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A guide to successful questioning

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Why is questioning important?

Teachers are almost always asking questions. But the types of questions asked and the kinds of responses students have to generate can have very different effects on students’ learning. Questions that engage students in complex thinking can increase students’ curiosity, develop their problem-solving skills, improve their engagement and strengthen their ability to persevere.

Well-crafted questions also help students to make connections between ideas, and to develop personal meaning and associations with previously learned content. When students are challenged to explain, listen and problem solve, they develop important thinking skills, strategies for working with content, and networks of ideas.

Instead of directly giving information to students, teachers can involve students actively in learning through carefully sequenced questions which encourage students to draw on current cues and past experiences to think through a problem for themselves. This typically leads to students experiencing a greater sense of success and self-efficacy. Questioning helps students discover, evaluate and apply content, and leads to better long-term recall.

How to improve your questioning

Effective teachers ask some direct and specific questions which help them to monitor students’ progress and understanding. However, they spend a significant proportion of time asking higher-order questions that encourage students to think (and provide students with time to think), and to give lengthy answers, including explanations and justifications.

In responding to questions, teachers should avoid designating a student as right or wrong , which effectively closes the dialogue. Instead effective teachers ask follow-up questions to probe and clarify a student’s thinking. Well-designed questions elicit evidence of students’ current understandings (and misunderstandings), and scaffold students’ thinking by helping students make connections between their existing knowledge and the new problems of learning.

Four ways to improve questioning

  • Make sure questions are demanding.
  • Allow enough time for students to think about answers.
  • Involve as many students as possible in thinking about answers to a question.
  • Follow up incorrect responses with probing or scaffolding for the correct answer.

How to make your questions more demanding

Although every lesson will involve questions that invite students to recall facts and knowledge (such as “what does a plant need to grow?”; “what is the answer to this maths problem?”), it is important to ask questions that get students to think at a higher level. You should therefore aim for a mix of product questions (which elicit a single correct/incorrect response from students) and process questions (such as asking students to give explanations).

When quickfire, factual questions predominate, classroom discourse takes the pattern of teacher initiation (the question), a student’s (short) response, and teacher evaluation (correct or incorrect). In these kinds of exchanges, teacher talk and direction dominate, and student apathy and boredom are common.

However, if questioning is used to encourage sustained dialogue , students are more intellectually stimulated and engaged, and do most of the talking, which means they are doing a lot more thinking. Student interest is engaged by stimulating discussion provoked by interesting questions . Try to ask questions that students have not been asked before .

Higher-level questions often involve the application of knowledge in ways that solidify students’ understanding. Questions should encourage students to think and construct answers, rather than to recite information . Higher-level questions involve students in using information and concepts to solve a problem , with at least two steps required to producing an answer, or a choice of steps or sources, necessitating strategic thinking . Compare, for example, asking students to describe the process of photosynthesis (recall) with asking students to suggest how they would go about determining the cause of a plant failing to thrive.

Good questions get students describing, summarising, evaluating, ranking, interpreting, explaining, assessing, planning, predicting, differentiating, classifying, concluding, relating and extending.

Note that making changes to your questioning practice can be challenging for students whose experience is of questions that require the recall of information or the repetitive performance of a procedure. Students might need time and support to go beyond their comfort zone.

Seven ways to make your questions more demanding

  • Pre-plan your questions. It’s often hard to think of higher-level questions on the spot. And often we default to asking low-level repetitive questions.
  • Make questions the cornerstones of learning . Consider having a ‘question plan’ rather than a ‘lesson plan’. Perhaps even set questions as learning objectives and explain to students that these are the questions they will be able to answer at the end of the lesson.
  • Follow factual questions with questions that inspire thought. This connects prior knowledge (recall) to problem solving and ongoing learning.
  • Use straightforward language . Formulate questions using simple language so that they remain understandable.
  • Keep questions short. This helps students not to lose the intent of the question. Consider breaking longer questions into several questions or split questions into parts.
  • Ensure students have the necessary knowledge to answer higher-order questions. Ensure that you teach the background information and concepts that students need in order to think at a deeper level (this might be new information for some students, or useful as a prompt to prior knowledge for others).
  • Ask questions that get students to make connections. Plan questions by considering the background knowledge and vocabulary that students need to understand the topic, what connections can be made with what students’ already know, and what real-world connections can be made to relate concepts to their purpose and importance outside of school.

Verbs to base questions upon

Remember/recall: define, describe, identify, label, match, list, name, select

Understand: clarify, demonstrate, describe, expand, explain, summarise, retell

Apply: calculate, compare, contrast, convert, demonstrate, determine, elaborate

Analyse : categorise, classify, compare, confirm, contrast, diagram, prove/disprove, illustrate, infer, simplify

Evaluate: criticise, decide, defend, discover, explain, interpret, judge, justify, predict

Create: construct, design, develop, devise, extrapolate, generate, illustrate, improve, produce

Adapted from Depka, E. (2017). Raising the rigour: Effective questioning strategies and techniques for the classroom. Bloomington, IN: Solution Tree Press.

“ Remember, expand, elaborate, add evidence ”

One way to promote fuller, more thoughtful and higher quality responses from students is to develop a classroom expectation for every response to include the following set of actions:

  • remember (recite or list information)
  • expand (add more information)
  • elaborate (add their own thinking)
  • add evidence or examples (give reasons for their opinions).

Templates can help students use the pattern until its components have been internalised and students can provide responses that include the four categories without it. Checking use of the format could also be an exercise for peer assessment.

‘ Wicked ’ questions

Ask ‘wicked’ questions to provoke discussion and reasoning and build students’ confidence with higher-level thinking. Wicked questions are questions with no obvious right answer, or with more than one answer. They can be questions that provoke or divide opinion, or that challenge students’ assumptions or present a paradox. These kinds of questions are open-ended and consider everyday topics in which all students could have an initial opinion as they are not solely dependent on background knowledge. They help students create a meaningful connection to a topic before learning more about it.

Through discussion of these kinds of questions, students with less experience with the topic have opportunities to build background knowledge by listening to other students. Wicked question can be used for collaborative work, and students can be asked to present, challenge or defend their positions. These questions can also be revisited after a unit of study so that new learning can be incorporated into students’ thinking about the topic.

Example ‘wicked’ questions:

Is there more love than hate in the world?

Is it OK to bully a bully?

Does charity simply increase the need for charities?

What causes conflict? In an argument, is one person always right?

How to allow enough time for student thinking 

Teachers often leave as little as a second for student thinking, which is not enough time for students to process the question or to formulate an answer. Think of questions as fast or slow: fast questions are low-level questions that students know the answer to without having to think, such as names or dates. Slow thinking questions are those that require a bit more cognitive processing, making students think, for example, by asking them to analyse or evaluate in order to arrive at an answer.

Try to keep a balance of fast and slow thinking questions. For example, if you check students’ knowledge of dates, names and places in a history lesson, go on to ask richer questions that compare and contrast events or explain why a date is important historically. In general, slow thinking questions make the greatest cognitive demand on students and lead to greater learning.

The use of a ‘wait time’ after asking a question can increase the amount of thinking time and increase student participation. Time your pause – use a timer, or your smartphone or a Powerpoint timer. The most effective wait time will probably vary from class to class, but three to five seconds should be sufficient. Pausing again after receiving an answer from a student can also increase student thinking and participation.

Pause … Pause … Share … (PPS)

P: The teacher asks a question and pauses without giving or taking an answer

P: The teacher signals they will take an answer, then reflects this answer back to the group, asking the group if they think the answer is correct or if anyone can expand on the answer. There then follows a second pause without the teacher giving or taking an answer.

S: The teacher takes a final answer and then shares and expands upon the answer with the group.

Spendlove, D. (2015). 100 ideas for secondary school teachers: Assessment for learning. London, England: Bloomsbury Education.

How to involve as many students as possible in thinking about answers

Only about 25 per cent of students are usually involved in classroom questioning. Research shows teachers tend to take more responses from those students that appear to know the answers to questions as well as from those in the front row of desks. It is often the same students who throw their hands up, eager to respond, which denies other students time to think about the answer. Those students who sit on the periphery (the back and corners) are asked fewest questions.

Have a ‘hands down, heads up’ rule .

Explain to students that this means that the question you are about to ask requires thinking about and everyone will need to have an answer. Then select a student to answer the question. This strategy is essential for increasing the amount of thinking taking place in a lesson. Finally, ensure your questions are directed to different students. Once students know that there is a high probability of being asked a question, they will participate in thinking about every question you pose, just in case. Therefore, it is important to ask the question before stating who is to respond.

Methods for the random selection of students for response

  • Alternate questions between boys and girls (also consider how you respond to students of different genders; research shows teachers tend to give fuller explanations to girls).
  • Move questions around in a pre-determined pattern, for example, starting at the corners and working your way in.
  • Use random name generators (lollysticks or counters with names on) so that all students are equally likely to be asked a question.
  • Throw a beanbag, call or other appropriate object for the person answering the question to hold – this is good for changing students’ point of attention too.

Three strategies for increasing participation

  • ‘Phone a friend’ : Make it your classroom culture that not knowing the answer is not a way of getting out of responding. Invent a ritual that you adopt for a “don’t know”, such as ‘phone a friend’ for a clue, for example.
  • Share with a partner : Have students share their thinking with a partner before taking answers to a question. Ask a big question, and give ‘wait time’ so that students consider their individual response. Then ask them to discuss the question with a partner to arrive at a joint response, and take as many joint response answers as desired. Experiment with pairings: try mixed ability and mixed gender pairings.
  • Targeted questioning : You might also try identifying specific questions you need to ask of particular students in your planning, which is called targeted questioning. Here a question is planned as an intervention in students’ learning, for example, relating to misconceptions, or to monitor their understanding of the learning so far.

How to follow up responses

If a student gives a wrong answer, don’t move on to the next student, but probe for, or scaffold, the student towards, the correct answer. Some strategies you could try:

  • Acknowledge if the student is partially correct, and affirm the correct part .
  • Use an ‘echo’ strategy to help students construct their answers, for example, when a student gives a partial answer, reflect their answer back to them, or ask clarifying questions, or rephrase the question to help them build a clearer and fuller response.
  • Use questioning to scaffold students to the right answer , for example, directing them to think about relevant information they have or to relate prior experiences to the problem.
  • Even where students’ responses are correct, challenge students’ accuracy and completeness in order to achieve a deeper understanding. However, it’s also important to be clear when students have provided the correct answer, for both that student’s learning and the learning of the class.

Taking questioning further

Use self-analysis, audio or video recording or peer observation to assess your questioning.

Ask a colleague to observe a lesson and map where the questions are directed to in your classroom, or to code the types of question you ask.

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  • Center for Innovative Teaching and Learning
  • Instructional Guide

Questioning Strategies to Engage Students

Asking students challenging and thought-provoking questions encourages students to tap their existing mental models and build upon previous knowledge. Faculty can ask key questions to get students to see the relevance of a topic. In turn, it is hoped that students will then ask follow-up questions, engaging in dialogue while critically analyzing viewpoints shared. Therefore, by encouraging students to ask questions faculty provide opportunities for students to become actively engaged in the learning process while also developing valuable metacognitive skills that will benefit them the rest of their lives.

. . . by encouraging students to ask questions faculty provide opportunities for students to...[develop] valuable metacognitive skills that will benefit them the rest of their lives.

This article shares tips for designing and asking effective questions, during the beginning, middle and end of class, as well as asking questions outside of class.

Tips for Designing and Asking Effective Questions

In his book, The Craft of Teaching , Kenneth E. Eble (1988) shows the essential connection between “the art of asking questions” with meaningful class discussions (p. 88-89). Eble suggests “three cardinal principles” when forming questions:

  • “Ask real questions even though they may seem off-hand, simple, or imprecise.” Avoid using stock questions that fail to match course content and worst of all, your teaching style. Instead, form questions that are related to course content, current and ongoing discussions, and ones that are interesting to your students. Finding students’ interests can be achieved through an early course survey and more intimate classroom discussions.
  • “Be ingeniously responsive to the students’ answers and questions.” Class conversations, as Eble suggests, should be accepting of all points of view, whether or not the answer is correct, “vague, wandering, irritating, or whatever” (1988, p. 89). In other words, everyone should feel comfortable answering questions without fear of ridicule, non-acceptance, or laughter. This is especially important when asking questions in a classroom of diverse learners. Some students not educated in western cultures may not be comfortable answering questions—they learned by listening to more autocratic instructors and did not ask questions because doing so questioned the authority of the instructor. Other students could have learning disabilities or are fearful of speaking in class. It is important, then, to create a learning environment in which you welcome and encourage questions. Model your expectations at the beginning of the semester and provide examples of ways you expect questions to be asked and answered. “Never deliberately ignore a question or demean the questioner” (Eble, 1988, p. 89). If class time is coming to an end and you feel students have questions yet to ask, have them write the questions on a note card that they submit before leaving class. You can address these questions at the beginning of the next class period or comment directly on the card which you can return to the student.
  • “Try to achieve a rhythm in a series of questions so that the group arrives at moments of larger understanding.” Prepare a series of questions that begin with less complicated content that eventually leads to more complex content. Present questions with just enough information to encourage students to think deeply and form a meaningful answer. Instead of expecting one person to answer the question, ask students to pair up and discuss the question and prepare a shared answer—this allows them to talk about and share their collective knowledge with the class.

Avoid using language that is ambiguous or not yet relevant to course content. Do not assume students know the “terminology du jour.” Asking vague questions by virtue of ambiguous or out-of-context language may elicit vague answers. Therefore, “questions should be definite and unmistakable” (Eble, 1988, p. 90, citing Fitch).

Avoid using language that is ambiguous or not yet relevant to course content.

The following tips and techniques have been compiled from of a number of sources (see references) that provide ways to prepare and deliver effective questions in the classroom. Although this list is not exhaustive, the points provide a range of ways to integrate questions in the classroom. The list begins with preparing questions and ends with ways questions can be used outside the classroom.

Preparing Questions

First and foremost, design course goals and learning objectives to help students achieve what you want them to learn. Once course goals and objectives have been developed you can begin to prepare complementary and effective questions.

Get acquainted with your students so you can customize questions that challenge them to think more critically about course content to help them learn. This does not mean that you must scrap the foundations, key concepts and content that drives your course. It means, however, that you can meet your students along the way—to challenge the knowledge they bring to the classroom and to present content through questions that is useful and relevant to them.

...customize questions that challenge them to think more critically about course content to help them learn.

