), whereas the other set depicted social interactions (among fish). The participants’ answers to questions about what they had seen suggested differences in attention to internal and external causes across the groups, but those differences depended on the domain (social or physical). The authors concluded that attribution of causality in the social domain is susceptible to cultural influences but that causality in the physical domain is not.

Beller and colleagues (2009) asked German, Chinese, and Tongan participants to indicate which entity they regarded as causally most relevant for statements such as “The fact that wood floats on water is basically due to . . . ”. Ratings varied by the cultural background of respondents and also by the phenomena participants were considering. In general, the German and Chinese participants, but not the Tongan participants, considered a carrier’s capability for buoyancy only when the floater was a solid object, such as wood, but not when it was a fluid, such as oil ( Beller et al., 2009 ; see also Bender et al., 2017 ). This is an area of research that has barely been explored, but results to date suggest that the perception of physical causality may in fact not be universal and may be learned in culturally mediated ways.

STRATEGIES TO SUPPORT LEARNING

People are naturally interested in strengthening their ability to acquire and retain knowledge and in ways to improve learning performance. Researchers have explored a variety of strategies to support learning and memory. They have identified several principles for structuring practice and engaging with information to be learned to improve memory, to make sense of new information, and to develop new knowledge.

Several scholars have looked across the research on the effectiveness of specific strategies for supporting learning ( Benassi et al., 2014 ; Dunlosky et al., 2013 ; Pashler et al., 2007 ). The authors of these three studies looked for strategies that (1) have been examined in several studies, using authentic educational materials in classroom settings; (2) show effects that can be generalized across learner characteristics and types of materials; (3) promote learning that is long-lasting; and (4) support comprehension, knowledge application, and problem solving in addition to recall of factual material. These three analyses identified five learning strategies as promising:

  • retrieval practice;
  • spaced practice;
  • interleaved and varied practice;
  • summarizing and drawing; and
  • explanations: elaborative interrogation, self-explanation, and teaching.

Strategies for Knowledge Retention

The first three strategies are ways of structuring practice that are particularly useful for increasing knowledge retention.

Retrieval Practice

Some evidence shows that the act of retrieval itself enhances learning and that when learners practice retrieval during an initial learning activity, their ability to retrieve and use knowledge again in the future is enhanced ( Karpicke, 2016 ; Roediger and Karpicke, 2006b ). The benefits of retrieval practice in general have been shown to generalize across individual differences in learners, variations in materials, and different assessments of learning. For example, researchers have found effects across learner characteristics in children ( Lipko-Speed et al., 2014 ; Marsh et al., 2012 ). Studies have also suggested that retrieval practice can be a useful memory remediation method among older adults ( Balota et al., 2006 ; Meyer and Logan, 2013 ; also see Dunlosky et al., 2013 , for a review of effective learning techniques). However, most of this research has addressed retrieval of relatively simple information (e.g., vocabulary), rather than deep understanding.

Research has also demonstrated the effects of retrieval practice on recall of texts and other information related to school subjects. For example, Roediger and Karpicke (2006a) had students read brief educational texts and practice recalling them. Students in one condition read the texts four times; students in a second group read three times and recalled the texts once by writing down as much as they could remember; and students in a third group read the material once and then recalled it during three retrieval practice periods. On a final test given 1 week after the initial learning session, students who practiced retrieval one time recalled more of the material than students who only read the texts, and the students who repeatedly retrieved the material performed the best. The results suggest that actively retrieving the material soon after studying it is more productive than spending the same amount of time repeatedly reading.

Attempting retrieval but failing has also been shown to promote learning. Failed retrievals provide feedback signals to learners, signaling that they may not know the information well and should adjust how they encode the material the next time they study it ( Pyc and Rawson, 2010 ). The act of failing to retrieve may thus enhance subsequent encoding ( Kornell, 2014 ).

Such studies suggest that self-testing can be an effective way for students to practice retrieval. However, evidence from surveys of students’ learning strategies and from experiments in which learners are given control over when and how often they can test themselves suggests that students may not test themselves often or effectively enough ( Karpicke et al., 2009 ; Kornell and Son, 2009 ). Many students do not engage in self-testing at all, and when students do test themselves, they often do so as a “knowledge check” to see whether they can or cannot remember what they are learning. While this is an important use of self-testing, few learners self-test because they view the act of retrieval as part of the process of learning. Instead, they are likely to retrieve something once and then, believing they have learned it for the long term, drop the item from further practice.

Spaced Practice

Researchers who have compared spaced and massed practice have shown that the way that learners schedule practice can have an impact on learning ( Carpenter et al., 2012 ; Kang, 2016 ). Massed practice concentrates all of the practice sessions in a short period of time (such as cramming for a test), whereas spaced practice distributes learning events over longer periods of time. Results show greater effects for spacing than for massed practice across learning materials (e.g., vocabulary learning, grammatical rules, history facts, pictures, motor skills) ( Carpenter et al., 2012 ; Dempster, 1996 ), stimulus formats (e.g., audiovisual, text) ( Janiszewski et al., 2003 ), and for both intentional and incidental learning ( Challis, 1993 ; Toppino et al., 2002 ). Studies have shown benefits of spaced practice for learners of ages 4 through 76 ( Balota et al., 1989 ; Rea and Modigliani, 1987 ; Simone et al., 2012 ; Toppino, 1991 ). Cepeda and colleagues (2006) found that spaced practice led to greater recall than massed practice regardless of the size of the lag between practice and recall.

There are many possible reasons why spaced practice might be more effective than massed practice. When an item, concept, or procedure is repeated after a spaced interval, learners have to fully engage in the mental operations they performed the first time because of forgetting that has occurred. But when repetitions are immediate and massed together, learners do not fully engage during repetitions. In the case of reading, one possible reason why massed re-readings do not promote learning is that when people reread immediately, they do not attend to the most informative and meaningful portions of the material during the second reading, as illustrated by Dunlosky and Rawson (2005) in a study of self-paced reading.

A few researchers have attempted to identify the spacing intervals that promote the most memory—a “sweet spot” where spaced practice confers benefits before too much forgetting has occurred ( Cepeda et al., 2008 ; Pavlik and Anderson, 2008 ). For example, a study of vocabulary learning among fifth

graders suggested that a 2-week interval showed the best results ( Sobel et al., 2011 ). Another classroom-based study of spacing effects focused on first-grade children learning to associate letters and sounds during phonics instruction ( Seabrook et al., 2005 ). The children who received spaced practice during the 2-week period significantly outperformed the children who received a single massed practice session each day.

In general, the literature on spaced practice suggests that separating learning episodes by at least 1 day, rather than focusing the learning into a single session, maximizes long-term retention of the material. However, it is important to note that wider spacing is not necessarily always better. The optimal distribution of learning sessions depends at least in part on how long the material needs to be retained in memory (i.e., when the material will be recalled or tested). For example, if the learner will be tested 1 month or more after the last learning session, then the learning should be distributed over weeks or months.

Interleaved and Variable Practice

The way information is presented can significantly affect both what is learned ( Schyns et al., 1998 ) and how well it is learned ( Goldstone, 1996 ). Variable learning generally refers to practicing skills in different ways, while interleaving refers to mixing in different activities. Varying or interleaving different skills, activities, or problems within a learning session—as opposed to focusing on one skill, activity, or problem throughout (called blocked learning)—may better promote learning. Both strategies may also involve spaced practice, and both also present learners with a variety of useful challenges, or “desirable difficulties.” Researchers have identified potential benefits of variable and interleaved practice learning, but they have also found a few benefits for blocked practice.

Several studies have shown benefits for blocking, at least for category learning ( Carpenter and Mueller, 2013 ; Goldstone, 1996 ; Higgins and Ross, 2011 ). Moreover, when given the option, a majority of learners preferred to block their study ( Carvalho et al., 2014 ; Tauber et al., 2013 ). Interleaving can boost learning of the structure of categories; that is, learning that some objects or ideas belong to the same category and others do not ( Birnbaum et al., 2013 ; Carvalho and Goldstone, 2014a , 2014b ; Kornell and Bjork; 2008 ). Other researchers have examined interleaved practice in mathematical problem-solving domains ( Rohrer, 2012 ; Rohrer et al., 2015 ).

Carvalho and Goldstone (2014a) found that the effectiveness of the presentation methods (interleaved or blocked) depended on whether the participant engaged in active or passive study. They also found that interleaving concepts improved students’ capacity to discriminate among different categories, while blocked practice emphasized similarities within each category. These results

suggest that interleaved study improves learning of highly similar categories (by facilitating between-category comparisons), whereas blocked study improves learning of low-similarity categories (by facilitating within-category comparisons).

Interleaved study naturally includes delays between learning blocks and thus easily allows for spaced practice, which has the potential benefits for long-term memory discussed above. However, it may be beneficial because it helps learners to make comparisons among categories, not because it allows time to elapse between learning blocks ( Carvalho and Goldstone, 2014b ). The mechanisms that underlie the benefits of either interleaved or blocked study (e.g, possible effects on attentional processes) are ongoing topics of research. As with other strategies, the optimal way to present material—interleaved or blocked—and the mechanisms most heavily involved will likely depend on the nature of the study task.

Strategies for Understanding and Integration

The other two strategies for which there is strong evidence—summarizing and drawing and developing explanations—draw on inferential processes that research shows to be effective for organizing and integrating information for learning.

Summarizing and Drawing

Summarizing and drawing are two common strategies for elaborating on what has been learned. To summarize is to create a verbal description that distills the most important information from a set of materials. Similarly, when learners create drawings, they use graphic strategies to portray important concepts and relationships. In both activities, learners must take the material they are learning and transform it into a different representation. There are differences between them, but both activities involve identifying important terms and concepts, organizing the information, and using prior knowledge to create verbal or pictorial representations.

Both summarization and drawing have been shown to benefit learning in school-age children ( Gobert and Clement, 1999 ; Van Meter, 2001 ; Van Meter and Garner, 2005 ). Literature reviews by Dunlosky and colleagues (2013) and Fiorella and Mayer (2015a , 2015b ) have identified factors that appear to contribute to the effectiveness of summarization and drawing activities.

A few studies have suggested that the quality of students’ summaries and drawings is directly related to how much they learn from the activities and that learners do these activities more effectively when they are trained and guided ( Bednall and Kehoe, 2011 ; Brown et al., 1983 ; Schmeck et al., 2014 ). For example, the effectiveness of drawing activities is enhanced when learners

compare their drawings to author-generated pictures ( Van Meter et al., 2006 ). Similarly, providing learners with a list of relevant elements to be included in drawings and partial drawings helps learners create more complete drawings and bolsters learning ( Schwamborn et al., 2010 ).

A group of researchers compared summarization and drawing and suggested that their effectiveness depends on the nature of the learning materials. For example, Leopold and Leutner (2012) asked high school students who were studying a science text about water molecules, which contained descriptions of several spatial relations, to either draw diagrams, write a summary of the text, or to re-read the text (the control condition). Those who created drawings performed better on a comprehension test than those who re-read the texts. However, those who created written summaries performed worse than those who re-read. The authors concluded that the drawing was more effective in this case because the learning involved spatial relations.

Note-taking, either writing by hand or typing on a laptop, is a form of summarizing that has also been studied. For example, Mueller and Oppenheimer (2014) found that students who hand-wrote notes learn more than those who typed notes using a laptop computer. The researchers asked students to take notes in these two ways and then tested their recall of factual details, conceptual understanding, and ability to synthesize and generalize the information. They found that students who typed took more voluminous notes than those who wrote by hand, but the hand-writers had a stronger conceptual understanding of the material and were more successful in applying and integrating the material than the typers. The researchers suggested that because writing notes by hand is slower, students doing this cannot take notes verbatim but must listen, digest, and summarize the material, capturing the main points. Students who type notes can do so quickly and without processing the information.

Mueller and Oppenheimer (2014) also examined the contents of notes taken by college students in these two ways across a number of disciplines. They found that the typed notes—which were closer to verbatim transcriptions—were associated with lower retention of the lecture material. Even when study participants using laptops were instructed to think about the information and type the notes in their own words, they were no better at synthesizing material than students who were not given the warning. The authors concluded that typing notes does not promote understanding or application of the information; they suggested that notes in the students’ own words and handwriting may serve as more effective memory prompts by recreating context (e.g., thought processes, conclusions) and content from the original lecture.

Developing Explanations

Encouraging learners to create explanations of what they are learning is a promising method of supporting understanding. Three techniques for doing this have been studied: elaborative interrogation, self-explanation, and teaching.

Elaborative interrogation is a strategy in which learners are asked, or are prompted to ask themselves, questions that invite deep reasoning, such as why, how, what-if, and what-if not (as opposed to shallow questions such as who, what, when, and where) ( Gholson et al., 2009 ). A curious student who applies intelligent elaborative interrogation asks deep-reasoning questions as she strives to comprehend difficult material and solve problems. However, elaborative interrogation does not come naturally to most children and adults; training people to use this skill—and particularly training in asking deep questions—has been shown to have a positive impact on comprehension, learning, and memory ( Gholson et al., 2009 ; Graesser and Lehman, 2012 ; Graesser and Olde, 2003 ; Rosenshine et al., 1996 ). For example, in an early study, people were asked either to provide “why” explanations for several unrelated sentences or to read and study the sentences. Both groups were then tested on their memory of the sentences. Those who asked questions performed better than the group that just studied the sentences ( Pressley et al., 1987 ). Studies with children have also shown benefits of elaborative interrogation ( Woloshyn et al., 1994 ), and the benefits of elaborative interrogation can persist over time (e.g., 1 or 2 weeks after learning), though few studies have examined effects of elaborative interrogation on long-term retention.

Most studies conducted by researchers in experimental psychology have used isolated facts as materials in studying the effects of elaboration and have assessed verbatim retention, but researchers in educational psychology have also looked at more complex text content and assessed inference making ( Dornisch and Sperling, 2006 ; Ozgungor and Guthrie, 2004 ). For example, McDaniel and Donnelly (1996) asked college students to study short descriptions of physics concepts, such as the conservation of angular momentum, and then answer a why question about the concept (e.g., “Why does an object speed up as its radius get smaller, as in conservation of angular momentum?”). A final assessment involved both factual questions and inference questions that tapped into deeper levels of comprehension. The authors found benefits of elaborative interrogation for complex materials and assessments and also found that those who engaged in elaborative interrogation outperformed learners who produced labeled diagrams of the concepts in each brief text.

Self-explanation is a strategy in which learners produce explanations of material or of their thought processes while they are reading, answering questions, or solving problems. In the most general case, learners may simply be asked to explain each step they take as they solve a problem ( Chi et al., 1989b ; McNamara, 2004 ) or explain a text sentence-by-sentence as they read it ( Chi

et al., 1994 ). Self-explanation involves more open-ended prompts than the specific “why” questions used in elaborative interrogation, but both strategies encourage learners to elaborate on the material by generating explanations. Other examples of this work include self-explanations of physics.

An early study of self-explanation was carried out by Chi and colleagues (1994) . Eighth-grade students learned about the circulatory system by reading an expository text. While one group just read the text, a second group of students produced explanations for each sentence in the text. The students who self-explained showed larger gains in comprehension of concepts in the text. A subsequent study showed similar results ( Wylie and Chi, 2014 ). Self-explanation has now been explored in a wide range of contexts, including comprehension of science texts in a classroom setting ( McNamara, 2004 ), learning of chess moves ( de Bruin et al., 2007 ), learning of mathematics concepts ( Rittle-Johnson, 2006 ), and learning from worked examples on problems that require reasoning ( Nokes-Malach et al., 2013 ). Self-explanation prompts have been included in intelligent tutoring systems ( Aleven and Koedinger, 2002 ) and systems with game components ( Jackson and McNamara, 2013 ; Mayer and Johnson, 2010 ). However, relatively few studies have examined the effects of self-explanation on long-term retention or explored the question of how much self-explanation is needed to produce notable results ( Jackson and McNamara, 2013 ).

A few studies have explored the relationship between self-explanation and prior knowledge in learning ( Williams and Lombrozo, 2013 ). For example, Ionas and colleagues (2012) investigated whether self-explanation was beneficial to college students who were asked to do chemistry problems. They found that prior knowledge moderated the effectiveness of self-explanation and that the more prior knowledge of chemistry the students reported having, the more self-explanation appeared to help them learn. Moreover, for students who had just a little prior knowledge, using self-explanation seemed to impede rather than support performance. The researchers suggested that learners search for concepts or processes in their prior knowledge to make sense of new material; when the prior knowledge is weak, the entire process fails. They concluded that educators should thoroughly assess the learners’ prior knowledge and use other cognitive support tools and methods during the early stages of the learning process, as learners strengthen their knowledge base.

Finally, teaching others can be an effective learning experience. When learners prepare to teach they must construct explanations, just as they do in elaborative interrogation and self-explanation activities. However, elaborative interrogation and self-explanation both require that the learner receive fairly specific prompts, whereas the act of preparing to teach can be more open-ended. Teaching others is often an excellent opportunity to hone one’s own knowledge ( Biswas et al., 2005 ; Palincsar and Brown, 1984 ), and learners in this kind of interaction are likely to feel empowered and responsible in a

way that they do not feel when they are the passive recipients of knowledge ( Scardamalia and Bereiter, 1993 ). Peers may be able to express themselves to each other in ways that are particularly relevant, immediate, and informative. Although peer learning and teaching are often quite effective, teachers and instructors typically come closer to injunctive norms and provide better models to observe.

A foundational study of the effects of teaching on learning by Bargh and Schul (1980) has served as a template for subsequent studies. Bargh and Schul asked participants to study a set of materials and either prepare to teach the material to a peer or simply study it for an upcoming test. Both groups were tested on the material without teaching it; only the expectation to teach had been manipulated. Students who prepared to teach others performed better on the assessment than students who simply read and studied the material. Effects of preparing to teach have been replicated in studies since Bargh and Schul’s foundational work (e.g., Fiorella and Mayer, 2014 ).

The benefits of teaching are evident in other contexts. For example, research on tutoring has shown that while students certainly learn by being tutored, the tutors themselves learn from the experience (see Roscoe and Chi, 2007 ). Reciprocal teaching is another strategy, used primarily in improving students’ reading comprehension ( Palincsar, 2013 ; Palincsar and Brown, 1984 ). In reciprocal teaching, students learn by taking turns teaching material to each other. The students are given guidance: training in four strategies to help them recognize and react to signs of comprehension breakdown (questioning, clarifying, summarizing, and predicting) ( Palincsar, 2013 ).

The research suggests several possible reasons why teaching may benefit learners. Preparing to teach requires elaborative processing because learners need to generate, organize, and integrate knowledge. Also, as mentioned, the explanations that people create may promote learning in the same way that elaborative interrogation and self-explanations promote learning. The process of explaining to others is active and generative, and it encourages learners to focus on deeper questions and levels of comprehension. Explaining in a teaching context also involves retrieval practice, as the teacher actively engages in retrieving knowledge in order to explain instructional content and answer questions. Although researchers have documented benefits of explanation, there are cautions to bear in mind. For example, a few researchers in this area have noted that in developing explanations learners may tend to make broad generalizations at the expense of significant specifics ( Lombrozo, 2012 ; Williams and Lombrozo, 2010 ; Williams et al., 2013 ). Children tend to prefer a single explanation for two different phenomena (e.g., a toy that both lights up and spins), even when there are two independent causes ( Bonawitz and Lombrozo, 2012 ). Likewise, when diagnosing diseases based on observable symptoms, adults tend to attribute the two symptoms to a single disease, even when it is more likely that there are two separate diseases ( Lombrozo, 2007 ;

Pacer and Lombrozo, 2017 ). The tendency to prefer simple, broad explanations over more complex ones may affect what people learn and the inferences they draw. For each of the different types of explanation strategies, researchers have noted reasons for educators to plan carefully when and how they can be used most effectively.

CONCLUSIONS

Learners identify and establish relationships among pieces of information and develop increasingly complex structures for using and categorizing what they have learned. Accumulating bodies of knowledge, structuring that knowledge, and developing the capacity to reason about the knowledge one has are key cognitive assets throughout the life span.

Strategies for supporting learning include those that focus on retention and retrieval of knowledge as well as those that support development of deeper and more sophisticated understanding of what is learned. The strategies that have shown promise for promoting learning help learners to develop the mental models they need to retain knowledge so they can use it adaptively and flexibly in making inferences and solving new problems.

CONCLUSION 5-1: Prior knowledge can reduce the attentional demands associated with engaging in well-learned activities, and it can facilitate new learning. However, prior knowledge can also lead to bias by causing people to not attend to new information and to rely on existing schema to solve new problems. These biases can be overcome but only through conscious effort.

CONCLUSION 5-2: Learners routinely generate their own novel understanding of the information they are accumulating and productively extend their knowledge by making logical connections between pieces of information. This capacity to generate novel understanding allows learners to use their knowledge to generalize, categorize, and solve problems.

CONCLUSION 5-3: The learning strategies for which there is evidence of effectiveness include ways to help students retrieve information and encourage them to summarize and explain material they are learning, as well as ways to space and structure the presentation of material. Effective strategies to create organized and distinctive knowledge structures encourage learners to go beyond the explicit material by elaborating

and to enrich their mental representation of information by calling up and applying it in various contexts.

CONCLUSION 5-4: The effectiveness of learning strategies is influenced by such contextual factors as the learner’s existing skills and prior knowledge, the nature of the material, and the goals for learning. Applying these approaches effectively therefore requires careful thought about how their specific mechanisms could be beneficial for particular learners, settings, and learning objectives.

This page intentionally left blank.

There are many reasons to be curious about the way people learn, and the past several decades have seen an explosion of research that has important implications for individual learning, schooling, workforce training, and policy.

In 2000, How People Learn: Brain, Mind, Experience, and School: Expanded Edition was published and its influence has been wide and deep. The report summarized insights on the nature of learning in school-aged children; described principles for the design of effective learning environments; and provided examples of how that could be implemented in the classroom.

Since then, researchers have continued to investigate the nature of learning and have generated new findings related to the neurological processes involved in learning, individual and cultural variability related to learning, and educational technologies. In addition to expanding scientific understanding of the mechanisms of learning and how the brain adapts throughout the lifespan, there have been important discoveries about influences on learning, particularly sociocultural factors and the structure of learning environments.

How People Learn II: Learners, Contexts, and Cultures provides a much-needed update incorporating insights gained from this research over the past decade. The book expands on the foundation laid out in the 2000 report and takes an in-depth look at the constellation of influences that affect individual learning. How People Learn II will become an indispensable resource to understand learning throughout the lifespan for educators of students and adults.

Welcome to OpenBook!

You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

Do you want to take a quick tour of the OpenBook's features?

Show this book's table of contents , where you can jump to any chapter by name.

...or use these buttons to go back to the previous chapter or skip to the next one.

Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

Switch between the Original Pages , where you can read the report as it appeared in print, and Text Pages for the web version, where you can highlight and search the text.

To search the entire text of this book, type in your search term here and press Enter .

Share a link to this book page on your preferred social network or via email.

View our suggested citation for this chapter.

Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

Get Email Updates

Do you enjoy reading reports from the Academies online for free ? Sign up for email notifications and we'll let you know about new publications in your areas of interest when they're released.