Questions to Ask Students at the Beginning of Class

  • Arrive in the classroom early to help students who have questions about previous lectures, readings and exam preparation.
  • Begin the semester—the very first class, by asking students the type of questions you plan to ask throughout the semester. This will set the stage for the class, and help students form more complete impressions and establish expectations
  • “How will the proposed economic stimulus package affect you as a college student?” 
  • “Why should we be concerned about melting arctic ice?”
  • “How will your successful completion of this class prepare you to enter the work force?”
  • Why did some societies get in boats and go bother other people while others stayed at home and tended to their own affairs?
  • Why are human beings occasionally willing to leave home and hearth and march off into the wilderness, desert, or jungle and kill each other in large numbers?
  • Why are some people poor and other people rich?
  • How does your brain work?
  • What is the chemistry of life?
  • Can people improve their basic intelligence?
Ask provocative questions to energize students into saying something.
  • Tell stories about your life, your friends, and other people that provide meaning to the topic of the day. Stories can provide the springboard some students might need to ask questions. For example, as an instructor in a University Experience class, you could tell the story of your first experiences away at college and some of your struggles with study and time management skills. Personal stories might compel students to ask questions about study skills, time management and taking exams.

Questions to Ask Students During Class

  • Teach with the notion that students are naturally curious and have them “develop an intrinsic interest that guides their quest for knowledge, and an intrinsic interest…that can diminish in the face of extrinsic rewards and punishments that appear to manipulate their focus” (Bain, 2004, pp. 46-47). In other words, provide content in such a way that students can see how it can be used in their professions and the relevance of course content to job-related skills. Provide meaningful comments on graded papers and exams—show them the “why” so they can learn “how” to improve.
. . . provide content in such a way that students can see how it can be used in their professions and the relevance of course content to job-related skills.
  • Be aware of how you present questions—do you ask questions in a friendly or authoritative manner? What is the purpose of asking questions? Do you want your students to learn from the question or are you asking the question “just because”?
  • Avoid “schooling” where “bulimic learners” (Bain, 2004, p. 40, citing Nelson) memorize facts and short-ranged information to later purge, “making room for the next feeding” (Bain, 2004, p. 41).  This “force fed” competitive-type of schooling reduces students to be mere receptors of information to compete for grades and have little interest in learning something new.
  • Incorporate relevant vocabulary when responding to a student’s question. For example, when a student asks why her computer is not operating as fast as it had been, you can tell her that she might need more RAM. The student can then ask, “What is RAM?” a question she would not have asked except in this context (the idea for this example was improvised from Bain, 2004, p. 104).
  • Ask students to bring one or two questions to class based on textbook readings or content covered in the previous class. Provide some sample questions to help students write meaningful questions. These questions can then be submitted (a good way to take attendance) and randomly addressed at the beginning of the class period or used to develop exam questions.
  • Avoid answering your own question by giving students a few seconds to form a good answer. If the first answer is not what you had expected, do not discount the effort the student has made. Instead, ask the student if they could re-phrase their answer or to elaborate a bit more. If they are still having some difficulty, ask another student to help form the correct answer. Ask questions that students can think for themselves (McComas & Abraham, 2004).
Avoid answering your own question by giving students a few seconds to form a good answer.
  • Engage other students by having them answer the question of one of their peers. It has been shown that students can learn from other students if given the opportunity to do so.

  Questions to Ask Students at the End of Class

  • “What questions do you still have about today’s topic?”
  • “If you were to ask one last question, what would it be?”
  • “What was the muddiest point today?”
  • “What was the most meaningful point we covered today?”
  • Ask end-of –class questions to help students synthesize the information and draw conclusions. Their responses to one last question and muddiest point can be submitted for your review—you can address student issues at the beginning of the next class period or review to clarify content.
  • Make notes about how students responded to questions asked during the class as well as the type of questions students asked of you. These notes can help you prepare for and modify subsequent classes (Gross Davis, 1993 citing Kasulis).

Questions to Ask Students Outside the Classroom

  • “Please take particular note of pages 13-14 of Kaisha’s article in which he comments on decision-making in Japanese business. Recall our discussion of decision-making in the American auto industry last week. What comparisons and contrasts can you draw between the two approaches to decision making? We will be using these two approaches in a simulated decision-making exercise Thursday” (Meyers and Jones, 1993, p. 129).
  • What [material from] the chapter do you think we should review?
  • What item in the chapter surprised you?
  • What topic in the chapter can you apply to your own experience? (Meyers and Jones, 1993, p. 130 citing Gaede).
  • Finally, use online discussion boards to pose questions that can help extend course content asynchronously. Online discussion boards give students extra time to form their answers and can benefit those students who are less inclined to join in on face-to-face class discussions.

Using questions in the classroom can help students engage with course content, the instructor, and other students. Good instructor-generated questions can also guide students in developing better answers and help them to form questions of their own.

Good instructor-generated questions can also guide students in developing ... questions of their own.

Bain, K. (2004). What the best college teachers do. Cambridge, MA: Harvard University Press.

Eble, K. E. (1988). The craft of teaching (2nd.ed.). San Francisco, CA: Jossey-Bass Publishers.

Gross Davis, B. (1993). Tools for teaching. San Francisco, CA: Jossey-Bass Publishers.

Meyers, C., & Jones, T. B. (1993). Promoting active learning: Strategies for the college classroom. San Francisco, CA: Jossey-Bass.

McComas, W. F., & Abraham, L. (2004). Asking more effective questions. http://cet.usc.edu/resources/teaching_learning/docs/Asking_Better_Questions.pdf

Selected Resources

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Suggested citation

Northern Illinois University Center for Innovative Teaching and Learning. (2012). Questioning strategies to engage students. In Instructional guide for university faculty and teaching assistants. Retrieved from https://www.niu.edu/citl/resources/guides/instructional-guide

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Practice makes perfect, but mix it up

By Fraser Scott 2022-03-24T08:30:00+00:00

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Does question bank design affect student performance?

We know it is important to provide students with repeated opportunities to practise solving questions. In a new study, researchers examined how the presentation and format of practice questions influences students’ problem-solving performance. The study revealed that mixed problem sets are better than questions arranged by topic.

There are two types of question practice teachers can give their students. The first, blocked practice, involves solving multiple problems of the same type, or about the same concept, before moving on to another. Practice worksheets and end-of-chapter questions in textbooks are often blocked practice type questions. They hone students’ algorithmic problem-solving skills, but at the expense of their conceptual understanding of the topic. The second, interleaved practice, shuffles between different types of questions in one session. It is more difficult, because students must identify the type of question being asked, or the concept it relates to, in addition to answering. Shuffled questions are thought to help with long-term learning and are similar to the questioning format in students’ exams.

The researchers investigated the effects of these two kinds of practice. They recruited 79 university students from general chemistry classes. They gave one group assignments with mixed questions and a control group assignments with questions organised into topics or chapters. They compared the groups’ performances through one pre-test and post-test after each of three problem-solving sessions.

Teaching tips

  • Source or compile more mixed practice question banks, and avoid solely using topic-specific question sets from textbooks.
  • To increase the difficulty and benefits of mixed problem question sets, do not include details identifying the relevant topics or chapters.
  • Blocked practice still has a place. Certain topics, particularly those to do with numerical problem-solving, may require extensive blocked practice before students can engage with the benefits of interleaved practice.

Probing the problems

Rather than looking at overall scores, the researchers used a more detailed analysis. They broke each problem into the sub-problems, or steps, required to answer the problem. They then categorised students’ answers to the steps as successful, neutral or unsuccessful. Subcategories provided more insight into the students’ work. For example, the neutral category contained the subcategories ‘not required’, ‘did not know to do’ and ‘did something else’.

The study revealed that students in the interleaved-practice group increased their problem-solving success more than those in the blocked-practice group. Significantly, the achievement gap between the experimental and control groups widened as the study progressed. Following interleaved practice, students’ neutral codes decreased by about 70%, unsuccessful codes decreased by about 40%, and the successful codes increased by about 52%. Even if students were not able to complete the entire problem, they still improved at individual steps.

Importantly, even though A-, B- and C-grade students showed different levels of improvement, they all benefited from interleaved practice. Perhaps unexpectedly, B- and C-grade students improved the most. This might relate to their poorer conceptual understanding of topics or assessment literacy beforehand, which interleaved practice helps to develop.

Fraser Scott

O. Gulacar et al, Chem. Educ. Res. Pract., 2022, DOI: 10.1039/D1RP00334H

O. Gulacar et al,  Chem. Educ. Res. Pract.,  2022,  23 , 422–435 ( DOI: 10.1039/D1RP00334H )

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Expert vs. novice problem solvers, communicate.

  • Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
  • If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
  • In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
  • When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

  • Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
  • Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
  • Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

  • Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

  • Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

questions to ask students about problem solving

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Guiding Students to Be Independent Problem-Solvers in STEM Classrooms

Teaching high school students how to plan to solve a problem in science, technology, engineering, and math is a crucial step.

High school students working together in class

Teaching students to become independent problem-solvers can be a challenging task, especially with virtual teaching during the pandemic. For some students, solving problems is not intuitive, and they need to learn how to think about solving problems from a general perspective. As experts, teachers often do not realize that there are implicit skills and ways of thinking that may not be obvious or known to our students.

5 Strategies to Explicitly Model and Teach Problem-Solving Skills

1. Model hidden thinking involved in solving a problem. When solving a problem, I talk about every aspect of what I am doing out loud. In fact, I over-talk, providing reasoning for every step. For example, when solving a dimensional-analysis problem, I will include descriptions like, “OK, I am going to look for any numbers that I can cancel. I know I can cancel or reduce if I see a number in the numerator and another number in the denominator that have a common factor.”

I will even include moments of vulnerability and model the fact that I don’t always know what to do, but I will discuss my options and my decision process. I sometimes intentionally make mistakes and then use methods to check my work to correct my errors. It’s essential that we explicitly show students this internal dialogue to model problem-solving.

2. Facilitate student talk during problem-solving. I do my best to never solve problems for students, even if they ask me. This includes whole-class lessons and working with students in small groups or individually. Using the Socratic method, I ask many questions of the students. The questions can be as simple as “What do we do next?” or “What are options of what we can do?”

Once during a classroom observation, I was told that in a span of 10 minutes, I asked more than 72 questions. This models the questions that the students can use in self-talk to guide them in the problem-solving process. After the first test, many students say that they could hear my voice asking them the same questions over and over, but what they’re really learning are advanced problem-solving skills they can extend to future contexts.

We can also provide deeper understanding with questions such as “Why do we do that?” These provide reasoning and value to the actions of each step in the problem-solving process, further solidifying the students’ understanding of the concepts and skills.

3. Include discussion for planning for each problem. Teachers instinctively plan problems. Students, as novice learners, often do not know how to plan a problem. They look at a problem, see it as foreign, and don’t know where to begin. They give up.

Research shows that planning how to solve the problem is an essential step for novice learners. Provide a structure or protocol for students. It can include the following: identify and write the data with units for a problem, identify equations to be used, identify and write what they’re trying to solve for, draw a relevant vector diagram, and brainstorm possible steps.

4. Emphasize the process, not final answers. Often, when checking individual work, we ask for the final answers. But what if instead of asking who has the answer, we ask who has the method to solve it? When students ask for correct answers, it’s natural to provide an immediate response. Instead, we should reply with guiding questions to facilitate the process of their solving the problems for themselves.

Often, I don’t even calculate the answer in the final step and ask if we all agree on the steps. The conversation is especially valuable when different methods are volunteered, and we can analyze the advantages of each. I want the students to check our work and not look at a simple result at the end of the problem to confirm their work. This shifts students’ attention to look at the details of the steps and not glance at the end of the work for the final answer. Further, grading can include points for steps and not the final solution.

5. Teach explicitly problem solving. After solving problems, students can create their own problem-solving strategy that they write on a note card. Collect responses from students and create a class protocol that you post on your learning management system or in your physical classroom space. Scaffold further with a two-column approach. In the left column, students show the work, and in the right column, they explain and justify what they did and why. The act of adding a justification will make students think about their actions. This will improve the connection between conceptual ideas and the problem-solving itself.

These are only a few strategies to get your students intentionally thinking about problem-solving from a general perspective beyond focusing on specific problems and memorizing steps. There are many ways to model and teach the skill of problem-solving that encourage them to think about the process explicitly.

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  • Solving Problems with Twenty Questions
  • Social Education
  • Social Education November/December 2021

William D. Edgington

Journal Issue:

How many times have we teachers thrown up our arms in exasperation and wanted to inquire of a student or a group of students, “What were you thinking?” How many times a day do we advise our students to “make good choices” and then cringe when they don’t?

All too often, students don’t, or can’t, simply because they don’t know how. Although we know that our students are constantly involved in a thinking process, we tend to take that process for granted, rationalizing that thinking is simply something that everybody does. The term thinking skills is itself broad and ambiguous. Turner refers to the “mental processes that individuals use to obtain, make sense of, and retain information, as well as how they process and use that information as a basis for solving problems.” 1 In social studies, we want to foster active citizens who have the ability to process information rationally to solve problems.

Yet many teachers are uncertain of how these skills are acquired. Too often, the idea of teaching thinking skills is synonymous with having students answer questions at the end of a chapter or recite material. My preservice methods students are often surprised that they will be responsible for teaching thinking skills in social studies instruction. Some students assume such an endeavor will be complicated and demanding; others believe that the questions written in blue ink in the margin of the teacher’s edition of textbooks will serve the purpose of “getting” children to think. But with planning and foresight, thinking skills strategies can be valuable tools in helping make the curriculum relevant, realistic, and stimulating to students. When teaching thinking skills through social studies instructions, teachers must not give these skills token attention or teach them in isolation, but must integrate them meaningfully into the curriculum.

An integral part of social studies instruction—and a key thinking skil#151;is problem solving. As defined by Hoge, problem solving is “finding the means to a distinctly conceived end or goal,” 2 and involves various formal strategies to reach that goal. As with the teaching of any thinking skill in social studies, problem solving skills need to be taught systematically, and this is next to impossible if teachers rely on the textbook for questions. As students become familiar with the process, they may need less time for actual instruction, practice, and feedback.

Steps in Problem Solving

The problem solving model, also referred to as discovery learning or inquiry , is a version of the scientific method and focuses on examining content. As applied to social studies instruction, the steps include the following:

• Define or perceive the problem. (The students are presented with a problem or question for which there is no immediate solution.)

• Formulate the hypothesis. (The students guess the causes of a problem.)

• Gather the data. (Information, either provided by the teacher or gathered by the students, is collected.)

• Evaluate or analyze the data. (The students examine and reflect on the information.)

• Use the data to confirm or reject the hypothesis. (The students use their reflections to help them consider whether their initial explanations are accurate.)

• Explain or reach a conclusion. (The students formulate and state their explanation for the original problem.)

Often, teachers see the practicality of such an approach in science but not in social studies. This misperception is ironic because social studies is filled with asking “why” and “how,” and most students are naturally curious about people and experiences, past and present.