  • Search Menu
  • Browse content in Arts and Humanities
  • Browse content in Archaeology
  • Anglo-Saxon and Medieval Archaeology
  • Archaeological Methodology and Techniques
  • Archaeology by Region
  • Archaeology of Religion
  • Archaeology of Trade and Exchange
  • Biblical Archaeology
  • Contemporary and Public Archaeology
  • Environmental Archaeology
  • Historical Archaeology
  • History and Theory of Archaeology
  • Industrial Archaeology
  • Landscape Archaeology
  • Mortuary Archaeology
  • Prehistoric Archaeology
  • Underwater Archaeology
  • Urban Archaeology
  • Zooarchaeology
  • Browse content in Architecture
  • Architectural Structure and Design
  • History of Architecture
  • Residential and Domestic Buildings
  • Theory of Architecture
  • Browse content in Art
  • Art Subjects and Themes
  • History of Art
  • Industrial and Commercial Art
  • Theory of Art
  • Biographical Studies
  • Byzantine Studies
  • Browse content in Classical Studies
  • Classical History
  • Classical Philosophy
  • Classical Mythology
  • Classical Literature
  • Classical Reception
  • Classical Art and Architecture
  • Classical Oratory and Rhetoric
  • Greek and Roman Epigraphy
  • Greek and Roman Law
  • Greek and Roman Papyrology
  • Greek and Roman Archaeology
  • Late Antiquity
  • Religion in the Ancient World
  • Digital Humanities
  • Browse content in History
  • Colonialism and Imperialism
  • Diplomatic History
  • Environmental History
  • Genealogy, Heraldry, Names, and Honours
  • Genocide and Ethnic Cleansing
  • Historical Geography
  • History by Period
  • History of Emotions
  • History of Agriculture
  • History of Education
  • History of Gender and Sexuality
  • Industrial History
  • Intellectual History
  • International History
  • Labour History
  • Legal and Constitutional History
  • Local and Family History
  • Maritime History
  • Military History
  • National Liberation and Post-Colonialism
  • Oral History
  • Political History
  • Public History
  • Regional and National History
  • Revolutions and Rebellions
  • Slavery and Abolition of Slavery
  • Social and Cultural History
  • Theory, Methods, and Historiography
  • Urban History
  • World History
  • Browse content in Language Teaching and Learning
  • Language Learning (Specific Skills)
  • Language Teaching Theory and Methods
  • Browse content in Linguistics
  • Applied Linguistics
  • Cognitive Linguistics
  • Computational Linguistics
  • Forensic Linguistics
  • Grammar, Syntax and Morphology
  • Historical and Diachronic Linguistics
  • History of English
  • Language Acquisition
  • Language Evolution
  • Language Reference
  • Language Variation
  • Language Families
  • Lexicography
  • Linguistic Anthropology
  • Linguistic Theories
  • Linguistic Typology
  • Phonetics and Phonology
  • Psycholinguistics
  • Sociolinguistics
  • Translation and Interpretation
  • Writing Systems
  • Browse content in Literature
  • Bibliography
  • Children's Literature Studies
  • Literary Studies (Asian)
  • Literary Studies (European)
  • Literary Studies (Eco-criticism)
  • Literary Studies (Romanticism)
  • Literary Studies (American)
  • Literary Studies (Modernism)
  • Literary Studies - World
  • Literary Studies (1500 to 1800)
  • Literary Studies (19th Century)
  • Literary Studies (20th Century onwards)
  • Literary Studies (African American Literature)
  • Literary Studies (British and Irish)
  • Literary Studies (Early and Medieval)
  • Literary Studies (Fiction, Novelists, and Prose Writers)
  • Literary Studies (Gender Studies)
  • Literary Studies (Graphic Novels)
  • Literary Studies (History of the Book)
  • Literary Studies (Plays and Playwrights)
  • Literary Studies (Poetry and Poets)
  • Literary Studies (Postcolonial Literature)
  • Literary Studies (Queer Studies)
  • Literary Studies (Science Fiction)
  • Literary Studies (Travel Literature)
  • Literary Studies (War Literature)
  • Literary Studies (Women's Writing)
  • Literary Theory and Cultural Studies
  • Mythology and Folklore
  • Shakespeare Studies and Criticism
  • Browse content in Media Studies
  • Browse content in Music
  • Applied Music
  • Dance and Music
  • Ethics in Music
  • Ethnomusicology
  • Gender and Sexuality in Music
  • Medicine and Music
  • Music Cultures
  • Music and Religion
  • Music and Media
  • Music and Culture
  • Music Education and Pedagogy
  • Music Theory and Analysis
  • Musical Scores, Lyrics, and Libretti
  • Musical Structures, Styles, and Techniques
  • Musicology and Music History
  • Performance Practice and Studies
  • Race and Ethnicity in Music
  • Sound Studies
  • Browse content in Performing Arts
  • Browse content in Philosophy
  • Aesthetics and Philosophy of Art
  • Epistemology
  • Feminist Philosophy
  • History of Western Philosophy
  • Metaphysics
  • Moral Philosophy
  • Non-Western Philosophy
  • Philosophy of Science
  • Philosophy of Language
  • Philosophy of Mind
  • Philosophy of Perception
  • Philosophy of Action
  • Philosophy of Law
  • Philosophy of Religion
  • Philosophy of Mathematics and Logic
  • Practical Ethics
  • Social and Political Philosophy
  • Browse content in Religion
  • Biblical Studies
  • Christianity
  • East Asian Religions
  • History of Religion
  • Judaism and Jewish Studies
  • Qumran Studies
  • Religion and Education
  • Religion and Health
  • Religion and Politics
  • Religion and Science
  • Religion and Law
  • Religion and Art, Literature, and Music
  • Religious Studies
  • Browse content in Society and Culture
  • Cookery, Food, and Drink
  • Cultural Studies
  • Customs and Traditions
  • Ethical Issues and Debates
  • Hobbies, Games, Arts and Crafts
  • Lifestyle, Home, and Garden
  • Natural world, Country Life, and Pets
  • Popular Beliefs and Controversial Knowledge
  • Sports and Outdoor Recreation
  • Technology and Society
  • Travel and Holiday
  • Visual Culture
  • Browse content in Law
  • Arbitration
  • Browse content in Company and Commercial Law
  • Commercial Law
  • Company Law
  • Browse content in Comparative Law
  • Systems of Law
  • Competition Law
  • Browse content in Constitutional and Administrative Law
  • Government Powers
  • Judicial Review
  • Local Government Law
  • Military and Defence Law
  • Parliamentary and Legislative Practice
  • Construction Law
  • Contract Law
  • Browse content in Criminal Law
  • Criminal Procedure
  • Criminal Evidence Law
  • Sentencing and Punishment
  • Employment and Labour Law
  • Environment and Energy Law
  • Browse content in Financial Law
  • Banking Law
  • Insolvency Law
  • History of Law
  • Human Rights and Immigration
  • Intellectual Property Law
  • Browse content in International Law
  • Private International Law and Conflict of Laws
  • Public International Law
  • IT and Communications Law
  • Jurisprudence and Philosophy of Law
  • Law and Politics
  • Law and Society
  • Browse content in Legal System and Practice
  • Courts and Procedure
  • Legal Skills and Practice
  • Primary Sources of Law
  • Regulation of Legal Profession
  • Medical and Healthcare Law
  • Browse content in Policing
  • Criminal Investigation and Detection
  • Police and Security Services
  • Police Procedure and Law
  • Police Regional Planning
  • Browse content in Property Law
  • Personal Property Law
  • Study and Revision
  • Terrorism and National Security Law
  • Browse content in Trusts Law
  • Wills and Probate or Succession
  • Browse content in Medicine and Health
  • Browse content in Allied Health Professions
  • Arts Therapies
  • Clinical Science
  • Dietetics and Nutrition
  • Occupational Therapy
  • Operating Department Practice
  • Physiotherapy
  • Radiography
  • Speech and Language Therapy
  • Browse content in Anaesthetics
  • General Anaesthesia
  • Neuroanaesthesia
  • Browse content in Clinical Medicine
  • Acute Medicine
  • Cardiovascular Medicine
  • Clinical Genetics
  • Clinical Pharmacology and Therapeutics
  • Dermatology
  • Endocrinology and Diabetes
  • Gastroenterology
  • Genito-urinary Medicine
  • Geriatric Medicine
  • Infectious Diseases
  • Medical Toxicology
  • Medical Oncology
  • Pain Medicine
  • Palliative Medicine
  • Rehabilitation Medicine
  • Respiratory Medicine and Pulmonology
  • Rheumatology
  • Sleep Medicine
  • Sports and Exercise Medicine
  • Clinical Neuroscience
  • Community Medical Services
  • Critical Care
  • Emergency Medicine
  • Forensic Medicine
  • Haematology
  • History of Medicine
  • Browse content in Medical Dentistry
  • Oral and Maxillofacial Surgery
  • Paediatric Dentistry
  • Restorative Dentistry and Orthodontics
  • Surgical Dentistry
  • Browse content in Medical Skills
  • Clinical Skills
  • Communication Skills
  • Nursing Skills
  • Surgical Skills
  • Medical Ethics
  • Medical Statistics and Methodology
  • Browse content in Neurology
  • Clinical Neurophysiology
  • Neuropathology
  • Nursing Studies
  • Browse content in Obstetrics and Gynaecology
  • Gynaecology
  • Occupational Medicine
  • Ophthalmology
  • Otolaryngology (ENT)
  • Browse content in Paediatrics
  • Neonatology
  • Browse content in Pathology
  • Chemical Pathology
  • Clinical Cytogenetics and Molecular Genetics
  • Histopathology
  • Medical Microbiology and Virology
  • Patient Education and Information
  • Browse content in Pharmacology
  • Psychopharmacology
  • Browse content in Popular Health
  • Caring for Others
  • Complementary and Alternative Medicine
  • Self-help and Personal Development
  • Browse content in Preclinical Medicine
  • Cell Biology
  • Molecular Biology and Genetics
  • Reproduction, Growth and Development
  • Primary Care
  • Professional Development in Medicine
  • Browse content in Psychiatry
  • Addiction Medicine
  • Child and Adolescent Psychiatry
  • Forensic Psychiatry
  • Learning Disabilities
  • Old Age Psychiatry
  • Psychotherapy
  • Browse content in Public Health and Epidemiology
  • Epidemiology
  • Public Health
  • Browse content in Radiology
  • Clinical Radiology
  • Interventional Radiology
  • Nuclear Medicine
  • Radiation Oncology
  • Reproductive Medicine
  • Browse content in Surgery
  • Cardiothoracic Surgery
  • Gastro-intestinal and Colorectal Surgery
  • General Surgery
  • Neurosurgery
  • Paediatric Surgery
  • Peri-operative Care
  • Plastic and Reconstructive Surgery
  • Surgical Oncology
  • Transplant Surgery
  • Trauma and Orthopaedic Surgery
  • Vascular Surgery
  • Browse content in Science and Mathematics
  • Browse content in Biological Sciences
  • Aquatic Biology
  • Biochemistry
  • Bioinformatics and Computational Biology
  • Developmental Biology
  • Ecology and Conservation
  • Evolutionary Biology
  • Genetics and Genomics
  • Microbiology
  • Molecular and Cell Biology
  • Natural History
  • Plant Sciences and Forestry
  • Research Methods in Life Sciences
  • Structural Biology
  • Systems Biology
  • Zoology and Animal Sciences
  • Browse content in Chemistry
  • Analytical Chemistry
  • Computational Chemistry
  • Crystallography
  • Environmental Chemistry
  • Industrial Chemistry
  • Inorganic Chemistry
  • Materials Chemistry
  • Medicinal Chemistry
  • Mineralogy and Gems
  • Organic Chemistry
  • Physical Chemistry
  • Polymer Chemistry
  • Study and Communication Skills in Chemistry
  • Theoretical Chemistry
  • Browse content in Computer Science
  • Artificial Intelligence
  • Computer Architecture and Logic Design
  • Game Studies
  • Human-Computer Interaction
  • Mathematical Theory of Computation
  • Programming Languages
  • Software Engineering
  • Systems Analysis and Design
  • Virtual Reality
  • Browse content in Computing
  • Business Applications
  • Computer Security
  • Computer Games
  • Computer Networking and Communications
  • Digital Lifestyle
  • Graphical and Digital Media Applications
  • Operating Systems
  • Browse content in Earth Sciences and Geography
  • Atmospheric Sciences
  • Environmental Geography
  • Geology and the Lithosphere
  • Maps and Map-making
  • Meteorology and Climatology
  • Oceanography and Hydrology
  • Palaeontology
  • Physical Geography and Topography
  • Regional Geography
  • Soil Science
  • Urban Geography
  • Browse content in Engineering and Technology
  • Agriculture and Farming
  • Biological Engineering
  • Civil Engineering, Surveying, and Building
  • Electronics and Communications Engineering
  • Energy Technology
  • Engineering (General)
  • Environmental Science, Engineering, and Technology
  • History of Engineering and Technology
  • Mechanical Engineering and Materials
  • Technology of Industrial Chemistry
  • Transport Technology and Trades
  • Browse content in Environmental Science
  • Applied Ecology (Environmental Science)
  • Conservation of the Environment (Environmental Science)
  • Environmental Sustainability
  • Environmentalist Thought and Ideology (Environmental Science)
  • Management of Land and Natural Resources (Environmental Science)
  • Natural Disasters (Environmental Science)
  • Nuclear Issues (Environmental Science)
  • Pollution and Threats to the Environment (Environmental Science)
  • Social Impact of Environmental Issues (Environmental Science)
  • History of Science and Technology
  • Browse content in Materials Science
  • Ceramics and Glasses
  • Composite Materials
  • Metals, Alloying, and Corrosion
  • Nanotechnology
  • Browse content in Mathematics
  • Applied Mathematics
  • Biomathematics and Statistics
  • History of Mathematics
  • Mathematical Education
  • Mathematical Finance
  • Mathematical Analysis
  • Numerical and Computational Mathematics
  • Probability and Statistics
  • Pure Mathematics
  • Browse content in Neuroscience
  • Cognition and Behavioural Neuroscience
  • Development of the Nervous System
  • Disorders of the Nervous System
  • History of Neuroscience
  • Invertebrate Neurobiology
  • Molecular and Cellular Systems
  • Neuroendocrinology and Autonomic Nervous System
  • Neuroscientific Techniques
  • Sensory and Motor Systems
  • Browse content in Physics
  • Astronomy and Astrophysics
  • Atomic, Molecular, and Optical Physics
  • Biological and Medical Physics
  • Classical Mechanics
  • Computational Physics
  • Condensed Matter Physics
  • Electromagnetism, Optics, and Acoustics
  • History of Physics
  • Mathematical and Statistical Physics
  • Measurement Science
  • Nuclear Physics
  • Particles and Fields
  • Plasma Physics
  • Quantum Physics
  • Relativity and Gravitation
  • Semiconductor and Mesoscopic Physics
  • Browse content in Psychology
  • Affective Sciences
  • Clinical Psychology
  • Cognitive Psychology
  • Cognitive Neuroscience
  • Criminal and Forensic Psychology
  • Developmental Psychology
  • Educational Psychology
  • Evolutionary Psychology
  • Health Psychology
  • History and Systems in Psychology
  • Music Psychology
  • Neuropsychology
  • Organizational Psychology
  • Psychological Assessment and Testing
  • Psychology of Human-Technology Interaction
  • Psychology Professional Development and Training
  • Research Methods in Psychology
  • Social Psychology
  • Browse content in Social Sciences
  • Browse content in Anthropology
  • Anthropology of Religion
  • Human Evolution
  • Medical Anthropology
  • Physical Anthropology
  • Regional Anthropology
  • Social and Cultural Anthropology
  • Theory and Practice of Anthropology
  • Browse content in Business and Management
  • Business Strategy
  • Business Ethics
  • Business History
  • Business and Government
  • Business and Technology
  • Business and the Environment
  • Comparative Management
  • Corporate Governance
  • Corporate Social Responsibility
  • Entrepreneurship
  • Health Management
  • Human Resource Management
  • Industrial and Employment Relations
  • Industry Studies
  • Information and Communication Technologies
  • International Business
  • Knowledge Management
  • Management and Management Techniques
  • Operations Management
  • Organizational Theory and Behaviour
  • Pensions and Pension Management
  • Public and Nonprofit Management
  • Strategic Management
  • Supply Chain Management
  • Browse content in Criminology and Criminal Justice
  • Criminal Justice
  • Criminology
  • Forms of Crime
  • International and Comparative Criminology
  • Youth Violence and Juvenile Justice
  • Development Studies
  • Browse content in Economics
  • Agricultural, Environmental, and Natural Resource Economics
  • Asian Economics
  • Behavioural Finance
  • Behavioural Economics and Neuroeconomics
  • Econometrics and Mathematical Economics
  • Economic Systems
  • Economic History
  • Economic Methodology
  • Economic Development and Growth
  • Financial Markets
  • Financial Institutions and Services
  • General Economics and Teaching
  • Health, Education, and Welfare
  • History of Economic Thought
  • International Economics
  • Labour and Demographic Economics
  • Law and Economics
  • Macroeconomics and Monetary Economics
  • Microeconomics
  • Public Economics
  • Urban, Rural, and Regional Economics
  • Welfare Economics
  • Browse content in Education
  • Adult Education and Continuous Learning
  • Care and Counselling of Students
  • Early Childhood and Elementary Education
  • Educational Equipment and Technology
  • Educational Strategies and Policy
  • Higher and Further Education
  • Organization and Management of Education
  • Philosophy and Theory of Education
  • Schools Studies
  • Secondary Education
  • Teaching of a Specific Subject
  • Teaching of Specific Groups and Special Educational Needs
  • Teaching Skills and Techniques
  • Browse content in Environment
  • Applied Ecology (Social Science)
  • Climate Change
  • Conservation of the Environment (Social Science)
  • Environmentalist Thought and Ideology (Social Science)
  • Natural Disasters (Environment)
  • Social Impact of Environmental Issues (Social Science)
  • Browse content in Human Geography
  • Cultural Geography
  • Economic Geography
  • Political Geography
  • Browse content in Interdisciplinary Studies
  • Communication Studies
  • Museums, Libraries, and Information Sciences
  • Browse content in Politics
  • African Politics
  • Asian Politics
  • Chinese Politics
  • Comparative Politics
  • Conflict Politics
  • Elections and Electoral Studies
  • Environmental Politics
  • European Union
  • Foreign Policy
  • Gender and Politics
  • Human Rights and Politics
  • Indian Politics
  • International Relations
  • International Organization (Politics)
  • International Political Economy
  • Irish Politics
  • Latin American Politics
  • Middle Eastern Politics
  • Political Methodology
  • Political Communication
  • Political Philosophy
  • Political Sociology
  • Political Behaviour
  • Political Economy
  • Political Institutions
  • Political Theory
  • Politics and Law
  • Public Administration
  • Public Policy
  • Quantitative Political Methodology
  • Regional Political Studies
  • Russian Politics
  • Security Studies
  • State and Local Government
  • UK Politics
  • US Politics
  • Browse content in Regional and Area Studies
  • African Studies
  • Asian Studies
  • East Asian Studies
  • Japanese Studies
  • Latin American Studies
  • Middle Eastern Studies
  • Native American Studies
  • Scottish Studies
  • Browse content in Research and Information
  • Research Methods
  • Browse content in Social Work
  • Addictions and Substance Misuse
  • Adoption and Fostering
  • Care of the Elderly
  • Child and Adolescent Social Work
  • Couple and Family Social Work
  • Developmental and Physical Disabilities Social Work
  • Direct Practice and Clinical Social Work
  • Emergency Services
  • Human Behaviour and the Social Environment
  • International and Global Issues in Social Work
  • Mental and Behavioural Health
  • Social Justice and Human Rights
  • Social Policy and Advocacy
  • Social Work and Crime and Justice
  • Social Work Macro Practice
  • Social Work Practice Settings
  • Social Work Research and Evidence-based Practice
  • Welfare and Benefit Systems
  • Browse content in Sociology
  • Childhood Studies
  • Community Development
  • Comparative and Historical Sociology
  • Economic Sociology
  • Gender and Sexuality
  • Gerontology and Ageing
  • Health, Illness, and Medicine
  • Marriage and the Family
  • Migration Studies
  • Occupations, Professions, and Work
  • Organizations
  • Population and Demography
  • Race and Ethnicity
  • Social Theory
  • Social Movements and Social Change
  • Social Research and Statistics
  • Social Stratification, Inequality, and Mobility
  • Sociology of Religion
  • Sociology of Education
  • Sport and Leisure
  • Urban and Rural Studies
  • Browse content in Warfare and Defence
  • Defence Strategy, Planning, and Research
  • Land Forces and Warfare
  • Military Administration
  • Military Life and Institutions
  • Naval Forces and Warfare
  • Other Warfare and Defence Issues
  • Peace Studies and Conflict Resolution
  • Weapons and Equipment

The Oxford Handbook of Thinking and Reasoning

  • < Previous chapter
  • Next chapter >

21 Problem Solving

Miriam Bassok, Department of Psychology, University of Washington, Seattle, WA

Laura R. Novick, Department of Psychology and Human Development, Vanderbilt University, Nashville, TN

  • Published: 21 November 2012
  • Cite Icon Cite
  • Permissions Icon Permissions

This chapter follows the historical development of research on problem solving. It begins with a description of two research traditions that addressed different aspects of the problem-solving process: ( 1 ) research on problem representation (the Gestalt legacy) that examined how people understand the problem at hand, and ( 2 ) research on search in a problem space (the legacy of Newell and Simon) that examined how people generate the problem's solution. It then describes some developments in the field that fueled the integration of these two lines of research: work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. Next, it presents examples of recent work on problem solving in science and mathematics that highlight the impact of visual perception and background knowledge on how people represent problems and search for problem solutions. The final section considers possible directions for future research.

People are confronted with problems on a daily basis, be it trying to extract a broken light bulb from a socket, finding a detour when the regular route is blocked, fixing dinner for unexpected guests, dealing with a medical emergency, or deciding what house to buy. Obviously, the problems people encounter differ in many ways, and their solutions require different types of knowledge and skills. Yet we have a sense that all the situations we classify as problems share a common core. Karl Duncker defined this core as follows: “A problem arises when a living creature has a goal but does not know how this goal is to be reached. Whenever one cannot go from the given situation to the desired situation simply by action [i.e., by the performance of obvious operations], then there has to be recourse to thinking” (Duncker, 1945 , p. 1). Consider the broken light bulb. The obvious operation—holding the glass part of the bulb with one's fingers while unscrewing the base from the socket—is prevented by the fact that the glass is broken. Thus, there must be “recourse to thinking” about possible ways to solve the problem. For example, one might try mounting half a potato on the broken bulb (we do not know the source of this creative solution, which is described on many “how to” Web sites).

The above definition and examples make it clear that what constitutes a problem for one person may not be a problem for another person, or for that same person at another point in time. For example, the second time one has to remove a broken light bulb from a socket, the solution likely can be retrieved from memory; there is no problem. Similarly, tying shoes may be considered a problem for 5-year-olds but not for readers of this chapter. And, of course, people may change their goal and either no longer have a problem (e.g., take the guests to a restaurant instead of fixing dinner) or attempt to solve a different problem (e.g., decide what restaurant to go to). Given the highly subjective nature of what constitutes a problem, researchers who study problem solving have often presented people with novel problems that they should be capable of solving and attempted to find regularities in the resulting problem-solving behavior. Despite the variety of possible problem situations, researchers have identified important regularities in the thinking processes by which people (a) represent , or understand, problem situations and (b) search for possible ways to get to their goal.

A problem representation is a model constructed by the solver that summarizes his or her understanding of the problem components—the initial state (e.g., a broken light bulb in a socket), the goal state (the light bulb extracted), and the set of possible operators one may apply to get from the initial state to the goal state (e.g., use pliers). According to Reitman ( 1965 ), problem components differ in the extent to which they are well defined . Some components leave little room for interpretation (e.g., the initial state in the broken light bulb example is relatively well defined), whereas other components may be ill defined and have to be defined by the solver (e.g., the possible actions one may take to extract the broken bulb). The solver's representation of the problem guides the search for a possible solution (e.g., possible attempts at extracting the light bulb). This search may, in turn, change the representation of the problem (e.g., finding that the goal cannot be achieved using pliers) and lead to a new search. Such a recursive process of representation and search continues until the problem is solved or until the solver decides to abort the goal.

Duncker ( 1945 , pp. 28–37) documented the interplay between representation and search based on his careful analysis of one person's solution to the “Radiation Problem” (later to be used extensively in research analogy, see Holyoak, Chapter 13 ). This problem requires using some rays to destroy a patient's stomach tumor without harming the patient. At sufficiently high intensity, the rays will destroy the tumor. However, at that intensity, they will also destroy the healthy tissue surrounding the tumor. At lower intensity, the rays will not harm the healthy tissue, but they also will not destroy the tumor. Duncker's analysis revealed that the solver's solution attempts were guided by three distinct problem representations. He depicted these solution attempts as an inverted search tree in which the three main branches correspond to the three general problem representations (Duncker, 1945 , p. 32). We reproduce this diagram in Figure 21.1 . The desired solution appears on the rightmost branch of the tree, within the general problem representation in which the solver aims to “lower the intensity of the rays on their way through healthy tissue.” The actual solution is to project multiple low-intensity rays at the tumor from several points around the patient “by use of lens.” The low-intensity rays will converge on the tumor, where their individual intensities will sum to a level sufficient to destroy the tumor.

A search-tree representation of one subject's solution to the radiation problem, reproduced from Duncker ( 1945 , p. 32).

Although there are inherent interactions between representation and search, some researchers focus their efforts on understanding the factors that affect how solvers represent problems, whereas others look for regularities in how they search for a solution within a particular representation. Based on their main focus of interest, researchers devise or select problems with solutions that mainly require either constructing a particular representation or finding the appropriate sequence of steps leading from the initial state to the goal state. In most cases, researchers who are interested in problem representation select problems in which one or more of the components are ill defined, whereas those who are interested in search select problems in which the components are well defined. The following examples illustrate, respectively, these two problem types.

The Bird-and-Trains problem (Posner, 1973 , pp. 150–151) is a mathematical word problem that tends to elicit two distinct problem representations (see Fig. 21.2a and b ):

Two train stations are 50 miles apart. At 2 p.m. one Saturday afternoon two trains start toward each other, one from each station. Just as the trains pull out of the stations, a bird springs into the air in front of the first train and flies ahead to the front of the second train. When the bird reaches the second train, it turns back and flies toward the first train. The bird continues to do this until the trains meet. If both trains travel at the rate of 25 miles per hour and the bird flies at 100 miles per hour, how many miles will the bird have flown before the trains meet? Fig. 21.2 Open in new tab Download slide Alternative representations of Posner's ( 1973 ) trains-and-bird problem. Adapted from Novick and Hmelo ( 1994 ).

Some solvers focus on the back-and-forth path of the bird (Fig. 21.2a ). This representation yields a problem that would be difficult for most people to solve (e.g., a series of differential equations). Other solvers focus on the paths of the trains (Fig. 21.2b ), a representation that yields a relatively easy distance-rate-time problem.

The Tower of Hanoi problem falls on the other end of the representation-search continuum. It leaves little room for differences in problem representations, and the primary work is to discover a solution path (or the best solution path) from the initial state to the goal state .

There are three pegs mounted on a base. On the leftmost peg, there are three disks of differing sizes. The disks are arranged in order of size with the largest disk on the bottom and the smallest disk on the top. The disks may be moved one at a time, but only the top disk on a peg may be moved, and at no time may a larger disk be placed on a smaller disk. The goal is to move the three-disk tower from the leftmost peg to the rightmost peg.

Figure 21.3 shows all the possible legal arrangements of disks on pegs. The arrows indicate transitions between states that result from moving a single disk, with the thicker gray arrows indicating the shortest path that connects the initial state to the goal state.

The division of labor between research on representation versus search has distinct historical antecedents and research traditions. In the next two sections, we review the main findings from these two historical traditions. Then, we describe some developments in the field that fueled the integration of these lines of research—work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. In the fifth section, we present some examples of recent work on problem solving in science and mathematics. This work highlights the role of visual perception and background knowledge in the way people represent problems and search for problem solutions. In the final section, we consider possible directions for future research.

Our review is by no means an exhaustive one. It follows the historical development of the field and highlights findings that pertain to a wide variety of problems. Research pertaining to specific types of problems (e.g., medical problems), specific processes that are involved in problem solving (e.g., analogical inferences), and developmental changes in problem solving due to learning and maturation may be found elsewhere in this volume (e.g., Holyoak, Chapter 13 ; Smith & Ward, Chapter 23 ; van Steenburgh et al., Chapter 24 ; Simonton, Chapter 25 ; Opfer & Siegler, Chapter 30 ; Hegarty & Stull, Chapter 31 ; Dunbar & Klahr, Chapter 35 ; Patel et al., Chapter 37 ; Lowenstein, Chapter 38 ; Koedinger & Roll, Chapter 40 ).

All possible problem states for the three-disk Tower of Hanoi problem. The thicker gray arrows show the optimum solution path connecting the initial state (State #1) to the goal state (State #27).

Problem Representation: The Gestalt Legacy

Research on problem representation has its origins in Gestalt psychology, an influential approach in European psychology during the first half of the 20th century. (Behaviorism was the dominant perspective in American psychology at this time.) Karl Duncker published a book on the topic in his native German in 1935, which was translated into English and published 10 years later as the monograph On Problem-Solving (Duncker, 1945 ). Max Wertheimer also published a book on the topic in 1945, titled Productive Thinking . An enlarged edition published posthumously includes previously unpublished material (Wertheimer, 1959 ). Interestingly, 1945 seems to have been a watershed year for problem solving, as mathematician George Polya's book, How to Solve It , also appeared then (a second edition was published 12 years later; Polya, 1957 ).

The Gestalt psychologists extended the organizational principles of visual perception to the domain of problem solving. They showed that various visual aspects of the problem, as well the solver's prior knowledge, affect how people understand problems and, therefore, generate problem solutions. The principles of visual perception (e.g., proximity, closure, grouping, good continuation) are directly relevant to problem solving when the physical layout of the problem, or a diagram that accompanies the problem description, elicits inferences that solvers include in their problem representations. Such effects are nicely illustrated by Maier's ( 1930 ) nine-dot problem: Nine dots are arrayed in a 3x3 grid, and the task is to connect all the dots by drawing four straight lines without lifting one's pencil from the paper. People have difficulty solving this problem because their initial representations generally include a constraint, inferred from the configuration of the dots, that the lines should not go outside the boundary of the imaginary square formed by the outer dots. With this constraint, the problem cannot be solved (but see Adams, 1979 ). Without this constraint, the problem may be solved as shown in Figure 21.4 (though the problem is still difficult for many people; see Weisberg & Alba, 1981 ).

The nine-dot problem is a classic insight problem (see van Steenburgh et al., Chapter 24 ). According to the Gestalt view (e.g., Duncker, 1945 ; Kohler, 1925 ; Maier, 1931 ; see Ohlsson, 1984 , for a review), the solution to an insight problem appears suddenly, accompanied by an “aha!” sensation, immediately following the sudden “restructuring” of one's understanding of the problem (i.e., a change in the problem representation): “The decisive points in thought-processes, the moments of sudden comprehension, of the ‘Aha!,’ of the new, are always at the same time moments in which such a sudden restructuring of the thought-material takes place” (Duncker, 1945 , p. 29). For the nine-dot problem, one view of the required restructuring is that the solver relaxes the constraint implied by the perceptual form of the problem and realizes that the lines may, in fact, extend past the boundary of the imaginary square. Later in the chapter, we present more recent accounts of insight.

The entities that appear in a problem also tend to evoke various inferences that people incorporate into their problem representations. A classic demonstration of this is the phenomenon of functional fixedness , introduced by Duncker ( 1945 ): If an object is habitually used for a certain purpose (e.g., a box serves as a container), it is difficult to see

A solution to the nine-dot problem.

that object as having properties that would enable it to be used for a dissimilar purpose. Duncker's basic experimental paradigm involved two conditions that varied in terms of whether the object that was crucial for solution was initially used for a function other than that required for solution.

Consider the candles problem—the best known of the five “practical problems” Duncker ( 1945 ) investigated. Three candles are to be mounted at eye height on a door. On the table, for use in completing this task, are some tacks and three boxes. The solution is to tack the three boxes to the door to serve as platforms for the candles. In the control condition, the three boxes were presented to subjects empty. In the functional-fixedness condition, they were filled with candles, tacks, and matches. Thus, in the latter condition, the boxes initially served the function of container, whereas the solution requires that they serve the function of platform. The results showed that 100% of the subjects who received empty boxes solved the candles problem, compared with only 43% of subjects who received filled boxes. Every one of the five problems in this study showed a difference favoring the control condition over the functional-fixedness condition, with average solution rates across the five problems of 97% and 58%, respectively.

The function of the objects in a problem can be also “fixed” by their most recent use. For example, Birch and Rabinowitz ( 1951 ) had subjects perform two consecutive tasks. In the first task, people had to use either a switch or a relay to form an electric circuit. After completing this task, both groups of subjects were asked to solve Maier's ( 1931 ) two-ropes problem. The solution to this problem requires tying an object to one of the ropes and making the rope swing as a pendulum. Subjects could create the pendulum using either the object from the electric-circuit task or the other object. Birch and Rabinowitz found that subjects avoided using the same object for two unrelated functions. That is, those who used the switch in the first task made the pendulum using the relay, and vice versa. The explanations subjects subsequently gave for their object choices revealed that they were unaware of the functional-fixedness constraint they imposed on themselves.

In addition to investigating people's solutions to such practical problems as irradiating a tumor, mounting candles on the wall, or tying ropes, the Gestalt psychologists examined how people understand and solve mathematical problems that require domain-specific knowledge. For example, Wertheimer ( 1959 ) observed individual differences in students' learning and subsequent application of the formula for finding the area of a parallelogram (see Fig. 21.5a ). Some students understood the logic underlying the learned formula (i.e., the fact that a parallelogram can be transformed into a rectangle by cutting off a triangle from one side and pasting it onto the other side) and exhibited “productive thinking”—using the same logic to find the area of the quadrilateral in Figure 21.5b and the irregularly shaped geometric figure in Figure 21.5c . Other students memorized the formula and exhibited “reproductive thinking”—reproducing the learned solution only to novel parallelograms that were highly similar to the original one.

The psychological study of human problem solving faded into the background after the demise of the Gestalt tradition (during World War II), and problem solving was investigated only sporadically until Allen Newell and Herbert Simon's ( 1972 ) landmark book Human Problem Solving sparked a flurry of research on this topic. Newell and Simon adopted and refined Duncker's ( 1945 ) methodology of collecting and analyzing the think-aloud protocols that accompany problem solutions and extended Duncker's conceptualization of a problem solution as a search tree. However, their initial work did not aim to extend the Gestalt findings

Finding the area of ( a ) a parallelogram, ( b ) a quadrilateral, and ( c ) an irregularly shaped geometric figure. The solid lines indicate the geometric figures whose areas are desired. The dashed lines show how to convert the given figures into rectangles (i.e., they show solutions with understanding).

pertaining to problem representation. Instead, as we explain in the next section, their objective was to identify the general-purpose strategies people use in searching for a problem solution.

Search in a Problem Space: The Legacy of Newell and Simon

Newell and Simon ( 1972 ) wrote a magnum opus detailing their theory of problem solving and the supporting research they conducted with various collaborators. This theory was grounded in the information-processing approach to cognitive psychology and guided by an analogy between human and artificial intelligence (i.e., both people and computers being “Physical Symbol Systems,” Newell & Simon, 1976 ; see Doumas & Hummel, Chapter 5 ). They conceptualized problem solving as a process of search through a problem space for a path that connects the initial state to the goal state—a metaphor that alludes to the visual or spatial nature of problem solving (Simon, 1990 ). The term problem space refers to the solver's representation of the task as presented (Simon, 1978 ). It consists of ( 1 ) a set of knowledge states (the initial state, the goal state, and all possible intermediate states), ( 2 ) a set of operators that allow movement from one knowledge state to another, ( 3 ) a set of constraints, and ( 4 ) local information about the path one is taking through the space (e.g., the current knowledge state and how one got there).

We illustrate the components of a problem space for the three-disk Tower of Hanoi problem, as depicted in Figure 21.3 . The initial state appears at the top (State #1) and the goal state at the bottom right (State #27). The remaining knowledge states in the figure are possible intermediate states. The current knowledge state is the one at which the solver is located at any given point in the solution process. For example, the current state for a solver who has made three moves along the optimum solution path would be State #9. The solver presumably would know that he or she arrived at this state from State #5. This knowledge allows the solver to recognize a move that involves backtracking. The three operators in this problem are moving each of the three disks from one peg to another. These operators are subject to the constraint that a larger disk may not be placed on a smaller disk.

Newell and Simon ( 1972 ), as well as other contemporaneous researchers (e.g., Atwood & Polson, 1976 ; Greeno, 1974 ; Thomas, 1974 ), examined how people traverse the spaces of various well-defined problems (e.g., the Tower of Hanoi, Hobbits and Orcs). They discovered that solvers' search is guided by a number of shortcut strategies, or heuristics , which are likely to get the solver to the goal state without an extensive amount of search. Heuristics are often contrasted with algorithms —methods that are guaranteed to yield the correct solution. For example, one could try every possible move in the three-disk Tower of Hanoi problem and, eventually, find the correct solution. Although such an exhaustive search is a valid algorithm for this problem, for many problems its application is very time consuming and impractical (e.g., consider the game of chess).

In their attempts to identify people's search heuristics, Newell and Simon ( 1972 ) relied on two primary methodologies: think-aloud protocols and computer simulations. Their use of think-aloud protocols brought a high degree of scientific rigor to the methodology used by Duncker ( 1945 ; see Ericsson & Simon, 1980 ). Solvers were required to say out loud everything they were thinking as they solved the problem, that is, everything that went through their verbal working memory. Subjects' verbalizations—their think-aloud protocols—were tape-recorded and then transcribed verbatim for analysis. This method is extremely time consuming (e.g., a transcript of one person's solution to the cryptarithmetic problem DONALD + GERALD = ROBERT, with D = 5, generated a 17-page transcript), but it provides a detailed record of the solver's ongoing solution process.

An important caveat to keep in mind while interpreting a subject's verbalizations is that “a protocol is relatively reliable only for what it positively contains, but not for that which it omits” (Duncker, 1945 , p. 11). Ericsson and Simon ( 1980 ) provided an in-depth discussion of the conditions under which this method is valid (but see Russo, Johnson, & Stephens, 1989 , for an alternative perspective). To test their interpretation of a subject's problem solution, inferred from the subject's verbal protocol, Newell and Simon ( 1972 ) created a computer simulation program and examined whether it solved the problem the same way the subject did. To the extent that the computer simulation provided a close approximation of the solver's step-by-step solution process, it lent credence to the researcher's interpretation of the verbal protocol.

Newell and Simon's ( 1972 ) most famous simulation was the General Problem Solver or GPS (Ernst & Newell, 1969 ). GPS successfully modeled human solutions to problems as different as the Tower of Hanoi and the construction of logic proofs using a single general-purpose heuristic: means-ends analysis . This heuristic captures people's tendency to devise a solution plan by setting subgoals that could help them achieve their final goal. It consists of the following steps: ( 1 ) Identify a difference between the current state and the goal (or subgoal ) state; ( 2 ) Find an operator that will remove (or reduce) the difference; (3a) If the operator can be directly applied, do so, or (3b) If the operator cannot be directly applied, set a subgoal to remove the obstacle that is preventing execution of the desired operator; ( 4 ) Repeat steps 1–3 until the problem is solved. Next, we illustrate the implementation of this heuristic for the Tower of Hanoi problem, using the problem space in Figure 21.3 .

As can be seen in Figure 21.3 , a key difference between the initial state and the goal state is that the large disk is on the wrong peg (step 1). To remove this difference (step 2), one needs to apply the operator “move-large-disk.” However, this operator cannot be applied because of the presence of the medium and small disks on top of the large disk. Therefore, the solver may set a subgoal to move that two-disk tower to the middle peg (step 3b), leaving the rightmost peg free for the large disk. A key difference between the initial state and this new subgoal state is that the medium disk is on the wrong peg. Because application of the move-medium-disk operator is blocked, the solver sets another subgoal to move the small disk to the right peg. This subgoal can be satisfied immediately by applying the move-small-disk operator (step 3a), generating State #3. The solver then returns to the previous subgoal—moving the tower consisting of the small and medium disks to the middle peg. The differences between the current state (#3) and the subgoal state (#9) can be removed by first applying the move-medium-disk operator (yielding State #5) and then the move-small-disk operator (yielding State #9). Finally, the move-large-disk operator is no longer blocked. Hence, the solver moves the large disk to the right peg, yielding State #11.

Notice that the subgoals are stacked up in the order in which they are generated, so that they pop up in the order of last in first out. Given the first subgoal in our example, repeated application of the means-ends analysis heuristic will yield the shortest-path solution, indicated by the large gray arrows. In general, subgoals provide direction to the search and allow solvers to plan several moves ahead. By assessing progress toward a required subgoal rather than the final goal, solvers may be able to make moves that otherwise seem unwise. To take a concrete example, consider the transition from State #1 to State #3 in Figure 21.3 . Comparing the initial state to the goal state, this move seems unwise because it places the small disk on the bottom of the right peg, whereas it ultimately needs to be at the top of the tower on that peg. But comparing the initial state to the solver-generated subgoal state of having the medium disk on the middle peg, this is exactly where the small disk needs to go.

Means-ends analysis and various other heuristics (e.g., the hill-climbing heuristic that exploits the similarity, or distance, between the state generated by the next operator and the goal state; working backward from the goal state to the initial state) are flexible strategies that people often use to successfully solve a large variety of problems. However, the generality of these heuristics comes at a cost: They are relatively weak and fallible (e.g., in the means-ends solution to the problem of fixing a hole in a bucket, “Dear Liza” leads “Dear Henry” in a loop that ends back at the initial state; the lyrics of this famous song can be readily found on the Web). Hence, although people use general-purpose heuristics when they encounter novel problems, they replace them as soon as they acquire experience with and sufficient knowledge about the particular problem space (e.g., Anzai & Simon, 1979 ).

Despite the fruitfulness of this research agenda, it soon became evident that a fundamental weakness was that it minimized the importance of people's background knowledge. Of course, Newell and Simon ( 1972 ) were aware that problem solutions require relevant knowledge (e.g., the rules of logical proofs, or rules for stacking disks). Hence, in programming GPS, they supplemented every problem they modeled with the necessary background knowledge. This practice highlighted the generality and flexibility of means-ends analysis but failed to capture how people's background knowledge affects their solutions. As we discussed in the previous section, domain knowledge is likely to affect how people represent problems and, therefore, how they generate problem solutions. Moreover, as people gain experience solving problems in a particular knowledge domain (e.g., math, physics), they change their representations of these problems (e.g., Chi, Feltovich, & Glaser, 1981 ; Haverty, Koedinger, Klahr, & Alibali, 2000 ; Schoenfeld & Herrmann, 1982 ) and learn domain-specific heuristics (e.g., Polya, 1957 ; Schoenfeld, 1979 ) that trump the general-purpose strategies.

It is perhaps inevitable that the two traditions in problem-solving research—one emphasizing representation and the other emphasizing search strategies—would eventually come together. In the next section we review developments that led to this integration.

The Two Legacies Converge

Because Newell and Simon ( 1972 ) aimed to discover the strategies people use in searching for a solution, they investigated problems that minimized the impact of factors that tend to evoke differences in problem representations, of the sort documented by the Gestalt psychologists. In subsequent work, however, Simon and his collaborators showed that such factors are highly relevant to people's solutions of well-defined problems, and Simon ( 1986 ) incorporated these findings into the theoretical framework that views problem solving as search in a problem space.

In this section, we first describe illustrative examples of this work. We then describe research on insight solutions that incorporates ideas from the two legacies described in the previous sections.

Relevance of the Gestalt Ideas to the Solution of Search Problems

In this subsection we describe two lines of research by Simon and his colleagues, and by other researchers, that document the importance of perception and of background knowledge to the way people search for a problem solution. The first line of research used variants of relatively well-defined riddle problems that had the same structure (i.e., “problem isomorphs”) and, therefore, supposedly the same problem space. It documented that people's search depended on various perceptual and conceptual inferences they tended to draw from a specific instantiation of the problem's structure. The second line of research documented that people's search strategies crucially depend on their domain knowledge and on their prior experience with related problems.

Problem Isomorphs

Hayes and Simon ( 1977 ) used two variants of the Tower of Hanoi problem that, instead of disks and pegs, involved monsters and globes that differed in size (small, medium, and large). In both variants, the initial state had the small monster holding the large globe, the medium-sized monster holding the small globe, and the large monster holding the medium-sized globe. Moreover, in both variants the goal was for each monster to hold a globe proportionate to its own size. The only difference between the problems concerned the description of the operators. In one variant (“transfer”), subjects were told that the monsters could transfer the globes from one to another as long as they followed a set of rules, adapted from the rules in the original Tower of Hanoi problem (e.g., only one globe may be transferred at a time). In the other variant (“change”), subjects were told that the monsters could shrink and expand themselves according to a set of rules, which corresponded to the rules in the transfer version of the problem (e.g., only one monster may change its size at a time). Despite the isomorphism of the two variants, subjects conducted their search in two qualitatively different problem spaces, which led to solution times for the change variant being almost twice as long as those for the transfer variant. This difference arose because subjects could more readily envision and track an object that was changing its location with every move than one that was changing its size.

Recent work by Patsenko and Altmann ( 2010 ) found that, even in the standard Tower of Hanoi problem, people's solutions involve object-bound routines that depend on perception and selective attention. The subjects in their study solved various Tower of Hanoi problems on a computer. During the solution of a particular “critical” problem, the computer screen changed at various points without subjects' awareness (e.g., a disk was added, such that a subject who started with a five-disc tower ended with a six-disc tower). Patsenko and Altmann found that subjects' moves were guided by the configurations of the objects on the screen rather than by solution plans they had stored in memory (e.g., the next subgoal).

The Gestalt psychologists highlighted the role of perceptual factors in the formation of problem representations (e.g., Maier's, 1930 , nine-dot problem) but were generally silent about the corresponding implications for how the problem was solved (although they did note effects on solution accuracy). An important contribution of the work on people's solutions of the Tower of Hanoi problem and its variants was to show the relevance of perceptual factors to the application of various operators during search for a problem solution—that is, to the how of problem solving. In the next section, we describe recent work that documents the involvement of perceptual factors in how people understand and use equations and diagrams in the context of solving math and science problems.

Kotovsky, Hayes, and Simon ( 1985 ) further investigated factors that affect people's representation and search in isomorphs of the Tower of Hanoi problem. In one of their isomorphs, three disks were stacked on top of each other to form an inverted pyramid, with the smallest disc on the bottom and the largest on top. Subjects' solutions of the inverted pyramid version were similar to their solutions of the standard version that has the largest disc on the bottom and the smallest on top. However, the two versions were solved very differently when subjects were told that the discs represent acrobats. Subjects readily solved the version in which they had to place a small acrobat on the shoulders of a large one, but they refrained from letting a large acrobat stand on the shoulders of a small one. In other words, object-based inferences that draw on people's semantic knowledge affected the solution of search problems, much as they affect the solution of the ill-defined problems investigated by the Gestalt psychologists (e.g., Duncker's, 1945 , candles problem). In the next section, we describe more recent work that shows similar effects in people's solutions to mathematical word problems.

The work on differences in the representation and solution of problem isomorphs is highly relevant to research on analogical problem solving (or analogical transfer), which examines when and how people realize that two problems that differ in their cover stories have a similar structure (or a similar problem space) and, therefore, can be solved in a similar way. This research shows that minor differences between example problems, such as the use of X-rays versus ultrasound waves to fuse a broken filament of a light bulb, can elicit different problem representations that significantly affect the likelihood of subsequent transfer to novel problem analogs (Holyoak & Koh, 1987 ). Analogical transfer has played a central role in research on human problem solving, in part because it can shed light on people's understanding of a given problem and its solution and in part because it is believed to provide a window onto understanding and investigating creativity (see Smith & Ward, Chapter 23 ). We briefly mention some findings from the analogy literature in the next subsection on expertise, but we do not discuss analogical transfer in detail because this topic is covered elsewhere in this volume (Holyoak, Chapter 13 ).

Expertise and Its Development

In another line of research, Simon and his colleagues examined how people solve ecologically valid problems from various rule-governed and knowledge-rich domains. They found that people's level of expertise in such domains, be it in chess (Chase & Simon, 1973 ; Gobet & Simon, 1996 ), mathematics (Hinsley, Hayes, & Simon, 1977 ; Paige & Simon, 1966 ), or physics (Larkin, McDermott, Simon, & Simon, 1980 ; Simon & Simon, 1978 ), plays a crucial role in how they represent problems and search for solutions. This work, and the work of numerous other researchers, led to the discovery (and rediscovery, see Duncker, 1945 ) of important differences between experts and novices, and between “good” and “poor” students.

One difference between experts and novices pertains to pattern recognition. Experts' attention is quickly captured by familiar configurations within a problem situation (e.g., a familiar configuration of pieces in a chess game). In contrast, novices' attention is focused on isolated components of the problem (e.g., individual chess pieces). This difference, which has been found in numerous domains, indicates that experts have stored in memory many meaningful groups (chunks) of information: for example, chess (Chase & Simon, 1973 ), circuit diagrams (Egan & Schwartz, 1979 ), computer programs (McKeithen, Reitman, Rueter, & Hirtle, 1981 ), medicine (Coughlin & Patel, 1987 ; Myles-Worsley, Johnston, & Simons, 1988 ), basketball and field hockey (Allard & Starkes, 1991 ), and figure skating (Deakin & Allard, 1991 ).

The perceptual configurations that domain experts readily recognize are associated with stored solution plans and/or compiled procedures (Anderson, 1982 ). As a result, experts' solutions are much faster than, and often qualitatively different from, the piecemeal solutions that novice solvers tend to construct (e.g., Larkin et al., 1980 ). In effect, experts often see the solutions that novices have yet to compute (e.g., Chase & Simon, 1973 ; Novick & Sherman, 2003 , 2008 ). These findings have led to the design of various successful instructional interventions (e.g., Catrambone, 1998 ; Kellman et al., 2008 ). For example, Catrambone ( 1998 ) perceptually isolated the subgoals of a statistics problem. This perceptual chunking of meaningful components of the problem prompted novice students to self-explain the meaning of the chunks, leading to a conceptual understanding of the learned solution. In the next section, we describe some recent work that shows the beneficial effects of perceptual pattern recognition on the solution of familiar mathematics problems, as well as the potentially detrimental effects of familiar perceptual chunks to understanding and reasoning with diagrams depicting evolutionary relationships among taxa.

Another difference between experts and novices pertains to their understanding of the solution-relevant problem structure. Experts' knowledge is highly organized around domain principles, and their problem representations tend to reflect this principled understanding. In particular, they can extract the solution-relevant structure of the problems they encounter (e.g., meaningful causal relations among the objects in the problem; see Cheng & Buehner, Chapter 12 ). In contrast, novices' representations tend to be bound to surface features of the problems that may be irrelevant to solution (e.g., the particular objects in a problem). For example, Chi, Feltovich, and Glaser ( 1981 ) examined how students with different levels of physics expertise group mechanics word problems. They found that advanced graduate students grouped the problems based on the physics principles relevant to the problems' solutions (e.g., conservation of energy, Newton's second law). In contrast, undergraduates who had successfully completed an introductory course in mechanics grouped the problems based on the specific objects involved (e.g., pulley problems, inclined plane problems). Other researchers have found similar results in the domains of biology, chemistry, computer programming, and math (Adelson, 1981 ; Kindfield, 1993 / 1994 ; Kozma & Russell, 1997 ; McKeithen et al., 1981 ; Silver, 1979 , 1981 ; Weiser & Shertz, 1983 ).

The level of domain expertise and the corresponding representational differences are, of course, a matter of degree. With increasing expertise, there is a gradual change in people's focus of attention from aspects that are not relevant to solution to those that are (e.g., Deakin & Allard, 1991 ; Hardiman, Dufresne, & Mestre, 1989 ; McKeithen et al., 1981 ; Myles-Worsley et al., 1988 ; Schoenfeld & Herrmann, 1982 ; Silver, 1981 ). Interestingly, Chi, Bassok, Lewis, Reimann, and Glaser ( 1989 ) found similar differences in focus on structural versus surface features among a group of novices who studied worked-out examples of mechanics problems. These differences, which echo Wertheimer's ( 1959 ) observations of individual differences in students' learning about the area of parallelograms, suggest that individual differences in people's interests and natural abilities may affect whether, or how quickly, they acquire domain expertise.

An important benefit of experts' ability to focus their attention on solution-relevant aspects of problems is that they are more likely than novices to recognize analogous problems that involve different objects and cover stories (e.g., Chi et al., 1989 ; Novick, 1988 ; Novick & Holyoak, 1991 ; Wertheimer, 1959 ) or that come from other knowledge domains (e.g., Bassok & Holyoak, 1989 ; Dunbar, 2001 ; Goldstone & Sakamoto, 2003 ). For example, Bassok and Holyoak ( 1989 ) found that, after learning to solve arithmetic-progression problems in algebra, subjects spontaneously applied these algebraic solutions to analogous physics problems that dealt with constantly accelerated motion. Note, however, that experts and good students do not simply ignore the surface features of problems. Rather, as was the case in the problem isomorphs we described earlier (Kotovsky et al., 1985 ), they tend to use such features to infer what the problem's structure could be (e.g., Alibali, Bassok, Solomon, Syc, & Goldin-Meadow, 1999 ; Blessing & Ross, 1996 ). For example, Hinsley et al. ( 1977 ) found that, after reading no more than the first few words of an algebra word problem, expert solvers classified the problem into a likely problem category (e.g., a work problem, a distance problem) and could predict what questions they might be asked and the equations they likely would need to use.

Surface-based problem categorization has a heuristic value (Medin & Ross, 1989 ): It does not ensure a correct categorization (Blessing & Ross, 1996 ), but it does allow solvers to retrieve potentially appropriate solutions from memory and to use them, possibly with some adaptation, to solve a variety of novel problems. Indeed, although experts exploit surface-structure correlations to save cognitive effort, they have the capability to realize that a particular surface cue is misleading (Hegarty, Mayer, & Green, 1992 ; Lewis & Mayer, 1987 ; Martin & Bassok, 2005 ; Novick 1988 , 1995 ; Novick & Holyoak, 1991 ). It is not surprising, therefore, that experts may revert to novice-like heuristic methods when solving problems under pressure (e.g., Beilock, 2008 ) or in subdomains in which they have general but not specific expertise (e.g., Patel, Groen, & Arocha, 1990 ).

Relevance of Search to Insight Solutions

We introduced the notion of insight in our discussion of the nine-dot problem in the section on the Gestalt tradition. The Gestalt view (e.g., Duncker, 1945 ; Maier, 1931 ; see Ohlsson, 1984 , for a review) was that insight problem solving is characterized by an initial work period during which no progress toward solution is made (i.e., an impasse), a sudden restructuring of one's problem representation to a more suitable form, followed immediately by the sudden appearance of the solution. Thus, solving problems by insight was believed to be all about representation, with essentially no role for a step-by-step solution process (i.e., search). Subsequent and contemporary researchers have generally concurred with the Gestalt view that getting the right representation is crucial. However, research has shown that insight solutions do not necessarily arise suddenly or full blown after restructuring (e.g., Weisberg & Alba, 1981 ); and even when they do, the underlying solution process (in this case outside of awareness) may reflect incremental progress toward the goal (Bowden & Jung-Beeman, 2003 ; Durso, Rea, & Dayton, 1994 ; Novick & Sherman, 2003 ).

“Demystifying insight,” to borrow a phrase from Bowden, Jung-Beeman, Fleck, and Kounios ( 2005 ), requires explaining ( 1 ) why solvers initially reach an impasse in solving a problem for which they have the necessary knowledge to generate the solution, ( 2 ) how the restructuring occurred, and ( 3 ) how it led to the solution. A detailed discussion of these topics appears elsewhere in this volume (van Steenburgh et al., Chapter 24 ). Here, we describe briefly three recent theories that have attempted to account for various aspects of these phenomena: Knoblich, Ohlsson, Haider, and Rhenius's ( 1999 ) representational change theory, MacGregor, Ormerod, and Chronicle's ( 2001 ) progress monitoring theory, and Bowden et al.'s ( 2005 ) neurological model. We then propose the need for an integrated approach to demystifying insight that considers both representation and search.

According to Knoblich et al.'s ( 1999 ) representational change theory, problems that are solved with insight are highly likely to evoke initial representations in which solvers place inappropriate constraints on their solution attempts, leading to an impasse. An impasse can be resolved by revising one's representation of the problem. Knoblich and his colleagues tested this theory using Roman numeral matchstick arithmetic problems in which solvers must move one stick to a new location to change a false numerical statement (e.g., I = II + II ) into a statement that is true. According to representational change theory, re-representation may occur through either constraint relaxation or chunk decomposition. (The solution to the example problem is to change II + to III – , which requires both methods of re-representation, yielding I = III – II ). Good support for this theory has been found based on measures of solution rate, solution time, and eye fixation (Knoblich et al., 1999 ; Knoblich, Ohlsson, & Raney, 2001 ; Öllinger, Jones, & Knoblich, 2008 ).

Progress monitoring theory (MacGregor et al., 2001 ) was proposed to account for subjects' difficulty in solving the nine-dot problem, which has traditionally been classified as an insight problem. According to this theory, solvers use the hill-climbing search heuristic to solve this problem, just as they do for traditional search problems (e.g., Hobbits and Orcs). In particular, solvers are hypothesized to monitor their progress toward solution using a criterion generated from the problem's current state. If solvers reach criterion failure, they seek alternative solutions by trying to relax one or more problem constraints. MacGregor et al. found support for this theory using several variants of the nine-dot problem (also see Ormerod, MacGregor, & Chronicle, 2002 ). Jones ( 2003 ) suggested that progress monitoring theory provides an account of the solution process up to the point an impasse is reached and representational change is sought, at which point representational change theory picks up and explains how insight may be achieved. Hence, it appears that a complete account of insight may require an integration of concepts from the Gestalt (representation) and Newell and Simon's (search) legacies.

Bowden et al.'s ( 2005 ) neurological model emphasizes the overlap between problem solving and language comprehension, and it hinges on differential processing in the right and left hemispheres. They proposed that an impasse is reached because initial processing of the problem produces strong activation of information irrelevant to solution in the left hemisphere. At the same time, weak semantic activation of alternative semantic interpretations, critical for solution, occurs in the right hemisphere. Insight arises when the weakly activated concepts reinforce each other, eventually rising above the threshold required for conscious awareness. Several studies of problem solving using compound remote associates problems, involving both behavioral and neuroimaging data, have found support for this model (Bowden & Jung-Beeman, 1998 , 2003 ; Jung-Beeman & Bowden, 2000 ; Jung-Beeman et al., 2004 ; also see Moss, Kotovsky, & Cagan, 2011 ).

Note that these three views of insight have received support using three quite distinct types of problems (Roman numeral matchstick arithmetic problems, the nine-dot problem, and compound remote associates problems, respectively). It remains to be established, therefore, whether these accounts can be generalized across problems. Kershaw and Ohlsson ( 2004 ) argued that insight problems are difficult because the key behavior required for solution may be hindered by perceptual factors (the Gestalt view), background knowledge (so expertise may be important; e.g., see Novick & Sherman, 2003 , 2008 ), and/or process factors (e.g., those affecting search). From this perspective, solving visual problems (e.g., the nine-dot problem) with insight may call upon more general visual processes, whereas solving verbal problems (e.g., anagrams, compound remote associates) with insight may call upon general verbal/semantic processes.

The work we reviewed in this section shows the relevance of problem representation (the Gestalt legacy) to the way people search the problem space (the legacy of Newell and Simon), and the relevance of search to the solution of insight problems that require a representational change. In addition to this inevitable integration of the two legacies, the work we described here underscores the fact that problem solving crucially depends on perceptual factors and on the solvers' background knowledge. In the next section, we describe some recent work that shows the involvement of these factors in the solution of problems in math and science.

Effects of Perception and Knowledge in Problem Solving in Academic Disciplines

Although the use of puzzle problems continues in research on problem solving, especially in investigations of insight, many contemporary researchers tackle problem solving in knowledge-rich domains, often in academic disciplines (e.g., mathematics, biology, physics, chemistry, meteorology). In this section, we provide a sampling of this research that highlights the importance of visual perception and background knowledge for successful problem solving.

The Role of Visual Perception

We stated at the outset that a problem representation (e.g., the problem space) is a model of the problem constructed by solvers to summarize their understanding of the problem's essential nature. This informal definition refers to the internal representations people construct and hold in working memory. Of course, people may also construct various external representations (Markman, 1999 ) and even manipulate those representations to aid in solution (see Hegarty & Stull, Chapter 31 ). For example, solvers often use paper and pencil to write notes or draw diagrams, especially when solving problems from formal domains (e.g., Cox, 1999 ; Kindfield, 1993 / 1994 ; S. Schwartz, 1971 ). In problems that provide solvers with external representation, such as the Tower of Hanoi problem, people's planning and memory of the current state is guided by the actual configurations of disks on pegs (Garber & Goldin-Meadow, 2002 ) or by the displays they see on a computer screen (Chen & Holyoak, 2010 ; Patsenko & Altmann, 2010 ).

In STEM (science, technology, engineering, and mathematics) disciplines, it is common for problems to be accompanied by diagrams or other external representations (e.g., equations) to be used in determining the solution. Larkin and Simon ( 1987 ) examined whether isomorphic sentential and diagrammatic representations are interchangeable in terms of facilitating solution. They argued that although the two formats may be equivalent in the sense that all of the information in each format can be inferred from the other format (informational equivalence), the ease or speed of making inferences from the two formats might differ (lack of computational equivalence). Based on their analysis of several problems in physics and math, Larkin and Simon further argued for the general superiority of diagrammatic representations (but see Mayer & Gallini, 1990 , for constraints on this general conclusion).

Novick and Hurley ( 2001 , p. 221) succinctly summarized the reasons for the general superiority of diagrams (especially abstract or schematic diagrams) over verbal representations: They “(a) simplify complex situations by discarding unnecessary details (e.g., Lynch, 1990 ; Winn, 1989 ), (b) make abstract concepts more concrete by mapping them onto spatial layouts with familiar interpretational conventions (e.g., Winn, 1989 ), and (c) substitute easier perceptual inferences for more computationally intensive search processes and sentential deductive inferences (Barwise & Etchemendy, 1991 ; Larkin & Simon, 1987 ).” Despite these benefits of diagrammatic representations, there is an important caveat, noted by Larkin and Simon ( 1987 , p. 99) at the very end of their paper: “Although every diagram supports some easy perceptual inferences, nothing ensures that these inferences must be useful in the problem-solving process.” We will see evidence of this in several of the studies reviewed in this section.

Next we describe recent work on perceptual factors that are involved in people's use of two types of external representations that are provided as part of the problem in two STEM disciplines: equations in algebra and diagrams in evolutionary biology. Although we focus here on effects of perceptual factors per se, it is important to note that such factors only influence performance when subjects have background knowledge that supports differential interpretation of the alternative diagrammatic depictions presented (Hegarty, Canham, & Fabricant, 2010 ).

In the previous section, we described the work of Patsenko and Altmann ( 2010 ) that shows direct involvement of visual attention and perception in the sequential application of move operators during the solution of the Tower of Hanoi problem. A related body of work documents similar effects in tasks that require the interpretation and use of mathematical equations (Goldstone, Landy, & Son, 2010 ; Landy & Goldstone, 2007a , b). For example, Landy and Goldstone ( 2007b ) varied the spatial proximity of arguments to the addition (+) and multiplication (*) operators in algebraic equations, such that the spatial layout of the equation was either consistent or inconsistent with the order-of-operations rule that multiplication precedes addition. In consistent equations , the space was narrower around multiplication than around addition (e.g., g*m + r*w = m*g + w*r ), whereas in inconsistent equations this relative spacing was reversed (e.g., s * n+e * c = n * s+c * e ). Subjects' judgments of the validity of such equations (i.e., whether the expressions on the two sides of the equal sign are equivalent) were significantly faster and more accurate for consistent than inconsistent equations.

In discussing these findings and related work with other external representations, Goldstone et al. ( 2010 ) proposed that experience with solving domain-specific problems leads people to “rig up” their perceptual system such that it allows them to look at the problem in a way that is consistent with the correct rules. Similar logic guides the Perceptual Learning Modules developed by Kellman and his collaborators to help students interpret and use algebraic equations and graphs (Kellman et al., 2008 ; Kellman, Massey, & Son, 2009 ). These authors argued and showed that, consistent with the previously reviewed work on expertise, perceptual training with particular external representations supports the development of perceptual fluency. This fluency, in turn, supports students' subsequent use of these external representations for problem solving.

This research suggests that extensive experience with particular equations or graphs may lead to perceptual fluency that could replace the more mindful application of domain-specific rules. Fisher, Borchert, and Bassok ( 2011 ) reported results from algebraic-modeling tasks that are consistent with this hypothesis. For example, college students were asked to represent verbal statements with algebraic equations, a task that typically elicits systematic errors (e.g., Clement, Lochhead, & Monk, 1981 ). Fisher et al. found that such errors were very common when subjects were asked to construct “standard form” equations ( y = ax ), which support fluent left-to-right translation of words to equations, but were relatively rare when subjects were asked to construct nonstandard division-format equations (x = y/a) that do not afford such translation fluency.

In part because of the left-to-right order in which people process equations, which mirrors the linear order in which they process text, equations have traditionally been viewed as sentential representations. However, Landy and Goldstone ( 2007a ) have proposed that equations also share some properties with diagrammatic displays and that, in fact, in some ways they are processed like diagrams. That is, spatial information is used to represent and to support inferences about syntactic structure. This hypothesis received support from Landy and Goldstone's ( 2007b ) results, described earlier, in which subjects' judgments of the validity of equations were affected by the Gestalt principle of grouping: Subjects did better when the grouping was consistent rather than inconsistent with the underlying structure of the problem (order of operations). Moreover, Landy and Goldstone ( 2007a ) found that when subjects wrote their own equations they grouped numbers and operators (+, *, =) in a way that reflected the hierarchical structure imposed by the order-of-operations rule.

In a recent line of research, Novick and Catley ( 2007 ; Novick, Catley, & Funk, 2010 ; Novick, Shade, & Catley, 2011 ) have examined effects of the spatial layout of diagrams depicting the evolutionary history of a set of taxa on people's ability to reason about patterns of relationship among those taxa. We consider here their work that investigates the role of another Gestalt perceptual principle—good continuation—in guiding students' reasoning. According to this principle, a continuous line is perceived as a single entity (Kellman, 2000 ). Consider the diagrams shown in Figure 21.6 . Each is a cladogram, a diagram that depicts nested sets of taxa that are related in terms of levels of most recent common ancestry. For example, chimpanzees and starfish are more closely related to each other than either is to spiders. The supporting evidence for their close relationship is their most recent common ancestor, which evolved the novel character of having radial cleavage. Spiders do not share this ancestor and thus do not have this character.

Cladograms are typically drawn in two isomorphic formats, which Novick and Catley ( 2007 ) referred to as trees and ladders. Although these formats are informationally equivalent (Larkin & Simon, 1987 ), Novick and Catley's ( 2007 ) research shows that they are not computationally equivalent (Larkin & Simon, 1987 ). Imagine that you are given evolutionary relationships in the ladder format, such as in Figure 21.6a (but without the four characters—hydrostatic skeleton, bilateral symmetry, radial cleavage, and trocophore larvae—and associated short lines indicating their locations on the cladogram), and your task is to translate that diagram to the tree format. A correct translation is shown in Figure 21.6b . Novick and Catley ( 2007 ) found that college students were much more likely to get such problems correct when the presented cladogram was in the nested circles (e.g., Figure 21.6d ) rather than the ladder format. Because the Gestalt principle of good continuation makes the long slanted line at the base of the ladder appear to represent a single hierarchical level, a common translation error for the ladder to tree problems was to draw a diagram such as that shown in Figure 21.6c .

The difficulty that good continuation presents for interpreting relationships depicted in the ladder format extends to answering reasoning questions as well. Novick and Catley (unpublished data) asked comparable questions about relationships depicted in the ladder and tree formats. For example, using the cladograms depicted in Figures 21.6a and 21.6b , consider the following questions: (a) Which taxon—jellyfish or earthworm—is the closest evolutionary relation to starfish, and what evidence supports your answer? (b) Do the bracketed taxa comprise a clade (a set of taxa consisting of the most recent common ancestor and all of its descendants), and what evidence supports your answer? For both such questions, students had higher accuracy and evidence quality composite scores when the relationships were depicted in the tree than the ladder format.

Four cladograms depicting evolutionary relationships among six animal taxa. Cladogram ( a ) is in the ladder format, cladograms ( b ) and ( c ) are in the tree format, and cladogram ( d ) is in the nested circles format. Cladograms ( a ), ( b ), and ( d ) are isomorphic.

If the difficulty in extracting the hierarchical structure of the ladder format is due to good continuation (which leads problem solvers to interpret continuous lines that depict multiple hierarchical levels as depicting only a single level), then a manipulation that breaks good continuation at the points where a new hierarchical level occurs should improve understanding. Novick et al. ( 2010 ) tested this hypothesis using a translation task by manipulating whether characters that are the markers for the most recent common ancestor of each nested set of taxa were included on the ladders. Figure 21.6a shows a ladder with such characters. As predicted, translation accuracy increased dramatically simply by adding these characters to the ladders, despite the additional information subjects had to account for in their translations.

The Role of Background Knowledge

As we mentioned earlier, the specific entities in the problems people encounter evoke inferences that affect how people represent these problems (e.g., the candle problem; Duncker, 1945 ) and how they apply the operators in searching for the solution (e.g., the disks vs. acrobats versions of the Tower of Hanoi problem; Kotovsky et al., 1985 ). Such object-based inferences draw on people's knowledge about the properties of the objects (e.g., a box is a container, an acrobat is a person who can be hurt). Here, we describe the work of Bassok and her colleagues, who found that similar inferences affect how people select mathematical procedures to solve problems in various formal domains. This work shows that the objects in the texts of mathematical word problems affect how people represent the problem situation (i.e., the situation model they construct; Kintsch & Greeno, 1985 ) and, in turn, lead them to select mathematical models that have a corresponding structure. To illustrate, a word problem that describes constant change in the rate at which ice is melting off a glacier evokes a model of continuous change, whereas a word problem that describes constant change in the rate at which ice is delivered to a restaurant evokes a model of discrete change. These distinct situation models lead subjects to select corresponding visual representations (e.g., Bassok & Olseth, 1995 ) and solutions methods, such as calculating the average change over time versus adding the consecutive changes (e.g., Alibali et al., 1999 ).

In a similar manner, people draw on their general knowledge to infer how the objects in a given problem are related to each other and construct mathematical solutions that correspond to these inferred object relations. For example, a word problem that involves doctors from two hospitals elicits a situation model in which the two sets of doctors play symmetric roles (e.g., work with each other), whereas a mathematically isomorphic problem that involves mechanics and cars elicits a situation model in which the sets play asymmetric roles (e.g., mechanics fix cars). The mathematical solutions people construct to such problems reflect this difference in symmetry (Bassok, Wu, & Olseth, 1995 ). In general, people tend to add objects that belong to the same taxonomic category (e.g., doctors + doctors) but divide functionally related objects (e.g., cars ÷ mechanics). People establish this correspondence by a process of analogical alignment between semantic and arithmetic relations, which Bassok and her colleagues refer to as “semantic alignment” (Bassok, Chase, & Martin, 1998 ; Doumas, Bassok, Guthormsen, & Hummel, 2006 ; Fisher, Bassok, & Osterhout, 2010 ).

Semantic alignment occurs very early in the solution process and can prime arithmetic facts that are potentially relevant to the problem solution (Bassok, Pedigo, & Oskarsson, 2008 ). Although such alignments can lead to erroneous solutions, they have a high heuristic value because, in most textbook problems, object relations indeed correspond to analogous mathematical relations (Bassok et al., 1998 ). Interestingly, unlike in the case of reliance on specific surface-structure correlations (e.g., the keyword “more” typically appears in word problems that require addition; Lewis & Mayer, 1987 ), people are more likely to exploit semantic alignment when they have more, rather than less modeling experience. For example, Martin and Bassok ( 2005 ) found very strong semantic-alignment effects when subjects solved simple division word problems, but not when they constructed algebraic equations to represent the relational statements that appeared in the problems. Of course, these subjects had significantly more experience with solving numerical word problems than with constructing algebraic models of relational statements. In a subsequent study, Fisher and Bassok ( 2009 ) found semantic-alignment effects for subjects who constructed correct algebraic models, but not for those who committed modeling errors.

Conclusions and Future Directions

In this chapter, we examined two broad components of the problem-solving process: representation (the Gestalt legacy) and search (the legacy of Newell and Simon). Although many researchers choose to focus their investigation on one or the other of these components, both Duncker ( 1945 ) and Simon ( 1986 ) underscored the necessity to investigate their interaction, as the representation one constructs for a problem determines (or at least constrains) how one goes about trying to generate a solution, and searching the problem space may lead to a change in problem representation. Indeed, Duncker's ( 1945 ) initial account of one subject's solution to the radiation problem was followed up by extensive and experimentally sophisticated work by Simon and his colleagues and by other researchers, documenting the involvement of visual perception and background knowledge in how people represent problems and search for problem solutions.

The relevance of perception and background knowledge to problem solving illustrates the fact that, when people attempt to find or devise ways to reach their goals, they draw on a variety of cognitive resources and engage in a host of cognitive activities. According to Duncker ( 1945 ), such goal-directed activities may include (a) placing objects into categories and making inferences based on category membership, (b) making inductive inferences from multiple instances, (c) reasoning by analogy, (d) identifying the causes of events, (e) deducing logical implications of given information, (f) making legal judgments, and (g) diagnosing medical conditions from historical and laboratory data. As this list suggests, many of the chapters in the present volume describe research that is highly relevant to the understanding of problem-solving behavior. We believe that important advancements in problem-solving research would emerge by integrating it with research in other areas of thinking and reasoning, and that research in these other areas could be similarly advanced by incorporating the insights gained from research on what has more traditionally been identified as problem solving.

As we have described in this chapter, many of the important findings in the field have been established by a careful investigation of various riddle problems. Although there are good methodological reasons for using such problems, many researchers choose to investigate problem solving using ecologically valid educational materials. This choice, which is increasingly common in contemporary research, provides researchers with the opportunity to apply their basic understanding of problem solving to benefit the design of instruction and, at the same time, allows them to gain a better understanding of the processes by which domain knowledge and educational conventions affect the solution process. We believe that the trend of conducting educationally relevant research is likely to continue, and we expect a significant expansion of research on people's understanding and use of dynamic and technologically rich external representations (e.g., Kellman et al., 2008 ; Mayer, Griffith, Jurkowitz, & Rothman, 2008 ; Richland & McDonough, 2010 ; Son & Goldstone, 2009 ). Such investigations are likely to yield both practical and theoretical payoffs.

Adams, J. L. ( 1979 ). Conceptual blockbusting: A guide to better ideas (2nd ed.). New York: Norton.

Google Scholar

Google Preview

Adelson, B. ( 1981 ). Problem solving and the development of abstract categories in programming languages.   Memory and Cognition , 9 , 422–433.

Alibali, M. W., Bassok, M., Solomon, K. O., Syc, S. E., & Goldin-Meadow, S. ( 1999 ). Illuminating mental representations through speech and gesture.   Psychological Science , 10 , 327–333.

Allard, F., & Starkes, J. L. ( 1991 ). Motor-skill experts in sports, dance, and other domains. In K. A. Ericsson & J. Smith (Eds.), Toward a general theory of expertise: Prospects and limits (pp. 126–152). New York: Cambridge University Press.