Twenty Questions

Perhaps the simplest example of inquiry thinking is the game of Twenty Questions. By asking questions that the teacher answers with yes or no responses, students attempt to solve a problem put before them before they ask their twentieth question. Usually it is a whole-group activity, but it may be played in small groups or individually. Questions may be asked in a variety of formats: The students may take turns asking questions or each student may ask a series of questions in a row. Students may also work in pairs to formulate questions.

When first exposed to the game, the students’ questions are often random and haphazard, but with practice and the aid of the teacher, the students learn that they are working their way through the steps of inquiry as they play the game, and their questioning strategies become more sophisticated. Gathering data by asking questions, students use the answers to analyze and confirm or reject their hypotheses. For example, students can discover what led to the death of Sir Thomas More (see Box A), why Dalmatians have traditionally been the mascots of fire fighters, or why civilizations generally began near water. Applying Twenty Questions to social studies instruction involves the following steps.

1. The students understand that they must find the answer to the problem that the teacher has put before them.

2. The students guess or reason what they believe is the answer to the problem.

3. By asking questions of the teacher, the students gather data to solve the problem.

4. The students use the information to reflect on and determine whether the data are congruent with their hypothesis.

5. On the basis of the information gathered, the students determine whether their hypothesis is correct. If incorrect, they may use the information to develop a new hypothesis.

6. If the students believe that their hypothesis is correct, they may state their explanation in the form of a question (“Is it. . . ?”). If they believe that their original explanation is incorrect, they may repeat steps 3-5 until they have a new conclusion.

Because the purpose is to let the students exercise problem solving thinking skills, the activity need not be limited to only twenty questions. What is important is that the teacher walk the students through the steps as the game is played, reminding them that they are solving a problem and that their questions will help them gather data, or information, which, through reflection, will help them determine whether their original hypothesis, or explanation, was correct.

Concrete objects may aid in the inquiry. In connection with a reading lesson, a preservice teacher displayed a farming tool that was typical of those used during the era of Sarah, Plain and Tall. Working with a fourth-grade reading group, the teacher showed the students the hand-held tool (which had belonged to her family for more than one hundred years) and explained that it was similar to those on the farm in Sarah, Plain and Tall. She informed the students that through their questions, they would discover the too#146;s purpose. Their initial questions centered on what they thought it was (“Does it plow?” and “Does it cut things?”), but through the teacher’s prompting, they soon asked questions that reflected data-gathering strategies in formal problem solving (“Is it used to prepare the soil somehow?” and “Is it used after the crop or plant is picked or harvested?”). The students then tested their hypotheses. They needed to ask more than twenty questions, but eventually they concluded that the object was used to separate residue cotton fibers from the plant—an explanation that their teacher affirmed. Although growing cotton was not mentioned in Sarah, Plain and Tall, the students, living in rural Alabama, could appreciate the difficulty that harvesting cotton presented to their ancestors, and in turn they understood the hardships that farmers, such as those in the book, must have faced.

Conflicting Statements as Problem Solving Tools

Twenty Questions is a highly effective method of problem solving, but other approaches also enable middle school students to focus on complex questions. For instance, Naylor and Diem suggest examining conflicting or opposing statements from the same source; an example might be Thomas Jefferson’s public writings on equality and his private ownership of slaves. 3 Students must struggle with the contradiction between Jefferson’s words and his actions.

The question for the students to consider could be “How could Thomas Jefferson write and speak of equality for all men and yet engage in the ownership of human beings?” Because the issue is complex, the question may serve as the overriding problem to be solved, while other related questions may guide the problem solving. Progressions in inquiry might include such questions: Was Jefferson a hypocrite? Was he a racist? Did others in similar positions and circumstances reflect this contradiction? What was the social and political climate at the time? Did events make this sort of contradiction seem acceptable? Did Jefferson show any acknowledgment of this contradiction in his writings or letters? What were his views on slavery? How were his slaves treated? Was this contradiction reflected in his views and dreams for the United States? Does this contradiction make his writings and accomplishments any less important or admirable? Working in groups, pairs, or individually, students can engage in problem solving steps.

Data gathering in such an exercise works well if the students examine primary and secondary documents from a variety of sources. For example, at the Thomas Jefferson Papers at the Library of Congress (memory.loc.gov/ammem/mtjhtml/ mtjhome.html), students can view formal documents that Jefferson wrote, personal letters, letters of his contemporaries, a timeline of his life, and assorted biographies.

Teachers need to emphasize and reiterate the steps in problem solving during the assignment. A culminating discussion of, or solution to, the problem may serve as a catalyst for further exploration of another issue or contradiction. In addition to exercising their problem solving skills, students better understand Jefferson the man, eighteenth-century political and social thought, and the philosophical principles that helped found the United States. Middle school students, curious about the people and the past, are ready to discuss how the past relates to their lives and the implications for their future.

Problem Solving for Creative Thinking

Although teaching problem solving skills is a vital part of social studies instruction, teachers are too often unwilling or unsure of how to incorporate problem solving into the curriculum. Not the nebulous beast that many educators assume, problem solving skills can be a viable centerpiece for instruction if we simply take a deep breath and examine the potential that they afford. If we wish for students to be creative thinkers, we must give them opportunity to think creatively, and if we want them to make judgments and reason logically, they must have the opportunity to practice these skills regularly. Through such models as Twenty Questions and Conflicting Statements, teachers can incorporate problem solving skills into the curriculum and give these skills the attention that they, and the students, deserve.

1. Thomas N. Turner, Essentials of Elementary Social Studies (2nd ed.) (Needham Heights, MA: Allyn & Bacon, 1999), 160.

2. John Douglas Hoge, Effective Elementary Social Studies (Belmont, CA: Wadsworth, 1996), 50.

3. David T. Naylor and Richard Diem, Elementary and Middle School Social Studies (New York: Random House, 1987), 254.

William D. Edgington is an assistant professor of social science education, Sam Houston State University, P.O. Box 2119, Huntsville, Texas 77341. He may be reached at [email protected] .

Twenty Questions and the Issue of Sir Thomas More

(sixth grade).

Teacher: We’ve been talking about England under Henry VIII, and today we’re going to investigate one of the most celebrated men of the day, Sir Thomas More. More was an author who wrote about the ideal society ( Utopia ); an attorney; and even the Lord Chancellor, the second most powerful man in England. But circumstances arose that cost More not only his position in the government, but also his life. He refused to change his stance on certain issues, although he was given opportunities to do so, choosing death over a compromise of his values and beliefs. He was beheaded on July 6, 1535.

Your mission today is to figure out what cost Sir Thomas More his life—what issues did he believe in so strongly that he chose death rather than deny his principles. Remember, you may ask questions to which I can answer with “yes” or “no” as we go through the problem solving process. You may already have a hypothesis or an idea, and my answers to your questions will help you determine whether your hypothesis is correct.

Student 1: Did it have to do with Henry VIII?

Teacher: Yes.

Student 2: Did More get in a fight with Henry?

Teacher: Be more specific.

Student 2: Did he and Henry disagree on something?

Student 3: Did it have to do with war?

Teacher: No. (At this point, the teacher emphasizes that the data were either supporting or disproving the students’ hypotheses and that they might need to rethink their hypotheses as they continue their questioning.)

Student 4: Did it have to do with Henry’s religion?

Student 4: Did it have to do with Henry starting his own church?

Teacher: Partially, yes. (At this time, the students review the data.)

Student 3: Was he not in favor of it?

Student 3: Was More not in favor of Henry’s church?

Teacher: No, he wasn’t in favor of it, but there is more to it.

Student 5: Did he not think that Henry should be the head of his church?

Teacher: No, he did not. Do you want to state your hypothesis?

Student 5: More didn’t think that Henry should be head of the church.

Teacher: Good! He refused to sign the Act of Supremacy, which named the king as the Supreme Head of the Church of England. But there was another issue on which More would not budge.

Student 1: Did it have to do with all of Henry’s wives?

Student 1: Did it have to do with his divorce? His first one?

Teacher: Partially. (The teacher prompts the students as they review the circumstances surrounding the end of Henry’s marriage to Catherine of Aragon.)

Student 6: Did it have to do with his ditching Catherine of Aragon and marrying Anne Boleyn?

Teacher: Yes. Keep going.

Student 7: Did More not think that Anne Boleyn should be queen?

Teacher: That’s correct. Do you want to state your hypothesis?

Student 7: More didn’t think that Anne Boleyn should be queen.

Teacher: Right! He refused to sign the Act of Succession, which stated that Henry’s marriage to Anne Boleyn was lawful. He wouldn’t sign either the Act of Supremacy or the Act of Succession. So what issues ultimately led to Sir Thomas More’s death?

Student 8: Henry’s marriage to Anne Boleyn and Henry making himself the Head of the Church of England.

Teacher: All right, let’s discuss why More felt so strongly about these issues . . . .

For a short biography of Sir Thomas More, see Encarta Online Encyclopedia, 2000 at encarta.msn.com.

Using Problem Solving Skills in a Fifth-Grade Classroom

Alan Rock and Nicole Halbert

Like most of our classmates, we were surprised to learn that we would be expected to teach thinking skills in social studies. Before our methods course, we equated social studies with maps, states, capitals, and presidents. We were astonished to discover that we would not just be teaching facts, we would also be helping students discover concepts, make generalizations, and enhance their observation, listening, graphing, mapping, and reference skills.

One of the requirements for our social studies methods course was to incorporate thinking skills into lessons that we would teach during our practicum. When we explained to our fifth-grade students that we would be doing activities that might be a little out of the ordinary, they seemed willing to assume the position of “thinker” rather than merely that of the traditional question-answering student.

We used a Twenty Questions activity for a problem solving skills lesson. To preface the lesson, we explained the rules and played a practice game of Twenty Questions. The mystery object or goal that they had to identify was a paper clip. The students’ first questions were random and nonsequential: “Is it a car?” “Is it the principal?” “Is it Jeff?” They called out the first thing that popped into their heads. As the game progressed, we discussed the need for asking questions that built on previous questions and that would narrow down the search. Eventually, their questions became more focused: “Is it in the classroom?” “Is it bigger than the desk?” “Does it have moveable parts?” “Is it red?” At the close of the game, we discussed the scientific method (they were familiar with the term from science class) and applied the steps to the practice game. When they thought that they knew what the object was, they were forming a hypothesis; by asking questions, they were gathering data; our answers helped them evaluate the data and reject or confirm their hypothesis.

We then explained their problem-solving activity: They had to figure out what actually happened to Paul Revere on the night of his famous ride. Having just played the practice game helped—their questions were not nearly as off-the-wall as at first. Instead of calling out any idea that came into their heads, their questions showed thought: “Does it have anything to do with his horse?” “Does it have to do with other people?” “Does it have to do with other minutemen?” “Does it have to do with the British?” “Did the British shoot him?” We stopped the questioning periodically to think about the scientific method and to have the students talk about their hypotheses. They did solve the problem—in fewer than twenty questions. Revere was captured by a British Patrol and spent much of the night in jail.

At their own initiation, they shared ideas with one another. For example, when the class discovered that the problem had something to do with the British, one student asked whether Revere had been killed. Another student dismissed that hypothesis because Revere was famous and therefore couldn’t have been killed. Other students immediately came to the first student’s defense, naming famous people who had been killed—John F. Kennedy, Abraham Lincoln, and Martin Luther King, Jr., for example. Once they solved the problem, they had plenty of follow-up questions: “Why have we never heard that part of the story before?” “How do we know that part of the story is true?” We hadn’t planned on such questions, but we addressed the issues of reliability and resources. In retrospect, we could have had the students compare the information that they had acquired with the information in their textbook.

We used the activity as a preview to our unit on the American Revolution. But we probably learned more than the students did. As future teachers, we clearly see that social studies can advance the thinking skills that the students use each day. Social studies is too often associated with tracing and memorizing, but we know it doesn’t have to be. We now look forward to using problem solving in our lessons.

Alan Rock and Nicole Halbert are Methods Students, Sam Houston State University, Huntsville, TX 

questions to ask students about problem solving

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  • Problem Solving in STEM

Solving problems is a key component of many science, math, and engineering classes.  If a goal of a class is for students to emerge with the ability to solve new kinds of problems or to use new problem-solving techniques, then students need numerous opportunities to develop the skills necessary to approach and answer different types of problems.  Problem solving during section or class allows students to develop their confidence in these skills under your guidance, better preparing them to succeed on their homework and exams. This page offers advice about strategies for facilitating problem solving during class.

How do I decide which problems to cover in section or class?

In-class problem solving should reinforce the major concepts from the class and provide the opportunity for theoretical concepts to become more concrete. If students have a problem set for homework, then in-class problem solving should prepare students for the types of problems that they will see on their homework. You may wish to include some simpler problems both in the interest of time and to help students gain confidence, but it is ideal if the complexity of at least some of the in-class problems mirrors the level of difficulty of the homework. You may also want to ask your students ahead of time which skills or concepts they find confusing, and include some problems that are directly targeted to their concerns.

You have given your students a problem to solve in class. What are some strategies to work through it?

  • Try to give your students a chance to grapple with the problems as much as possible.  Offering them the chance to do the problem themselves allows them to learn from their mistakes in the presence of your expertise as their teacher. (If time is limited, they may not be able to get all the way through multi-step problems, in which case it can help to prioritize giving them a chance to tackle the most challenging steps.)
  • When you do want to teach by solving the problem yourself at the board, talk through the logic of how you choose to apply certain approaches to solve certain problems.  This way you can externalize the type of thinking you hope your students internalize when they solve similar problems themselves.
  • Start by setting up the problem on the board (e.g you might write down key variables and equations; draw a figure illustrating the question).  Ask students to start solving the problem, either independently or in small groups.  As they are working on the problem, walk around to hear what they are saying and see what they are writing down. If several students seem stuck, it might be a good to collect the whole class again to clarify any confusion.  After students have made progress, bring the everyone back together and have students guide you as to what to write on the board.
  • It can help to first ask students to work on the problem by themselves for a minute, and then get into small groups to work on the problem collaboratively.
  • If you have ample board space, have students work in small groups at the board while solving the problem.  That way you can monitor their progress by standing back and watching what they put up on the board.
  • If you have several problems you would like to have the students practice, but not enough time for everyone to do all of them, you can assign different groups of students to work on different – but related - problems.

When do you want students to work in groups to solve problems?

  • Don’t ask students to work in groups for straightforward problems that most students could solve independently in a short amount of time.
  • Do have students work in groups for thought-provoking problems, where students will benefit from meaningful collaboration.
  • Even in cases where you plan to have students work in groups, it can be useful to give students some time to work on their own before collaborating with others.  This ensures that every student engages with the problem and is ready to contribute to a discussion.

What are some benefits of having students work in groups?