Anderson, J. R. ( 1982 ). Acquisition of cognitive skill.   Psychological Review , 89 , 369–406.

Anzai, Y., & Simon, H. A. ( 1979 ). The theory of learning by doing.   Psychological Review , 86 , 124–140.

Atwood, M. E, & Polson, P.G. ( 1976 ). A process model for water jug problems.   Cognitive Psychology , 8 , 191–216.

Barwise, J., & Etchemendy, J. ( 1991 ). Visual information and valid reasoning. In W. Zimmermann & S. Cunningham (Eds.), Visualization in teaching and learning mathematics (pp. 9–24). Washington, DC: Mathematical Association of America.

Bassok, M., Chase, V. M., & Martin, S. A. ( 1998 ). Adding apples and oranges: Alignment of semantic and formal knowledge.   Cognitive Psychology , 35 , 99–134.

Bassok, M., & Holyoak, K. J. ( 1989 ). Interdomain transfer between isomorphic topics in algebra and physics.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 15 , 153–166.

Bassok, M., & Olseth, K. L. ( 1995 ). Object-based representations: Transfer between cases of continuous and discrete models of change.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 21 , 1522–1538.

Bassok, M., Pedigo, S. F., & Oskarsson, A. T. ( 2008 ). Priming addition facts with semantic relations.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 34 , 343–352.

Bassok, M., Wu, L., & Olseth, L. K. ( 1995 ). Judging a book by its cover: Interpretative effects of content on problem solving transfer.   Memory and Cognition , 23 , 354–367.

Beilock, S. L. ( 2008 ). Math performance in stressful situations.   Current Directions in Psychological Science , 17 , 339–343.

Birch, H. G. & Rabinowitz, H. S. ( 1951 ). The negative effect of previous experience on productive thinking.   Journal of Experimental Psychology , 41 , 122–126.

Blessing, S. B., & Ross, B. H. ( 1996 ). Content effects in problem categorization and problem solving.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 22 , 792–810.

Bowden, E. M., & Jung-Beeman, M. ( 1998 ). Getting the right idea: Semantic activation in the right hemisphere may help solve insight problems.   Psychological Science , 6 , 435–440.

Bowden, E. M., & Jung-Beeman, M. ( 2003 ). Aha! Insight experience correlates with solution activation in the right hemisphere.   Psychonomic Bulletin and Review , 10 , 730–737.

Bowden, E. M., Jung-Beeman, M., Fleck, J., & Kounios, J. ( 2005 ). New approaches to demystifying insight.   Trends in Cognitive Sciences , 9 , 322–328.

Catrambone, R. ( 1998 ). The subgoal-learning model: Creating better examples so that students can solve novel problems.   Journal of Experimental Psychology: General , 127 , 355–376.

Chase, W. G., & Simon, H. A. ( 1973 ). Perception in chess.   Cognitive Psychology , 4 , 55–81.

Chen, D., & Holyoak, K. J. ( 2010 ). Enhancing acquisition of intuition versus planning in problem solving. In S. Ohlsson & R. Catrambone (Eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society (pp. 1875–1880). Austin, TX: Cognitive Science Society.

Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. ( 1989 ). Self-explanations: How students study and use examples in learning to solve problems.   Cognitive Science , 13 , 145–182.

Chi, M. T. H., Feltovich, P. J., & Glaser, R. ( 1981 ). Categorization and representation of physics problems by experts and novices.   Cognitive Science , 5 , 121–152.

Clement, J., Lochhead, J., & Monk, G. S. ( 1981 ). Translation difficulties in learning mathematics.   The American Mathematical Monthly , 88 , 286–290.

Coughlin, L. D., & Patel, V. L. ( 1987 ). Processing of critical information by physicians and medical students.   Journal of Medical Education , 62 , 818–828.

Cox, R. ( 1999 ). Representation construction, externalised cognition and individual differences.   Learning and Instruction , 9 , 343–363.

Deakin, J. M., & Allard, F. ( 1991 ). Skilled memory in expert figure skaters.   Memory and Cognition , 19 , 79–86.

Doumas, L. A. A., Bassok, M., Guthormsen, A., & Hummel, J. E. ( 2006 ). Theory of reflexive relational generalization. In R. Sun & N. Miyake (Eds.), Proceedings of the 28th Annual Conference of the Cognitive Science Society (pp. 1246–1250). Mahwah, NJ: Erlbaum.

Dunbar, K. ( 2001 ). The analogical paradox: Why analogy is so easy in naturalistic settings, yet so difficult in the psychological laboratory. In D. Gentner, K. J. Holyoak, & B. Kokinov (Eds.), Analogy: Perspectives from cognitive science (pp. 313–362). Cambridge, MA: MIT Press.

Duncker, K. ( 1945 ). On problem-solving (L. S. Lees, Trans.). Psychological Monographs , 58 (Whole No. 270). (Original work published 1935).

Durso, F. T., Rea, C. B., & Dayton, T. ( 1994 ). Graph-theoretic confirmation of restructuring during insight.   Psychological Science , 5 , 94–98.

Egan, D. E., & Schwartz, B. J. ( 1979 ). Chunking in the recall of symbolic drawings.   Memory and Cognition , 7 , 149–158.

Ericsson, K. A., & Simon, H. A. ( 1980 ). Verbal reports as data.   Psychological Review , 87 , 215–251.

Ernst, G. W., & Newell, A. ( 1969 ). GPS: A case study in generality and problem solving . New York: Academic Press.

Fisher, K. J., & Bassok, M. ( 2009 ). Analogical alignments in algebraic modeling. In B. Kokinov, D. Gentner, & K. J. Holyoak (Eds.), Proceedings of the 2nd International Analogy Conference (pp. 137–144). Sofia, Bulgaria: New Bulgarian University Press.

Fisher, K. J., Bassok, M., & Osterhout, L. ( 2010 ). When two plus two does not equal four: Event-related potential responses to semantically incongruous arithmetic word problems. In S. Ohlsson & R. Catrambone (Eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society (pp. 1571–1576). Austin, TX: Cognitive Science Society.

Fisher, K. J., Borchert, K., & Bassok, M. ( 2011 ). Following the standard form: Effects of equation format on algebraic modeling.   Memory and Cognition , 39 , 502–515.

Garber, P., & Goldin-Meadow, S. ( 2002 ). Gesture offers insight into problem solving in adults and children.   Cognitive Science , 26 , 817–831.

Gobet, F., & Simon, H. ( 1996 ). Recall of rapidly presented random chess positions is a function of skill.   Psychonomic Bulletin and Review , 3 , 159–163.

Goldstone, R. L., Landy, D. H., & Son, J. Y. ( 2010 ). The education of perception.   Topics in Cognitive Science , 2 , 265–284.

Goldstone, R. L., & Sakamoto, J. Y. ( 2003 ). The transfer of abstract principles governing complex adaptive systems.   Cognitive Psychology , 46 , 414–466.

Greeno, J. G. ( 1974 ). Hobbits and orcs: Acquisition of a sequential concept.   Cognitive Psychology , 6 , 270–292.

Hardiman, P. T., Dufresne, R., & Mestre, J. P. ( 1989 ). The relation between problem categorization and problem solving among experts and novices.   Memory and Cognition , 17 , 627–638.

Haverty, L. A., Koedinger, K. R., Klahr, D., & Alibali, M. W. ( 2000 ). Solving induction problems in mathematics: Not-so-trivial Pursuit.   Cognitive Science , 24 , 249–298.

Hayes, J. R., & Simon, H. A. ( 1977 ). Psychological differences among problem isomorphs. In N. J. Castellan, D. B. Pisoni, & G. R. Potts (Eds.), Cognitive theory (Vol. 2, pp. 21–44). Hillsdale, NJ: Erlbaum.

Hegarty, M., Canham, M. S., & Fabricant, S. I. ( 2010 ). Thinking about the weather: How display salience and knowledge affect performance in a graphic inference task.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 36 , 37–53.

Hegarty, M., Mayer, R. E., & Green, C. E. ( 1992 ). Comprehension of arithmetic word problems: Evidence from students' eye fixations.   Journal of Educational Psychology , 84 , 76–84.

Hinsley, D. A., Hayes, J. R., & Simon, H. A. ( 1977 ). From words to equations: Meaning and representation in algebra word problems. In D. Hinsley, M. Just., & P. Carpenter (Eds.), Cognitive processes in comprehension (pp. 89–106). Hillsdale, NJ: Erlbaum.

Holyoak, K. J., & Koh, K. ( 1987 ). Surface and structural similarity in analogical transfer.   Memory and Cognition , 15 , 332–340.

Jones, G. ( 2003 ). Testing two cognitive theories of insight.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 29 , 1017–1027.

Jung-Beeman, M., & Bowden, E. M. ( 2000 ). The right hemisphere maintains solution-related activation for yet-to-be solved insight problems.   Memory and Cognition , 28 , 1231–1241.

Jung-Beeman, M., Bowden, E. M., Haberman, J., Frymiare, J. L., Arambel-Liu, S., Greenblatt, R., … Kounios, J. ( 2004 ). Neural activity when people solve verbal problems with insight.   PLOS Biology , 2 , 500–510.

Kellman, P. J. ( 2000 ). An update on Gestalt psychology. In B. Landau, J. Sabini, J. Jonides, & E. Newport (Eds.), Perception, cognition, and language: Essays in honor of Henry and Lila Gleitman (pp. 157–190). Cambridge, MA: MIT Press.

Kellman, P. J., Massey, C. M., & Son, J. Y ( 2009 ). Perceptual learning modules in mathematics: Enhancing students' pattern recognition, structure extraction, and fluency.   Topics in Cognitive Science , 1 , 1–21.

Kellman, P. J., Massey, C., Roth, Z., Burke, T., Zucker, J., Saw, A., … Wise, J. A. ( 2008 ). Perceptual learning and the technology of expertise.   Pragmatics and Cognition , 16 , 356–405.

Kershaw, T. C., & Ohlsson, S. ( 2004 ). Multiple causes of difficulty in insight: The case of the nine-dot problem.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 30 , 3–13.

Kindfield, A. C. H. ( 1993 /1994). Biology diagrams: Tools to think with.   Journal of the Learning Sciences , 3 , 1–36.

Kintsch, W., & Greeno, J. G. ( 1985 ). Understanding and solving word arithmetic problems.   Psychological Review , 92 , 109–129.

Knoblich, G., Ohlsson, S., Haider, H., & Rhenius, D. ( 1999 ). Constraint relaxation and chunk decomposition in insight problem solving.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 25 , 1534–1555.

Knoblich, G., Ohlsson, S., & Raney, G. E. ( 2001 ). An eye movement study of insight problem solving.   Memory and Cognition , 29 , 1000–1009.

Kohler, W. ( 1925 ). The mentality of apes . New York: Harcourt Brace.

Kotovsky, K., Hayes, J. R., & Simon, H. A. ( 1985 ). Why are some problems hard? Evidence from Tower of Hanoi.   Cognitive Psychology , 17 , 248–294.

Kozma, R. B., & Russell, J. ( 1997 ). Multimedia and understanding: Expert and novice responses to different representations of chemical phenomena.   Journal of Research in Science Teaching , 34 , 949–968.

Landy, D., & Goldstone, R. L. ( 2007 a). Formal notations are diagrams: Evidence from a production task.   Memory and Cognition , 35, 2033–2040.

Landy, D., & Goldstone, R. L. ( 2007 b). How abstract is symbolic thought?   Journal of Experimental Psychology: Learning, Memory, and Cognition , 33, 720–733.

Larkin, J. H., McDermott, J., Simon, D. P., & Simon, H. A. ( 1980 ). Models of competence in solving physics problems.   Cognitive Science , 4 , 317–345.

Larkin, J. H., & Simon, H. A. ( 1987 ). Why a diagram is (sometimes) worth ten thousand words.   Cognitive Science , 11 , 65–99.

Lewis, A. B., & Mayer, R. E. ( 1987 ). students' miscomprehension of relational statements in arithmetic word problems.   Journal of Educational Psychology , 79 , 363–371.

Lynch, M. ( 1990 ). The externalized retina: Selection and mathematization in the visual documentation of objects in the life sciences. In M. Lynch & S. Woolgar (Eds.), Representation in scientific practice (pp. 153–186). Cambridge, MA: MIT Press.

MacGregor, J. N., Ormerod, T. C., & Chronicle, E. P. ( 2001 ). Information processing and insight: A process model of performance on the nine-dot and related problems.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 27 , 176–201.

Maier, N. ( 1930 ). Reasoning in humans. I. On direction.   Journal of Comparative Psychology , 10 , 15–43.

Maier, N. ( 1931 ). Reasoning in humans. II. The solution of a problem and its appearance in consciousness.   Journal of Comparative Psychology , 12 , 181–194.

Markman, A. B. ( 1999 ). Knowledge representation . Mahwah, NJ: Erlbaum.

Martin, S. A., & Bassok, M. ( 2005 ). Effects of semantic cues on mathematical modeling: Evidence from word-problem solving and equation construction tasks.   Memory and Cognition , 33 , 471–478.

Mayer, R. E., & Gallini, J. K. ( 1990 ). When is an illustration worth ten thousand words?   Journal of Educational Psychology , 82 , 715–726.

Mayer, R. E., Griffith, E., Jurkowitz, I. T. N., & Rothman, D. ( 2008 ). Increased interestingness of extraneous details in a multimedia science presentation leads to decreased learning.   Journal of Experimental Psychology: Applied , 14 , 329–339.

McKeithen, K. B., Reitman, J. S., Rueter, H. H., & Hirtle, S. C. ( 1981 ). Knowledge organization and skill differences in computer programmers.   Cognitive Psychology , 13 , 307–325.

Medin, D. L., & Ross, B. H. ( 1989 ). The specific character of abstract thought: Categorization, problem solving, and induction. In R. J. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 5, pp. 189–223). Hillsdale, NJ: Erlbaum.

Moss, J., Kotovsky, K., & Cagan, J. ( 2011 ). The effect of incidental hints when problems are suspended before, during, and after an impasse.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 37 , 140–148.

Myles-Worsley, M., Johnston, W. A., & Simons, M. A ( 1988 ). The influence of expertise on X-ray image processing.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 14 , 553–557.

Newell, A., & Simon, H. A. ( 1972 ). Human problem solving . Englewood Cliffs, NJ: Prentice-Hall.

Newell, A., & Simon, H. A. ( 1976 ). Computer science as empirical enquiry: Symbols and search.   Communications of the ACM , 19 , 113–126.

Novick, L. R. ( 1988 ). Analogical transfer, problem similarity, and expertise.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 14 , 510–520.

Novick, L. R. ( 1995 ). Some determinants of successful analogical transfer in the solution of algebra word problems.   Thinking and Reasoning , 1 , 5–30.

Novick, L. R., & Catley, K. M. ( 2007 ). Understanding phylogenies in biology: The influence of a Gestalt perceptual principle.   Journal of Experimental Psychology: Applied , 13 , 197–223.

Novick, L. R., Catley, K. M., & Funk, D. J. ( 2010 ). Characters are key: The effect of synapomorphies on cladogram comprehension.   Evolution: Education and Outreach , 3 , 539–547.

Novick, L. R., & Hmelo, C. E. ( 1994 ). Transferring symbolic representations across non-isomorphic problems.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 20 , 1296–1321.

Novick, L. R., & Holyoak, K. J. ( 1991 ). Mathematical problem solving by analogy.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 17 , 398–415.

Novick, L. R., & Hurley, S. M. ( 2001 ). To matrix, network, or hierarchy: That is the question.   Cognitive Psychology , 42 , 158–216.

Novick, L. R., Shade, C. K., & Catley, K. M. ( 2011 ). Linear versus branching depictions of evolutionary history: Implications for diagram design.   Topics in Cognitive Science , 3 (3), 536–559.

Novick, L. R., & Sherman, S. J. ( 2003 ). On the nature of insight solutions: Evidence from skill differences in anagram solution.   The Quarterly Journal of Experimental Psychology , 56A , 351–382.

Novick, L. R., & Sherman, S. J. ( 2008 ). The effects of superficial and structural information on on-line problem solving for good versus poor anagram solvers.   The Quarterly Journal of Experimental Psychology , 61 , 1098–1120.

Ohlsson, S. ( 1984 ). Restructuring revisited I. Summary and critique of the Gestalt theory of problem solving.   Scandinavian Journal of Psychology , 25 , 65–78.

Öllinger, M., Jones, G., & Knoblich, G. ( 2008 ). Investigating the effect of mental set on insight problem solving.   Experimental Psychology , 55 , 269–282.

Ormerod, T. C., MacGregor, J. N., & Chronicle, E. P. ( 2002 ). Dynamics and constraints in insight problem solving.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 28 , 791–799.

Paige, J. M., & Simon, H. A. ( 1966 ). Cognitive processes in solving algebra word problems. In B. Kleinmuntz (Ed.), Problem solving: Research, method, and theory (pp. 51–119). New York: Wiley

Patel, V. L., Groen, G. J., & Arocha, J. F. ( 1990 ). Medical expertise as a function of task difficulty.   Memory and Cognition , 18 , 394–406.

Patsenko, E. G., & Altmann, E. M. ( 2010 ). How planful is routine behavior? A selective attention model of performance in the Tower of Hanoi.   Journal of Experimental Psychology: General , 139 , 95–116.

Polya, G. ( 1957 ). How to solve it (2nd ed.). Princeton, NJ: Princeton University Press.

Posner, M. I. ( 1973 ). Cognition: An introduction . Glenview, IL: Scott, Foresman and Company.

Reitman, W. R. ( 1965 ). Cognition and thought . New York: Wiley.

Richland, L. E., & McDonough, I. M. ( 2010 ), Learning by analogy: Discriminating between potential analogs.   Contemporary Educational Psychology , 35 , 28–43.

Russo, J. E., Johnson, E. J., & Stephens, D. L. ( 1989 ). The validity of verbal protocols.   Memory and Cognition , 17 , 759–769.

Schoenfeld, A. H. ( 1979 ). Explicit heuristic training as a variable in problem-solving performance.   Journal for Research in Mathematics Education , 10 , 173–187.

Schoenfeld, A. H., & Herrmann, D. J. ( 1982 ). Problem perception and knowledge structure in expert and novice mathematical problem solvers.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 8 , 484–494.

Schwartz, S. H. ( 1971 ). Modes of representation and problem solving: Well evolved is half solved.   Journal of Experimental Psychology , 91 , 347–350.

Silver, E. A. ( 1979 ). Student perceptions of relatedness among mathematical verbal problems.   Journal for Research in Mathematics Education , 10 , 195–210.

Silver, E. A. ( 1981 ). Recall of mathematical problem information: Solving related problems.   Journal for Research in Mathematics Education , 12 , 54–64.

Simon, D. P., & Simon, H. A. ( 1978 ). Individual differences in solving physics problems. In R. Siegler (Ed.), Children's thinking: What develops? (pp. 325–348). Hillsdale, NJ: Erlbaum.

Simon, H. A. ( 1978 ). Information-processing theory of human problem solving. In W. K. Estes (Ed.), Handbook of learning and cognitive processes (Vol. 5, pp. 271–295). Hillsdale, NJ: Erlbaum.

Simon, H. A. ( 1986 ). The information processing explanation of Gestalt Phenomena.   Computers in Human Behavior , 2 , 241–255.

Simon, H. A. ( 1990 ). Invariants of human behavior.   Annual Review of Psychology , 41 , 1–19.

Son, J. Y., & Goldstone, R. L. ( 2009 ). Fostering general transfer with specific simulations.   Pragmatics and Cognition , 17 , 1–42.

Thomas, J. C., Jr., ( 1974 ). An analysis of behavior in the hobbits-orcs problem.   Cognitive Psychology , 6 , 257–269.

Weisberg, R. W., & Alba, J. W. ( 1981 ). An examination of the alleged role of “fixation” in the solution of several “insight” problems.   Journal of Experimental Psychology: General , 110 , 169–192.

Weiser, M., & Shertz, J. ( 1983 ). Programming problem representation in novice and expert programmers.   International Journal of Man-Machine Studies , 19 , 391–398.

Wertheimer, M. ( 1959 ). Productive thinking (Rev. ed.). Chicago, IL: University of Chicago Press.

Winn, W. ( 1989 ). The design and use of instructional graphics. In H. Mandl & J. R. Levin (Eds.), Knowledge acquisition from text and pictures (pp. 125–144). Amsterdam, Netherlands: Elsevier

  • About Oxford Academic
  • Publish journals with us
  • University press partners
  • What we publish
  • New features  
  • Open access
  • Institutional account management
  • Rights and permissions
  • Get help with access
  • Accessibility
  • Advertising
  • Media enquiries
  • Oxford University Press
  • Oxford Languages
  • University of Oxford

Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide

  • Copyright © 2024 Oxford University Press
  • Cookie settings
  • Cookie policy
  • Privacy policy
  • Legal notice

This Feature Is Available To Subscribers Only

Sign In or Create an Account

This PDF is available to Subscribers Only

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.

U.S. flag

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

  • Publications
  • Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

  • Advanced Search
  • Journal List
  • HHS Author Manuscripts

Logo of nihpa

Associations Between Conceptual Reasoning, Problem Solving, and Adaptive Ability in High-functioning Autism

Diane l. williams.

Department of Speech-Language Pathology, Duquesne University, Pittsburgh, PA, USA

Carla A. Mazefsky

Department of Psychiatry, University of Pittsburgh, Pittsburgh, PA, USA

Jon D. Walker

VA Pittsburgh Healthcare System, University Drive, Pittsburgh, PA 15240, USA

Nancy J. Minshew

Departments of Psychiatry and Neurology, University of Pittsburgh, Pittsburgh, PA, USA

Gerald Goldstein

VA Pittsburgh Healthcare System, University Drive, Pittsburgh, PA 15240, USA, ten.bn@dlogG

Abstract thinking is generally highly correlated with problem-solving ability which is predictive of better adaptive functioning. Measures of conceptual reasoning, an ecologically-valid laboratory measure of problem-solving, and a report measure of adaptive functioning in the natural environment, were administered to children and adults with and without autism. The individuals with autism had weaker conceptual reasoning ability than individuals with typical development of similar age and cognitive ability. For the autism group, their flexible thinking scores were significantly correlated with laboratory measures of strategy formation and rule shifting and with reported overall adaptive behavior but not socialization scores. Therefore, in autism, flexibility of thought is potentially more important for adaptive functioning in the natural environment than conceptual reasoning or problem-solving.

Introduction

An important goal of treatment in autism is to help the individual successfully function as independently as possible. This notion is captured by the construct of “adaptive behavior ability,” which is an index of how one is able to function in the natural social environment across a multidimensional set of skills ( Oswald and DiSalvo 2003 ). Individuals with autism spectrum disorders (ASDs) have extremely high variability in adaptive behavior ( Klin et al. 2007 ; MacLean et al. 1999 ; Mazefsky et al. 2008 ). For example, Mazefsky et al. (2008) found that a sample of individuals with autism without intellectual developmental disorder had standard scores ranging from 19 (Impaired Range) to 162 (Very Superior) on the Vineland Adaptive Behavior Scales (VABS; Sparrow et al. 1984 ), a commonly used measure of adaptive behavior. Whereas the variability in adaptive behavior in ASD is well-documented, the source of this variability is less clear. Understanding factors that influence this variability in adaptive behavior would inform the design of interventions that might improve the outcome for individuals with autism.

Most of the research conducted to understand adaptive behavior in ASD has focused on its relationship to age and intelligence quotient (IQ). This research has been fairly consistent in finding that adaptive behavior skills in autism tend to be much lower than would be expected based on IQ (e.g. Boltë and Poustka 2002 ; Fenton et al. 2001 ; Kanne et al. 2011 ; Mazefsky et al. 2008 ). It is also clear that the IQ-adaptive behavior discrepancy becomes even more apparent with increasing age, and that the gap between IQ and adaptive behavior ability is often quite significant in samples with higher IQs ( Boltë and Poustka 2002 ; Kanne et al. 2011 ; Klin et al. 2007 ; Liss et al. 2001 ; Mazefsky et al. 2008 ). Even a recent study with children with ASD (ages 4–17 years) that reported that IQ was a strong predictor of adaptive behavior, noted that having a higher IQ did not indicate that the children would perform well socially ( Kanne et al. 2011 ). The unclear nature of the relationship between IQ and adaptive behavior would suggest that the failure of verbal individuals with IQ scores in the normal range to achieve age and ability appropriate adaptive behavior is related to some other aspect of the disorder than general intellectual ability.

We have conceptualized the pattern of abilities in verbal individuals with autism as a deficit in information processing with the major tenet being that autism is characterized by impairment in complex cognitive processing in multiple domains while simpler abilities in those same domains are intact or sometimes better than normal ( Minshew et al. 1997 ). This general principle has been demonstrated in several individual cognitive domains including attention ( Goldstein et al. 2001 ), memory ( Minshew and Goldstein 2001 ; Williams et al. 2005 , 2006b ), language ( Minshew et al. 1995 ; Peppeé et al. 2007 ), and perceptual and motor skills ( Minshew et al. 1999 , 2004 ). The results from this body of research has suggested that conceptual development, and more specifically, conceptual reasoning, may function somewhat differently in individuals with autism than typically developing individuals with similar cognitive ability. Indeed, we have previously reported that individuals with autism perform well on tasks requiring concept identification or the ability to learn already established rules and have more difficulty with concept formation or the ability to develop new concepts based upon experience ( Minshew et al. 2002 ).

In individuals with typical development, the ability to think abstractly, particularly with regard to forming new concepts is thought to be highly related to the ability to solve problems. In turn, the ability to solve problems is generally thought to be predictive of better adaptive functioning ( Goldstein 1996 ). Individuals with autism, despite the presence of average or above general intelligence often have prominent deficits in the areas of conceptual reasoning and problem solving ( Adams and Sheslow 1983 ; Rutter 1983 ; Hill and Bird 2006 ; Pennington and Ozonoff 1996 ; Bogte et al. 2007 ). However, this finding is not universal across the autism spectrum, as there are some reports, particularly of individuals with Asperger Syndrome (AS), of intact or superior abstract reasoning or fluid thinking skills ( Hayashi et al. 2008 ; Soulières et al. 2011 ). In addition, significant numbers of children and adults on the autism spectrum, including those with AS, have challenges in negotiating social situations in the real world that have to be addressed with explicit training and intervention ( Krasny et al. 2003 ). Furthermore, even those individuals with autism who develop adequate conceptual reasoning abilities and the ability to problem solve in contrived situations may have difficulty in applying these abilities to situations that they encounter in daily life.

The relationship between conceptual reasoning, problem solving, and adaptive functioning may differ in individuals with autism. This would occur if they were depending on the application of rules to determine what the solution to the problem is but had difficulty with creating new concepts based upon environmental experience. Consistent with this hypothesis, social cognitive deficits in autism have been reported to be related to a decreased ability to implicitly encode and integrate contextual information with improved performance when social information is made explicit or rule-based ( Baez et al. 2012 ). Alternately, other research indicates that implicit learning is relatively intact in autism with the important factor being a deficit in the flexibility of response to novel contexts ( Kourkoulou et al. 2012 ).

The relationship between conceptual reasoning and adaptive functioning may also vary by age in individuals with autism. For example, a study of abstract reasoning and social functioning found impairments in both concept identification and concept formation in verbal children ages 8–12 years with ASD and normal intelligence ( Solomon et al. 2011 ). These results suggest that developmental differences may occur with respect to these two components of abstract reasoning; therefore, developmental differences should be considered when investigating the nature of the relationship between conceptual reasoning, problem solving, and adaptive functioning in autism.

The purpose of this study was to examine the relationship between performance on measures of conceptual reasoning, ecologically valid measures of problem solving, and measures of adaptive behavior in verbal children and adults with autism with IQs in the normal range. The hypothesis was that, unlike individuals with typical development, for individuals with autism, conceptual reasoning and problem solving abilities would be correlated with each other but would not be correlated with adaptive function. That is, while aspects of conceptual reasoning might be intact in autism, particularly in concept identification, the ability to adapt to various aspects of the environment will not be related to the overall level of conceptual reasoning ability. Rather, consistent with recent work on learning in autism, adaptive function will be related to the level of flexible thinking or the ability to respond to contextual change.

Participants

Participants for this study were a group of 65 verbal children and adults with autism with IQ scores in the normal range and an age- and IQ-matched group of 65 children and adults with typical development. Participants ranged in age from 8 to 46 years. Demographic data for the sample are presented in Table 1 . For purposes of making age group comparisons, the participants were divided into three groups: 8–12, 13–20 years, and 21+ years, representing children, adolescents, and adults. The study is retrospective in nature, and these data were collected over a number of years; therefore, many of the participants in the present study were the same individuals as those used in previous studies, notably Minshew et al. (1997 , 2002 ), and Williams et al. (2006a) .

Demographic data

The diagnosis of autism was made by a detailed evaluation using expert clinical judgment, the Autism Diagnostic Interview-Revised (ADI-R; LeCouteur et al. 1989 ; Lord et al. 1994 ), and the Autism Diagnostic Observation Schedule-Generic (ADOS; Lord et al. 1989 , 2000 ). All participants were required to have evidence of delayed and disordered language development, thus excluding individuals with Asperger’s Disorder as defined at that time in the DSM system (DSM-IV-R; American Psychiatric Association 2000 ). Participants with autism were excluded if they had associated neurologic, genetic, infectious, or metabolic disorders, such as tuberous sclerosis, fragile-X syndrome, or fetal cytomegalovirus infection.

The control participants were community volunteers recruited to match the autism participants on age, Verbal IQ, Full Scale IQ, gender, race, and years of education, and socioeconomic status of family of origin ( Hollingshead 1957 ). Potential control participants were recruited through advertisement and contacts with community organizations and were screened by questionnaire, telephone, personal interview, and observation during screening tests. Potential control participants were excluded if they had a history of birth or developmental abnormalities; brain injury; poor school attendance; current or past history of psychiatric or significant neurological disorder; family history of autism, developmental cognitive disorder, or learning disability; mood or anxiety disorder; or other neuropsychiatric disorder thought to have a genetic etiological component.

Conceptual Reasoning Tests

Tests were neuropsychological measures that were selected to target different aspects of conceptual reasoning or problem solving such as forming and changing hypotheses or plans, concept formation or deductive reasoning, concept identification or abstract reasoning based on rules or general knowledge, planning and organization to accomplish a goal, and formation of mental representations. The tests used in this analysis varied in modality of presentation, some involving language, others visual perceptual analysis, and others purposeful movements associated with problem solving. Tests included the: the Verbal Absurdities and Picture Absurdities subtests from the Stanford-Binet scales ( Thorndike et al. 1986 ), Tower of Hanoi (TOH) ( Simon 1975 ), the Wisconsin Card Sorting Test (WCST) ( Heaton et al. 1993 ), the Halstead Category Test (HCT) ( Halstead and Settlage 1943 ), the Hooper Visual Organization Test ( Hooper 1983 ), the Tactual Performance Test ( Reitan and Wolfson 1993 ), the 20 Questions Task ( Laine and Butters 1982 ), and the Trail Making Test, Part B ( Reitan and Wolfson 1993 ).

Ecologically Valid Measures of Problem-Solving

Behavioural Assessment of the Dysexecutive Syndrome (BADS; Wilson et al. 1996 ). The BADS is an assessment procedure that is individually administered in a laboratory setting. It provides a micro level of analysis of the skills needed for carrying out specific types of adaptive challenge by characterizing the ability to shift rules, develop a plan of action to solve a problem, develop a plan for a course of action, make temporal judgments, create a plan when structure is minimal as contrasted to use of an externally imposed strategy, and plan and organize multiple tasks. The BADS has been reported to have a higher ecological validity than similar tests of executive function and to be useful when evaluating skills for vocational planning ( Chamberlain 2003 ). Consistent with these prior characterizations of the usefulness of the BADS, for purposes of the present study, we used the instrument as a means of evaluating cognitive function or problem solving ability that underlies adaptive function.

The BADS contains six subtests. Rule Shift requires the subject to initially go through a deck of cards, saying ‘Yes’ for red or ‘No’ for black cards. Then, the rule is shifted by asking the subject to tell whether the card just turned over is the same as or different from the previous card. Scores are time and errors. In Action Sequences the subject attempts to remove a cork from a tube in a beaker filled with water using materials made available. The score is the number of problem solving stages completed independently. Key Search assesses the subject’s ability to plan an effective course of action to find a lost key. The score is the sum of 8 components of the search process, such as entering the field at the bottom. Temporal Judgment asks questions about the duration of events, an ability that contributes to organizing and planning. The Zoo Map Test evaluates planning when constrained by a set of rules. The task is for the subject to plan to visit a series of locations on a map of a zoo while obeying a set of rules (e.g., starting at the entrance and finishing at a designated area). An error score is used. The Modified Six Elements Test requires the subject to perform a dictation, arithmetic, and picture naming task. The test is scored for organizing ability, including the number of sub-tasks completed, rule-breaking on the tasks, and maximum amount of time spent on a subtask. The raw score for each BADS subtest was converted to a profile score ranging from 0 to 4. The profile scores were used in the analyses.