  • Students bring different strengths, different knowledge, and different ideas for how to solve a problem; collaboration can help students work through problems that are more challenging than they might be able to tackle on their own.
  • In working in a group, students might consider multiple ways to approach a problem, thus enriching their repertoire of strategies.
  • Students who think they understand the material will gain a deeper understanding by explaining concepts to their peers.

What are some strategies for helping students to form groups?  

  • Instruct students to work with the person (or people) sitting next to them.
  • Count off.  (e.g. 1, 2, 3, 4; all the 1’s find each other and form a group, etc)
  • Hand out playing cards; students need to find the person with the same number card. (There are many variants to this.  For example, you can print pictures of images that go together [rain and umbrella]; each person gets a card and needs to find their partner[s].)
  • Based on what you know about the students, assign groups in advance. List the groups on the board.
  • Note: Always have students take the time to introduce themselves to each other in a new group.

What should you do while your students are working on problems?

  • Walk around and talk to students. Observing their work gives you a sense of what people understand and what they are struggling with. Answer students’ questions, and ask them questions that lead in a productive direction if they are stuck.
  • If you discover that many people have the same question—or that someone has a misunderstanding that others might have—you might stop everyone and discuss a key idea with the entire class.

After students work on a problem during class, what are strategies to have them share their answers and their thinking?

  • Ask for volunteers to share answers. Depending on the nature of the problem, student might provide answers verbally or by writing on the board. As a variant, for questions where a variety of answers are relevant, ask for at least three volunteers before anyone shares their ideas.
  • Use online polling software for students to respond to a multiple-choice question anonymously.
  • If students are working in groups, assign reporters ahead of time. For example, the person with the next birthday could be responsible for sharing their group’s work with the class.
  • Cold call. To reduce student anxiety about cold calling, it can help to identify students who seem to have the correct answer as you were walking around the class and checking in on their progress solving the assigned problem. You may even want to warn the student ahead of time: "This is a great answer! Do you mind if I call on you when we come back together as a class?"
  • Have students write an answer on a notecard that they turn in to you.  If your goal is to understand whether students in general solved a problem correctly, the notecards could be submitted anonymously; if you wish to assess individual students’ work, you would want to ask students to put their names on their notecard.  
  • Use a jigsaw strategy, where you rearrange groups such that each new group is comprised of people who came from different initial groups and had solved different problems.  Students now are responsible for teaching the other students in their new group how to solve their problem.
  • Have a representative from each group explain their problem to the class.
  • Have a representative from each group draw or write the answer on the board.

What happens if a student gives a wrong answer?

  • Ask for their reasoning so that you can understand where they went wrong.
  • Ask if anyone else has other ideas. You can also ask this sometimes when an answer is right.
  • Cultivate an environment where it’s okay to be wrong. Emphasize that you are all learning together, and that you learn through making mistakes.
  • Do make sure that you clarify what the correct answer is before moving on.
  • Once the correct answer is given, go through some answer-checking techniques that can distinguish between correct and incorrect answers. This can help prepare students to verify their future work.

How can you make your classroom inclusive?

  • The goal is that everyone is thinking, talking, and sharing their ideas, and that everyone feels valued and respected. Use a variety of teaching strategies (independent work and group work; allow students to talk to each other before they talk to the class). Create an environment where it is normal to struggle and make mistakes.
  • See Kimberly Tanner’s article on strategies to promoste student engagement and cultivate classroom equity. 

A few final notes…

  • Make sure that you have worked all of the problems and also thought about alternative approaches to solving them.
  • Board work matters. You should have a plan beforehand of what you will write on the board, where, when, what needs to be added, and what can be erased when. If students are going to write their answers on the board, you need to also have a plan for making sure that everyone gets to the correct answer. Students will copy what is on the board and use it as their notes for later study, so correct and logical information must be written there.

For more information...

Tipsheet: Problem Solving in STEM Sections

Tanner, K. D. (2013). Structure matters: twenty-one teaching strategies to promote student engagement and cultivate classroom equity . CBE-Life Sciences Education, 12(3), 322-331.

  • Designing Your Course
  • A Teaching Timeline: From Pre-Term Planning to the Final Exam
  • The First Day of Class
  • Group Agreements
  • Classroom Debate
  • Flipped Classrooms
  • Leading Discussions
  • Polling & Clickers
  • Teaching with Cases
  • Engaged Scholarship
  • Devices in the Classroom
  • Beyond the Classroom
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8 Chapter 6 Supporting Student Problem-Solving

Across content areas, the standards address problem-solving in the form of being able to improvise, decide, inquire, and research. In fact, math and science standards are premised almost completely on problem-solving and inquiry. According to the literature, however, problem-solving and inquiry are often overlooked or addressed only superficially in classrooms, and in some subject areas, are not attended to at all.

OVERVIEW OF PROBLEM-SOLVING AND INQUIRY IN K–12 CLASSROOMS

In keeping with a learning focus, this chapter first discusses problem-solving and inquiry to provide a basis from which teachers can provide support for these goals with technology.

What Is Problem-solving?

Whereas production is a process that focuses on an end-product, problem-solving is a process that centers on a problem. Students apply critical and creative thinking skills to prior knowledge during the problem-solving process. The end result of problem-solving is typically some kind of decision, in other words, choosing a solution and then evaluating it.

There are two general kinds of problems. Close-ended problems are those with known solutions to which students can apply a process similar to one that they have already used. For example, if a student understands the single-digit process in adding 2 plus 2 to make 4, she most likely will be able to solve a problem that asks her to add 1 plus 1. Open-ended or loosely structured problems, on the other hand, are those with many or unknown solutions rather than one correct answer. These types of problems require the ability to apply a variety of strategies and knowledge to finding a solution. For example, an open-ended problem statement might read:

A politician has just discovered information showing that a statement he made to the public earlier in the week was incorrect. If he corrects himself he will look like a fool, but if he doesn’t and someone finds out the truth, he will be in trouble. What should he do or say about this?

Obviously, there is no simple answer to this question, and there is a lot of information to consider.

Many textbooks, teachers, and tests present or ask only for the results of problem-solving and not the whole process that students must go through in thinking about how to arrive at a viable solution. As a result, according to the literature, most people use their personal understandings to try to solve open-ended problems, but the bias of limited experience makes it hard for people to understand the trade-offs or contradictions that these problems present. To solve such problems, students need to be able to use both problem-solving skills and an effective inquiry process.

What Is Inquiry?

Inquiry in education is also sometimes called research, investigation, or guided discovery. During inquiry, students ask questions and then search for answers to those questions. In doing so, they come to new understandings in content and language. Although inquiry is an instructional strategy in itself, it is also a central component of problem-solving when students apply their new understandings to the problem at hand. Each question that the problem raises must be addressed by thorough and systematic investigation to arrive at a well-grounded solution. Therefore, the term “problem-solving” can be considered to include inquiry.

For students to understand both the question and ways of looking at the answer(s), resources such as historical accounts, literature, art, and eyewitness experiences must be used. In addition, each resource must be examined in light of what each different type of material contributes to the solution. Critical literacy, or reading beyond the text, then, is a fundamental aspect of inquiry and so of problem-solving. Search for critical literacy resources by using “critical literacy” and your grade level, and be sure to look at the tools provided in this text’s Teacher Toolbox.

What Is Problem-Based Learning?

Problem-based learning (PBL) is a teaching approach that combines critical thinking, problem- solving skills, and inquiry as students explore real-world problems. It is based on unstructured, complex, and authentic problems that are often presented as part of a project. PBL addresses many of the learning goals presented in this text and across the standards, including communication, creativity, and often production.

Research is being conducted in every area from business to education to see how we solve problems, what guides us, what information we have and use during problem-solving, and how we can become more efficient problem solvers. There are competing theories of how people learn to and do solve problems, and much more research needs to be done. However, we do know several things. First, problem-solving can depend on the context, the participants, and the stakeholders. In addition, studies show that content appears to be covered better by “traditional” instruction, but students retain better after problem-solving. PBL has been found effective at teaching content and problem-solving, and the use of technology can make those gains even higher (Chauhan, 2017). Research clearly shows that the more parts of a problem there are, the less successful students will be at solving it. However, effective scaffolding can help to support students’ problem-solving and overcomes some of the potential issues with it (Belland, Walker, Kim, & Lefler, 2017).

The PBL literature points out that both content knowledge and problem-solving skills are necessary to arrive at solutions, but individual differences among students affect their success, too. For example, field-independent students in general do better than field-dependent students in tasks. In addition, students from some cultures will not be familiar with this kind of learning, and others may not have the language to work with it. Teachers must consider all of these ideas and challenges in supporting student problem-solving.

Characteristics of effective technology-enhanced problem-based learning tasks

PBL tasks share many of the same characteristics of other tasks in this book, but some are specific to PBL. Generally, PBL tasks:

Involve learners in gaining and organizing knowledge of content. Inspiration and other concept-mapping tools like the app Popplet are useful for this.

Help learners link school activities to life, providing the “why” for doing the activity.

Give students control of their learning.

Have built-in and just-in-time scaffolding to help students. Tutorials are available all over the Web for content, language, and technology help.

Are fun and interesting.

Contain specific objectives for students to meet along the way to a larger goal.

Have guidance for the use of tools, especially computer technologies.

Include communication and collaboration (described in chapter 3).

Emphasize the process and the content.

Are central to the curriculum, not peripheral or time fillers.

Lead to additional content learning.

Have a measurable, although not necessarily correct, outcome.

More specifically, PBL tasks:

Use a problem that “appeals to human desire for resolution/stasis/harmony” and “sets up need for and context of learning which follows” (IMSA, 2005, p. 2).

Help students understand the range of problem-solving mechanisms available.

Focus on the merits of the question, the concepts involved, and student research plans.

Provide opportunities for students to examine the process of getting the answer (for example, looking back at the arguments).

Lead to additional “transfer” problems that use the knowledge gained in a different context.

Not every task necessarily exhibits all of these characteristics completely, but these lists can serve as guidelines for creating and evaluating tasks.

Student benefits of problem-solving

There are many potential benefits of using PBL in classrooms at all levels; however, the benefits depend on how well this strategy is employed. With effective PBL, students can become more engaged in their learning and empowered to become more autonomous in classroom work. This, in turn, may lead to improved attitudes about the classroom and thus to other gains such as increased abilities for social-problem solving. Students can gain a deeper understanding of concepts, acquire skills necessary in the real world, and transfer skills to become independent and self-directed learners and thinkers outside of school. For example, when students are encouraged to practice using problem-solving skills across a variety of situations, they gain experience in discovering not only different methods but which method to apply to what kind of problem. Furthermore, students can become more confident when their self-esteem and grade does not depend only on the specific answer that the teacher wants. In addition, during the problem-solving process students can develop better critical and creative thinking skills.

Students can also develop better language skills (both knowledge and communication) through problems that require a high level of interaction with others (Verga & Kotz, 2013). This is important for all learners, but especially for ELLs and others who do not have grade-level language skills. For students who may not understand the language or content or a specific question, the focus on process gives them more opportunities to access information and express their knowledge.

The problem-solving process

The use of PBL requires different processes for students and teachers. The teacher’s process involves careful planning. There are many ways for this to happen, but a general outline that can be adapted includes the following steps:

After students bring up a question, put it in the greater context of a problem to solve (using the format of an essential question; see chapter 4) and decide what the outcome should be–a recommendation, a summary, a process?

Develop objectives that represent both the goal and the specific content, language, and skills toward which students will work.

List background information and possible materials and content that will need to be addressed. Get access to materials and tools and prepare resource lists if necessary.

Write the specific problem. Make sure students know what their role is and what they are expected to do. Then go back and check that the problem and task meet the objectives and characteristics of effective PBL and the relevant standards. Reevaluate materials and tools.

Develop scaffolds that will be needed.

Evaluate and prepare to meet individual students’ needs for language, assistive tools, content review, and thinking skills and strategies

Present the problem to students, assess their understanding, and provide appropriate feedback as they plan and carry out their process.

The student process focuses more on the specific problem-solving task. PBL sources list different terms to describe each step, but the process is more or less the same. Students:

Define and frame the problem: Describe it, recognize what is being asked for, look at it from all sides, and say why they need to solve it.

Plan: Present prior knowledge that affects the problem, decide what further information and concepts are needed, and map what resources will be consulted and why.

Inquire: Gather and analyze the data, build and test hypotheses.

Look back: Review and evaluate the process and content. Ask “What do I understand from this result? What does it tell me?”

questions to ask students about problem solving

These steps are summarized in Figure 6.1.

Problem-solving strategies that teachers can demonstrate, model, and teach directly include trial and error, process of elimination, making a model, using a formula, acting out the problem, using graphics or drawing the problem, discovering patterns, and simplifying the problem (e.g., rewording, changing the setting, dividing it into simpler tasks). Even the popular KWL (Know, Want to Know, Learned) chart can help students frame questions. A KWL for a project asking whether a superstore should be built in the community might look like the one in Figure 6.2. Find out more about these strategies at http://literacy.kent.edu/eureka/strategies/discuss-prob.html .

Teaching problem-solving in groups involves the use of planning and other technologies. Using these tools, students post, discuss, and reflect on their joint problem-solving process using visual cues that they create. This helps students focus on both their process and the content. Throughout the teacher and student processes, participants should continue to examine cultural, emotional, intellectual, and other possible barriers to problem-solving.

questions to ask students about problem solving

Teachers and Problem-solving

The teacher’s role in PBL

During the teacher’s process of creating the problem context, the teacher must consider what levels of authenticity, complexity, uncertainty, and self-direction students can access and work within. Gordon (1998) broke loosely structured problems into three general types with increasing levels of these aspects. Still in use today, these are:

Academic challenges. An academic challenge is student work structured as a problem arising directly from an area of study. It is used primarily to promote greater understanding of selected subject matter. The academic challenge is crafted by transforming existing curricular material into a problem format.

Scenario challenges. These challenges cast students in real-life roles and ask them to perform these roles in the context of a reality-based or fictional scenario.

Real-life problems. These are actual problems in need of real solutions by real people or organizations. They involve students directly and deeply in the exploration of an area of study. And the solutions have the potential for actual implementation at the classroom, school, community, regional, national, or global level. (p. 3)

To demonstrate the application of this simple categorization, the learning activities presented later in this chapter follow this outline.

As discussed in other chapters in this book, during student work the teacher’s role can vary from director to shepherd, but when the teacher is a co-learner rather than a taskmaster, learners become experts. An often-used term for the teacher’s role in the literature about problem-solving is “coach.” As a coach, the teacher works to facilitate thinking skills and process, including working out group dynamics, keeping students on task and making sure they are participating, assessing their progress and process, and adjusting levels of challenge as students’ needs change. Teachers can provide hints and resources and work on a gradual release of responsibility to learners.