Measures of Adaptive Ability

Vineland Adaptive Behavior Scales (VABS; Sparrow et al. 1984 ). As has been done in prior research examining the relationship between IQ and adaptive behavior, we used the VABS as a measure of functioning in the natural environment. The VABS Survey is a 261 item form that is administered to parents as a measure of how many age-appropriate, socially adaptive behaviors a child or adult exhibits in their natural environment. It is a well-recognized instrument, with demonstrable reliability and validity both for individuals who are typically developing and those with disabilities. It is also the preeminent measure for the assessment of adaptive functioning in children with autism ( Newsom and Hovanitz 1997 ). The VABS assesses three skill domains, each with three subdomains: Communication (receptive, expressive, and written language skills), Daily Living skills (personal self-care, domestic, and community living skills), and Socialization (interpersonal, play or leisure, and coping skills). The VABS provides standard scores ( m = 100, SD = 15) with higher scores indicating better functioning. Domain scores and the Adaptive Behavior composite score were used in the data analysis.

Data Analysis

For purposes of data reduction, the conceptual reasoning tests were factor analyzed in order to assess the latent variables that underlie the series of tests that were used. The principal components method was used with Varimax rotation. Regression based factor scores were computed. Factor scores are composite variables for use in subsequent analyses following performance of a factor analysis. For this study, the factor scores were then correlated with the BADS and VABS scores. Because of narrow distributions of the factor scores in some cases, Spearman’s Rho was used as the correlation coefficient rather than Pearson’s r. Preliminary inspection of the data indicated that comparable results were obtained between the two coefficients. These correlations were computed separately for each group.

Differences between the autism and control groups and among the three age groups on the eleven conceptual reasoning tests were compared using a 3×2 factorial design analysis of variance for independent samples, with presence or absence of autism constituting one independent variable and age group the other. This form of analysis was also conducted for the BADS and VABS.

Comparisons were made between the autism and control groups on the BADS and VABS using t -tests. We also wanted to evaluate the differences in discrepancies on the various abilities measured by these two instruments. While individuals with autism may generally do more poorly than typically developing individuals at adaptive abilities, this discrepancy may not be of the same order of magnitude for all abilities. Specifically, it was hypothesized that adaptive functions requiring relatively high levels of conceptual ability will show a relatively greater level of discrepancy between individuals with autism and groups with typical development. Such differences can be evaluated through obtaining effect sizes and statistical power assessing the magnitude of the statistical significance of group differences. Effect size determination and power analyses were accomplished for all variables; the items were ranked by effect size from largest to smallest. Cohen’s d ( Cohen 1988 ) was the statistic used to obtain effect sizes; it is computed by taking the difference between the two obtained means and dividing by the pooled standard deviation. The effect size reflects the magnitude of a difference, whereas power reflects the capacity to reject the null hypothesis given a particular effect size. Thus, some differences may be so robust that acceptance of a false hypothesis is unlikely, whereas minimally significant findings with low power might raise the possibility of having made a Type I error or making false discoveries ( Benjamini and Hochberg 1995 ). Correspondingly, borderline non-significant findings raise the possibility of rejecting a true hypothesis or making a Type II error. The magnitude of the test performance difference between participants with autism and demographically matched normal control participants should provide an index of the extent to which the ability measured by the test characterizes the performance of the individuals with autism. Thus, those tests found to have larger effect sizes reflected by higher d’s and relatively greater statistical power to reject the null hypothesis of no difference between autism and normal control groups could be understood as reflecting specific aspects of dysfunction in autism, whereas those tests that do not discriminate measure abilities at which individuals with autism performed relatively similarly to individuals with typical development.

To estimate a more global association between conceptual reasoning and adaptive abilities, entry method and stepwise multiple regression analyses were performed. The three factor scores were the predictor variables and the summary scores (i.e., the Total Standard Score from the BADS and the Adaptive Behavior Composite Score from the VABS) were the dependent variables. The following method was used. Group was coded 1 for autism and 0 for control and multiplied by the factor scores. These new variables, often characterized as “dummy variables”, represent interaction between group and factor score. They were entered into the regression equations along with the unweighted diagnostic code itself (Autism or Control) and the factor scores were used as predictor variables with either the BADS or VABS summary score as the dependent variable. The analyses were performed using both the enter all variables and stepwise methods. In addition to the multiple regression coefficients (R), this analysis also provides Beta coefficients for the predictor variables. β represents the independent contributions of each independent variable to the prediction of the dependent variable. t tests were performed to determine the significance of the difference in β between groups for the predictor variables. Thus, for example, a significant difference for one of the factors would indicate that the groups differed with regard to their association with the dependent variable.

Factor Analysis of Conceptual Reasoning Tests

As a way of assessing the relationship between conceptual ability, problem solving, and adaptive function, we first performed a principal components factor analysis with Varimax rotation of the scores from the conceptual reasoning tests and then computed correlations between the obtained factor scores and the BADS and VABS. Using Kaiser’s Rule requiring stopping extraction of factors when an eigenvalue of below 1 is obtained, a three factor solution was obtained for the conceptual tests. The rotated component matrix is presented in Table 2 . The first factor received exceptionally high (>.5) loadings on the Verbal and Picture Absurdities test, the perseverative errors score from the WCST, and the number of constraint seeking questions from the 20 Questions task. These measures assess a high degree of flexibility of thought that underlies concept formation or the ability to spontaneously organize strategies for problem solving. We therefore named it the Flexible Thinking factor. The second factor received high loadings from the Tactual Performance test and the Hooper Visual Organization test, and a moderately high loading from the Picture Absurdities test. It would, therefore, appear to mainly describe reasoning based on perceptual characteristics. We named this the Perceptual Reasoning factor. The third factor received high loadings from the Category and Trail Making Tests and the Tower of Hanoi task. These procedures assess what we have described as concept identification or applying a previously established organizational strategy, and so we called it a Rule Application factor.

Rotated factor loadings for the conceptual reasoning tests

Relationship of Conceptual Reasoning Factors to Problem Solving and Adaptive Ability

Spearman Rho correlations between the conceptual reasoning factor scores and the scores from the BADS and VABS are presented Table 3 . In general, there were few statistically significant correlations ( p <.05), with only four significant correlations in the autism group and three in the control group. Significant correlations in the autism group for the BADS were found between the Flexible Thinking factor and the BADS Key Search (strategy formation) and Rule Shift (changing an established pattern of responding) scores, and between the Perceptual Reasoning Factor and BADS Zoo Map (which involves topographical planning) score. Significant correlations in the autism group for the VABS were obtained between the Flexible Thinking factor and the VABS Adaptive Behavior composite score. In the control group, for the BADS, there were significant correlations between the Perceptual Reasoning factor and the Modified Six Elements (planning and performance monitoring). Significant correlations were found in the control group for the Flexible Thinking factor and the Socialization Domain and Adaptive Composite Behavior Scores on the VABS.

Rho correlations between factor scores, BADS, and VABS

Relationship Between Problem Solving and Adaptive Function

We ranked differences between autism and control groups on the measures from the BADS and VABS with regard to effect sizes and statistical power to evaluate what aspects of problem solving and adaptive behavior distinguish most strongly between the two groups (see Table 4 ). It was thought that the functions that made the greatest discrimination would have the largest effect size and greatest statistical power to reject the null hypothesis, with less discriminating abilities having lower effect sizes and power. Using Cohen’s (1988) conventions indicating that an effect size in the .2 range is small, one in the .5 range is medium, and one in the .8 range is large, then it is clear that there is a wide range of effect sizes. Only one of the BADS subtests, Action Sequences which involves practical problem solving, adequately discriminated between the autism and control groups. On the VABS, the Adaptive Behavior Composite score and Socialization Domain score had highly significant group differences and large effect sizes. The VABS Daily Living Skills and Communication Domains did not distinguish between individuals with autism and controls. Apparently adaptive function as measured by the VABS was more sensitive to differences between the autism and control groups than was the case for most of the tasks on the BADS, even though they are generally considered to have ecological validity (i.e., Chamberlain 2003 ).

Differences between autism and control groups on adaptive functioning ranked by effect size (d)

Overall and Age Group Differences

Given previous reports of differences in the relationship between cognitive abilities and adaptive functioning at different ages for individuals with ASD (e.g., Kanne et al. 2011 ) and the possibility that the components of abstract reasoning, concept identification and concept formation, are influenced by developmental factors in autism ( Solomon et al. 2011 ), we conducted some analyses by age group. As described earlier, the data was separated into three age groupings for children, adolescents, and adults. ANOVA results for comparisons on the conceptual reasoning tests between the participants with and without autism and among the age groups are presented in Tables 5 and ​ and6. 6 . Overall, the autism group performed significantly differently from the control group on all tests but the Halstead Category Test. These results suggest that the autism group as a whole was weaker in conceptual reasoning than the age and IQ-matched controls. As indicated in Table 6 , there were also several significant differences among the age groups. However, there were no significant interactions, leading to the conclusion that there are no significant differences in the age related changes in conceptual reasoning test performance between the autism and control groups.

Means and SDs of the three age groups in the autism and control groups on the cognitive tests

F-ratios for main effects and interaction for conceptual reasoning tests

The only significant group difference for the BADS was for Action Sequences which involves practical problem solving, with the autism group performing significantly poorer than the group with typical development. However, no significant age by diagnostic group interaction was obtained.

With regard to the adaptive functioning scale, only the age group main effect was significant for the VABS Daily Living Domain scale. In the autism group the 8–12 year olds group did more poorly than the older groups while in the control group there were very small mean differences among the age groups. Thus, the significant main effect was probably attributable to poor performance by the 8–12 year old autism group. There were two significant age group X diagnostic group interactions one for the VABS Socialization Domain Scale and the other for the VABS Adaptive Behavior Composite Score. Essentially the same patterns appeared in the Socialization Domain and Adaptive Behavior Scale. There were substantially higher mean scores obtained by the controls in the younger age groups, but essentially equal mean scores obtained by adult members of the autism and control groups. These findings would suggest that there were substantial differences in adaptive functioning in individuals with autism and typical development at younger ages, but that this difference was no longer evident in adulthood ( Tables 7 and ​ and8 8 ).

Means and SDs for adaptive function variables of the three age groups in the autism and control groups

F-ratios for main effects and interaction for BADS and VABS

Multiple Regression Analyses

Results for the BADS Total Standard Score are presented in Table 9 . This score shows a high Multiple R (R = .459, p < .001). Using the stepwise method only the factor scores weighted by group membership were entered. Group membership alone and the three factor scores themselves were not entered. This finding would indicate that the multivariate association between the conceptual reasoning factors and the BADS measure interacts with group membership. If group membership is not considered, as when only the factor scores themselves are used, they are not entered.

Multiple regression analyses using conceptual reasoning factor scores as predictor variables and BADS total standard or VABS adaptive behavior composite summary scores as dependent measures

For the VABS Adaptive Behavior variable, the enter method also yields a significant multiple R of .428. However, the stepwise method entered group alone (autism vs. control) and Group weighted by Factor Score 1 (Flexible Thinking). It would appear that membership in the control group has little or no influence on the factor scores while membership in the autism group has a substantial influence. However, the analysis of the data presented in Table 3 indicates that the Rho correlation between the VABS Adaptive Behavior Scale and the Flexible Thinking factor is positive (.299) in the autism group while it is negative (−.263) in the control group. This discrepancy would not appear to justify the conclusion that adaptive behavior is negatively correlated with flexible thinking, particularly since the entire set of correlations considered are non-significant. However, this pattern of correlations might affirm the result of the regression analysis indicating that in typically developing individuals, level of adaptive functioning does not appear to be associated with intelligence.

In general, individuals with autism have relatively weaker conceptual reasoning abilities than individuals with typical development of similar age and overall cognitive ability. Despite this weakness, individuals with autism appear to be able to apply these conceptual reasoning abilities on most of the laboratory measures of adaptive flexibility, planning, and problem solving, resulting in a lack of differentiation from controls. The level of conceptual reasoning for most of these children and adults with autism allowed them to demonstrate problem solving abilities in a variety of structured or hypothetical situations as measured by the BADS. However, as indicated by the VABS data, individuals with autism may fail to apply these reasoning abilities to real life situations, resulting in dissociation between overall level of cognition and adaptive functioning. This result is consistent with reports of problems with adaptive functioning in children and adults with autism who have average or above IQs ( Kanne et al. 2011 ; Mazefsky et al. 2008 ). This dissociation between performance on structured tasks and observed daily performance may help explain the rather poor outcome in adult life of verbal individuals with autism despite their academic success in school programs ( Farley et al. 2009 ).

The underlying reason for the disconnect between the ability to apply reasoning in a controlled setting and the ability to demonstrate reasoning in real life situations is not clear, but some understanding may be gained by examining the obtained relationships between the measures of conceptual reasoning and the measures of problem solving and adaptive functioning. For the autism group, the Flexible Thinking factor was significantly correlated with the BADS subtests that assess strategy formation and rule shifting. This relationship suggests that individuals with autism who had more ability to think flexibly were able to form strategies and were more flexible in applying rules. It was not surprising to find that the Flexible Thinking factor was also associated with overall better adaptive functioning in autism. Taken together, these results suggest that the ability to flexibly form concepts is particularly important for better adaptive behavior in individuals with autism.

In a related area of research, it has been proposed that learning difficulties encountered in social situations by individuals with autism are not related to the implicit nature of the information but to a problem with flexibility of response to novel contexts ( Kourkoulou et al. 2012 ). In that study, intact implicit learning was found for contextual cuing tasks; however, deficits occurred in novel contexts, particularly when the paradigm biased learning to local stimuli, suggesting that flexibility of response to novel contexts was the underlying problem not implicit learning per se ( Kourkoulou et al. 2012 ).

The conclusion about the importance of flexible thinking to adaptive functioning in autism is generally supported by the results of the multiple regression analysis. These modest findings may suggest several potential explanations for this reversal of patterns of relationships. First, it may be due to the BADS being a laboratory-based assessment that provides a more micro-level analysis of the conceptual skills needed for carrying out a specific type of adaptive challenge, whereas the VABS scores reflect the integrative use and flexible application of these skills to solve real world problems. It is possible that individuals with autism can demonstrate problem solving and planning when there are reduced temporal demands and the problems are clearer and the solutions more limited. That is, they have adequate cognitive resources to meet these challenges and, therefore, can explain what should be done in a hypothetical situation. However, real world problems are seldom this structured and explicit, beginning with the necessity to identify what the problem to be solved is. Therefore, individuals with autism would have difficulty translating their knowledge into success in real life situations because the complexity of the processing task has increased exponentially. The impact of conceptual reasoning deficits in autism may not be as apparent in highly structured settings that provide rules like schools but is likely to become more evident under open field conditions such as jobs and independent living where there are few established rules that address a particular situation with constantly changing contexts that demand flexibility of thought. Individuals with autism who have a relatively stronger ability to manipulate and form new concepts, to think flexibly, would be at an advantage even as the environmental demands increase.

In addition to Flexible Thinking, another significant relationship was obtained between the Perceptual Reasoning factor and performance on the BADS Zoo Map subtest for the autism group. Abilities associated with the Perceptual Reasoning factor include ideational planning as measured by the TPT and visual imagery and integration assessed with the Hooper Visual Organization Test. Perceptual ability, involving the requirement of the tactual and visual processing demanded by these two measures, may be particularly important for individuals with autism for the aspect of adaptive functioning that involves imaging and planning. Therefore, perceptual reasoning is a type of process that might be capitalized on when helping individuals with autism develop skills to negotiate ever-changing social environments.

The results regarding age differences are of particular interest. It is understood that this was a cross-sectional study and inferences may not be made to the effect that differences noted would be observed in the development of individuals, as could be determined only by a longitudinal study. However, it has been noted for some time that the results of cross-sectional and longitudinal studies are typically the same ( Heaton and Drexler 1987 ). The cross-sectional results obtained here reflect differences among age groups that are not always the same for the autism and control groups, and may reflect differences in developmental course. The pattern for both the measures of conceptual reasoning and problem solving of improved performance from childhood until young adulthood is comparable in individuals with typical development and individuals with autism. Test scores were fairly consistently lower in the autism group, although linear trajectories were noted in both groups. A different pattern emerged for adaptive behavior as measured by the VABS with significant interactions between autism status and age group on the Socialization Doman and Adaptive Behavior Composite scores. We made the remarkable finding that, while the scores of the group with typical development far exceeded those of the autism group in the child and adolescent age groups, they were essentially equal in the adult groups, and, furthermore, were in the average range on these scales. In summary, age differences in cognitive abilities were found to be linear in both groups but at differing performance levels; however, some adaptive abilities do not have parallel trajectories in the autism and groups with typical development. Rather, the child and adolescent groups showed marked group differences between autism and control groups, while in the adult groups there was essentially no difference. Because this is not longitudinal data, we cannot infer the source for this difference to be developmental in nature. It is, however, important to note that this relatively high functioning group of adults with autism has been able to achieve strong adaptive skills even if they are continuing to be challenged in functioning in the social domain.

The results regarding age differences raise the obviously major question of whether or not individuals with autism undergo a course of development in which they possess certain normal adaptive abilities during adulthood they did not have during childhood, perhaps as a result of lifelong treatment or developmental changes associated with the course of the disorder. Longitudinal data, even retrospective information, might ultimately clarify this matter.

Clinical Implications

The findings from this study have important implications related to the provision of services to verbal individuals with autism who are relatively higher functioning. First, we provide further support for the argument that adults with autism should not be denied social support services because they have an IQ in the average range if they are demonstrating difficulties with real world functioning. Unlike individuals with typical development, the ability to perform well on formal measures such as the BADS may not necessarily reflect actual functioning for individuals with autism.

In particular, better adaptive functioning in autism appears to be related to the development of concept formation, flexible thinking and perceptual reasoning. Given that successful independent living is a goal for individuals with autism, cognitive remediation therapies explicitly targeting these skills seem warranted. However, the way in which this intervention is delivered would appear to be of particular importance for successful skill acquisition in individuals with autism.

Even when individuals with autism can explain what should be done in a hypothetical situation, they may not be able to translate this knowledge into success in real life situations. Based on the results of this study, we would predict that interventions that are limited to answering questions about hypothetical situations and artificial problem solving would have little to no impact on adaptive functioning in individuals with autism. Knowing how to solve a problem does not appear to be enough. Similarly, approaches that emphasize the acquisition of social skills through explicitly teaching social rules or engaging through role playing of social interactions (e.g. MacAfee 2002 ) may also result in a failure to translate this knowledge into a change in adaptive behavior unless these skills are practiced in the contexts in which they are to be applied.

Although time-consuming and resource intensive, practice of skills in the real world, appears to be essential for individuals with autism ( Rao et al. 2008 ). In fact, this recommendation is consistent with the conclusions of a recent review of research on behavioral interventions for adaptive skills in verbal young adults with autism with normal IQ scores ( Palmen et al. 2012 ). To further facilitate the transfer of reasoning abilities to everyday problem solving, the primary interaction partners of the individuals with autism should be trained to recognize opportunities for learning and to assist the individual with autism in the application of problem solving when faced with real world challenges.

Alternative intervention approaches such as those that incorporated virtual reality techniques may serve as cost efficient alternatives to training in the real world. Virtual reality has reportedly been used to successfully develop the social interaction and theory-of-mind skills in young adults who were on the autism spectrum ( Kandalaft et al. 2013 ). A similar approach could present individuals with autism with more realistic challenges, requiring them to develop solutions to common problems in a contextually-rich environment that might facilitate flexible thinking and generalization to real world settings.

Acknowledgments

This research was supported by Grant Sponsor: National Institute of Child Health and Human Development (NICHD), Grant Number: HD35469, a Collaborative Program of Excellence in Autism (CPEA); Grant Sponsor: National Institute on Deafness and other Communication Disorders (NIDCD), Grant Number K23DC006691 to Dr. Williams and by the VISN IV Mental Illness Research, Education and Clinical Center (MIRECC), VA Pittsburgh Healthcare System Pittsburgh PA.

The research described here has been approved by the appropriate IRB and full informed consent or assent has been obtained for all subjects.

Contributor Information

Diane L. Williams, Department of Speech-Language Pathology, Duquesne University, Pittsburgh, PA, USA.

Carla A. Mazefsky, Department of Psychiatry, University of Pittsburgh, Pittsburgh, PA, USA.

Jon D. Walker, VA Pittsburgh Healthcare System, University Drive, Pittsburgh, PA 15240, USA.

Nancy J. Minshew, Departments of Psychiatry and Neurology, University of Pittsburgh, Pittsburgh, PA, USA.

Gerald Goldstein, VA Pittsburgh Healthcare System, University Drive, Pittsburgh, PA 15240, USA, ten.bn@dlogG .

  • Adams WV, Sheslow BV. A developmental perspective of adolescence. In: Schopler E, Mesibov GB, editors. Autism in adolescents and adults. New York, NY: Plenum Press; 1983. pp. 11–36. [ Google Scholar ]
  • American Psychiatric Association. Diagnostic and statistical manual of mental disorders. 4. Washington, D.C: Author; 2000. rev. ed. [ Google Scholar ]
  • Baez S, Rattazzi A, Gonzalez-Gadea ML, Torralva T, Vigliecca NS, Decety J, et al. Integrating intention and context: Assessing social cognition in adults with Asperger syndrome. Frontiers in Human Neuroscience. 2012; 6 (302):1–21. [ PMC free article ] [ PubMed ] [ Google Scholar ]
  • Benjamini Y, Hochberg Y. Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B (Methodological) 1995; 57 :289–300. [ Google Scholar ]
  • Bogte H, Flamma B, van der Meere J, van Engeland H. Cognitive flexibility in adults with high functioning autism. Journal of Clinical and Experimental Neuropsychology. 2007; 11 :1–9. [ PubMed ] [ Google Scholar ]
  • Boltë S, Poustka F. The relation between general cognitive level and adaptive behavior domains in individuals with autism with and without co-morbid mental retardation. Child Psychiatric and Human Development. 2002; 33 :165–172. [ PubMed ] [ Google Scholar ]
  • Chamberlain E. Behavioural assessment of the dysexecutive syndrome (BADS): Test review. Journal of Occupational Psychology, Employment and Disability. 2003; 5 :33–37. [ Google Scholar ]
  • Cohen J. Statistical power analysis for the behavioral sciences. 2. Hillside, NJ: Lawrence Erlbaum Associates; 1988. [ Google Scholar ]
  • Farley MA, McMahon WM, Fombonne E, Jenson WR, Miller J, Gardner M, et al. Twenty-year outcome for individuals with autism and average or near-average cognitive abilities. Autism Research. 2009; 2 :109–118. [ PubMed ] [ Google Scholar ]
  • Fenton G, D’Ardia C, Valente D, Del Vecchio I, Fabrizi A, Bernabei P. Vineland adaptive behavior profiles in children with autism and moderate to severe developmental delay. Autism. 2001; 7 :269–287. [ PubMed ] [ Google Scholar ]
  • Goldstein G. Functional considerations in neuropsychology. In: Shordone RJ, Long CJ, editors. Ecological validity of neuropsychological testing. Delray Beach, FL: Gr Press/St Lucie Press; 1996. pp. 75–89. [ Google Scholar ]
  • Goldstein G, Johnson CR, Minshew NJ. Attentional processes in autism. Journal of Autism and Developmental Disorders. 2001; 31 :433–440. [ PubMed ] [ Google Scholar ]
  • Halstead WC, Settlage PH. Grouping behavior of normal persons and persons with lesions of the brain. Archives of Neurology and Psychiatry. 1943; 49 :489–506. [ Google Scholar ]
  • Hayashi M, Kato M, Igarashi K, Kashima H. Superior fluid intelligence in children with Asperger’s disorder. Brain and Cognition. 2008; 66 (3):306–310. [ PubMed ] [ Google Scholar ]
  • Heaton RK, Chelune CJ, Talley JL, Kay GG, Curtiss G. Wisconsin card sorting test manual, revised and expanded. Odessa, FL: Psychological Assessment Resources; 1993. [ Google Scholar ]
  • Heaton RK, Drexler M. Clinical and neuropsychological findings in schizophrenia and aging. In: Miller NE, Cohen GD, editors. Schizophrenia and aging. New York, NY: Guilford Press; 1987. pp. 145–161. [ Google Scholar ]
  • Hill EL, Bird CM. Executive processes in Asperger syndrome: Patterns of performance in a multiple case series. Neuropsychologia. 2006; 44 :2822–2835. [ PubMed ] [ Google Scholar ]
  • Hollingshead AB. Two-factor index of social position. New Haven, CT: Yale University, Department of Sociology; 1957. [ Google Scholar ]
  • Hooper HE. Hooper visual organization test (VOT) Los Angeles: Western Psychological Services; 1983. [ Google Scholar ]
  • Kandalaft MR, Didehbani N, Krawczyk DC, Allen TT, Chapman SB. Virtual reality social cognition training for young adults with high-functioning autism. Journal of Autism and Developmental Disorders. 2013; 43 (1):34–44. [ PMC free article ] [ PubMed ] [ Google Scholar ]
  • Kanne SM, Gerber AJ, Quirmbach LM, Sparrow SS, Cicchetti DV, Saulnier CA. The role of adaptive behavior in autism spectrum disorders: Implications for functional outcome. Journal of Autism and Developmental Disorders. 2011; 41 :1007–1018. [ PubMed ] [ Google Scholar ]
  • Klin A, Saulnier CA, Sparrow SS, Cicchetti DV, Volkmar FR, Lord C. Social and communication abilities and disabilities in higher-functioning individuals with autism spectrum disorders: The Vineland and ADOS. Journal of Autism and Developmental Disorders. 2007; 37 :748–759. [ PubMed ] [ Google Scholar ]
  • Kourkoulou A, Leekam SR, Findlay JM. Implicit learning of local context in autism spectrum disorder. Journal of Autism and Developmental Disorders. 2012; 42 (2):244–256. [ PubMed ] [ Google Scholar ]
  • Krasny L, Williams BJ, Provencal S, Ozonoff S. Social skills interventions for the autism spectrum: Essential ingredients and a model curriculum. Child and Adolescent Psychiatric Clinics in North America. 2003; 12 (1):107–122. [ PubMed ] [ Google Scholar ]
  • Laine M, Butters N. A preliminary study of the problem solving strategies of detoxified long-tern alcoholics. Drug and Alcohol Dependence. 1982; 10 :235–242. [ PubMed ] [ Google Scholar ]
  • LeCouteur A, Rutter M, Lord C, Rios P, Robertson S, Holdgrafer M, et al. Autism diagnostic interview: A standardized investigator-based instrument. Journal of Autism and Developmental Disorders. 1989; 19 :363–387. [ PubMed ] [ Google Scholar ]
  • Liss M, Harel B, Fein D, Allen D, Dunn M, Feinstein C, et al. Predictors and correlates of adaptive functioning in children with developmental disorders. Journal of Autism and Developmental Disorders. 2001; 31 :219–230. [ PubMed ] [ Google Scholar ]
  • Lord C, Risi S, Lambrecht L, Cook EH, Jr, Leventhal BL, DiLavore PC, et al. The autism diagnostic observation schedule—generic: A standard measure of social and communication deficits associated with the spectrum of autism. Journal of Autism and Developmental Disorders. 2000; 30 :205–223. [ PubMed ] [ Google Scholar ]
  • Lord C, Rutter M, Goode S. Autism diagnostic observation schedule: A standardized investigator-based instrument. Journal of Autism and Developmental Disorders. 1989; 19 :185–212. [ PubMed ] [ Google Scholar ]
  • Lord C, Rutter M, LeCouteur AL. Autism diagnostic interview revised: A revised version of a diagnostic interview for caregivers of individuals with possible pervasive developmental disorders. Journal of Autism and Developmental Disorders. 1994; 24 :659–685. [ PubMed ] [ Google Scholar ]
  • MacAfee J. Navigating the social world: A curriculum for individuals with Asperger’s syndrome, high functioning autism and related disorders. Arlington, TX: Future Horizons Inc; 2002. [ Google Scholar ]
  • MacLean JE, Szatmari P, Jones MB, Bryson SE, Mahoney WJ, Bartolucci G, et al. Familial factors influence level of functioning in pervasive developmental disorder. Journal of the American Academy of Child and Adolescent Psychiatry. 1999; 38 :746–753. [ PubMed ] [ Google Scholar ]
  • Mazefsky CA, Williams DL, Minshew NJ. Variability in adaptive behavior in Autism: Evidence for the importance of family history. Journal of Abnormal Child Psychology. 2008; 36 :591–599. [ PMC free article ] [ PubMed ] [ Google Scholar ]
  • Minshew NJ, Goldstein G. The pattern of intact and impaired memory functions in autism. Journal of Child Psychology and Psychiatry. 2001; 42 :1095–1101. [ PubMed ] [ Google Scholar ]
  • Minshew NJ, Goldstein G, Siegel DJ. Speech and language in high-functioning autistic individuals. Neuropsychology. 1995; 9 :255–261. [ PubMed ] [ Google Scholar ]
  • Minshew NJ, Goldstein G, Siegel DJ. Neuropsychologic functioning in autism: Profile of a complex information processing disorder. Journal of the International Neuropsychological Society. 1997; 3 :303–316. [ PubMed ] [ Google Scholar ]
  • Minshew N, Luna B, Sweeney J. Oculomotor evidence for neocortical systems but not cerebellar dysfunctions in autism. Neurology. 1999; 52 :917–922. [ PMC free article ] [ PubMed ] [ Google Scholar ]
  • Minshew NJ, Meyer J, Goldstein G. Abstract reasoning in autism: A dissociation between concept formation and concept identification. Neuropsychology. 2002; 16 :327–334. [ PubMed ] [ Google Scholar ]
  • Minshew NJ, Sung K, Jones B, Furman J. Underdevelopment of the postural control system in autism. Neurology. 2004; 63 :2056–2061. [ PubMed ] [ Google Scholar ]
  • Newsom C, Hovanitz CA. Autistic disorder. In: Mash EJ, Terdal LG, editors. Assessment of childhood disorders. 3. New York, NY: Guilford; 1997. pp. 408–452. [ Google Scholar ]
  • Oswald DP, DiSalvo CA. Adaptive behavior assessment. In: Ollendick TH, Schroeder CS, editors. The encyclopedia of pediatric and clinical child psychology. New York: Kluwer Academic/Plenum Publishers; 2003. [ Google Scholar ]
  • Palmen A, Didden R, Lang R. A systematic review of behavioral intervention research on adaptive skill building in high-functioning young adults with autism spectrum disorder. Research in Autism Spectrum Disorders. 2012; 6 :602–617. [ Google Scholar ]
  • Pennington BF, Ozonoff S. Executive functions and developmental psychopathology. Journal of Child Psychology and Psychiatry. 1996; 37 :51–87. [ PubMed ] [ Google Scholar ]
  • Peppeé S, McCann J, Gibbon F, O’Hare A, Rutherford M. Receptive and expressive prosodic ability in children with high-functioning autism. Journal of Speech, Language and Hearing Research. 2007; 50 :1015–1028. [ PubMed ] [ Google Scholar ]
  • Rao PA, Beidel DC, Murray MJ. Social skills interventions for children with Asperger’s syndrome or high-functioning autism: A review and recommendations. Journal of Autism and Developmental Disorders. 2008; 38 (2):353–361. [ PubMed ] [ Google Scholar ]
  • Reitan RM, Wolfson D. The Halstead-retain neuro-psychological test battery: Theory and clinical interpretation. 2. Tucson, AZ: Neuropsychology Press; 1993. [ Google Scholar ]
  • Rutter M. Cognitive deficits in the pathogenesis of autism. Journal of Child Psychology and Psychiatry and Allied Disciplines. 1983; 24 :513–531. [ PubMed ] [ Google Scholar ]
  • Simon H. The functional equivalence of problem solving skills. Cognitive Psychology. 1975; 7 :268–288. [ Google Scholar ]
  • Solomon M, Buaminger N, Rogers SJ. Abstract reasoning and friendship in high functioning preadolescents with autism spectrum disorders. Journal of Autism and Developmental Disorders. 2011; 41 (1):32–43. [ PMC free article ] [ PubMed ] [ Google Scholar ]
  • Soulieères I, Dawson M, Gernsbacher MA, Mottron L. The level and nature of autistic intelligence II: What about Asperger syndrome? PLoS ONE. 2011; 6 :e25372. [ PMC free article ] [ PubMed ] [ Google Scholar ]
  • Sparrow SS, Balla DA, Cicchetti DV. Vineland adaptive behavior scales. Circle Pines, MN: American Guidance Service; 1984. [ Google Scholar ]
  • Thorndike RL, Hagen EP, Sattler JM. The stanford-binet intelligence scale. 4. Chicago: Riverside Publishing; 1986. [ Google Scholar ]
  • Williams DL, Goldstein G, Minshew NJ. Impaired memory for faces and social scenes in autism: Clinical implications of the memory disorder. Archives of Clinical Neuropsychology. 2005; 20 :1–15. [ PubMed ] [ Google Scholar ]
  • Williams DL, Goldstein G, Minshew NJ. Neuropsychologic functioning in children with autism: Further evidence of disordered complex information processing. Child Neuropsychology. 2006a; 12 :279–298. [ PMC free article ] [ PubMed ] [ Google Scholar ]
  • Williams DL, Goldstein G, Minshew NJ. Profile of memory function in children with autism. Neuropsychology. 2006b; 20 :21–29. [ PMC free article ] [ PubMed ] [ Google Scholar ]
  • Wilson BA, Alderman N, Burgess PW, Emslie H, Evans JJ. Behavioural assessment dysexecutive syndrome. Bury St. Edmunds, Suffolk, England: Thames Valley Test Company; 1996. [ Google Scholar ]

Logo for Maricopa Open Digital Press

6 Thinking and Intelligence

Three side by side images are shown. On the left is a person lying in the grass with a book, looking off into the distance. In the middle is a sculpture of a person sitting on rock, with chin rested on hand, and the elbow of that hand rested on knee. The third is a drawing of a person sitting cross-legged with his head resting on his hand, elbow on knee.

What is the best way to solve a problem? How does a person who has never seen or touched snow in real life develop an understanding of the concept of snow? How do young children acquire the ability to learn language with no formal instruction? Psychologists who study thinking explore questions like these and are called cognitive psychologists.

Cognitive psychologists also study intelligence. What is intelligence, and how does it vary from person to person? Are “street smarts” a kind of intelligence, and if so, how do they relate to other types of intelligence? What does an IQ test really measure? These questions and more will be explored in this chapter as you study thinking and intelligence.

In other chapters, we discussed the cognitive processes of perception, learning, and memory. In this chapter, we will focus on high-level cognitive processes. As a part of this discussion, we will consider thinking and briefly explore the development and use of language. We will also discuss problem solving and creativity before ending with a discussion of how intelligence is measured and how our biology and environments interact to affect intelligence. After finishing this chapter, you will have a greater appreciation of the higher-level cognitive processes that contribute to our distinctiveness as a species.

Learning Objectives

By the end of this section, you will be able to:

  • Describe cognition
  • Distinguish concepts and prototypes
  • Explain the difference between natural and artificial concepts
  • Describe how schemata are organized and constructed

Imagine all of your thoughts as if they were physical entities, swirling rapidly inside your mind. How is it possible that the brain is able to move from one thought to the next in an organized, orderly fashion? The brain is endlessly perceiving, processing, planning, organizing, and remembering—it is always active. Yet, you don’t notice most of your brain’s activity as you move throughout your daily routine. This is only one facet of the complex processes involved in cognition. Simply put,  cognition  is thinking, and it encompasses the processes associated with perception, knowledge, problem solving, judgment, language, and memory. Scientists who study cognition are searching for ways to understand how we integrate, organize, and utilize our conscious cognitive experiences without being aware of all of the unconscious work that our brains are doing (for example, Kahneman, 2011).

Upon waking each morning, you begin thinking—contemplating the tasks that you must complete that day. In what order should you run your errands? Should you go to the bank, the cleaners, or the grocery store first? Can you get these things done before you head to class or will they need to wait until school is done? These thoughts are one example of cognition at work. Exceptionally complex, cognition is an essential feature of human consciousness, yet not all aspects of cognition are consciously experienced.

Cognitive psychology  is the field of psychology dedicated to examining how people think. It attempts to explain how and why we think the way we do by studying the interactions among human thinking, emotion, creativity, language, and problem solving, in addition to other cognitive processes. Cognitive psychologists strive to determine and measure different types of intelligence, why some people are better at problem solving than others, and how emotional intelligence affects success in the workplace, among countless other topics. They also sometimes focus on how we organize thoughts and information gathered from our environments into meaningful categories of thought, which will be discussed later.

Concepts and Prototypes

The human nervous system is capable of handling endless streams of information. The senses serve as the interface between the mind and the external environment, receiving stimuli and translating it into nerve impulses that are transmitted to the brain. The brain then processes this information and uses the relevant pieces to create thoughts, which can then be expressed through language or stored in memory for future use. To make this process more complex, the brain does not gather information from external environments only. When thoughts are formed, the mind synthesizes information from emotions and memories ( Figure 7.2 ). Emotion and memory are powerful influences on both our thoughts and behaviors.

The outline of a human head is shown. There is a box containing “Information, sensations” in front of the head. An arrow from this box points to another box containing “Emotions, memories” located where the front of the person's brain would be. An arrow from this second box points to a third box containing “Thoughts” located where the back of the person's brain would be. There are two arrows coming from “Thoughts.” One arrow points back to the second box, “Emotions, memories,” and the other arrow points to a fourth box, “Behavior.”

In order to organize this staggering amount of information, the mind has developed a “file cabinet” of sorts in the mind. The different files stored in the file cabinet are called concepts.  Concepts  are categories or groupings of linguistic information, images, ideas, or memories, such as life experiences. Concepts are, in many ways, big ideas that are generated by observing details, and categorizing and combining these details into cognitive structures. You use concepts to see the relationships among the different elements of your experiences and to keep the information in your mind organized and accessible.

Concepts are informed by our semantic memory (you will learn more about semantic memory in a later chapter) and are present in every aspect of our lives; however, one of the easiest places to notice concepts is inside a classroom, where they are discussed explicitly. When you study United States history, for example, you learn about more than just individual events that have happened in America’s past. You absorb a large quantity of information by listening to and participating in discussions, examining maps, and reading first-hand accounts of people’s lives. Your brain analyzes these details and develops an overall understanding of American history. In the process, your brain gathers details that inform and refine your understanding of related concepts like democracy, power, and freedom.

Concepts can be complex and abstract, like justice, or more concrete, like types of birds. In psychology, for example, Piaget’s stages of development are abstract concepts. Some concepts, like tolerance, are agreed upon by many people because they have been used in various ways over many years. Other concepts, like the characteristics of your ideal friend or your family’s birthday traditions, are personal and individualized. In this way, concepts touch every aspect of our lives, from our many daily routines to the guiding principles behind the way governments function.

Another technique used by your brain to organize information is the identification of prototypes for the concepts you have developed. A  prototype  is the best example or representation of a concept. For example, what comes to your mind when you think of a dog? Most likely your early experiences with dogs will shape what you imagine. If your first pet was a Golden Retriever, there is a good chance that this would be your prototype for the category of dogs.

Natural and Artificial Concepts

In psychology, concepts can be divided into two categories, natural and artificial.  Natural concepts  are created “naturally” through your experiences and can be developed from either direct or indirect experiences. For example, if you live in Essex Junction, Vermont, you have probably had a lot of direct experience with snow. You’ve watched it fall from the sky, you’ve seen lightly falling snow that barely covers the windshield of your car, and you’ve shoveled out 18 inches of fluffy white snow as you’ve thought, “This is perfect for skiing.” You’ve thrown snowballs at your best friend and gone sledding down the steepest hill in town. In short, you know snow. You know what it looks like, smells like, tastes like, and feels like. If, however, you’ve lived your whole life on the island of Saint Vincent in the Caribbean, you may never have actually seen snow, much less tasted, smelled, or touched it. You know snow from the indirect experience of seeing pictures of falling snow—or from watching films that feature snow as part of the setting. Either way, snow is a natural concept because you can construct an understanding of it through direct observations, experiences with snow, or indirect knowledge (such as from films or books) ( Figure 7.3 ).

Photograph A shows a snow covered landscape with the sun shining over it. Photograph B shows a sphere shaped object perched atop the corner of a cube shaped object. There is also a triangular object shown.

An  artificial concept , on the other hand, is a concept that is defined by a specific set of characteristics. Various properties of geometric shapes, like squares and triangles, serve as useful examples of artificial concepts. A triangle always has three angles and three sides. A square always has four equal sides and four right angles. Mathematical formulas, like the equation for area (length × width), are artificial concepts defined by specific sets of characteristics that are always the same. Artificial concepts can enhance the understanding of a topic by building on one another. For example, before learning the concept of “area of a square” (and the formula to find it), you must understand what a square is. Once the concept of “area of a square” is understood, an understanding of area for other geometric shapes can be built upon the original understanding of area. The use of artificial concepts to define an idea is crucial to communicating with others and engaging in complex thought. According to Goldstone and Kersten (2003), concepts act as building blocks and can be connected in countless combinations to create complex thoughts.

A  schema  is a mental construct consisting of a cluster or collection of related concepts (Bartlett, 1932). There are many different types of schemata, and they all have one thing in common: schemata are a method of organizing information that allows the brain to work more efficiently. When a schema is activated, the brain makes immediate assumptions about the person or object being observed.

There are several types of schemata. A  role schema  makes assumptions about how individuals in certain roles will behave (Callero, 1994). For example, imagine you meet someone who introduces himself as a firefighter. When this happens, your brain automatically activates the “firefighter schema” and begins making assumptions that this person is brave, selfless, and community-oriented. Despite not knowing this person, already you have unknowingly made judgments about him. Schemata also help you fill in gaps in the information you receive from the world around you. While schemata allow for more efficient information processing, there can be problems with schemata, regardless of whether they are accurate: Perhaps this particular firefighter is not brave, he just works as a firefighter to pay the bills while studying to become a children’s librarian.

An  event schema , also known as a  cognitive script , is a set of behaviors that can feel like a routine. Think about what you do when you walk into an elevator ( Figure 7.4 ). First, the doors open and you wait to let exiting passengers leave the elevator car. Then, you step into the elevator and turn around to face the doors, looking for the correct button to push. You never face the back of the elevator, do you? And when you’re riding in a crowded elevator and you can’t face the front, it feels uncomfortable, doesn’t it? Interestingly, event schemata can vary widely among different cultures and countries. For example, while it is quite common for people to greet one another with a handshake in the United States, in Tibet, you greet someone by sticking your tongue out at them, and in Belize, you bump fists (Cairns Regional Council, n.d.)

A crowded elevator is shown. There are many people standing close to one another.

Because event schemata are automatic, they can be difficult to change. Imagine that you are driving home from work or school. This event schema involves getting in the car, shutting the door, and buckling your seatbelt before putting the key in the ignition. You might perform this script two or three times each day. As you drive home, you hear your phone’s ring tone. Typically, the event schema that occurs when you hear your phone ringing involves locating the phone and answering it or responding to your latest text message. So without thinking, you reach for your phone, which could be in your pocket, in your bag, or on the passenger seat of the car. This powerful event schema is informed by your pattern of behavior and the pleasurable stimulation that a phone call or text message gives your brain. Because it is a schema, it is extremely challenging for us to stop reaching for the phone, even though we know that we endanger our own lives and the lives of others while we do it (Neyfakh, 2013) ( Figure 7.5 ).

A person’s right hand is holding a cellular phone. The person is in the driver’s seat of an automobile while on the road.

Remember the elevator? It feels almost impossible to walk in and  not  face the door. Our powerful event schema dictates our behavior in the elevator, and it is no different with our phones. Current research suggests that it is the habit, or event schema, of checking our phones in many different situations that make refraining from checking them while driving especially difficult (Bayer & Campbell, 2012). Because texting and driving has become a dangerous epidemic in recent years, psychologists are looking at ways to help people interrupt the “phone schema” while driving. Event schemata like these are the reason why many habits are difficult to break once they have been acquired. As we continue to examine thinking, keep in mind how powerful the forces of concepts and schemata are to our understanding of the world.

  • Define language and demonstrate familiarity with the components of language
  • Understand the development of language
  • Explain the relationship between language and thinking

Language  is a communication system that involves using words and systematic rules to organize those words to transmit information from one individual to another. While language is a form of communication, not all communication is language. Many species communicate with one another through their postures, movements, odors, or vocalizations. This communication is crucial for species that need to interact and develop social relationships with their conspecifics. However, many people have asserted that it is language that makes humans unique among all of the animal species (Corballis & Suddendorf, 2007; Tomasello & Rakoczy, 2003). This section will focus on what distinguishes language as a special form of communication, how the use of language develops, and how language affects the way we think.

Components of Language

Language, be it spoken, signed, or written, has specific components: a lexicon and grammar.  Lexicon  refers to the words of a given language. Thus, lexicon is a language’s vocabulary.  Grammar  refers to the set of rules that are used to convey meaning through the use of the lexicon (Fernández & Cairns, 2011). For instance, English grammar dictates that most verbs receive an “-ed” at the end to indicate past tense.

Words are formed by combining the various phonemes that make up the language. A  phoneme  (e.g., the sounds “ah” vs. “eh”) is a basic sound unit of a given language, and different languages have different sets of phonemes. Phonemes are combined to form  morphemes , which are the smallest units of language that convey some type of meaning (e.g., “I” is both a phoneme and a morpheme). We use semantics and syntax to construct language. Semantics and syntax are part of a language’s grammar.  Semantics  refers to the process by which we derive meaning from morphemes and words.  Syntax  refers to the way words are organized into sentences (Chomsky, 1965; Fernández & Cairns, 2011).

We apply the rules of grammar to organize the lexicon in novel and creative ways, which allow us to communicate information about both concrete and abstract concepts. We can talk about our immediate and observable surroundings as well as the surface of unseen planets. We can share our innermost thoughts, our plans for the future, and debate the value of a college education. We can provide detailed instructions for cooking a meal, fixing a car, or building a fire. Through our use of words and language, we are able to form, organize, and express ideas, schema, and artificial concepts.

Language Development

Given the remarkable complexity of a language, one might expect that mastering a language would be an especially arduous task; indeed, for those of us trying to learn a second language as adults, this might seem to be true. However, young children master language very quickly with relative ease. B. F.  Skinner  (1957) proposed that language is learned through reinforcement. Noam  Chomsky  (1965) criticized this behaviorist approach, asserting instead that the mechanisms underlying language acquisition are biologically determined. The use of language develops in the absence of formal instruction and appears to follow a very similar pattern in children from vastly different cultures and backgrounds. It would seem, therefore, that we are born with a biological predisposition to acquire a language (Chomsky, 1965; Fernández & Cairns, 2011). Moreover, it appears that there is a critical period for language acquisition, such that this proficiency at acquiring language is maximal early in life; generally, as people age, the ease with which they acquire and master new languages diminishes (Johnson & Newport, 1989; Lenneberg, 1967; Singleton, 1995).

Children begin to learn about language from a very early age ( Table 7.1 ). In fact, it appears that this is occurring even before we are born. Newborns show a preference for their mother’s voice and appear to be able to discriminate between the language spoken by their mother and other languages. Babies are also attuned to the languages being used around them and show preferences for videos of faces that are moving in synchrony with the audio of spoken language versus videos that do not synchronize with the audio (Blossom & Morgan, 2006; Pickens, 1994; Spelke & Cortelyou, 1981).

DIG DEEPER: The Case of Genie

In the fall of 1970, a social worker in the Los Angeles area found a 13-year-old girl who was being raised in extremely neglectful and abusive conditions. The girl, who came to be known as Genie, had lived most of her life tied to a potty chair or confined to a crib in a small room that was kept closed with the curtains drawn. For a little over a decade, Genie had virtually no social interaction and no access to the outside world. As a result of these conditions, Genie was unable to stand up, chew solid food, or speak (Fromkin, Krashen, Curtiss, Rigler, & Rigler, 1974; Rymer, 1993). The police took Genie into protective custody.

Genie’s abilities improved dramatically following her removal from her abusive environment, and early on, it appeared she was acquiring language—much later than would be predicted by critical period hypotheses that had been posited at the time (Fromkin et al., 1974). Genie managed to amass an impressive vocabulary in a relatively short amount of time. However, she never developed a mastery of the grammatical aspects of language (Curtiss, 1981). Perhaps being deprived of the opportunity to learn language during a critical period impeded Genie’s ability to fully acquire and use language.

You may recall that each language has its own set of phonemes that are used to generate morphemes, words, and so on. Babies can discriminate among the sounds that make up a language (for example, they can tell the difference between the “s” in vision and the “ss” in fission); early on, they can differentiate between the sounds of all human languages, even those that do not occur in the languages that are used in their environments. However, by the time that they are about 1 year old, they can only discriminate among those phonemes that are used in the language or languages in their environments (Jensen, 2011; Werker & Lalonde, 1988; Werker & Tees, 1984).

After the first few months of life, babies enter what is known as the babbling stage, during which time they tend to produce single syllables that are repeated over and over. As time passes, more variations appear in the syllables that they produce. During this time, it is unlikely that the babies are trying to communicate; they are just as likely to babble when they are alone as when they are with their caregivers (Fernández & Cairns, 2011). Interestingly, babies who are raised in environments in which sign language is used will also begin to show babbling in the gestures of their hands during this stage (Petitto, Holowka, Sergio, Levy, & Ostry, 2004).

Generally, a child’s first word is uttered sometime between the ages of 1 year to 18 months, and for the next few months, the child will remain in the “one word” stage of language development. During this time, children know a number of words, but they only produce one-word utterances. The child’s early vocabulary is limited to familiar objects or events, often nouns. Although children in this stage only make one-word utterances, these words often carry larger meaning (Fernández & Cairns, 2011). So, for example, a child saying “cookie” could be identifying a cookie or asking for a cookie.

As a child’s lexicon grows, she begins to utter simple sentences and to acquire new vocabulary at a very rapid pace. In addition, children begin to demonstrate a clear understanding of the specific rules that apply to their language(s). Even the mistakes that children sometimes make provide evidence of just how much they understand about those rules. This is sometimes seen in the form of  overgeneralization . In this context, overgeneralization refers to an extension of a language rule to an exception to the rule. For example, in English, it is usually the case that an “s” is added to the end of a word to indicate plurality. For example, we speak of one dog versus two dogs. Young children will overgeneralize this rule to cases that are exceptions to the “add an s to the end of the word” rule and say things like “those two gooses” or “three mouses.” Clearly, the rules of the language are understood, even if the exceptions to the rules are still being learned (Moskowitz, 1978).

Language and Thought

When we speak one language, we agree that words are representations of ideas, people, places, and events. The given language that children learn is connected to their culture and surroundings. But can words themselves shape the way we think about things? Psychologists have long investigated the question of whether language shapes thoughts and actions, or whether our thoughts and beliefs shape our language. Two researchers, Edward Sapir and Benjamin Lee Whorf began this investigation in the 1940s. They wanted to understand how the language habits of a community encourage members of that community to interpret language in a particular manner (Sapir, 1941/1964). Sapir and Whorf proposed that language determines thought. For example, in some languages, there are many different words for love. However, in English, we use the word love for all types of love. Does this affect how we think about love depending on the language that we speak (Whorf, 1956)? Researchers have since identified this view as too absolute, pointing out a lack of empiricism behind what Sapir and Whorf proposed (Abler, 2013; Boroditsky, 2011; van Troyer, 1994). Today, psychologists continue to study and debate the relationship between language and thought.

  • Describe problem solving strategies
  • Define algorithm and heuristic
  • Explain some common roadblocks to effective problem solving and decision making

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe is doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

Problem-Solving Strategies

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A  problem-solving strategy  is a plan of action used to find a solution. Different strategies have different action plans associated with them ( Table 7.2 ). For example, a well-known strategy is  trial and error . The old adage, “If at first, you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Another type of strategy is an algorithm. An  algorithm  is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a  heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of the five conditions is met (Pratkanis, 1989):

  • When one is faced with too much information
  • When the time to make a decision is limited
  • When the decision to be made is unimportant
  • When there is access to very little information to use in making the decision
  • When an appropriate heuristic happens to come to mind in the same moment

Working backward is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C., and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backward heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or a long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

EVERYDAY CONNECTION: Solving Puzzles

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( Figure 7.7 ) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

A four column by four row Sudoku puzzle is shown. The top left cell contains the number 3. The top right cell contains the number 2. The bottom right cell contains the number 1. The bottom left cell contains the number 4. The cell at the intersection of the second row and the second column contains the number 4. The cell to the right of that contains the number 1. The cell below the cell containing the number 1 contains the number 2. The cell to the left of the cell containing the number 2 contains the number 3.

Here is another popular type of puzzle ( Figure 7.8 ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

A square shaped outline contains three rows and three columns of dots with equal space between them.

Take a look at the “Puzzling Scales” logic puzzle below ( Figure 7.9 ). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

A puzzle involving a scale is shown. At the top of the figure it reads: “Sam Loyds Puzzling Scales.” The first row of the puzzle shows a balanced scale with 3 blocks and a top on the left and 12 marbles on the right. Below this row it reads: “Since the scales now balance.” The next row of the puzzle shows a balanced scale with just the top on the left, and 1 block and 8 marbles on the right. Below this row it reads: “And balance when arranged this way.” The third row shows an unbalanced scale with the top on the left side, which is much lower than the right side. The right side is empty. Below this row it reads: “Then how many marbles will it require to balance with that top?”

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A  mental set  is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness  is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. Duncker (1945) conducted foundational research on functional fixedness. He created an experiment in which participants were given a candle, a book of matches, and a box of thumbtacks. They were instructed to use those items to attach the candle to the wall so that it did not drip wax onto the table below. Participants had to use functional fixedness to solve the problem ( Figure 7.10 ). During the  Apollo 13  mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Figure a shows a book of matches, a box of thumbtacks, and a candle. Figure b shows the candle standing in the box that held the thumbtacks. A thumbtack attaches the box holding the candle to the wall.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An  anchoring bias  occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The  confirmation bias  is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis.  Hindsight bias  leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did.  Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the  availability heuristic  is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision .  Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in  Table 7.3 .

Were you able to determine how many marbles are needed to balance the scales in  Figure 7.9 ? You need nine. Were you able to solve the problems in  Figure 7.7  and  Figure 7.8 ? Here are the answers ( Figure 7.11 ).

The first puzzle is a Sudoku grid of 16 squares (4 rows of 4 squares) is shown. Half of the numbers were supplied to start the puzzle and are colored blue, and half have been filled in as the puzzle’s solution and are colored red. The numbers in each row of the grid, left to right, are as follows. Row 1: blue 3, red 1, red 4, blue 2. Row 2: red 2, blue 4, blue 1, red 3. Row 3: red 1, blue 3, blue 2, red 4. Row 4: blue 4, red 2, red 3, blue 1.The second puzzle consists of 9 dots arranged in 3 rows of 3 inside of a square. The solution, four straight lines made without lifting the pencil, is shown in a red line with arrows indicating the direction of movement. In order to solve the puzzle, the lines must extend beyond the borders of the box. The four connecting lines are drawn as follows. Line 1 begins at the top left dot, proceeds through the middle and right dots of the top row, and extends to the right beyond the border of the square. Line 2 extends from the end of line 1, through the right dot of the horizontally centered row, through the middle dot of the bottom row, and beyond the square’s border ending in the space beneath the left dot of the bottom row. Line 3 extends from the end of line 2 upwards through the left dots of the bottom, middle, and top rows. Line 4 extends from the end of line 3 through the middle dot in the middle row and ends at the right dot of the bottom row.

  • Define intelligence
  • Explain the triarchic theory of intelligence
  • Identify the difference between intelligence theories
  • Explain emotional intelligence
  • Define creativity

Classifying Intelligence

What exactly is intelligence? The way that researchers have defined the concept of intelligence has been modified many times since the birth of psychology. British psychologist Charles Spearman believed intelligence consisted of one general factor, called  g , which could be measured and compared among individuals. Spearman focused on the commonalities among various intellectual abilities and de-emphasized what made each unique. Long before modern psychology developed, however, ancient philosophers, such as Aristotle, held a similar view (Cianciolo & Sternberg, 2004).

Other psychologists believe that instead of a single factor, intelligence is a collection of distinct abilities. In the 1940s, Raymond Cattell proposed a theory of intelligence that divided general intelligence into two components: crystallized intelligence and fluid intelligence (Cattell, 1963). Crystallized intelligence  is characterized as acquired knowledge and the ability to retrieve it. When you learn, remember, and recall information, you are using crystallized intelligence. You use crystallized intelligence all the time in your coursework by demonstrating that you have mastered the information covered in the course.  Fluid intelligence  encompasses the ability to see complex relationships and solve problems. Navigating your way home after being detoured onto an unfamiliar route because of road construction would draw upon your fluid intelligence. Fluid intelligence helps you tackle complex, abstract challenges in your daily life, whereas crystallized intelligence helps you overcome concrete, straightforward problems (Cattell, 1963).

Other theorists and psychologists believe that intelligence should be defined in more practical terms. For example, what types of behaviors help you get ahead in life? Which skills promote success? Think about this for a moment. Being able to recite all 45 presidents of the United States in order is an excellent party trick, but will knowing this make you a better person?

Robert Sternberg developed another theory of intelligence, which he titled the  triarchic theory of intelligence  because it sees intelligence as comprised of three parts (Sternberg, 1988): practical, creative, and analytical intelligence ( Figure 7.12 ).

Three boxes are arranged in a triangle. The top box contains “Analytical intelligence; academic problem solving and computation.” There is a line with arrows on both ends connecting this box to another box containing “Practical intelligence; street smarts and common sense.” Another line with arrows on both ends connects this box to another box containing “Creative intelligence; imaginative and innovative problem solving.” Another line with arrows on both ends connects this box to the first box described, completing the triangle.

Practical intelligence , as proposed by Sternberg, is sometimes compared to “street smarts.” Being practical means you find solutions that work in your everyday life by applying knowledge based on your experiences. This type of intelligence appears to be separate from the traditional understanding of IQ; individuals who score high in practical intelligence may or may not have comparable scores in creative and analytical intelligence (Sternberg, 1988).

Analytical intelligence is closely aligned with academic problem solving and computations. Sternberg says that analytical intelligence is demonstrated by an ability to analyze, evaluate, judge, compare, and contrast. When reading a classic novel for a literature class, for example, it is usually necessary to compare the motives of the main characters of the book or analyze the historical context of the story. In a science course such as anatomy, you must study the processes by which the body uses various minerals in different human systems. In developing an understanding of this topic, you are using analytical intelligence. When solving a challenging math problem, you would apply analytical intelligence to analyze different aspects of the problem and then solve it section by section.

Creative intelligence  is marked by inventing or imagining a solution to a problem or situation. Creativity in this realm can include finding a novel solution to an unexpected problem or producing a beautiful work of art or a well-developed short story. Imagine for a moment that you are camping in the woods with some friends and realize that you’ve forgotten your camp coffee pot. The person in your group who figures out a way to successfully brew coffee for everyone would be credited as having higher creative intelligence.

Multiple Intelligences Theory  was developed by Howard Gardner, a Harvard psychologist and former student of Erik Erikson. Gardner’s theory, which has been refined for more than 30 years, is a more recent development among theories of intelligence. In Gardner’s theory, each person possesses at least eight intelligences. Among these eight intelligences, a person typically excels in some and falters in others (Gardner, 1983).  Table 7.4  describes each type of intelligence.

Gardner’s theory is relatively new and needs additional research to better establish empirical support. At the same time, his ideas challenge the traditional idea of intelligence to include a wider variety of abilities, although it has been suggested that Gardner simply relabeled what other theorists called “cognitive styles” as “intelligences” (Morgan, 1996). Furthermore, developing traditional measures of Gardner’s intelligences is extremely difficult (Furnham, 2009; Gardner & Moran, 2006; Klein, 1997).

Gardner’s inter- and intrapersonal intelligences are often combined into a single type: emotional intelligence.  Emotional intelligence  encompasses the ability to understand the emotions of yourself and others, show empathy, understand social relationships and cues, and regulate your own emotions and respond in culturally appropriate ways (Parker, Saklofske, & Stough, 2009). People with high emotional intelligence typically have well-developed social skills. Some researchers, including Daniel Goleman, the author of  Emotional Intelligence: Why It Can Matter More than IQ , argue that emotional intelligence is a better predictor of success than traditional intelligence (Goleman, 1995). However, emotional intelligence has been widely debated, with researchers pointing out inconsistencies in how it is defined and described, as well as questioning results of studies on a subject that is difficult to measure and study empirically (Locke, 2005; Mayer, Salovey, & Caruso, 2004)

The most comprehensive theory of intelligence to date is the Cattell-Horn-Carroll (CHC) theory of cognitive abilities (Schneider & McGrew, 2018). In this theory, abilities are related and arranged in a hierarchy with general abilities at the top, broad abilities in the middle, and narrow (specific) abilities at the bottom. The narrow abilities are the only ones that can be directly measured; however, they are integrated within the other abilities. At the general level is general intelligence. Next, the broad level consists of general abilities such as fluid reasoning, short-term memory, and processing speed. Finally, as the hierarchy continues, the narrow level includes specific forms of cognitive abilities. For example, short-term memory would further break down into memory span and working memory capacity.

Intelligence can also have different meanings and values in different cultures. If you live on a small island, where most people get their food by fishing from boats, it would be important to know how to fish and how to repair a boat. If you were an exceptional angler, your peers would probably consider you intelligent. If you were also skilled at repairing boats, your intelligence might be known across the whole island. Think about your own family’s culture. What values are important for Latinx families? Italian families? In Irish families, hospitality and telling an entertaining story are marks of the culture. If you are a skilled storyteller, other members of Irish culture are likely to consider you intelligent.

Some cultures place a high value on working together as a collective. In these cultures, the importance of the group supersedes the importance of individual achievement. When you visit such a culture, how well you relate to the values of that culture exemplifies your  cultural intelligence , sometimes referred to as cultural competence.

Creativity  is the ability to generate, create, or discover new ideas, solutions, and possibilities. Very creative people often have intense knowledge about something, work on it for years, look at novel solutions, seek out the advice and help of other experts, and take risks. Although creativity is often associated with the arts, it is actually a vital form of intelligence that drives people in many disciplines to discover something new. Creativity can be found in every area of life, from the way you decorate your residence to a new way of understanding how a cell works.

Creativity is often assessed as a function of one’s ability to engage in  divergent thinking . Divergent thinking can be described as thinking “outside the box;” it allows an individual to arrive at unique, multiple solutions to a given problem. In contrast,  convergent thinking describes the ability to provide a correct or well-established answer or solution to a problem (Cropley, 2006; Gilford, 1967)

  • Explain how intelligence tests are developed
  • Describe the history of the use of IQ tests
  • Describe the purposes and benefits of intelligence testing

While you’re likely familiar with the term “IQ” and associate it with the idea of intelligence, what does IQ really mean? IQ stands for  intelligence quotient  and describes a score earned on a test designed to measure intelligence. You’ve already learned that there are many ways psychologists describe intelligence (or more aptly, intelligences). Similarly, IQ tests—the tools designed to measure intelligence—have been the subject of debate throughout their development and use.

When might an IQ test be used? What do we learn from the results, and how might people use this information? While there are certainly many benefits to intelligence testing, it is important to also note the limitations and controversies surrounding these tests. For example, IQ tests have sometimes been used as arguments in support of insidious purposes, such as the eugenics movement (Severson, 2011). The infamous Supreme Court Case,  Buck v. Bell , legalized the forced sterilization of some people deemed “feeble-minded” through this type of testing, resulting in about 65,000 sterilizations ( Buck v. Bell , 274 U.S. 200; Ko, 2016). Today, only professionals trained in psychology can administer IQ tests, and the purchase of most tests requires an advanced degree in psychology. Other professionals in the field, such as social workers and psychiatrists, cannot administer IQ tests. In this section, we will explore what intelligence tests measure, how they are scored, and how they were developed.

Measuring Intelligence

It seems that the human understanding of intelligence is somewhat limited when we focus on traditional or academic-type intelligence. How then, can intelligence be measured? And when we measure intelligence, how do we ensure that we capture what we’re really trying to measure (in other words, that IQ tests function as valid measures of intelligence)? In the following paragraphs, we will explore the how intelligence tests were developed and the history of their use.

The IQ test has been synonymous with intelligence for over a century. In the late 1800s, Sir Francis Galton developed the first broad test of intelligence (Flanagan & Kaufman, 2004). Although he was not a psychologist, his contributions to the concepts of intelligence testing are still felt today (Gordon, 1995). Reliable intelligence testing (you may recall from earlier chapters that reliability refers to a test’s ability to produce consistent results) began in earnest during the early 1900s with a researcher named Alfred Binet ( Figure 7.13 ). Binet was asked by the French government to develop an intelligence test to use on children to determine which ones might have difficulty in school; it included many verbally based tasks. American researchers soon realized the value of such testing. Louis Terman, a Stanford professor, modified Binet’s work by standardizing the administration of the test and tested thousands of different-aged children to establish an average score for each age. As a result, the test was normed and standardized, which means that the test was administered consistently to a large enough representative sample of the population that the range of scores resulted in a bell curve (bell curves will be discussed later).  Standardization  means that the manner of administration, scoring, and interpretation of results is consistent.  Norming  involves giving a test to a large population so data can be collected comparing groups, such as age groups. The resulting data provide norms, or referential scores, by which to interpret future scores. Norms are not expectations of what a given group  should  know but a demonstration of what that group  does  know. Norming and standardizing the test ensures that new scores are reliable. This new version of the test was called the Stanford-Binet Intelligence Scale (Terman, 1916). Remarkably, an updated version of this test is still widely used today.

Photograph A shows a portrait of Alfred Binet. Photograph B shows six sketches of human faces. Above these faces is the label “Guide for Binet-Simon Scale. 223” The faces are arranged in three rows of two, and these rows are labeled “1, 2, and 3.” At the bottom it reads: “The psychological clinic is indebted for the loan of these cuts and those on p. 225 to the courtesy of Dr. Oliver P. Cornman, Associate Superintendent of Schools of Philadelphia, and Chairman of Committee on Backward Children Investigation. See Report of Committee, Dec. 31, 1910, appendix.”