Challenges for teachers

For many teachers, the roles suggested above are easier said than done. To use a PBL approach, teachers must break out of the content-dissemination mode and help their students to do the same. Even when this happens, in many classrooms students have been trained to think that problem-solving is getting the one right answer, and it takes time, practice, and patience for them to understand otherwise. Some teachers feel that they are obligated to cover too much in the curriculum to spend time on PBL or that using real-world problems does not mesh well with the content, materials, and context of the classroom. However, twenty years ago Gordon (1998) noted, “whether it’s a relatively simple matter of deciding what to eat for breakfast or a more complex one such as figuring out how to reduce pollution in one’s community, in life we make decisions and do things that have concrete results. Very few of us do worksheets” (p. 2). He adds that not every aspect of students’ schoolwork needs to be real, but that connections should be made from the classroom to the real world. Educators around the world are still working toward making school more like life.

In addition, many standardized district and statewide tests do not measure process, so students do not want to spend time on it. However, teachers can overcome this thinking by demonstrating to students the ways in which they need to solve problems every day and how these strategies may transfer to testing situations.

Furthermore, PBL tasks and projects may take longer to develop and assess than traditional instruction. However, teachers can start slowly by helping students practice PBL in controlled environments with structure, then gradually release them to working independently. The guidelines in this chapter address some of these challenges.

GUIDELINES FOR TECHNOLOGY-SUPPORTED PROBLEM-SOLVING

Obviously, PBL is more than simply giving students a problem and asking them to solve it. The following guidelines describe other issues in PBL.

Designing Problem-Solving Opportunities

The guidelines described here can assist students in developing a PBL opportunity.

Guideline #1: Integrate reading and writing. Although an important part of solving problems, discussion alone is not enough for students to develop and practice problem-solving skills. Effective problem-solving and inquiry require students to think clearly and deeply about content, language, and process. Reading and writing tasks can encourage students to take time to think about these issues and to contextualize their thinking practice. They can also provide vehicles for teachers to understand student progress and to provide concrete feedback. Students who have strengths in these areas will be encouraged and those who need help can learn from their stronger partners, just as those who have strengths in speaking can model for and assist their peers during discussion. Even in courses that do not stress reading and writing, integrating these skills into tasks and projects can promote successful learning.

Guideline #2: Avoid plagiarism. The Internet is a great resource for student inquiry and problem-solving. However, when students read and write using Internet resources, they often cut and paste directly from the source. Sometimes this is an innocent mistake; students may be uneducated about the use of resources, perhaps they come from a culture where the concept of ownership is completely different than in the United States, or maybe their language skills are weak and they want to be able to express themselves better. In either case, two strategies can help avoid plagiarism: 1) The teacher can teach directly about plagiarism and copyright issues. Strategies including helping students learn how to cite sources, paraphrase, summarize, and restate; 2) The teacher can be as familiar as possible with the resources that students will use and check for plagiarism when it is suspected. To do so, the teacher can enter a sentence or phrase into any Web browser with quote marks around it and if the entry is exact, the original source will come up in the browser window. Essay checkers such as Turnitin (http://turnitin.com/) are also available online that will check a passage or an entire essay.

Guideline #3: Do not do what students can do. Teaching, and particularly teaching with technology, is often a difficult job, due in part to the time it takes teachers to prepare effective learning experiences. Planning, developing, directing, and assessing do not have to be solely the teacher’s domain, however. Students should take on many of these responsibilities, and at the same time gain in problem-solving, language, content, critical thinking, creativity, and other crucial skills. Teachers do not always need to click the mouse, write on the whiteboard, decide

criteria for a rubric, develop questions, decorate the classroom, or perform many classroom and learning tasks. Students can take ownership and feel responsibility. Although it is often difficult for teachers to give up some of their power, the benefits of having more time and shared responsibility can be transformational. Teachers can train themselves to ask, “Is this something students can do?”

Guideline #4: Make mistakes okay. Problem-solving often involves coming to dead ends, having to revisit data and reformulate ideas, and working with uncertainty. For students used to striving for correct answers and looking to the teacher as a final authority, the messiness of problem-solving can be disconcerting, frustrating, and even scary. Teachers can create environments of acceptance where reasoned, even if wrong, answers are recognized, acknowledged, and given appropriate feedback by the teacher and peers. Teachers already know that students come to the task with a variety of beliefs and information. In working with students’ prior knowledge, they can model how to be supportive of students’ faulty ideas and suggestions. They can also ask positive questions to get the students thinking about what they still need to know and how they can come to know it. They can both encourage and directly teach students to be supportive of mistakes and trials as part of their team-building and leadership skills.

In addition, teachers may need to help students to understand that even a well-reasoned argument or answer can meet with opposition. Students must not feel that they have made a bad decision just because everyone else, particularly the teacher, does not agree. Teachers can model for students that they are part of the learning process and they are impartial as to the outcome when the student’s position has been well defended.

PROBLEM-SOLVING AND INQUIRY TECHNOLOGIES

As with all the goals in this book, the focus of technology in problem-solving is not on the technology itself but on the learning experiences that the technology affords. Different tools exist to support different parts of the process. Some are as simple as handouts that students can print and complete, others as complex as modeling and visualization software. Many software tools that support problem-solving are made for experts in the field and are relatively difficult to learn and use. Examples of these more complicated programs include many types of computer-aided design software, advanced authoring tools, and complex expert systems. In the past there were few software tools for K–12 students that addressed the problem-solving process directly and completely, but more apps are being created all the time that do so. See the Teacher Tools for this text for examples.

Simple inquiry tools that help students perform their investigations during PBL are much more prevalent. The standard word processor, database, concept mapping/graphics and spreadsheet software can all assist students in answering questions and organizing and presenting data, but there are other tools more specifically designed to support inquiry. Software programs that can be used within the PBL framework are mentioned in other chapters in this text. These programs, such as the Tom Snyder Productions/Scholastic programs mentioned in chapter 2 address the overlapping goals of collaboration, production, critical thinking, creativity, and problem-solving. Interestingly, even video games might be used as problem-solving tools. Many of these games require users to puzzle out directions, to find missing artifacts, or to follow clues that are increasingly difficult to find and understand. One common tool with which students at all levels might be familiar is Minecraft (Mojang; https://minecraft.net/en-us/). The Internet has as many resources as teachers might need to use Minecraft across the disciplines to teach whole units and even gamify the classroom.

The following section presents brief descriptions of tools that can support the PBL process. The examples are divided into stand-alone tools that can be used on one or more desktops and Web-based tools.

Stand-Alone Tools

Example 1: Fizz and Martina’s Math Adventures (Tom Snyder Productions/Scholastic)

Students help Fizz and Martina, animated characters in this software, to solve problems by figuring out which data is relevant, performing appropriate calculations, and presenting their solutions. The five titles in this series are perfect for a one-computer classroom. Each software package combines computer-based video, easy navigation, and handouts and other resources as scaffolds. This software is useful in classrooms with ELLs because of the combination of visual, audio, and text-based reinforcement of input. It is also accessible to students with physical disabilities because it can run on one computer; students do not have to actually perform the mouse clicks to run the software themselves.

This software is much more than math. It includes a lot of language, focuses on cooperation and collaboration in teams, and promotes critical thinking as part of problem-solving. Equally important, it helps students to communicate mathematical ideas orally and in writing. See Figure 6.6 for the “getting started” screen from Fizz and Martina to view some of the choices that teachers and students have in using this package.

Example 2: I Spy Treasure Hunt, I Spy School Days, I Spy Spooky Mansion (Scholastic)

The language in these fun simulations consists of isolated, discrete words and phrases, making these programs useful for word study but not for overall concept learning. School Days, for example, focuses on both objects and words related to school. However, students work on extrapolation, trial and error, process of elimination, and other problem-solving strategies. It is difficult to get students away from the computer once they start working on any of the simulations in this series. Each software package has several separate hunts with a large number of riddles that, when solved, allow the user to put together a map or other clues to find the surprise at the end. Some of the riddles involve simply finding an item on the screen, but others require more thought such as figuring out an alternative representation for the item sought or using a process of elimination to figure out where to find it. All of the riddles are presented in both text and audio and can be repeated as many times as the student requires, making it easier for language learners, less literate students, and students with varied learning preferences to access the information. Younger students can also work with older students or an aide for close support so that students are focused. Free versions of the commercial software and similar types of programs such as escape rooms (e.g., escapes at 365 Escape {http://www.365escape.com/Room-Escape-Games.html] and www.primarygames.com) can be found across the Web.

There are many more software packages like these that can be part of a PBL task. See the Teacher Toolbox for ideas.

Example 3: Science Court (Tom Snyder Productions/Scholastic)

Twelve different titles in this series present humorous court cases that students must help to resolve. Whether the focus is on the water cycle, soil, or gravity, students use animated computer-based video, hands-on science activities, and group work to learn and practice science and the inquiry process. As students work toward solving the case, they examine not only the facts but also their reasoning processes. Like Fizz and Martina and much of TSP’s software, Science Court uses multimedia and can be used in the one-computer classroom (as described in chapter 2), making it accessible to diverse students.

Example 4: Geographic Information Systems (GIS)

The use of GIS to track threatened species, map hazardous waste or wetlands in the community, or propose solutions for other environmental problems supports student “spatial literacy and geographic competence” (Baker, 2005, n.p.), in addition to experimental and inquiry techniques, understanding of scale and resolution, and verification skills. Popular desktop-based GIS that students can access include Geodesy and ArcVoyager; many Web-based versions also exist. A GIS is not necessarily an easy tool to learn or use, but it can lead to real-world involvement and language, concept, and thinking skills development.

Web-Based Tools

Many technology-enhanced lessons and tools on the Web come premade. In other words, they were created for someone else’s students and context. Teachers must adapt these tools to fit their own teaching styles, student needs, goals, resources, and contextual variables. Teachers must learn to modify these resources to make them their own and help them to work effectively in their unique teaching situation. With this in mind, teachers can take advantage of the great ideas in the Web-based tools described below.

Example 1: WebQuest

A WebQuest is a Web-based inquiry activity that is highly structured in a preset format. Most teachers are aware of WebQuests—a Web search finds them mentioned in every state, subject area, and grade level, and they are popular topics at conferences and workshops. Created by Bernie Dodge and Tom March in 1995 (see http://webquest.org/), this activity has proliferated wildly.

Each WebQuest has six parts. The Quest starts with an introduction to excite student interest. The task description then explains to students the purpose of the Quest and what the outcome will be. Next, the process includes clear steps and the scaffolds, including resources, that students will need to accomplish the steps. The evaluation section provides rubrics and assessment guidelines, and the conclusion section provides closure. Finally, the teacher section includes hints and tips for other teachers to use the WebQuest.

Advantages to using WebQuests as inquiry and problem-solving tools include:

Students are focused on a specific topic and content and have a great deal of scaffolding.

Students focus on using information rather than looking for it, because resources are preselected.

Students use collaboration, critical thinking, and other important skills to complete their Quest.

Teachers across the United States have reported significant successes for students participating in Quests. However, because Quests can be created and posted by anyone, many found on the Web do not meet standards for inquiry and do not allow students autonomy to work in authentic settings and to solve problems. Teachers who want to use a WebQuest to meet specific goals should examine carefully both the content and the process of the Quest to make sure that they offer real problems as discussed in this chapter. A matrix of wonderful Quests that have been evaluated as outstanding by experts is available on the site.

Although very popular, WebQuests are also very structured. This is fine for students who have not moved to more open-ended problems, but to support a higher level of student thinking, independence, and concept learning, teachers can have students work in teams on Web Inquiry Projects ( http://webinquiry.org/ ).

Example 2: Virtual Field Trips

Virtual field trips are great for concept learning, especially for students who need extra support from photos, text, animation, video, and audio. Content for field trips includes virtual walks through museums, underwater explorations, house tours, and much more (see online field trips suggested by Steele-Carlin [2014] at http://www.educationworld.com/a_tech/tech/tech071.shtml ). However, the format of virtual field trips ranges from simple postcard-like displays to interactive video simulations, and teachers must review the sites before using them to make sure that they meet needs and goals.

With a virtual reality headset (now available for sale cheaply even at major department stores), teachers and students can go on Google Expeditions ( https://edu.google.com/expeditions/ ), 3D immersive field trips from Nearpod ( http://nearpod.com ), and even create their using resources from Larry Ferlazzo’s “Best Resources for Finding and Creating Virtual Field Trips” at http://larryferlazzo.edublogs.org/2009/08/11/the-best-resources-for-finding-and-creating-virtual-field-trips/.

Example 3: Raw Data Sites

Raw data sites abound on the Web, from the U.S. Census to the National Climatic Data Center, from databases full of language data to the Library of Congress. These sites can be used for content learning and other learning goals. Some amazing sites can be found where students can collect their own data. These include sites like John Walker’s (2003) Your Sky (www.fourmilab.to/yoursky) and Water on the Web (2005, waterontheweb.org). When working with raw data students have to draw their own conclusions based on evidence. This is another important problem-solving skill. Note that teachers must supervise and verify that data being entered for students across the world is accurate or

Example 4: Filamentality

Filamentality (https://keithstanger.com/filamentality.html) presents an open-ended problem with a lot of scaffolding. Students and/or teachers start with a goal and then create a Web site in one of five formats that range in level of inquiry and problem-solving from treasure hunts to WebQuests. The site provides lots of help and hints for those who need it, including “Mentality Tips” to help accomplish goals. It is free and easy to use, making it accessible to any teacher (or student) with an Internet connection.

Example 5: Problem Sites

Many education sites offer opportunities for students to solve problems. Some focus on language (e.g., why do we say “when pigs fly”?) or global history (e.g., what’s the real story behind Tut’s tomb?); see, for example, the resources and questions in The Ultimate STEM Guide for Students at http://www.mastersindatascience.org/blog/the-ultimate-stem-guide-for-kids-239-cool-sites-about-science-technology-engineering-and-math/. These problems range in level from very structured, academic problems to real-world unsolved mysteries.

The NASA SciFiles present problems in a format similar to WebQuests at https://knowitall.org/series/nasa-scifiles. In other parts of the Web site there are video cases, quizzes, and tools for problem-solving.

There is an amazing number of tools, both stand-alone and Web-based, to support problem-solving and inquiry, but no tool can provide all the features that meet the needs of all students. Most important in tool choice is that it meets the language, content, and skills goals of the project and students and that there is a caring and supportive teacher guiding the students in their choice and use of the tool.

Teacher Tools

There are many Web sites addressed specifically to teachers who are concerned that they are not familiar enough with PBL or that they do not have the tools to implement this instructional strategy. For example, from Now On at http://www.fno.org/ toolbox.html provides specific suggestions for how to integrate technology and inquiry. Search “problem-solving” on the amazing Edutopia site ( https://www.edutopia.org/ ) for ideas, guidelines, examples, and more.