In 1939, David Wechsler, a psychologist who spent part of his career working with World War I veterans, developed a new IQ test in the United States. Wechsler combined several subtests from other intelligence tests used between 1880 and World War I. These subtests tapped into a variety of verbal and nonverbal skills because Wechsler believed that intelligence encompassed “the global capacity of a person to act purposefully, to think rationally, and to deal effectively with his environment” (Wechsler, 1958, p. 7). He named the test the Wechsler-Bellevue Intelligence Scale (Wechsler, 1981). This combination of subtests became one of the most extensively used intelligence tests in the history of psychology. Although its name was later changed to the Wechsler Adult Intelligence Scale (WAIS) and has been revised several times, the aims of the test remain virtually unchanged since its inception (Boake, 2002). Today, there are three intelligence tests credited to Wechsler, the Wechsler Adult Intelligence Scale-fourth edition (WAIS-IV), the Wechsler Intelligence Scale for Children (WISC-V), and the Wechsler Preschool and Primary Scale of Intelligence—IV (WPPSI-IV) (Wechsler, 2012). These tests are used widely in schools and communities throughout the United States, and they are periodically normed and standardized as a means of recalibration. As a part of the recalibration process, the WISC-V was given to thousands of children across the country, and children taking the test today are compared with their same-age peers ( Figure 7.13 ).

The WISC-V is composed of 14 subtests, which comprise five indices, which then render an IQ score. The five indices are Verbal Comprehension, Visual Spatial, Fluid Reasoning, Working Memory, and Processing Speed. When the test is complete, individuals receive a score for each of the five indices and a Full Scale IQ score. The method of scoring reflects the understanding that intelligence is comprised of multiple abilities in several cognitive realms and focuses on the mental processes that the child used to arrive at his or her answers to each test item.

Interestingly, the periodic recalibrations have led to an interesting observation known as the Flynn effect. Named after James Flynn, who was among the first to describe this trend, the  Flynn effect  refers to the observation that each generation has a significantly higher IQ than the last. Flynn himself argues, however, that increased IQ scores do not necessarily mean that younger generations are more intelligent per se (Flynn, Shaughnessy, & Fulgham, 2012).

Ultimately, we are still left with the question of how valid intelligence tests are. Certainly, the most modern versions of these tests tap into more than verbal competencies, yet the specific skills that should be assessed in IQ testing, the degree to which any test can truly measure an individual’s intelligence, and the use of the results of IQ tests are still issues of debate (Gresham & Witt, 1997; Flynn, Shaughnessy, & Fulgham, 2012; Richardson, 2002; Schlinger, 2003).

The Bell Curve

The results of intelligence tests follow the bell curve, a graph in the general shape of a bell. When the bell curve is used in psychological testing, the graph demonstrates a normal distribution of a trait, in this case, intelligence, in the human population. Many human traits naturally follow the bell curve. For example, if you lined up all your female schoolmates according to height, it is likely that a large cluster of them would be the average height for an American woman: 5’4”–5’6”. This cluster would fall in the center of the bell curve, representing the average height for American women ( Figure 7.14 ). There would be fewer women who stand closer to 4’11”. The same would be true for women of above-average height: those who stand closer to 5’11”. The trick to finding a bell curve in nature is to use a large sample size. Without a large sample size, it is less likely that the bell curve will represent the wider population. A  representative sample  is a subset of the population that accurately represents the general population. If, for example, you measured the height of the women in your classroom only, you might not actually have a representative sample. Perhaps the women’s basketball team wanted to take this course together, and they are all in your class. Because basketball players tend to be taller than average, the women in your class may not be a good representative sample of the population of American women. But if your sample included all the women at your school, it is likely that their heights would form a natural bell curve.

A graph of a bell curve is labeled “Height of U.S. Women.” The x axis is labeled “Height” and the y axis is labeled “Frequency.” Between the heights of five feet tall and five feet and five inches tall, the frequency rises to a curved peak, then begins dropping off at the same rate until it hits five feet ten inches tall.

The same principles apply to intelligence test scores. Individuals earn a score called an intelligence quotient (IQ). Over the years, different types of IQ tests have evolved, but the way scores are interpreted remains the same. The average IQ score on an IQ test is 100. Standard deviations  describe how data are dispersed in a population and give context to large data sets. The bell curve uses the standard deviation to show how all scores are dispersed from the average score ( Figure 7.15 ). In modern IQ testing, one standard deviation is 15 points. So a score of 85 would be described as “one standard deviation below the mean.” How would you describe a score of 115 and a score of 70? Any IQ score that falls within one standard deviation above and below the mean (between 85 and 115) is considered average, and 68% of the population has IQ scores in this range. An IQ score of 130 or above is considered a superior level.

A graph of a bell curve is labeled “Intelligence Quotient Score.” The x axis is labeled “IQ,” and the y axis is labeled “Population.” Beginning at an IQ of 60, the population rises to a curved peak at an IQ of 100 and then drops off at the same rate ending near zero at an IQ of 140.

Only 2.2% of the population has an IQ score below 70 (American Psychological Association [APA], 2013). A score of 70 or below indicates significant cognitive delays. When these are combined with major deficits in adaptive functioning, a person is diagnosed with having an intellectual disability (American Association on Intellectual and Developmental Disabilities, 2013). Formerly known as mental retardation, the accepted term now is intellectual disability, and it has four subtypes: mild, moderate, severe, and profound ( Table 7.5 ).  The Diagnostic and Statistical Manual of Psychological Disorders  lists criteria for each subgroup (APA, 2013).

On the other end of the intelligence spectrum are those individuals whose IQs fall into the highest ranges. Consistent with the bell curve, about 2% of the population falls into this category. People are considered gifted if they have an IQ score of 130 or higher, or superior intelligence in a particular area. Long ago, popular belief suggested that people of high intelligence were maladjusted. This idea was disproven through a groundbreaking study of gifted children. In 1921, Lewis Terman began a longitudinal study of over 1500 children with IQs over 135 (Terman, 1925). His findings showed that these children became well-educated, successful adults who were, in fact, well-adjusted (Terman & Oden, 1947). Additionally, Terman’s study showed that the subjects were above average in physical build and attractiveness, dispelling an earlier popular notion that highly intelligent people were “weaklings.” Some people with very high IQs elect to join Mensa, an organization dedicated to identifying, researching, and fostering intelligence. Members must have an IQ score in the top 2% of the population, and they may be required to pass other exams in their application to join the group.

DIG DEEPER: What’s in a Name? 

In the past, individuals with IQ scores below 70 and significant adaptive and social functioning delays were diagnosed with mental retardation. When this diagnosis was first named, the title held no social stigma. In time, however, the degrading word “retard” sprang from this diagnostic term. “Retard” was frequently used as a taunt, especially among young people, until the words “mentally retarded” and “retard” became an insult. As such, the DSM-5 now labels this diagnosis as “intellectual disability.” Many states once had a Department of Mental Retardation to serve those diagnosed with such cognitive delays, but most have changed their name to the Department of Developmental Disabilities or something similar in language.

Erin Johnson’s younger brother Matthew has Down syndrome. She wrote this piece about what her brother taught her about the meaning of intelligence:

His whole life, learning has been hard. Entirely possible – just different. He has always excelled with technology – typing his thoughts was more effective than writing them or speaking them. Nothing says “leave me alone” quite like a text that reads, “Do Not Call Me Right Now.” He is fully capable of reading books up to about a third-grade level, but he didn’t love it and used to always ask others to read to him. That all changed when his nephew came along, because he willingly reads to him, and it is the most heart-swelling, smile-inducing experience I have ever had the pleasure of witnessing.

When it comes down to it, Matt can learn. He does learn. It just takes longer, and he has to work harder for it, which if we’re being honest, is not a lot of fun. He is extremely gifted in learning things he takes an interest in, and those things often seem a bit “strange” to others. But no matter. It just proves my point – he  can  learn. That does not mean he will learn at the same pace, or even to the same level. It also, unfortunately, does not mean he will be allotted the same opportunities to learn as many others.

Here’s the scoop. We are all wired with innate abilities to retain and apply our learning and natural curiosities and passions that fuel our desire to learn. But our abilities and curiosities may not be the same.

The world doesn’t work this way though, especially not for my brother and his counterparts. Have him read aloud a book about skunks, and you may not get a whole lot from him. But have him tell you about skunks straight out of his memory, and hold onto your hats. He can hack the school’s iPad system, but he can’t tell you how he did it. He can write out every direction for a drive to our grandparents’ home in Florida, but he can’t drive.

Society is quick to deem him disabled and use demeaning language like the r-word to describe him, but in reality, we haven’t necessarily given him opportunities to showcase the learning he can do. In my case, I can escape the need to memorize how to change the oil in my car without anyone assuming I can’t do it, or calling me names when they find out I can’t. But Matthew can’t get through a day at his job without someone assuming he needs help. He is bright. Brighter than most anyone would assume. Maybe we need to redefine what is smart.

My brother doesn’t fit in the narrow schema of intelligence that is accepted in our society. But intelligence is far more than being able to solve 525 x 62 or properly introduce yourself to another. Why can’t we assume the intelligence of someone who can recite all of a character’s lines in a movie or remember my birthday a year after I told him/her a single time? Why is it we allow a person’s diagnosis or appearance to make us not just wonder if, but entirely doubt that they are capable? Maybe we need to cut away the sides of the box we have created for people so everyone can fit.

My brother can learn. It may not be what you know. It may be knowledge you would deem unimportant. It may not follow a traditional learning trajectory. But the fact remains – he can learn. Everyone can learn. And even though it is harder for him and harder for others still, he is not a “retard.” Nobody is.

When you use the r-word, you are insinuating that an individual, whether someone with a disability or not, is unintelligent, foolish, and purposeless. This in turn tells a person with a disability that they too are unintelligent, foolish, and purposeless. Because the word was historically used to describe individuals with disabilities and twisted from its original meaning to fit a cruel new context, it is forevermore associated with people like my brother. No matter how a person looks or learns or behaves, the r-word is never a fitting term. It’s time we waved it goodbye.

Why Measure Intelligence?

The value of IQ testing is most evident in educational or clinical settings. Children who seem to be experiencing learning difficulties or severe behavioral problems can be tested to ascertain whether the child’s difficulties can be partly attributed to an IQ score that is significantly different from the mean for her age group. Without IQ testing—or another measure of intelligence—children and adults needing extra support might not be identified effectively. In addition, IQ testing is used in courts to determine whether a defendant has special or extenuating circumstances that preclude him from participating in some way in a trial. People also use IQ testing results to seek disability benefits from the Social Security Administration.

  • Describe how genetics and environment affect intelligence
  • Explain the relationship between IQ scores and socioeconomic status
  • Describe the difference between a learning disability and a developmental disorder

High Intelligence: Nature or Nurture?

Where does high intelligence come from? Some researchers believe that intelligence is a trait inherited from a person’s parents. Scientists who research this topic typically use twin studies to determine the  heritability  of intelligence. The Minnesota Study of Twins Reared Apart is one of the most well-known twin studies. In this investigation, researchers found that identical twins raised together and identical twins raised apart exhibit a higher correlation between their IQ scores than siblings or fraternal twins raised together (Bouchard, Lykken, McGue, Segal, & Tellegen, 1990). The findings from this study reveal a genetic component to intelligence ( Figure 7.15 ). At the same time, other psychologists believe that intelligence is shaped by a child’s developmental environment. If parents were to provide their children with intellectual stimuli from before they are born, it is likely that they would absorb the benefits of that stimulation, and it would be reflected in intelligence levels.

A chart shows correlations of IQs for people of varying relationships. The bottom is labeled “Percent IQ Correlation” and the left side is labeled “Relationship.” The percent IQ Correlation for relationships where no genes are shared, including adoptive parent-child pairs, similarly aged unrelated children raised together, and adoptive siblings are around 21 percent, 30 percent, and 32 percent, respectively. The percent IQ Correlation for relationships where 25 percent of genes are shared, as in half-siblings, is around 33 percent. The percent IQ Correlation for relationships where 50 percent of genes are shared, including parent-children pairs, and fraternal twins raised together, are roughly 44 percent and 62 percent, respectively. A relationship where 100 percent of genes are shared, as in identical twins raised apart, results in a nearly 80 percent IQ correlation.

The reality is that aspects of each idea are probably correct. In fact, one study suggests that although genetics seem to be in control of the level of intelligence, the environmental influences provide both stability and change to trigger manifestation of cognitive abilities (Bartels, Rietveld, Van Baal, & Boomsma, 2002). Certainly, there are behaviors that support the development of intelligence, but the genetic component of high intelligence should not be ignored. As with all heritable traits, however, it is not always possible to isolate how and when high intelligence is passed on to the next generation.

Range of Reaction  is the theory that each person responds to the environment in a unique way based on his or her genetic makeup. According to this idea, your genetic potential is a fixed quantity, but whether you reach your full intellectual potential is dependent upon the environmental stimulation you experience, especially in childhood. Think about this scenario: A couple adopts a child who has average genetic intellectual potential. They raise her in an extremely stimulating environment. What will happen to the couple’s new daughter? It is likely that the stimulating environment will improve her intellectual outcomes over the course of her life. But what happens if this experiment is reversed? If a child with an extremely strong genetic background is placed in an environment that does not stimulate him: What happens? Interestingly, according to a longitudinal study of highly gifted individuals, it was found that “the two extremes of optimal and pathological experience are both represented disproportionately in the backgrounds of creative individuals”; however, those who experienced supportive family environments were more likely to report being happy (Csikszentmihalyi & Csikszentmihalyi, 1993, p. 187).

Another challenge to determining the origins of high intelligence is the confounding nature of our human social structures. It is troubling to note that some ethnic groups perform better on IQ tests than others—and it is likely that the results do not have much to do with the quality of each ethnic group’s intellect. The same is true for socioeconomic status. Children who live in poverty experience more pervasive, daily stress than children who do not worry about the basic needs of safety, shelter, and food. These worries can negatively affect how the brain functions and develops, causing a dip in IQ scores. Mark Kishiyama and his colleagues determined that children living in poverty demonstrated reduced prefrontal brain functioning comparable to children with damage to the lateral prefrontal cortex (Kishyama, Boyce, Jimenez, Perry, & Knight, 2009).

The debate around the foundations and influences on intelligence exploded in 1969 when an educational psychologist named Arthur Jensen published the article “How Much Can We Boost I.Q. and Achievement” in the Harvard Educational Review . Jensen had administered IQ tests to diverse groups of students, and his results led him to the conclusion that IQ is determined by genetics. He also posited that intelligence was made up of two types of abilities: Level I and Level II. In his theory, Level I is responsible for rote memorization, whereas Level II is responsible for conceptual and analytical abilities. According to his findings, Level I remained consistent among the human race. Level II, however, exhibited differences among ethnic groups (Modgil & Routledge, 1987). Jensen’s most controversial conclusion was that Level II intelligence is prevalent among Asians, then Caucasians, then African Americans. Robert Williams was among those who called out racial bias in Jensen’s results (Williams, 1970).

Obviously, Jensen’s interpretation of his own data caused an intense response in a nation that continued to grapple with the effects of racism (Fox, 2012). However, Jensen’s ideas were not solitary or unique; rather, they represented one of many examples of psychologists asserting racial differences in IQ and cognitive ability. In fact, Rushton and Jensen (2005) reviewed three decades worth of research on the relationship between race and cognitive ability. Jensen’s belief in the inherited nature of intelligence and the validity of the IQ test to be the truest measure of intelligence are at the core of his conclusions. If, however, you believe that intelligence is more than Levels I and II, or that IQ tests do not control for socioeconomic and cultural differences among people, then perhaps you can dismiss Jensen’s conclusions as a single window that looks out on the complicated and varied landscape of human intelligence.

In a related story, parents of African American students filed a case against the State of California in 1979, because they believed that the testing method used to identify students with learning disabilities was culturally unfair as the tests were normed and standardized using white children ( Larry P. v. Riles ). The testing method used by the state disproportionately identified African American children as mentally retarded. This resulted in many students being incorrectly classified as “mentally retarded.”

What are Learning Disabilities?

Learning disabilities are cognitive disorders that affect different areas of cognition, particularly language or reading. It should be pointed out that learning disabilities are not the same thing as intellectual disabilities. Learning disabilities are considered specific neurological impairments rather than global intellectual or developmental disabilities. A person with a language disability has difficulty understanding or using spoken language, whereas someone with a reading disability, such as dyslexia, has difficulty processing what he or she is reading.

Often, learning disabilities are not recognized until a child reaches school age. One confounding aspect of learning disabilities is that they most often affect children with average to above-average intelligence. In other words, the disability is specific to a particular area and not a measure of overall intellectual ability. At the same time, learning disabilities tend to exhibit comorbidity with other disorders, like attention-deficit hyperactivity disorder (ADHD). Anywhere between 30–70% of individuals with diagnosed cases of ADHD also have some sort of learning disability (Riccio, Gonzales, & Hynd, 1994). Let’s take a look at three examples of common learning disabilities: dysgraphia, dyslexia, and dyscalculia.

Children with  dysgraphia  have a learning disability that results in a struggle to write legibly. The physical task of writing with a pen and paper is extremely challenging for the person. These children often have extreme difficulty putting their thoughts down on paper (Smits-Engelsman & Van Galen, 1997). This difficulty is inconsistent with a person’s IQ. That is, based on the child’s IQ and/or abilities in other areas, a child with dysgraphia should be able to write, but can’t. Children with dysgraphia may also have problems with spatial abilities.

Students with dysgraphia need academic accommodations to help them succeed in school. These accommodations can provide students with alternative assessment opportunities to demonstrate what they know (Barton, 2003). For example, a student with dysgraphia might be permitted to take an oral exam rather than a traditional paper-and-pencil test. Treatment is usually provided by an occupational therapist, although there is some question as to how effective such treatment is (Zwicker, 2005).

Dyslexia is the most common learning disability in children. An individual with  dyslexia  exhibits an inability to correctly process letters. The neurological mechanism for sound processing does not work properly in someone with dyslexia. As a result, dyslexic children may not understand sound-letter correspondence. A child with dyslexia may mix up letters within words and sentences—letter reversals, such as those shown in  Figure 7.17 , are a hallmark of this learning disability—or skip whole words while reading. A dyslexic child may have difficulty spelling words correctly while writing. Because of the disordered way that the brain processes letters and sounds, learning to read is a frustrating experience. Some dyslexic individuals cope by memorizing the shapes of most words, but they never actually learn to read (Berninger, 2008).

Two columns and five rows all containing the word “teapot” are shown. “Teapot” is written ten times with the letters jumbled, sometimes appearing backwards and upside down.

Dyscalculia

Dyscalculia  is difficulty in learning or comprehending arithmetic. This learning disability is often first evident when children exhibit difficulty discerning how many objects are in a small group without counting them. Other symptoms may include struggling to memorize math facts, organize numbers, or fully differentiate between numerals, math symbols, and written numbers (such as “3” and “three”).

Additional Supplemental Resources

  • Use Google’s QuickDraw web app on your phone to quickly draw 5 things for Google’s artificially intelligent neural net. When you are done, the app will show you what it thought each of the drawings was. How does this relate to the psychological idea of concepts, prototypes, and schemas? Check out here.  Works best in Chrome if used in a web browser
  • This article lists information about a variety of different topics relating to speech development, including how speech develops and what research is currently being done regarding speech development.
  • The Human intelligence site includes biographical profiles of people who have influenced the development of intelligence theory and testing, in-depth articles exploring current controversies related to human intelligence, and resources for teachers.

Preview the document

  • In 2000, psychologists Sheena Iyengar and Mark Lepper from Columbia and Stanford University published a study about the paradox of choice.  This is the original journal article.
  • Mensa , the high IQ society, provides a forum for intellectual exchange among its members. There are members in more than 100 countries around the world.  Anyone with an IQ in the top 2% of the population can join.
  • This test developed in the 1950s is used to refer to some kinds of behavioral tests for the presence of mind, or thought, or intelligence in putatively minded entities such as machines.
  • Your central “Hub” of information and products created for the network of Parent Centers serving families of children with disabilities.
  • How have average IQ levels changed over time? Hear James Flynn discuss the “Flynn Effect” in this Ted Talk. Closed captioning available.
  • We all want customized experiences and products — but when faced with 700 options, consumers freeze up. With fascinating new research, Sheena Iyengar demonstrates how businesses (and others) can improve the experience of choosing. This is the same researcher that is featured in your midterm exam.
  • What does an IQ Score distribution look like?  Where do most people fall on an IQ Score distribution?  Find out more in this video. Closed captioning available.
  • How do we solve problems?  How can data help us to do this?  Follow Amy Webb’s story of how she used algorithms to help her find her way to true love. Closed captioning available.
  • In this Ted-Ed video, explore some of the ways in which animals communicate, and determine whether or not this communication qualifies as language.  A variety of discussion and assessment questions are included with the video (free registration is required to access the questions). Closed captioning available.
  • Watch this Ted-Ed video to learn more about the benefits of speaking multiple languages, including how bilingualism helps the brain to process information, strengthens the brain, and keeps the speaker more engaged in their world.  A variety of discussion and assessment questions are included with the video (free registration is required to access the questions). Closed captioning available.
  • This video is on how your mind can amaze and betray you includes information on topics such as concepts, prototypes, problem-solving and mistakes in thinking. Closed captioning available.
  • This video on language includes information on topics such as the development of language, language theories, and brain areas involved in language, as well as language disorders. Closed captioning available.
  • This video on the controversy of intelligence includes information on topics such as theories of intelligence, emotional intelligence, and measuring intelligence. Closed captioning available.
  • This video on the brains vs. bias includes information on topics such as intelligence testing, testing bias, and stereotype threat. Closed captioning available.

Access for free at  https://openstax.org/books/psychology-2e/pages/1-introduction

Introduction to Psychology Copyright © 2020 by Julie Lazzara is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

Share This Book

Chapter 7: Thinking and Intelligence

What is cognition.

what is problem solving why does it is always associated with the word reasoning

Imagine all of your thoughts as if they were physical entities, swirling rapidly inside your mind. How is it possible that the brain is able to move from one thought to the next in an organized, orderly fashion? The brain is endlessly perceiving, processing, planning, organizing, and remembering—it is always active. Yet, you don’t notice most of your brain’s activity as you move throughout your daily routine. This is only one facet of the complex processes involved in cognition. Simply put, cognition is thinking, and it encompasses the processes associated with perception, knowledge, problem-solving, judgment, language, and memory. Scientists who study cognition are searching for ways to understand how we integrate, organize, and utilize our conscious cognitive experiences without being aware of all of the unconscious work that our brains are doing (for example, Kahneman, 2011).

Categories and Concepts

Concepts and prototypes.

The human nervous system is capable of handling endless streams of information. The senses serve as the interface between the mind and the external environment, receiving stimuli and translating them into nerve impulses that are transmitted to the brain. The brain then processes this information and uses the relevant pieces to create thoughts, which can then be expressed through language or stored in memory for future use. To make this process more complex, the brain does not gather information from external environments only. When thoughts are formed, the brain also pulls information from emotions and memories (Figure 1). Emotion and memory are powerful influences on both our thoughts and behaviors.

The outline of a human head is shown. There is a box containing “Information, sensations” in front of the head. An arrow from this box points to another box containing “Emotions, memories” located where the person’s brain would be. An arrow from this second box points to a third box containing “Thoughts” behind the head.

Figure 1 . Sensations and information are received by our brains, filtered through emotions and memories, and processed to become thoughts.

In order to organize this staggering amount of information, the brain has developed a file cabinet of sorts in the mind. The different files stored in the file cabinet are called concepts. Concepts are categories or groupings of linguistic information, images, ideas, or memories, such as life experiences. Concepts are, in many ways, big ideas that are generated by observing details, and categorizing and combining these details into cognitive structures. You use concepts to see the relationships among the different elements of your experiences and to keep the information in your mind organized and accessible.

Concepts are informed by our semantic memory (you will learn more about this concept when you study memory) and are present in every aspect of our lives; however, one of the easiest places to notice concepts is inside a classroom, where they are discussed explicitly. When you study United States history, for example, you learn about more than just individual events that have happened in America’s past. You absorb a large quantity of information by listening to and participating in discussions, examining maps, and reading first-hand accounts of people’s lives. Your brain analyzes these details and develops an overall understanding of American history. In the process, your brain gathers details that inform and refine your understanding of related concepts like democracy, power, and freedom.

Concepts can be complex and abstract, like justice, or more concrete, like types of birds. In psychology, for example, Piaget’s stages of development are abstract concepts. Some concepts, like tolerance, are agreed upon by many people because they have been used in various ways over many years. Other concepts, like the characteristics of your ideal friend or your family’s birthday traditions, are personal and individualized. In this way, concepts touch every aspect of our lives, from our many daily routines to the guiding principles behind the way governments function.

Concepts are at the core of intelligent behavior. We expect people to be able to know what to do in new situations and when confronting new objects. If you go into a new classroom and see chairs, a blackboard, a projector, and a screen, you know what these things are and how they will be used. You’ll sit on one of the chairs and expect the instructor to write on the blackboard or project something onto the screen. You do this even if you have never seen any of these particular objects before , because you have concepts of classrooms, chairs, projectors, and so forth, that tell you what they are and what you’re supposed to do with them. Furthermore, if someone tells you a new fact about the projector—for example, that it has a halogen bulb—you are likely to extend this fact to other projectors you encounter. In short, concepts allow you to extend what you have learned about a limited number of objects to a potentially infinite set of entities.

A photograph of Mohandas Gandhi is shown. There are several people walking with him.

Figure 2 . In 1930, Mohandas Gandhi led a group in peaceful protest against a British tax on salt in India.

Another technique used by your brain to organize information is the identification of prototypes for the concepts you have developed. A prototype is the best example or representation of a concept. For example, for the category of civil disobedience, your prototype could be Rosa Parks. Her peaceful resistance to segregation on a city bus in Montgomery, Alabama, is a recognizable example of civil disobedience. Or your prototype could be Mohandas Gandhi, sometimes called Mahatma Gandhi (“Mahatma” is an honorific title) (Figure 2).

Mohandas Gandhi served as a nonviolent force for independence for India while simultaneously demanding that Buddhist, Hindu, Muslim, and Christian leaders—both Indian and British—collaborate peacefully. Although he was not always successful in preventing violence around him, his life provides a steadfast example of the civil disobedience prototype (Constitutional Rights Foundation, 2013). Just as concepts can be abstract or concrete, we can make a distinction between concepts that are functions of our direct experience with the world and those that are more artificial in nature.

link to learning

Test how well you can match the computer’s prototype for certain objects by  playing this interactive game, Quick Draw!

Natural and Artificial Concepts

In psychology, concepts can be divided into two categories, natural and artificial. Natural concepts are created “naturally” through your experiences and can be developed from either direct or indirect experiences. For example, if you live in Essex Junction, Vermont, you have probably had a lot of direct experience with snow. You’ve watched it fall from the sky, you’ve seen lightly falling snow that barely covers the windshield of your car, and you’ve shoveled out 18 inches of fluffy white snow as you’ve thought, “This is perfect for skiing.” You’ve thrown snowballs at your best friend and gone sledding down the steepest hill in town. In short, you know snow. You know what it looks like, smells like, tastes like, and feels like. If, however, you’ve lived your whole life on the island of Saint Vincent in the Caribbean, you may never have actually seen snow, much less tasted, smelled, or touched it. You know snow from the indirect experience of seeing pictures of falling snow—or from watching films that feature snow as part of the setting. Either way, snow is a natural concept because you can construct an understanding of it through direct observations or experiences of snow (Figure 3).

Photograph A shows a snow covered landscape with the sun shining over it. Photograph B shows a sphere shaped object perched atop the corner of a cube shaped object. There is also a triangular object shown.

Figure 3 . (a) Our concept of snow is an example of a natural concept—one that we understand through direct observation and experience. (b) In contrast, artificial concepts are ones that we know by a specific set of characteristics that they always exhibit, such as what defines different basic shapes. (credit a: modification of work by Maarten Takens; credit b: modification of work by “Shayan (USA)”/Flickr)

An artificial concept , on the other hand, is a concept that is defined by a specific set of characteristics. Various properties of geometric shapes, like squares and triangles, serve as useful examples of artificial concepts. A triangle always has three angles and three sides. A square always has four equal sides and four right angles. Mathematical formulas, like the equation for area (length × width) are artificial concepts defined by specific sets of characteristics that are always the same. Artificial concepts can enhance the understanding of a topic by building on one another. For example, before learning the concept of “area of a square” (and the formula to find it), you must understand what a square is. Once the concept of “area of a square” is understood, an understanding of area for other geometric shapes can be built upon the original understanding of area. The use of artificial concepts to define an idea is crucial to communicating with others and engaging in complex thought. According to Goldstone and Kersten (2003), concepts act as building blocks and can be connected in countless combinations to create complex thoughts.

A schema is a mental construct consisting of a cluster or collection of related concepts (Bartlett, 1932). There are many different types of schemata, and they all have one thing in common: schemata are a method of organizing information that allows the brain to work more efficiently. When a schema is activated, the brain makes immediate assumptions about the person or object being observed.

There are several types of schemata. A role schema makes assumptions about how individuals in certain roles will behave (Callero, 1994). For example, imagine you meet someone who introduces himself as a firefighter. When this happens, your brain automatically activates the “firefighter schema” and begins making assumptions that this person is brave, selfless, and community-oriented. Despite not knowing this person, already you have unknowingly made judgments about him. Schemata also help you fill in gaps in the information you receive from the world around you. While schemata allow for more efficient information processing, there can be problems with schemata, regardless of whether they are accurate: Perhaps this particular firefighter is not brave, he just works as a firefighter to pay the bills while studying to become a children’s librarian.

An event schema , also known as a cognitive script , is a set of behaviors that can feel like a routine. Think about what you do when you walk into an elevator (Figure 4). First, the doors open and you wait to let exiting passengers leave the elevator car. Then, you step into the elevator and turn around to face the doors, looking for the correct button to push. You never face the back of the elevator, do you? And when you’re riding in a crowded elevator and you can’t face the front, it feels uncomfortable, doesn’t it? Interestingly, event schemata can vary widely among different cultures and countries. For example, while it is quite common for people to greet one another with a handshake in the United States, in Tibet, you greet someone by sticking your tongue out at them, and in Belize, you bump fists (Cairns Regional Council, n.d.)

A crowded elevator is shown. There are many people standing close to one another.

Figure 4 . What event schema do you perform when riding in an elevator? (credit: “Gideon”/Flickr)

Because event schemata are automatic, they can be difficult to change. Imagine that you are driving home from work or school. This event schema involves getting in the car, shutting the door, and buckling your seatbelt before putting the key in the ignition. You might perform this script two or three times each day. As you drive home, you hear your phone’s ring tone. Typically, the event schema that occurs when you hear your phone ringing involves locating the phone and answering it or responding to your latest text message. So without thinking, you reach for your phone, which could be in your pocket, in your bag, or on the passenger seat of the car. This powerful event schema is informed by your pattern of behavior and the pleasurable stimulation that a phone call or text message gives your brain. Because it is a schema, it is extremely challenging for us to stop reaching for the phone, even though we know that we endanger our own lives and the lives of others while we do it (Neyfakh, 2013) (Figure 5).

A person’s right hand is holding a cellular phone. The person is in the driver’s seat of an automobile while on the road.

Figure 5 . Texting while driving is dangerous, but it is a difficult event schema for some people to resist.

Remember the elevator? It feels almost impossible to walk in and not face the door. Our powerful event schema dictates our behavior in the elevator, and it is no different with our phones. Current research suggests that it is the habit, or event schema, of checking our phones in many different situations that make refraining from checking them while driving especially difficult (Bayer & Campbell, 2012). Because texting and driving has become a dangerous epidemic in recent years, psychologists are looking at ways to help people interrupt the “phone schema” while driving. Event schemata like these are the reason why many habits are difficult to break once they have been acquired. As we continue to examine thinking, keep in mind how powerful the forces of concepts and schemata are to our understanding of the world.

  • Modification, adaptation, and original content. Provided by : Lumen Learning. License : CC BY: Attribution
  • What is Cognition?. Authored by : OpenStax College. Located at : http://cnx.org/contents/[email protected]:u8MlFxBQ@7/What-Is-Cognition . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/content/col11629/latest/.
  • Paragraphs on categories and concepts. Authored by : Gregory Murphy. Provided by : New York University. Located at : http://nobaproject.com/textbooks/wendy-king-introduction-to-psychology-the-full-noba-collection/modules/categories-and-concepts . Project : The Noba Project. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
  • A Thinking Man Image. Authored by : Wesley Nitsckie. Located at : https://www.flickr.com/photos/nitsckie/5507777269 . License : CC BY-SA: Attribution-ShareAlike
  • Cognition: How Your Mind Can Amaze and Betray You - Crash Course Psychology #15. Provided by : CrashCourse. Located at : https://www.youtube.com/watch?v=R-sVnmmw6WY&feature=youtu.be&list=PL8dPuuaLjXtOPRKzVLY0jJY-uHOH9KVU6 . License : All Rights Reserved . License Terms : Standard YouTube License

Footer Logo Lumen Candela

Privacy Policy

42 Problem Solving

[latexpage]

Learning Objectives

By the end of this section, you will be able to:

  • Describe problem solving strategies
  • Define algorithm and heuristic
  • Explain some common roadblocks to effective problem solving

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

PROBLEM-SOLVING STRATEGIES

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them ( [link] ). For example, a well-known strategy is trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

  • When one is faced with too much information
  • When the time to make a decision is limited
  • When the decision to be made is unimportant
  • When there is access to very little information to use in making the decision
  • When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( [link] ) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

A four column by four row Sudoku puzzle is shown. The top left cell contains the number 3. The top right cell contains the number 2. The bottom right cell contains the number 1. The bottom left cell contains the number 4. The cell at the intersection of the second row and the second column contains the number 4. The cell to the right of that contains the number 1. The cell below the cell containing the number 1 contains the number 2. The cell to the left of the cell containing the number 2 contains the number 3.