LEARNING ACTIVITIES: PROBLEM-SOLVING AND INQUIRY

In addition to using the tools described in the previous section to teach problem-solving and inquiry, teachers can develop their own problems according to the guidelines throughout this chapter. Gordon’s (1998) scheme of problem-solving levels (described previously)—academic, scenario, and real life—is a simple and useful one. Teachers can refer to it to make sure that they are providing appropriate structure and guidance and helping students become independent thinkers and learners. This section uses Gordon’s levels to demonstrate the variety of problem-solving and inquiry activities in which students can participate. Each example is presented with the question/problem to be answered or solved, a suggestion of a process that students might follow, and some of the possible electronic tools that might help students to solve the problem.

Academic problems

Example 1: What Will Harry Do? (Literature)

Problem: At the end of the chapter, Harry Potter is faced with a decision to make. What will he do?

Process: Discuss the choices and consequences. Choose the most likely, based on past experience and an understanding of the story line. Make a short video to present the solution. Test it against Harry’s decision and evaluate both the proposed solution and the real one.

Tools: Video camera and video editing software.

Example 2: Treasure Hunt (History)

Problem: Students need resources to learn about the Civil War.

Process: Teacher provides a set of 10 questions to find specific resources online.

Tools: Web browser.

Example 3: Problem of the Week (Math)

Problem: Students should solve the math problem of the week.

Process: Students simplify the problem, write out their solution, post it to the site for feedback, then revise as necessary.

Tools: Current problems from the Math Forum@Drexel, http://mathforum.org/pow/

Example 1: World’s Best Problem Solver

Problem: You are a member of a committee that is going to give a prestigious international award for the world’s best problem-solver. You must nominate someone and defend your position to the committee, as the other committee members must do.

Process: Consult and list possible nominees. Use the process of elimination to determine possible nominees. Research the nominees using several different resources. Weigh the evidence and make a choice. Prepare a statement and support.

Tools: Biography.com has over 25,000 biographies, and Infoplease (infoplease.com) and the Biographical Dictionary (http://www.s9.com/) provide biographies divided into categories for easy searching.

Example 2: Curator

Problem: Students are a committee of curators deciding what to hang in a new community art center. They have access to any painting in the world but can only hang 15 pieces in their preset space. Their goals are to enrich art appreciation in the community, make a name for their museum, and make money.

Process: Students frame the problem, research and review art from around the world, consider characteristics of the community and other relevant factors, choose their pieces, and lay them out for presentation to the community.

Tools: Art museum Web sites, books, and field trips for research and painting clips; computer-aided design, graphics, or word processing software to lay out the gallery for viewing.

Example 3: A New National Anthem

Problem: Congress has decided that the national anthem is too difficult to remember and sing and wants to adopt a new, easier song before the next Congress convenes. They want input from musicians across the United States. Students play the roles of musicians of all types.

Process: Students define the problem (e.g., is it that “The Star-Spangled Banner” is too difficult or that Congress needs to be convinced that it is not?). They either research and choose new songs or research and defend the current national anthem. They prepare presentations for members of Congress.

Tools: Music sites and software, information sites on the national anthem.

Real-life problems

Example 1: Racism in School

Problem: There have been several incidents in our school recently that seem to have been racially motivated. The principal is asking students to consider how to make our school a safe learning environment for all students.

Process: Determine what is being asked—the principal wants help. Explore the incidents and related issues. Weigh the pros and cons of different solutions. Prepare solutions to present to the principal.

Tools: Web sites and other resources about racism and solutions, graphic organizers to organize the information, word processor or presentation software for results. Find excellent free tools for teachers and students at the Southern Poverty Law Center’s Teaching Tolerance Web site at www.tolerance.org.

Example 2: Homelessness vs. Education

Problem: The state legislature is asking for public input on the next budget. Because of a projected deficit, political leaders are deciding which social programs, including education and funding for the homeless, should be cut and to what extent. They are interested in hearing about the effects of these programs on participants and on where cuts could most effectively be made.

Process: Decide what the question is (e.g., how to deal with the deficit? How to cut education or funding for the homeless? Which programs are more important? Something else?). Perform a cost-benefit analysis using state data. Collect other data by interviewing and researching. Propose and weigh different solution schemes and propose a suggestion. Use feedback to improve or revise.

Tools: Spreadsheet for calculations, word processor for written solution, various Web sites and databases for costs, electronic discussion list or email for interviews.

Example 3: Cleaning Up

Problem: Visitors and residents in our town have been complaining about the smell from the university’s experimental cattle farms drifting across the highway to restaurants and stores in the shopping center across the street. They claim that it makes both eating and shopping unpleasant and that something must be done.

Process: Conduct onsite interviews and investigation. Determine the source of the odor. Measure times and places where the odor is discernible. Test a variety of solutions. Choose the most effective solution and write a proposal supported by a poster for evidence.

Tools: Online and offline sources of information on cows, farming, odor; database to organize and record data; word processing and presentation software for describing the solution.

These activities can all be adapted and different tools and processes used. As stated previously, the focus must be both on the content to be learned and the skills to be practiced and acquired. More problem-solving activity suggestions and examples can be found at site at http://www.2learn.ca/.

ASSESSING LEARNER PROBLEM-SOLVING AND INQUIRY

Many of the assessments described in other chapters of this text, for example, rubrics, performance assessments, observation, and student self-reflection, can also be employed to assess problem-solving and inquiry. Most experts on problem-solving and inquiry agree that schools need to get away from testing that does not involve showing process or allowing students to problem-solve; rather, teachers should evaluate problem-solving tasks as if they were someone in the real-world context of the problem. For example, if students are studying an environmental issue, teachers can evaluate their work throughout the project from the standpoint of someone in the field, being careful that their own biases do not cloud their judgment on controversial issues. Rubrics, multiple-choice tests, and other assessment tools mentioned in other chapters of this text can account for the multiple outcomes that are possible in content, language, and skills learning. These resources can be used as models for assessing problem-solving skills in a variety of tasks. Find hundreds of problem-solving rubrics by searching the Web for “problem-solving rubrics” or check Pinterest for teacher-created rubrics.

In addition to the techniques mentioned above, many teachers suggest keeping a weekly problem-solving notebook (also known as a math journal or science journal), in which students record problem solutions, strategies they used, similarities with other problems, extensions of the problem, and an investigation of one or more of the extensions. Using this notebook to assess students’ location and progress in problem-solving could be very effective, and it could even be convenient if learners can keep them online as a blog or in a share cloud space.

FROM THE CLASSROOM

Research and Plagiarism

We’ve been working on summaries all year and the idea that copying word for word is plagiarism. When they come to me (sixth grade) they continue to struggle with putting things in their own words so [Microsoft Encarta] Researcher not only provides a visual (a reference in APA format) that this is someone else’s work, but allows me to see the information they used to create their report as Researcher is an electronic filing system. It’s as if students were printing out the information and keeping it in a file that they will use to create their report. But instead of having them print everything as they go to each individual site they can copy and paste until later. When they finish their research they come back to their file, decide what information they want to use, and can print it out all at once. This has made it easier for me because the students turn this in with their report. So, I would say it not only allows students to learn goals of summarizing, interpreting, or synthesizing, it helps me to address them in greater depth and it’s easier on me! (April, middle school teacher)

I evaluated a WebQuest for middle elementary (third–fourth grades), although it seems a little complicated for that age group. The quest divides students into groups and each person in the group is given a role to play (a botanist, museum curator, ethnobotanist, etc.). The task is for students to find out how plants were used for medicinal purposes in the Southwest many years ago. Students then present their findings, in a format that they can give to a national museum. Weird. It was a little complicated and not well done. I liked the topic and thought it was interesting, but a lot of work would need to be done to modify it so that all students could participate. (Jennie, first-grade teacher).

CHAPTER REVIEW

Define problem-solving and inquiry.

The element that distinguishes problem-solving or problem-based learning from other strategies is that the focal point is a problem that students must work toward solving. A proposed solution is typically the outcome of problem-solving. During the inquiry part of the process, students ask questions and then search for answers to those questions.

Understand the interaction between problem-solving and other instructional goals. Although inquiry is also an important instructional strategy and can stand alone, it is also a central component of problem-solving because students must ask questions and investigate the answers to solve the problem. In addition, students apply critical and creative thinking skills to prior knowledge during the problem-solving process, and they communicate, collaborate, and often produce some kind of concrete artifact.

Discuss guidelines and tools for encouraging effective student problem-solving.

It is often difficult for teachers to not do what students can do, but empowering students in this way can lead to a string of benefits. Other guidelines, such as avoiding plagiarism, integrating reading and writing, and making it okay for students to make mistakes, keep the problem-solving process on track. Tools to assist in this process range from word processing to specially designed inquiry tools.

Create and adapt effective technology-enhanced tasks to support problem-solving. Teachers can design their own tasks following guidelines from any number of sources, but they can also find ready-made problems in books, on the Web, and in some software pack-ages. Teachers who do design their own have plenty of resources available to help. A key to task development is connecting classroom learning to the world outside of the classroom.

Assess student technology-supported problem-solving.

In many ways the assessment of problem-solving and inquiry tasks is similar to the assessment of other goals in this text. Matching goals and objectives to assessment and ensuring that students receive formative feedback throughout the process will make success more likely.

Baker, T. (2005). The history and application of GIS in education. KANGIS: K12 GIS Community. Available from http://kangis.org/learning/ed_docs/gisNed1.cfm.

Belland, B., Walker, A., Kim, N., & Lefler, M. (2017). Synthesizing results from empirical research on computer-based scaffolding in STEM education: A meta-analysis. Review of Educational Research, 87(2), pp. 309-344.

Chauhan, S. (2017). A meta-analysis of the impact of technology on learning effectiveness of elementary students. Computers & Education, 105, pp. 14-30.

Dooly, M. (2005, March/April). The Internet and language teaching: A sure way to interculturality? ESL Magazine, 44, 8–10.

Gordon, R. (1998, January).Balancing real-world problems with real-world results. Phi Delta Kappan, 79(5), 390–393. [electronic version]

IMSA (2005). How does PBL compare with other instructional approaches? Available: http://www2 .imsa.edu/programs/pbln/tutorials/intro/intro7.php.

Molebash, P., & Dodge, B. (2003). Kickstarting inquiry with WebQuests and web inquiry projects. Social Education, 671(3), 158–162.

Verga, L., & Kotz, S. A. (2013). How relevant is social interaction in second language learning? Frontiers in Human Neuroscience, 7, 550. http://doi.org/10.3389/fnhum.2013.00550

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Helping Students Ask the Right Questions

Thinking skills and constructivism, appropriate strategies, practical examples, questions and constructivism, implementing the theory.

  • The complexity of the world is increasing rapidly with the rise of technology. We have access to much more information than the generations before us did, and that information changes with intimidating speed. The half-life of an engineering degree is currently estimated at four years. That is, in four years, half of what an engineering graduate has learned becomes obsolete (Rubenstein, 1998)—a daunting statistic. Unless that engineer can access and integrate new information, he or she cannot remain current. In the face of such rapid and exponential change, no one can rely solely on experience and accumulated knowledge. Content mastery is not a static state but an evolving and lifelong process.
  • The workplace and schools increasingly call for teams of people to work effectively to analyze and resolve issues. It is important not only to ask the right questions but also to ask them in a logical sequence. Without a sequential questioning strategy, groups often flounder, go off track, or overlook essential information.
  • Most questioning strategies, although effective at stimulating thought about a given point, do little to help students integrate their thinking and produce a logical, well-considered conclusion or point of view that builds on previous questioning or thinking. Questions appear to be almost random.
  • The questions still reside with the teacher. But to develop the thinking and questioning abilities of students, the questions must reside with the students. We need to help students develop the capability to ask tough and meaningful questions. Effective teacher-generated questioning strategies encourage students to think but not necessarily to become better questioners. Indeed, Carin and Sund demonstrated that students attain significantly higher levels of thinking when they are encouraged to develop skill in generating critical and creative questions and when they are provided opportunities for dialogue with classmates about the questions posed and conclusions derived from information they encounter. (Cecil, 1995, p. 36)
  • comprehensive—they invite consideration of all relevant variables, perspectives, and information;
  • adaptable—they apply to student populations that vary by grade level and by ability and to different curriculum material;
  • discriminating—they accommodate the requirements of different situations;
  • productive—they produce some outcome, resolution, or conclusion; and
  • transferable—students can be taught these strategies so that they ask the questions.

Figure 1. Problem-Solving Strategies from CompassQuest

Helping Students Ask the Right Questions - table

  • NASA used them to avert disaster on its Apollo 13 mission.
  • Honda uses all four strategies in its quality assurance program.
  • Uniroyal Chemical uses the strategies to help its quality improvement teams work effectively.
  • Hewlett-Packard's customer engineers better serve customers by using these techniques.
  • Students at John Witherspoon Middle School in Princeton, New Jersey, pose as members of the Supreme Court to consider the Brown v. Board of Education decision and make a ruling.
  • At Whitman Middle School in Wauwatosa, Wisconsin, a 7th grade social studies class examines the U.S.-China trade policy from the standpoint of various stakeholders, such as Chinese citizens, U.S. citizens, human rights advocates, U.S. businesses, and the U.S. military.
  • Students in a science class at Gonzales, Louisiana, Middle School select topics for their science project.
  • Students in 8th grade consumer home economics at Scranton Middle School in Brighton, Michigan, identify how best to respond to typical job-related issues or problems, such as finding that a coworker is stealing from the cash register.

CompassQuest

The 12 schools in the compassquest consortium are working to infuse into their curriculums decision-making and problem-solving skills that are based on proven and successful corporate models., begun in 1998, the consortium is a three-year collaboration among four groups. the tregoe education forum provides and teaches problem-solving strategies to school teams. the school teams create classroom-based lessons and models that enable their middle school students to use rational decision-making and problem-solving techniques and strategies., corporate partners, who are trained in the kepner-tregoe methods and use them in their own corporate operations, coach the school teams throughout the three years. ascd provides the logistical support for the consortium and, with the help of consortium team members, is developing resources that will enable the wider education community to use these skills in their own school settings., figure 2. the select problem-solving matrix.

Helping Students Ask the Right Questions-table2

  • See the issues: What are you concerned about in this situation? What fears or hopes do you have? What needs must you address?
  • Clarify the issues: Why does each one of these issues concern you?
  • Assess priorities: Which issues are your priorities and why?
  • Name next steps: How will you address your high-priority issues?
  • Relevance for the students increases as they use these questioning strategies. Students become more invested as they apply their judgments and conclusions to the situation. They become interested in seeing what really happened or in comparing their conclusions with those of others. In addition, they see opportunities to apply the strategy to their own situations. As Mike Roche, a high school English teacher from Laguna Beach, California, High School says, It puts the students in a position to recognize that when they leave school as young adults, they are going to face many situations that they will have to sort through. No one is going to be there with the right answers—if there even is a right answer. They are going to have to make a decision or formulate an action plan on the basis of the best information available.
  • These strategies encourage and make visible student thinking and points of view. This allows teachers not only to assess student perspective and understanding before introducing a concept, and thus make meaningful linkages, but also to assess learning afterward. As Bob Klempen, deputy superintendent of Orange County, Florida, Public Schools, says, The process reinforces that everything said is important. And that brings dignity and respect into the discussion. It doesn't matter if the participants are students or faculty; the mutual respect that the process builds enables everyone to participate and listen.
  • These approaches provide a road map to guide group work. This questioning framework becomes a jumping-off point for further student inquiry and allows the teacher to always have some notion of where each group is in its analysis.
  • By learning these question-based problem-solving strategies, students become more effective questioners, thinkers, and learners. They learn from one another as well as from the teacher and the materials.
  • As students examine and work with content, they acquire a deeper understanding of curriculum material, which helps move material from mimetic, short-term memory to comprehension and long-term understanding.
  • The tools or strategies themselves become relevant to students as they see opportunities to apply the questions to real-life situations. For example, high school students in Warren County, New Jersey, used all four strategies in developing a countywide substance abuse policy.
The central problem that Constructivist educators face is not a [lack of] guiding theory, but concrete strategies and tools for institutionalizing these theoretical and practical understandings into more inclusive classrooms. (Hyerle, 1996, p. 15)
  • express, evaluate, and reevaluate their own opinions and comprehension;
  • expand their understanding on a given topic;
  • seek out and consider alternative viewpoints;
  • experience the dilemmas of others by sorting through and weighing similar issues;
  • refine their understanding by accommodating and considering relevant data and alternative perspectives; and
  • demonstrate their understanding by considering relevant facts and issues.

Bourgeois, P., & Clark, B. (1995). Franklin wants a pet. New York: Scholastic.

Cecil, N. (1995). The art of inquiry: Questioning strategies for K–6 classrooms. Winnipeg, Canada: Peguis.

Fiske, E. (1991). Smart schools, smart kids: Why do some schools work? New York: Touchstone.

Hyerle, D. (1996). Visual tools for constructing knowledge. Alexandria VA: ASCD.

Rubenstein, R. (1998, March 18). Invest in brains. Electronics Weekly, p. 17.

questions to ask students about problem solving

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20 Math Critical Thinking Questions to Ask in Class Tomorrow

chaput.caroline

  • November 20, 2023

give intentional and effective feedback for students with 10 critical thinking prompts for algebra 1

The level of apathy towards math is only increasing as each year passes and it’s up to us as teachers to make math class more meaningful . This list of math critical thinking questions will give you a quick starting point for getting your students to think deeper about any concept or problem. 

Since artificial intelligence has basically changed schooling as we once knew it, I’ve seen a lot of districts and teachers looking for ways to lean into AI rather than run from it.

The idea of memorizing formulas and regurgitating information for a test is becoming more obsolete. We can now teach our students how to use their resources to make educated decisions and solve more complex problems.

With that in mind, teachers have more opportunities to get their students thinking about the why rather than the how.

Table of Contents

Looking for more about critical thinking skills? Check out these blog posts:

  • Why You Need to Be Teaching Writing in Math Class Today
  • How to Teach Problem Solving for Mathematics
  • Turn the Bloom’s Taxonomy Verbs into Engaging Math Activities

critical thinking questions for any math class

What skills do we actually want to teach our students?

As professionals, we talk a lot about transferable skills that can be valuable in multiple jobs, such as leadership, event planning, or effective communication. The same can be said for high school students. 

It’s important to think about the skills that we want them to have before they are catapulted into the adult world. 

Do you want them to be able to collaborate and communicate effectively with their peers? Maybe you would prefer that they can articulate their thoughts in a way that makes sense to someone who knows nothing about the topic.

Whatever you decide are the most essential skills your students should learn, make sure to add them into your lesson objectives.

algebra 1 critical thinking questions. 10 topics. 190+ prompts. click to learn more

When should I ask these math critical thinking questions?

Critical thinking doesn’t have to be complex or fill an entire lesson. There are simple ways that you can start adding these types of questions into your lessons daily!

Start small

Add specific math critical thinking questions to your warm up or exit ticket routine. This is a great way to start or end your class because your students will be able to quickly show you what they understand. 

Asking deeper questions at the beginning of your class can end up leading to really great discussions and get your students talking about math.

questions to ask students about problem solving

Add critical thinking questions to word problems

Word problems and real-life applications are the perfect place to add in critical thinking questions. Real-world applications offer a more choose-your-own-adventure style assignment where your students can expand on their thought processes. 

They also allow your students to get creative and think outside of the box. These problem-solving skills play a critical role in helping your students develop critical thinking abilities.

connect algebra concepts to geometry applications

Keep reading for math critical thinking questions that can be applied to any subject or topic!

When you want your students to defend their answers.

  • Explain the steps you took to solve this problem
  • How do you know that your answer is correct?
  • Draw a diagram to prove your solution.
  • Is there a different way to solve this problem besides the one you used?
  • How would you explain _______________ to a student in the grade below you?
  • Why does this strategy work?
  • Use evidence from the problem/data to defend your answer in complete sentences.

When you want your students to justify their opinions

  • What do you think will happen when ______?
  • Do you agree/disagree with _______?
  • What are the similarities and differences between ________ and __________?
  • What suggestions would you give to this student?
  • What is the most efficient way to solve this problem?
  • How did you decide on your first step for solving this problem?

questions to ask students about problem solving

When you want your students to think outside of the box

  • How can ______________ be used in the real world?
  • What might be a common error that a student could make when solving this problem?
  • How is _____________ topic similar to _______________ (previous topic)?
  • What examples can you think of that would not work with this problem solving method?
  • What would happen if __________ changed?
  • Create your own problem that would give a solution of ______________.
  • What other math skills did you need to use to solve this problem?

Let’s Recap:

  • Rather than running from AI, help your students use it as a tool to expand their thinking.
  • Identify a few transferable skills that you want your students to learn and make a goal for how you can help them develop these skills.
  • Add critical thinking questions to your daily warm ups or exit tickets.
  • Ask your students to explain their thinking when solving a word problem.
  • Get a free sample of my Algebra 1 critical thinking questions ↓

10 free math critical thinking writing prompts for algebra 1 and algebra 2

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7 thoughts on “20 math critical thinking questions to ask in class tomorrow”.

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I would love to see your free math writing prompts, but there is no place for me to sign up. thank you

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August 20, 2013 / 8 Comments

Questions to ask while problem solving

I’m working on a set of possible questions one can ask their students (and teach their students to ask themselves) while they are problem solving in math. Note that these questions are related to the work of George Pólya from his book How to Solve It .

What would you add?

Questions to ask during problem solving

What are your assumptions?

  • What happens if you change those assumptions?
  • What assumptions have other people made?

Is there another way to solve it?

  • Within your current assumptions?
  • With different assumptions?

How is this problem related to other problems you have done?

  • Can you solve a related problem?
  • Can you simplify the problem, and then solve it?
  • Can you find connections between this problem and other problems?

Can you explain the solution to someone else?

  • Can they explain your solution to you?
  • Can they explain your solution to someone else?
  • Can you explain your solution without words?
  • Can you explain your solution using only words (no symbols or drawings)?

What tools could you use to help you solve this problem?

  • Are there any technological tools that might make the problem easier to visualize or manipulate?
  • Are there any mathematical techniques that might be connected to this problem?

How can you justify your solution?

  • How can you prove your answer is unique (if it is unique)?
  • If your answer is not unique, how many different answers are there?
  • How do you know your answer is reasonable?

Can you reflect on your problem solving process?

  • How could you change this problem?
  • Can you think of related problems?
  • What is interesting about this problem?
  • How could you generalize this problem?
  • Author info

Add yours →

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Kristina Buenafe says:

I might use this for my beginning of year problem solving challenge (this year it will incorporate building a gumdrop structure)! Cool way to think about it abstractly!

August 20, 2013 — 3:39 pm

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Howard Phillips says:

I grew up with the books of Polya and also W.W.Sawyer, both geniuses in the ‘What is going on? Have I seen anything like this before? Are there other ways of looking at it?’ business. Polya asks other questions, often really useful ones such as ‘Is there a simpler problem buried in here, which I might have more success with?’ and ‘Are there any special cases?’. Questions I like to ask are “If you had the solution, what would it look like?’ and ‘So you have a solution, how can you convince me,or anybody else, that it is right?’. Also, ‘Can you visualise the situation, draw a picture or two or a diagram?’, and ‘Is there any structure in the situation that I have overlooked?’. Advice I have often given is ‘Give it a break, think of something else, let the brain get on with the job, it doesn’t need your attention constantly’.

August 20, 2013 — 6:26 pm

David: There are two other books by Polya: Induction and Analogy in Mathematics, and Patterns of Plausible Reasoning

Well worth a read if you havent already done so

August 23, 2013 — 9:36 pm

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Kayla Szymanski says:

Hi, my name is Kayla Szymanski and I am currently enrolled in the EDM310 course. I have been assigned your blog for this week, and by this being done I have read your current post. I think that it is a very good idea to give your students questions they can ask themselves while problem solving. As a former math student myself, sometimes just seeing a math problem will freak you out enough to where you don’t even want to begin. I think by giving your students these quick questions it will ease this sensation that I repeatedly felt while taking math courses. Also just a tip I think maybe you could condense these rules into about 10 quick easy steps. This would be a great class motto or easy memorizing learning tool for each of your students. They could use it as a way to self check themselves while solving problems too. I had a teacher that once gave us a saying, and each word meant; subtract, multiply, etc.,and it worked. You will be surprised what works and sticks in your students heads.

August 27, 2013 — 6:49 pm

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My name is asad.Sir please answer me of this question.

When student solve mathematics problem then some question would create in mind like “Yes i understood” or “i have not understood” or “I have not learned that” or ” i have no idea to solve problem” or “what does means of one third” so please any can know that what is name of this cognitive/meta cognitive activity. Thanks

December 9, 2014 — 6:29 pm

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David Wees says:

I don’t know if there is a more specific name to it or not. I would call it “questioning oneself” and classify it broadly as a meta-cognitive strategy.

December 10, 2014 — 5:51 am

Thanks Sir. You said  “questioning onself” so can we say it “Self questioning ” ?

December 11, 2014 — 5:01 pm

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25 Powerful Creative Problem Solving Questions You Can Use for Any Challenge

January 19, 2016 by adminsmartstrm

Asking powerful questions can be a highly effective method for enhancing group discovery and creative problem solving. The right question, asked at the appropriate moment, can transform the unknown into new understanding, simplify complex issues, stimulate leaps in imagination, shift a group out of the doldrums, and quickly refocus efforts that have veered off onto unproductive tangents.

Effective questions are typically simple, concise, and easy to understand; they are also intentionally provocative to prompt a group to think, imagine, reflect, and challenge any pre-existing assumptions, beliefs, and conventional thinking.

Here are twenty-five effective creative problem solving questions you can ask when tackling virtually any challenge. Questions like these will help you stimulate your group’s imagination, and allow them to generate a wider range of fresh, innovative ideas.

“What is the simplest, most obvious solution to this challenge?”

“What are three other ways to approach this challenge?”

“If all limitations were removed, what could we do?”

“If we knew we couldn’t fail, what would we try?”

“Let’s quickly free-associate all the things that __(subject)__ reminds us of.”

“What else is similar to/different from this?”

“What is the most audacious thing we can do, say, or imagine?”

“What would Apple, Google, or Nike do in this situation?”

“What haven’t we considered yet?”

“What’s the single most important thing to focus on here?”

“What are some radically new or different ways to approach this challenge?”

“What idea(s) can we push even further?”

“What possibilities have we missed or not considered yet?”

“What if we…?”

“What can we simplify, combine, reverse, modify, or eliminate?”

“If we dug deeper, what would we discover?”

“How would a five-year-old solve this challenge?”

“What opportunities haven’t we recognized or taken advantage of yet?”

“Where is there an unmet need we can fulfill?”

“How would they solve this challenge fifty years in the future?”

“What are some of the worst ideas we can think of?” (Pause for answers, then ask…) “How can we reverse them to find the seeds of a good idea?”

“How can we take this wild idea and make it more practical?”

“What do our customers really want, need, or desire?”

“What would an insanely great idea or solution look like?”

“In what ways can we turn this challenge into a golden opportunity?”

Tip: Create a “cheat sheet” of great questions

If you prepare a list of provocative, “ready-to-go” questions before your next meeting or brainstorm session , you can significantly improve your leadership performance. A questioning “cheat sheet” will not only provide you with greater peace of mind, but also help keep the momentum of your meeting or session flowing in a positive direction. With a series of prepared questions at the ready, you will never be at a loss for a question to ask.  

Excerpt from the book,  SmartStorming: The Game-Changing Process for Generating Bigger, Better Ideas .

questions to ask students about problem solving

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questions to ask students about problem solving

How to Ask Problem-Solving Questions

  • November 29, 2021

The importance of asking questions (the right questions) is one of the foundations of my work. 

There are all kinds of questions we can ask.

3 Tips to break the telling habit

Some are more effective, and some are less effective, at fostering thinking and supporting problem-solving.

Asking the right questions is often about intention .

I’ve written before about the types of questions that support problem-solving , how to ask effective questions , and how to ask questions even if you already know “the answer” . 

I’ve even developed a guide with “3 Tips to Break the ‘Telling Habit’” – which you can download here .

One of my articles for TheLeanMag was titled “Solve More Problems By Asking Better Questions: The Impact of Breaking Your Telling Habit” — which you can download here .

But what does the practice of asking questions to support problem-solving actually look like?

This was one of the questions I’ve been asked by leaders enrolled in my Leading to Learn Accelerator program. 

In this post, I provide some resources for you to ask better questions to support problem-solving, and a video sharing the framework that I use in my head to guide the questions I ask.

Inspired by questions asked to me

As of the publishing of this post, I’m leading the second live community cohort of my Leading to Learn Accelerator program. Part of this program is a live group coaching component. 

These are always really interesting and useful sessions where we all get to learn by asking questions and sharing reflections.

In fact, in this particular session, we were talking about exactly that: how to ask more effective questions to support problem-solving.

My answer: for me, it looks like the A3 thinking process.

A3 Problem-Solving Framework

When I’m coaching others to solve problems, I’ve developed a pattern of thinking that helps me structure what questions I ask to help somebody solve a problem. I use this same process when working through solving my own problems too!

Having this structure in my head gives me a framework for asking questions, and allows me to stay more focused on what the other person is saying, rather than trying to think of the “next best question” to ask. 