Here is another popular type of puzzle ( [link] ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

A square shaped outline contains three rows and three columns of dots with equal space between them.

Take a look at the “Puzzling Scales” logic puzzle below ( [link] ). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

A puzzle involving a scale is shown. At the top of the figure it reads: “Sam Loyds Puzzling Scales.” The first row of the puzzle shows a balanced scale with 3 blocks and a top on the left and 12 marbles on the right. Below this row it reads: “Since the scales now balance.” The next row of the puzzle shows a balanced scale with just the top on the left, and 1 block and 8 marbles on the right. Below this row it reads: “And balance when arranged this way.” The third row shows an unbalanced scale with the top on the left side, which is much lower than the right side. The right side is empty. Below this row it reads: “Then how many marbles will it require to balance with that top?”

PITFALLS TO PROBLEM SOLVING

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

what is problem solving why does it is always associated with the word reasoning

Check out this Apollo 13 scene where the group of NASA engineers are given the task of overcoming functional fixedness.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in [link] .

Please visit this site to see a clever music video that a high school teacher made to explain these and other cognitive biases to his AP psychology students.

Were you able to determine how many marbles are needed to balance the scales in [link] ? You need nine. Were you able to solve the problems in [link] and [link] ? Here are the answers ( [link] ).

The first puzzle is a Sudoku grid of 16 squares (4 rows of 4 squares) is shown. Half of the numbers were supplied to start the puzzle and are colored blue, and half have been filled in as the puzzle’s solution and are colored red. The numbers in each row of the grid, left to right, are as follows. Row 1:  blue 3, red 1, red 4, blue 2. Row 2: red 2, blue 4, blue 1, red 3. Row 3: red 1, blue 3, blue 2, red 4. Row 4: blue 4, red 2, red 3, blue 1.The second puzzle consists of 9 dots arranged in 3 rows of 3 inside of a square. The solution, four straight lines made without lifting the pencil, is shown in a red line with arrows indicating the direction of movement. In order to solve the puzzle, the lines must extend beyond the borders of the box. The four connecting lines are drawn as follows. Line 1 begins at the top left dot, proceeds through the middle and right dots of the top row, and extends to the right beyond the border of the square. Line 2 extends from the end of line 1, through the right dot of the horizontally centered row, through the middle dot of the bottom row, and beyond the square’s border ending in the space beneath the left dot of the bottom row. Line 3 extends from the end of line 2 upwards through the left dots of the bottom, middle, and top rows. Line 4 extends from the end of line 3 through the middle dot in the middle row and ends at the right dot of the bottom row.

Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

Review Questions

A specific formula for solving a problem is called ________.

  • an algorithm
  • a heuristic
  • a mental set
  • trial and error

A mental shortcut in the form of a general problem-solving framework is called ________.

Which type of bias involves becoming fixated on a single trait of a problem?

  • anchoring bias
  • confirmation bias
  • representative bias
  • availability bias

Which type of bias involves relying on a false stereotype to make a decision?

Critical Thinking Questions

What is functional fixedness and how can overcoming it help you solve problems?

Functional fixedness occurs when you cannot see a use for an object other than the use for which it was intended. For example, if you need something to hold up a tarp in the rain, but only have a pitchfork, you must overcome your expectation that a pitchfork can only be used for garden chores before you realize that you could stick it in the ground and drape the tarp on top of it to hold it up.

How does an algorithm save you time and energy when solving a problem?

An algorithm is a proven formula for achieving a desired outcome. It saves time because if you follow it exactly, you will solve the problem without having to figure out how to solve the problem. It is a bit like not reinventing the wheel.

Personal Application Question

Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

Creative Commons License

Share This Book

  • Increase Font Size
  • Trending Categories

Data Structure

  • Selected Reading
  • UPSC IAS Exams Notes
  • Developer's Best Practices
  • Questions and Answers
  • Effective Resume Writing
  • HR Interview Questions
  • Computer Glossary

Reasoning and Problem Solving

The ability that sets human beings apart from other animals is cognitive capacity. Humans have a larger brain with a neocortex that helps them think, reason or solve problems. This ability is what gives us an edge over other living beings. Every day, we face numerous challenges and problems, and we attempt to solve these through many techniques. Humans have the power of thinking and reasoning. These are essential tools that help humans survive in the face of adversity and help us live meaningful lives. It enables us to navigate through the challenges that life throws at us.

What is the Reasoning?

In psychology, the reasoning is the process through which people reason or come to conclusions. This involves studying the process humans use to solve problems and come to a decision. The same reasoning is also covered in several other fields, such as philosophy, science, literature, logic, etc. In everyday life, people mostly use two processes for reasoning: deductive and inductive reasoning.

Types of Reasoning

Major types of reasoning are

what is problem solving why does it is always associated with the word reasoning

How does reasoning develop?

As a person initially learns a language, associating sounds with meanings they are familiar with requires an abstract thinking capacity. They start using more critical thinking and logic skills when they can analyze other people's noises and send sounds that others can receive. As they age, they start using more critical thinking involving logical reasoning.

According to Jean Piaget's theory of the development of cognition, reasoning develops in stages from infancy to childhood. According to him, as children grow and their capacity for working memory enlarges, their speed of processing increases. This leads to enhanced executive functions and better control over them. During these stages, children become increasingly self-aware. In the final stage of Piaget's theory, children gain enough experience, leading to increased logic. They started looking at problems in an abstract manner and began to look for multiple solutions to the problem. They start thinking scientifically about the world around them. The way one justifies things also affects how one reason. Erroneous thinking frequently results from illogical reasoning. Logic is the study of sound reasoning, which aids in rational thought. Therefore, we should encourage our kids to use reason daily. They use various methods of reasoning. Two of the most well-known methods are as follows  −

what is problem solving why does it is always associated with the word reasoning

Inductive vs. Deductive Reasoning

Inductive reasoning refers to finding a solution from specific information to a more generalized principle, also known as a "bottom-up" approach. For instance, penguins cannot fly, a penguin is also a bird, and all birds cannot fly. Deductive reasoning is a top-down approach where one derives specific conclusions from a generalized principle. This means that one moves from general premises to specific ideas. A person starts with a theory and develops a hypothesis, and they further empirically test the hypothesis. Data is collected from multiple sources, and a statistical test helps to conclude the hypothesis. For example, all birds have wings; a penguin has wings; therefore, a penguin is a bird.

Why is this Reasoning Important?

Being able to reason determines how people understand, assess, and accept statements and arguments, which significantly affects one's capacity to learn from new information and experiences. Your capacity for decision-making, aspect analysis, and other mental abilities are all tested via reasoning. Making decisions sensibly and successfully requires reasoning, which reasoning fosters. Your reasoning assesses decision-making capacity, aspect analysis, and other mental skills. Making wise and effective decisions involves reasoning, which is what reasoning encourages.

What is the problem solving?

Problem-solving refers to a mental process wherein individuals are dedicated to solving a problem. They achieve this by acknowledging the problem, analyzing it, and taking effective steps toward solving it. It is not just about solving any problem or finding any solution; it involves attempting to come up with the best solution to any problem. A problem can have several solutions, and there is never just one way to solve a problem. In psychology, problem-solving is not just about finding solutions to psychological or mental health-related issues. It is also associated with the cognitive processes involved in solving any problem in life, and this involves using the thought process that leads to solutions.

There are many steps to solving a problem, referred to as problem-solving methods. This is a step-by-step process, and while dealing with a problem, one may have to go through them repeatedly to devise a viable solution. Here are the steps

Identifying the problem − This may seem easy, but it is the most important step. It involves acknowledging the problem and then trying to find out the source of the problem. If one does not understand the problem or identifies an incorrect one, one might waste time trying to solve an incorrect problem. For instance, if a child is having trouble playing an instrument, they must identify the problem (they cannot play the instrument). Later, they identify that they have not been holding the instrument correctly or have not dedicated enough time to practice.

Defining the problem − It is crucial to adequately define the problem at hand once it has been acknowledged. Once a person has defined a problem, they can take the right steps to solve it. At this stage, it is important to look at the problem from different angles to find many possible solutions. For instance, one can find playing an instrument difficult if one is not holding it properly.

Forming a strategy − Finding a solution requires developing a plan of action. Different tactics must be developed for each circumstance, considering each person's particular preferences. One cannot simply become a good musician overnight. If a person realizes that they cannot play the instrument, they will have to make a plan of action for effective playing.

Resource allocation − There are finite amounts of time, money, and other resources. One can choose the resources they need in the course to find the solution by deciding how important it is to solve the challenge. If the issue is significant, more resources can be devoted to its resolution. Without appropriate planning, one might spend time and money on a problem that is less significant than one thinks.

Monitoring Progress − It is important to keep track of the progress while working on the problem. Effective problem-solvers are known to assess their performance regularly. Furthermore, they will reconsider their strategy or hunt for alternatives if they do not make the necessary advancements.

Reasoning and problem-solving are higher-order functions that humans use in their day-to-day lives. Maturity in reasoning and problem-solving is achieved with increasing age, life experience, and the ability to learn from mistakes. These are important skills that help us navigate simple and complex problems. The reasoning is arriving at a decision or conclusion, whereas problem-solving is finding the best solution to a problem.

Utkarsh Shukla

Related Articles

  • Attention and Problem Solving
  • Problem Solving: Meaning, Theory, and Strategies
  • Barriers to Problem Solving
  • Facilitating and Hindering Factors in Problem Solving
  • Problem Solving - Steps, Techniques, & Best Practices
  • Problem-solving on Boolean Model and Vector Space Model
  • How Can Leaders Improve Problem-Solving Abilities?
  • Tips for Effective Problem-solving in Quality Management
  • Explain The Scientific Method Used By A Scientist In Solving Problem?
  • Inductive Vs. Deductive Reasoning
  • Difference between Forward and Backward Reasoning in AI
  • Solving Cryptarithmetic Puzzles
  • Sudoku Solving algorithms
  • Signals and Systems – Solving Differential Equations with Laplace Transform
  • What are the applications of Memory Based Reasoning?

Kickstart Your Career

Get certified by completing the course

what is problem solving why does it is always associated with the word reasoning

What Is Problem Solving?

You will often see beach clean-up drives being publicized in coastal cities. There are already dustbins available on the beaches,…

What Is Problem Solving?

You will often see beach clean-up drives being publicized in coastal cities. There are already dustbins available on the beaches, so why do people need to organize these drives? It’s evident that despite advertising and posting anti-littering messages, some of us don’t follow the rules.

Temporary food stalls and shops make it even more difficult to keep the beaches clean. Since people can’t ask the shopkeepers to relocate or prevent every single person from littering, the clean-up drive is needed.  This is an ideal example of problem-solving psychology in humans. ( 230-fifth.com ) So, what is problem-solving? Let’s find out.

What Is Problem-Solving?

At its simplest, the meaning of problem-solving is the process of defining a problem, determining its cause, and implementing a solution. The definition of problem-solving is rooted in the fact that as humans, we exert control over our environment through solutions. We move forward in life when we solve problems and make decisions. 

We can better define the problem-solving process through a series of important steps.

Identify The Problem: 

This step isn’t as simple as it sounds. Most times, we mistakenly identify the consequences of a problem rather than the problem itself. It’s important that we’re careful to identify the actual problem and not just its symptoms. 

Define The Problem: 

Once the problem has been identified correctly, you should define it. This step can help clarify what needs to be addressed and for what purpose.

Form A Strategy: 

Develop a strategy to solve your problem. Defining an approach will provide direction and clarity on the next steps. 

Organize The Information:  

Organizing information systematically will help you determine whether something is missing. The more information you have, the easier it’ll become for you to arrive at a solution.  

Allocate Resources:  

We may not always be armed with the necessary resources to solve a problem. Before you commit to implementing a solution for a problem, you should determine the availability of different resources—money, time and other costs.

Track Progress: 

The true meaning of problem-solving is to work towards an objective. If you measure your progress, you can evaluate whether you’re on track. You could revise your strategies if you don’t notice the desired level of progress. 

Evaluate The Results:  

After you spot a solution, evaluate the results to determine whether it’s the best possible solution. For example, you can evaluate the success of a fitness routine after several weeks of exercise.

Meaning Of Problem-Solving Skill

Now that we’ve established the definition of problem-solving psychology in humans, let’s look at how we utilize our problem-solving skills.  These skills help you determine the source of a problem and how to effectively determine the solution. Problem-solving skills aren’t innate and can be mastered over time. Here are some important skills that are beneficial for finding solutions.

Communication

Communication is a critical skill when you have to work in teams.  If you and your colleagues have to work on a project together, you’ll have to collaborate with each other. In case of differences of opinion, you should be able to listen attentively and respond respectfully in order to successfully arrive at a solution.

As a problem-solver, you need to be able to research and identify underlying causes. You should never treat a problem lightly. In-depth study is imperative because often people identify only the symptoms and not the actual problem.

Once you have researched and identified the factors causing a problem, start working towards developing solutions. Your analytical skills can help you differentiate between effective and ineffective solutions.

Decision-Making

You’ll have to make a decision after you’ve identified the source and methods of solving a problem. If you’ve done your research and applied your analytical skills effectively, it’ll become easier for you to take a call or a decision.

Organizations really value decisive problem-solvers. Harappa Education’s   Defining Problems course will guide you on the path to developing a problem-solving mindset. Learn how to identify the different types of problems using the Types of Problems framework. Additionally, the SMART framework, which is a five-point tool, will teach you to create specific and actionable objectives to address problem statements and arrive at solutions. 

Explore topics & skills such as Problem Solving Skills , PICK Chart , How to Solve Problems & Barriers to Problem Solving from our Harappa Diaries blog section and develop your skills.

Thriversitybannersidenav

Book cover

Enabling Mathematics Learning of Struggling Students pp 265–290 Cite as

Additive Reasoning and Problem-Solving

  • Yan Ping Xin 6 &
  • Signe Kastberg 7  
  • First Online: 12 July 2022

737 Accesses

Part of the book series: Research in Mathematics Education ((RME))

In this chapter we illustrate how a computer-assisted intervention program, COMPS-A that integrates a constructivist view of learning and explicit teaching of mathematical model-based problem-solving, can help students with learning disabilities or difficulties in mathematics. Building on students’ development of fundamental ideas such as “number as the composite unit” (which naturally leads to the part-part-whole additive relationships), COMPS-A emphasizes students’ understanding and representation of mathematics relations in algebraic equations and, thus, supports growth in generalized problem-solving skills. Findings from empirical studies indicate that elementary students with learning difficulties in mathematics can be expected to move beyond concrete operations and toward thinking symbolically or algebraically. Algebraic conceptualizations of mathematical relations and model-based problem-solving can be taught through systematic strategy instruction. Introducing symbolic representation and algebraic thinking in earlier grades may facilitate a smoother transition from elementary to higher level mathematics and improve middle- and high school mathematics performance.

  • Learning disabilities
  • Learning difficulties
  • Elementary mathematics
  • Problem-solving
  • Computer-assisted instruction
  • Instructional strategies
  • Intervention
  • Word problem-solving
  • Model-based learning
  • Mathematical models
  • Mathematical relations
  • Additive reasoning
  • abstract level of representation
  • algebra readiness.

This is a preview of subscription content, log in via an institution .

Buying options

  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
  • Available as EPUB and PDF
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
  • Durable hardcover edition

Tax calculation will be finalised at checkout

Purchases are for personal use only

Effect size (ES) is used to measure the effectiveness of a treatment. EF is defined as the standardized mean difference between the experimental and the control group (Glass et al., 1981 ; Hedges & Olkin, 1985 ). An ES of 2.00 means 97.5% of students in the experimental group (e.g., received instruction in mathematical model-based representation and solving) performed better than the control group.

Blum, W., & Leiss, D. (2005). Modellieren mit der “Tanken”-Aufgaben. Mathematic Lehren, 128 , 18–21.

Google Scholar  

Blomhøj, M. (2004). Mathematical modelling – a theory for practice. In B. Clarke et al. (Eds.), International perspectives on learning and teaching mathematics (pp. 145–159). National Center for Mathematics Education.

Boulineau, T., Fore, C., Hagan-Burke, S., & Burke, M. D. (2004). Use of story-mapping to increase the story-grammar text comprehension of elementary students with learning disabilities. Learning Disability Quarterly, 27 (2), 105–121.

Article   Google Scholar  

Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Duran, R., Reed, B. S., et al. (1997). Learning by understanding: The role of multiple representations in learning algebra. American Educational Research Journal, 34 , 663–689.

Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2006). Learning mathematics in elementary and middle schools: A learner-centered approach (4th ed.). Pearson Merrill Prentice Hall.

Chappell, M. F., & Strutchens, M. E. (2001). Creating connections: Promoting algebraic thinking with concrete models. Mathematics Teaching in the Middle School, 7 (1), 20–25.

National Governors Association Center, & for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics . Authors.

Common Core State Standards Initiative. (2012). Introduction: Standards for mathematical practice. Retrieved from http://www.corestandards.org/the-standards/mathematics .

Cobb, P., & Merkel, G. (1989). Thinking strategies as an example of teaching arithmetic through problem solving. In P. Trafton (Ed.), New directions for elementary school mathematics: 1989 yearbook of the National Council of Teachers of Mathematics (pp. 70–81). NCTM.

Cobb, P., & Wheatley, G. (1988). Children’s initial understandings of ten. Focus on Learning Problems in Mathematics, 10 (3), 1–28.

Davydov, V. V. (1982). Psychological characteristics of the formation of mathematical operations in children. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and subtraction: Cognitive perspective (pp. 225–238). Lawrence Erlbaum Associates.

Dundar, S., Gokkurt, B., & Soylu, Y. (2012). Mathematical Modelling at a Glance: A Theoretical Study, Procedia – Social and Behavioral Sciences, 46 , 3465–3470.

Fuson, K. C., & Willis, G. B. (1988). Subtracting by counting up: More evidence. Journal for Research in Mathematics Education, 19 , 402–420.

Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79 , 1202–1242. https://doi.org/10.3102/0034654309334431

Glass, G. V., McGaw, B., & Smith, M. L. (1981). Meta-analysis in social research . Sage Publication.

Greer, B. (1992). Multiplication and division as models of situations. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 276–295). Macmillan.

Gurney, D., Gersten, R., Dimino, J., & Carnine, D. (1990). Story grammar: Effective literature instruction for high school students with learning disabilities. Journal of Learning Disabilities, 23 (6), 335–342, 348. https://doi.org/10.1177/002221949002300603

Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis . Academic Press.

Hughes, E. M., Witzel, B. S., Riccomini, P. J., Fries, K. M., & Kanyongo, G. Y. (2014). A meta-analysis of algebra interventions for learners with disabilities and struggling learners. The Journal of the International Association of Special Education, 15 (1), 36–47.

Jonassen, D. H. (2003). Designing research-based instruction for story problems. Educational Psychology Review, 15 , 267–296.

Karp, K. S., Bush, S. B., & Dougherty, B. J. (2014). 13 rules that expire. Teaching Children Mathematics, 21 (1), 18–25.

Kim, S. J., & Xin, Y. P. (2022). A Synthesis of Computer-Assisted Mathematical Word Problem-Solving Instruction for Students with Learning Disabilities or difficulties. Learning Disabilities: A Contemporary Journal, 20 (1). https://www.ldw-ldcj.org/images/Kim__Xin_2022.pdf

Lesh, R., Doerr, H. M., Carmona, G., & Hjalmarson, M. (2003). Beyond constructivism. Mathematical Thinking and Learning, 5 (2&3), 211–233.

Lewis, A. B., & Mayer, R. E. (1987). Students’ miscomprehension of relational statements in arithmetic word problems. Journal of Education & Psychology, 79 , 361–371.

Mayer, R. E. (1999). The promise of educational psychology Vol. I: Learning in the content areas . Merrill Prentice Hall.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Author.

National Assessment of Educational Progress result. (NAEP, 2019). Extracted from https://www.nationsreportcard.gov/mathematics/nation/scores/?grade=4

Olive, J. (2001). Children’s number sequences: An exploration of Steffe’s constructs and an extrapolation to rational numbers of arithmetic. Mathematical Education, 11 (1), 1–9.

Polotskaiaa, E., & Savardb, A. (2018). Using the Relational Paradigm: Effects on pupils’ reasoning in solving additive word problems. Research in Mathematics Education, 20 (1), 70–90. https://doi.org/10.1080/14794802.2018.1442740

Polya, G. (1957). How to solve it (2nd ed.). Doubleday.

Rand, R.H. (1984). Computer algebra in applied mathematics: An introduction to MACSYMA. Boston: Pitman.

Seel, N. M. (2017). Model-based learning: a synthesis of theory and research. Educational Technology Research and Development, 65 (4), 931–966. https://doi.org/10.1007/s11423-016-9507-9

Sowder, L. (1988). Children’s solutions of story problems. The Journal of Mathematical Behavior, 7 , 227–238.

Steffe, L. P., von Glasersfeld, E., Richards, J., & Cobb, P. (1983). Children’s counting types . Praeger.

Thompson, P. W. (1993). Quantitative reasoning, complexity, and additive structures. Educational Studies in Mathematics, 25 (3), 165–208. https://doi.org/10.1007/BF01273861

Tzur, R., Johnson, H. L., McClintock, E., Kenney, R. H., Xin, Y. P., Si, L., Woodward, J., Hord, C., & Jin, X. (2013). Distinguishing schemes and tasks in children’s development of multiplicative reasoning. PNA, 7 (3), 85–101.

Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching developmentally (5th ed.). Allyn & Bacon.

Walker, D. W., & Poteet, J. A. (1989–90). A comparison of two methods of teaching mathematics story problem-solving with learning disabled students. National Forum of Special Education Journal, 1 , 44–51.

Witzel, B. S. (2005). Using CRA to teach algebra to students with math difficulties in inclusive settings. Learning Disabilities: A Contemporary Journal, 3 (2), 49–60.

Wright, R., Stanger, G., Stafford, A., & Martland, J. (2007). Teaching number in the classroom with 4–8 year olds . Sage.

Xin, Y. P. (2012). Conceptual model-based problem solving: Teach students with learning difficulties to solve math problems. Sense. https://doi.org/10.1007/978-94-6209-104-7_1

Xin, Y. P. (2016). Conceptual model-based problem solving. In P. Fermer, J. Kilpatrick, & E. Pehkonen (Eds.), Posing and solving mathematical problems: Advances and new perspectives (pp. 231–254). Springers.

Chapter   Google Scholar  

Xin, Y. P. (2007). Word-problem-solving tasks presented in textbooks and their relation to student performance: A cross-curriculum comparison case study. The Journal of Educational Research, 100 , 347–359.

Xin, Y. P., Kim, S. J., Lei, Q., Wei, S., Liu, B., Wang, W., Kastberg, S., Chen, Y., Yang, X., Ma, X., & Richardson, S. E. (2020). The Impact of a Conceptual Model-based Intervention Program on math problem-solving performance of at-risk English learners. Reading and Writing Quarterly: Overcoming Learning Difficulties, 36 (2), 104-123. https://www.tandfonline.com/doi/full/10.1080/10573569.2019.1702909

Xin, Y. P., Kastberg, S., & Chen, V. (2015). Conceptual Model-based Problem Solving (COMPS): A response to intervention program for students with LDM . National Science Foundation (NSF) funded project.

Xin, Y. P., Liu, J., & Zheng, X. (2011). A cross-cultural lesson comparison on teaching the connection between multiplication and division. School Science and Mathematics, 111 (7), 354–367.

Xin, Y. P. (PI)., Wang, W., Van Nahmen, M. A., & Sanders, D. (2018). Conceptual Model-based Mathematics Intelligent Tutors (COMMIT), NSF I-Corps funded project.

Xin, Y. P., Wiles, B., & Lin, Y. (2008). Teaching conceptual model-based word-problem story grammar to enhance mathematics problem solving. Journal of Special Education, 42 (3), 163–178. https://doi.org/10.1177/0022466907312895

Zhang, D., & Xin, Y. P. (2012). A follow-up meta-analysis of word problem solving interventions for students with learning problems. The Journal of Educational Research, 105 (5), 303–318.

Zheng, X., Flynn, L. J., & Swanson, L. (2012). Experimental intervention studies on word problem solving and math disabilities: A selective analysis of the literature. Learning Disability Quarterly, 36 (2), 97–111. https://doi.org/10.1177/07319487124442

Download references

Acknowledgement

©All screenshots from the COMPS-A computer tutor presented in this chapter are copyrighted by the COMPS-RtI project ( i Xin et al., 2015 -2018). All rights reserved. Therefore, reproduction, modification, storage, in any form or by any means is strictly prohibited without prior written permission from the project director ([email protected]) and the authors.

i This research was funded by the National Science Foundation, under grant1503451. The opinions expressed do not necessarily reflect the views of the Foundation.

Author information

Authors and affiliations.

Department of Educational Studies, Purdue University, West Lafayette, IN, USA

Yan Ping Xin

Department of Curriculum and Instruction, Purdue University, West Lafayette, IN, USA

Signe Kastberg

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Yan Ping Xin .

Editor information

Editors and affiliations.

School of Education and Human Development, University of Colorado Denver, Denver, CO, USA

Institute of Education, St Mary’s University Twickenham, London, UK

Helen Thouless

Mixed Additive Word Problem-Solving Worksheet (Adapted from Xin, 2012 )

Kelsie said she had 82 apples. If Lee had 32 fewer apples than Kelsie, how many apples did Lee have?

Selina had some video games. Then, her brother Andy gave her 24 more video games. Now Selina has 67 video games. How many video games did Selina have in the beginning?

Taylor and her friend Wendy collect marbles. As of today, Taylor has 93 marbles. Taylor has 53 more marbles than Wendy. How many marbles does Wendy have?

Dana has 28 goldfish in her aquarium. She has 32 fewer goldfish than her friend Gesell. How many goldfish does Gisela have in her aquarium?

Gilbert had 56 paperback books. Then his brother, Sean, gave him some more paperback books. Now Gilbert has 113 paperback books. How many paperback books did Sean give Gilbert?

Adriana has 70 cows. Michelle has 35 fewer cows than Adriana. How many cows does Michelle have?

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Cite this chapter.

Xin, Y.P., Kastberg, S. (2022). Additive Reasoning and Problem-Solving. In: Xin, Y.P., Tzur, R., Thouless, H. (eds) Enabling Mathematics Learning of Struggling Students. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-95216-7_13

Download citation

DOI : https://doi.org/10.1007/978-3-030-95216-7_13

Published : 12 July 2022

Publisher Name : Springer, Cham

Print ISBN : 978-3-030-95215-0

Online ISBN : 978-3-030-95216-7

eBook Packages : Education Education (R0)

Share this chapter

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • Publish with us

Policies and ethics

  • Find a journal
  • Track your research

COMMENTS

  1. 7 Module 7: Thinking, Reasoning, and Problem-Solving

    Module 7: Thinking, Reasoning, and Problem-Solving. This module is about how a solid working knowledge of psychological principles can help you to think more effectively, so you can succeed in school and life. You might be inclined to believe that—because you have been thinking for as long as you can remember, because you are able to figure ...

  2. Fluency, Reasoning and Problem Solving: What They REALLY Look Like

    In that paper he produces this pyramid: This is important for two reasons: 1) It splits up reasoning skills and problem solving into two different entities. 2) It demonstrates that fluency is not something to be rushed through to get to the 'problem solving' stage but is rather the foundation of problem solving.

  3. Fluency, Reasoning & Problem Solving: What They REALLY Are

    This was a frequent feature of my lessons up until last academic year: teach a mathematical procedure; get the students to do about 10 of them in their books; mark these and if the majority were correct, model some reasoning/problem solving questions from the same content as the fluency content; give the students some reasoning and word problem ...

  4. Ch 8: Thinking and Language

    A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A "rule of thumb" is an example of a heuristic.

  5. The Problem-Solving Process

    Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue. The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything ...

  6. 7.3 Problem-Solving

    Additional Problem Solving Strategies:. Abstraction - refers to solving the problem within a model of the situation before applying it to reality.; Analogy - is using a solution that solves a similar problem.; Brainstorming - refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal ...

  7. Thinking, Language, and Problem Solving

    Cognitive psychology is the field of psychology dedicated to examining how people think. It attempts to explain how and why we think the way we do by studying the interactions among human thinking, emotion, creativity, language, and problem solving, in addition to other cognitive processes. Cognitive psychologists strive to determine and ...

  8. Solving Problems

    Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (Figure 1) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4.

  9. 5 Knowledge and Reasoning

    Problem-based learning emphasizes that memories are not simply stored to allow future reminiscing, but are formed so that they can be used, reshaped, and flexibly adapted to serve broad reasoning needs. The goal of problem-based learning is to instill in learners flexible knowledge use, effective problem-solving skills, self-directed learning ...

  10. Problem Solving

    Abstract. This chapter follows the historical development of research on problem solving. It begins with a description of two research traditions that addressed different aspects of the problem-solving process: (1) research on problem representation (the Gestalt legacy) that examined how people understand the problem at hand, and (2) research on search in a problem space (the legacy of Newell ...

  11. What is Problem Solving? Steps, Process & Techniques

    Finding a suitable solution for issues can be accomplished by following the basic four-step problem-solving process and methodology outlined below. Step. Characteristics. 1. Define the problem. Differentiate fact from opinion. Specify underlying causes. Consult each faction involved for information. State the problem specifically.

  12. Associations Between Conceptual Reasoning, Problem Solving, and

    Abstract thinking is generally highly correlated with problem-solving ability which is predictive of better adaptive functioning. Measures of conceptual reasoning, an ecologically-valid laboratory measure of problem-solving, and a report measure of adaptive functioning in the natural environment, were administered to children and adults with and without autism.

  13. Problem-Solving Strategies: Definition and 5 Techniques to Try

    In insight problem-solving, the cognitive processes that help you solve a problem happen outside your conscious awareness. 4. Working backward. Working backward is a problem-solving approach often ...

  14. What Are Critical Thinking Skills and Why Are They Important?

    Problem-solving: Problem-solving is perhaps the most important skill that critical thinkers can possess. The ability to solve issues and bounce back from conflict is what helps you succeed, be a leader, and effect change. One way to properly solve problems is to first recognize there's a problem that needs solving.

  15. Thinking and Intelligence

    When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution. A problem-solving strategy is ...

  16. What Is Cognition?

    Cognitive psychology is the field of psychology dedicated to examining how people think. It attempts to explain how and why we think the way we do by studying the interactions among human thinking, emotion, creativity, language, and problem solving, in addition to other cognitive processes. Cognitive psychologists strive to determine and ...

  17. Word problems in mathematics education: a survey

    Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and debates that have dominated the field. After a ...

  18. Problem Solving in Mathematics Education

    1.1 Role of Heuristics for Problem Solving—Regina Bruder. The origin of the word heuristic dates back to the time of Archimedes and is said to have come out of one of the famous stories told about this great mathematician and inventor. The King of Syracuse asked Archimedes to check whether his new wreath was really made of pure gold. Archimedes struggled with this task and it was not until ...

  19. Problem Solving

    Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( [link]) is a 4×4 grid.

  20. Reasoning and Problem Solving

    Maturity in reasoning and problem-solving is achieved with increasing age, life experience, and the ability to learn from mistakes. These are important skills that help us navigate simple and complex problems. The reasoning is arriving at a decision or conclusion, whereas problem-solving is finding the best solution to a problem.

  21. PDF Conceptual Understanding, Procedural Knowledge and Problem- Solving

    Standards for School Mathematics (National Council of Teachers of Mathematics, 2000). Problem solving involves students applying four processes: reasoning, communication, connections, and representation. Problem solving can also provide opportunities for students to apply content knowledge in all five mathematic domains. Problem solving

  22. What Is Problem Solving?

    At its simplest, the meaning of problem-solving is the process of defining a problem, determining its cause, and implementing a solution. The definition of problem-solving is rooted in the fact that as humans, we exert control over our environment through solutions. We move forward in life when we solve problems and make decisions.

  23. Additive Reasoning and Problem-Solving

    The goal of the COMPS-A program was to help elementary students construct mathematical model-based reasoning and problem-solving. The program includes two modules. Module A nurtures children to develop more sophisticated ways of counting, as a spring board to the construction of part-part-whole relations.