The pattern of questions follows the problem-solving A3 thinking structure that I learned many years ago when I was first exposed to Lean and the Toyota Way. And one that I’ve learned more deeply about from Isao Yoshino when I first moved to Japan in 2015. 

What is an A3 and the A3 thinking process?

questions to ask students about problem solving

A3 thinking is collaborative. 

It’s a process management and improvement system that was developed by Toyota, and it can be used for problem-solving, decision-making, planning, or reporting.

I describe the flow of problem-solving A3s in my book Learning to Lead, Leading to Learn: Lessons from Toyota Leader Isao Yoshino on a Lifetime of Continuous Learning (see image here) and the history of how A3 thinking became the standard for communication and problem-solving at Toyota.

You can also learn more about A3 thinking in this post, “Toyota Leadership Lessons: Part 8 – The A3 Isn’t a Magical Tool,  which I wrote in 2017 based on my discussions with Mr. Yoshino about A3 as a management and thinking process.

While the A3 can be a tool and framework for communication and problem-solving, it’s important to remember, as I highlighted in about in this popular article “When to ‘A3’: 3 Problem-Solving Tools to Match the Complexity of Your Problem”:

It’s not about the tool(s), but rather the thinking process, the coaching process that supports problem-solving, and the learning process the comes out of it.”

A structured flow for problem-solving thinking

The A3 provides the structure for problem-solving and communicating one’s thinking about solving problems.

And it’s become my habit for structuring my thinking and questions for problem-solving.

We can use the A3 framework to guide what types of open questions we ask. 

In the video below I explore the structure of A3 thinking, how it works, and how it can be used to ask effective questions that help to solve problems. 

Below is a lightly edited version of the video’s transcript

Today I want to respond to a question that was asked in my recent Leading to Learn Accelerator program in one of our live group coaching sessions focusing on how to ask more effective questions to support problem-solving.

In our discussion, I shared how I like to ask questions and some of the patterns of thinking that are always going through my head when I’m thinking about how to ask a question to help somebody solve a problem.

Start with A3 Problem-Solving Thinking

It usually goes along the pattern that I learned from practicing A3 thinking — an A3 being a size of paper that they use at Toyota to support problem-solving and other documentation of projects and other things.

But from a problem-solving context, it follows the following flow (see image) below.

I want to share this here and talk about the different questions that happen in my head when I think about what questions to ask.

There are many more questions you can ask in all of these elements but this is the flow of thinking that happens for me.

The Flow of Problem-Solving

questions to ask students about problem solving

In this card (see picture to the right),  you can see it’s like an A3 divided into a left side and a right side.

The left side is about understanding the problem you’re trying to solve, and then the right side goes into more of the experimentation and closing the gap.

Here is how I use this A3 framework to guide questions I ask for problem-solving.

Questions that I like to start off with are around the background, like:

  • What is the context for this problem?
  • Why is it important? 
  • What led you to be addressing this?
  • How does this fit into priorities?

Current Condition

Then, ask questions to understand the current condition:

  • What’s actually happening here? 
  • How are you going to see?
  • What are you learning? 
  • How can you describe that in words and pictures? What’s really happening? 

Target / Goals

Then, understand the target by asking:

  • What’s the target?
  • What should be happening? 
  • What’s the goal, what do we need to accomplish?
  • What is the outcome we need to be seeing? 

What is the actual target?

Then we can define the problem.

There is a simple equation to define a problem that I learned a long time ago:

questions to ask students about problem solving

Target-Actual = Problem (the gap to close)

It’s a mantra that an executive I worked with would always say when he would go see and help support problem-solving in our organization: “Target, Actual, Please Explain”:

  • What’s actually happening?
  • What’s the gap? That’s the problem.
  • Please explain your thinking: What are you thinking is causing the problem? How are you solving it?

You can read more about this problem-solving equation in these articles: “Leading Daily Improvement: Creating New Habits and Practices to Support Continuous Improvement” and “When to ‘A3’: 3 Problem-Solving Tools to Match the Complexity of Your Problem”.

Once we’ve defined what the problem is in a quantifiable, measurable way, then we can move into what are the causes of the problem.

How are you learning and understanding what was actually causing the problem and getting into the root cause?

And this might be where we start asking more of the ‘why’ questions.

Countermeasures / Experiments to Close the Gap

When we really understand some of the causes — or maybe we haven’t got to the root cause yet, but we understand what our problem is and some of the causes — then we can start moving into countermeasures.

These are potential solutions to close the gap between what’s currently happening and what should be happening.

Then you can list out the different ideas and creative ideas and things that you’re going to try as countermeasures to close that gap.

And you can prioritize based on… what are we going to try first?

What’s our first step?

And then we put together our plan – what are we going to do?

Reflections

Then, really importantly: what are you learning from this? 

A Thinking Process to Support Problem-Solving

An A3 document is not a static document. It’s iterative — one you continue to revise as you go through and learn.

You do not have know “A3 thinking”, or use an A3 format or an A3-sized piece of paper, to use the same thinking process.

This structure of A3-thinking is in the back of my mind of how I’m guiding people through a problem-solving process.

Starting with context — what leads you to be focused on this problem? Why is it important to you?

Understanding what’s currently happening? What’s actually happening?

What should be happening? Then, you can quantify that problem.

Then you can start doing some root cause analysis and start coming up with some creative solutions, and there may be some things you already know that you can take action on that are just do-its.

This is a problem-solving process for framing your questions and thinking

It’s correlated to the simple equation that you can use for any problem.

T his A3 framework correlates with problem-solving thinking using either an A3 format or just structured thinking for problem-solving of any scope.

Go through this problem-solving process flow and ask questions to help somebody else think more deeply about the problem he or she has ownership for.

How can you get started with asking more intentional questions, and developing continuous learning supported by A3 thinking?

Breaking the Telling Habit Workshop

You break the telling habit!

Asking more effective questions to support problem-solving is one of the most important skills we can learn. However, we often have a habit of “telling” our answers more than asking to help others think and learn.

If you can learn to break the “telling habit” and start tapping into the power of effective questions, you open up whole new horizons of possibility for your organization, your team, and yourself!

Join my self-paced “Breaking the ‘Telling Habit’” workshop, and unlock your team’s potential by discovering how to ask more effective questions. You can take the class at any time, at your own pace.

Get the guide

If you don’t have it yet you can download my free guide “3 Tips to Break the ‘Telling Habit’” !

Accelerate your leadership

I also invite you to join my next Leading to Lean Accelerato r or enroll in the self-paced option to dive deeply into these topics of problem-solving, people development, asking effective questions, and more! 

And, I’m always happy to design custom learning experiences for your team or organization to accelerate your problem-solving thinking and coaching! Let’s talk!

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IMAGES

  1. Problem Solving Printable Flash Cards Social Skills Cards

    questions to ask students about problem solving

  2. Free Problem Solving for Kids School Counseling Printable in 2021

    questions to ask students about problem solving

  3. The ABCs of Problem Solving Steps {Free Printable Included!}

    questions to ask students about problem solving

  4. Probing Questions

    questions to ask students about problem solving

  5. Introduction to Problem Solving Skills

    questions to ask students about problem solving

  6. Problem Solving Skill

    questions to ask students about problem solving

VIDEO

  1. solving questions harsh rajput

  2. Problem Solving Method & Checklist: Sample Problem

  3. problem solving 😳👍.reaction. #school #crazymath #mathhumor #trendingdshorts #viral #funny #shorts

  4. Enigmas Unveiled Delving into Riddles and Brain Teasers

  5. Problem Solving IQ Pedestal

COMMENTS

  1. Effective Questions to Support Problem-Solving Thinking

    It's always inspiring to see, with some dedicated thinking time and practice time, how much people's skills in problem solving, question asking, and listening can advance. For example, in this class over two days, people got at least 90-120 minutes to work through a problem they own, and then practice 3-4 sessions of "catchball" (asking ...

  2. Helping Students Ask Questions and Define Problems

    Question Formulation Technique: QFT is a structured approach to asking questions. It improves communication skills, critical thinking, and problem-solving skills as well as metacognition. It also increases student autonomy and ownership of learning. Need to Know Questions: These questions are used to guide students' inquiry and drive their ...

  3. 15 Questions to Encourage Critical Thinking

    We'll explore why, as parents and teachers, the questions we ask our kids matter — and what we can be asking to help them excel. ... Analyzing why something is a problem — rather than just accepting that it is — will help students develop strong problem-solving skills of their own. The Hun School of Princeton Teaches Critical Thinking.

  4. 3 Ways to Improve Student Problem-Solving

    Research provides a striking revelation about problem solvers. The best problem solvers approach problems much differently than novices. For instance, one meta-study showed that when experts evaluate graphs, they tend to spend less time on tasks and answer choices and more time on evaluating the axes' labels and the relationships of variables within the graphs.

  5. A guide to successful questioning

    Questions that engage students in complex thinking can increase students' curiosity, develop their problem-solving skills, improve their engagement and strengthen their ability to persevere. Well-crafted questions also help students to make connections between ideas, and to develop personal meaning and associations with previously learned ...

  6. Questioning Strategies to Engage Students

    Questions to Ask Students at the Beginning of Class. Arrive in the classroom early to help students who have questions about previous lectures, readings and exam preparation. Begin the semester—the very first class, by asking students the type of questions you plan to ask throughout the semester. This will set the stage for the class, and ...

  7. 50+ Higher-Order Thinking Questions and Stems

    Source: University of Michigan. Bloom's Taxonomy is a way of classifying cognitive thinking skills. The six main categories—remember, understand, apply, analyze, evaluate, create—are broken into lower-order thinking skills (LOTS) and higher-order thinking skills (HOTS). LOTS includes remember, understand, and apply.

  8. Tweak your questions to improve students' problem-solving skills

    In a new study, researchers examined how the presentation and format of practice questions influences students' problem-solving performance. The study revealed that mixed problem sets are better than questions arranged by topic. There are two types of question practice teachers can give their students. The first, blocked practice, involves ...

  9. Teaching Problem Solving

    Make students articulate their problem solving process . In a one-on-one tutoring session, ask the student to work his/her problem out loud. This slows down the thinking process, making it more accurate and allowing you to access understanding. When working with larger groups you can ask students to provide a written "two-column solution.".

  10. Guiding Students to Be Independent Problem-Solvers in STEM ...

    This shifts students' attention to look at the details of the steps and not glance at the end of the work for the final answer. Further, grading can include points for steps and not the final solution. 5. Teach explicitly problem solving. After solving problems, students can create their own problem-solving strategy that they write on a note ...

  11. Solving Problems with Twenty Questions

    1. The students understand that they must find the answer to the problem that the teacher has put before them. 2. The students guess or reason what they believe is the answer to the problem. 3. By asking questions of the teacher, the students gather data to solve the problem. 4.

  12. Problem Solving in STEM

    Problem Solving in STEM. Solving problems is a key component of many science, math, and engineering classes. If a goal of a class is for students to emerge with the ability to solve new kinds of problems or to use new problem-solving techniques, then students need numerous opportunities to develop the skills necessary to approach and answer ...

  13. 8 Chapter 6 Supporting Student Problem-Solving

    During inquiry, students ask questions and then search for answers to those questions. In doing so, they come to new understandings in content and language. Although inquiry is an instructional strategy in itself, it is also a central component of problem-solving when students apply their new understandings to the problem at hand.

  14. Helping Students Ask the Right Questions

    The constructivist toolbox needs many tools, but surely one is a systematic approach that helps students ask important questions to successfully assess or resolve a difficult issue or problem. Ernest Boyer, president of the Carnegie Foundation for the Advancement of Teaching, proclaimed, "An educated person today is someone who knows the right ...

  15. Asking Questions Help Students in Learning & Problem Solving

    Four Question-Based Problem Solving Techniques. The article presented four strategies outlined in the ASCD CompassQuest consortium that help students become better questioners. First, when students are faced with a complex situation, with multiple variables and opinions, they use the SCAN technique. This acronym stands for: See the issues.

  16. 6 Essential Questions for Problem Solving

    The first step in developing essential questions for problem solving was to identify a specific skill set that would support reliable and consistent suc-cess at problem solving for all students. It involved ... Some students hesitate to ask questions. Others ask for help without putting effort into refining their questions or identifying what ...

  17. 20 Math Critical Thinking Questions to Ask in Class Tomorrow

    Identify a few transferable skills that you want your students to learn and make a goal for how you can help them develop these skills. Add critical thinking questions to your daily warm ups or exit tickets. Ask your students to explain their thinking when solving a word problem. Get a free sample of my Algebra 1 critical thinking questions ↓

  18. Questions to ask while problem solving

    I think that it is a very good idea to give your students questions they can ask themselves while problem solving. As a former math student myself, sometimes just seeing a math problem will freak you out enough to where you don't even want to begin. I think by giving your students these quick questions it will ease this sensation that I ...

  19. Helping Students with Word Problems

    These questions and prompts are a great way to have regular discussion around word problems. 5. Model your thinking when reading and solving word problems during instruction. 6. Provide students with a step-by-step way to work through understanding and solving a word problem. 7. Get hands-on. Use hands-on sorts and interactive digital activities.

  20. 25 Powerful Creative Problem Solving Questions You Can Use for Any

    Asking powerful questions can be a highly effective method for enhancing group discovery and creative problem solving. The right question, asked at the appropriate moment, can transform the unknown into new understanding, simplify complex issues, stimulate leaps in imagination, shift a group out of the doldrums, and quickly refocus efforts that have veered off onto …

  21. How to Ask Problem-Solving Questions

    The A3 provides the structure for problem-solving and communicating one's thinking about solving problems. And it's become my habit for structuring my thinking and questions for problem-solving. We can use the A3 framework to guide what types of open questions we ask. In the video below I explore the structure of A3 thinking, how it works ...

  22. 9 problem-solving examples for students (plus benefits)

    The following are problem-solving examples for students: 1. Brainstorming. Brainstorming is a creative process that can generate many potential solutions to an issue. When brainstorming, involve your students in creating lists. For example, if you want to focus on some historical figures and their significance, you can ask students to come up ...

  23. Study: How professors should respond to student questions

    Asking a question in a college classroom can be intimidating. And a recent study suggests that how professors respond to students' questions matters, both to how students think about themselves and their desire to be involved in the field in question. "Instructors' responses to students' questions, while being a minimal cue in the environment, can be beneficial to students, especially ...

  24. 8 Common Problem-Solving Interview Questions and Answers

    2. Tell me about a time when you faced an unexpected challenge at work. Tip: For this question, you'll want to choose a specific example from your work history to demonstrate your ability to be flexible while solving problems. To stay focused, you can use the STAR method to answer this question.

  25. Inequalities and Restrictions

    Inequalities Use inequalities to automatically shade above or below lines and curves. Combine implicit relations and inequalities to shade the interior of a circle, or the concave part of a hyper...