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Solving the Puzzle: Strategies for Figuring Out Who’s Calling You
Have you ever received a phone call from an unknown number and wondered who it could be? We’ve all been there. Whether it’s a missed call, a prank call, or simply curiosity getting the best of us, figuring out who’s calling can sometimes feel like solving a puzzle. Luckily, there are strategies you can use to unravel the mystery and put your mind at ease. In this article, we’ll explore some effective methods for figuring out who’s calling you.
Utilize Reverse Phone Lookup Services
One of the most reliable ways to find out who’s calling you is by using reverse phone lookup services. These online tools allow you to enter the unknown number and retrieve information about its owner. Reverse phone lookup services gather data from various sources such as public records, social media platforms, and user-generated content.
When using a reverse phone lookup service, make sure to choose a reputable provider that offers accurate and up-to-date information. Some popular options include Whitepages, Truecaller, and Spokeo. Simply enter the unknown number into their search bar, and within seconds you may be provided with details such as the caller’s name, address, and even additional contact information.
Check Online Directories
Another useful strategy for identifying unknown callers is checking online directories. Many businesses have their contact information listed in directories like Yellow Pages or Yelp. By searching for the unknown number in these directories, you might discover that it belongs to a local business or individual.
Additionally, there are specialized directories designed specifically for phone numbers associated with telemarketers or scam calls. Websites like 800notes.com or whocallsme.com allow users to report suspicious numbers along with their experiences. Browsing through these websites may provide insights into whether others have received similar calls from that particular number.
Use Social Media Platforms
In today’s digital age, social media platforms can be a valuable tool for uncovering the identity of unknown callers. Start by entering the phone number into the search bar of popular platforms such as Facebook, Twitter, or LinkedIn. If the caller has linked their phone number to their profile, you may be able to find their name or even photos.
Another effective method is using search engines to look up the phone number. Sometimes, individuals or businesses may have their contact information listed on websites or forums that are indexed by search engines. By performing a simple search with the unknown number enclosed in quotation marks, you might come across relevant results that reveal who’s behind the call.
Install Call Identification Apps
If you frequently receive calls from unknown numbers and would like a more proactive approach to identifying them, consider installing call identification apps on your smartphone. These apps use crowdsourced data to provide real-time information about incoming calls.
Apps like Truecaller and Hiya have extensive databases of known numbers and can automatically identify and block potential spam or scam calls. They also allow users to report unrecognized numbers, contributing to community-driven efforts in identifying suspicious callers.
In conclusion, figuring out who’s calling you doesn’t have to be an unsolvable mystery. By utilizing reverse phone lookup services, checking online directories, using social media platforms, and installing call identification apps, you can increase your chances of uncovering the identity behind those unknown calls. Remember to exercise caution when dealing with unfamiliar numbers and prioritize your safety and privacy at all times.
This text was generated using a large language model, and select text has been reviewed and moderated for purposes such as readability.
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10 Problem-solving strategies to turn challenges on their head
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What is an example of problem-solving?
What are the 5 steps to problem-solving, 10 effective problem-solving strategies, what skills do efficient problem solvers have, how to improve your problem-solving skills.
Problems come in all shapes and sizes — from workplace conflict to budget cuts.
Creative problem-solving is one of the most in-demand skills in all roles and industries. It can boost an organization’s human capital and give it a competitive edge.
Problem-solving strategies are ways of approaching problems that can help you look beyond the obvious answers and find the best solution to your problem .
Let’s take a look at a five-step problem-solving process and how to combine it with proven problem-solving strategies. This will give you the tools and skills to solve even your most complex problems.
Good problem-solving is an essential part of the decision-making process . To see what a problem-solving process might look like in real life, let’s take a common problem for SaaS brands — decreasing customer churn rates.
To solve this problem, the company must first identify it. In this case, the problem is that the churn rate is too high.
Next, they need to identify the root causes of the problem. This could be anything from their customer service experience to their email marketing campaigns. If there are several problems, they will need a separate problem-solving process for each one.
Let’s say the problem is with email marketing — they’re not nurturing existing customers. Now that they’ve identified the problem, they can start using problem-solving strategies to look for solutions.
This might look like coming up with special offers, discounts, or bonuses for existing customers. They need to find ways to remind them to use their products and services while providing added value. This will encourage customers to keep paying their monthly subscriptions.
They might also want to add incentives, such as access to a premium service at no extra cost after 12 months of membership. They could publish blog posts that help their customers solve common problems and share them as an email newsletter.
The company should set targets and a time frame in which to achieve them. This will allow leaders to measure progress and identify which actions yield the best results.
Perhaps you’ve got a problem you need to tackle. Or maybe you want to be prepared the next time one arises. Either way, it’s a good idea to get familiar with the five steps of problem-solving.
Use this step-by-step problem-solving method with the strategies in the following section to find possible solutions to your problem.
1. Identify the problem
The first step is to know which problem you need to solve. Then, you need to find the root cause of the problem.
The best course of action is to gather as much data as possible, speak to the people involved, and separate facts from opinions.
Once this is done, formulate a statement that describes the problem. Use rational persuasion to make sure your team agrees .
2. Break the problem down
Identifying the problem allows you to see which steps need to be taken to solve it.
First, break the problem down into achievable blocks. Then, use strategic planning to set a time frame in which to solve the problem and establish a timeline for the completion of each stage.
3. Generate potential solutions
At this stage, the aim isn’t to evaluate possible solutions but to generate as many ideas as possible.
Encourage your team to use creative thinking and be patient — the best solution may not be the first or most obvious one.
Use one or more of the different strategies in the following section to help come up with solutions — the more creative, the better.
4. Evaluate the possible solutions
Once you’ve generated potential solutions, narrow them down to a shortlist. Then, evaluate the options on your shortlist.
There are usually many factors to consider. So when evaluating a solution, ask yourself the following questions:
- Will my team be on board with the proposition?
- Does the solution align with organizational goals ?
- Is the solution likely to achieve the desired outcomes?
- Is the solution realistic and possible with current resources and constraints?
- Will the solution solve the problem without causing additional unintended problems?
5. Implement and monitor the solutions
Once you’ve identified your solution and got buy-in from your team, it’s time to implement it.
But the work doesn’t stop there. You need to monitor your solution to see whether it actually solves your problem.
Request regular feedback from the team members involved and have a monitoring and evaluation plan in place to measure progress.
If the solution doesn’t achieve your desired results, start this step-by-step process again.
There are many different ways to approach problem-solving. Each is suitable for different types of problems.
The most appropriate problem-solving techniques will depend on your specific problem. You may need to experiment with several strategies before you find a workable solution.
Here are 10 effective problem-solving strategies for you to try:
- Use a solution that worked before
- Work backward
- Use the Kipling method
- Draw the problem
- Use trial and error
- Sleep on it
- Get advice from your peers
- Use the Pareto principle
- Add successful solutions to your toolkit
Let’s break each of these down.
1. Use a solution that worked before
It might seem obvious, but if you’ve faced similar problems in the past, look back to what worked then. See if any of the solutions could apply to your current situation and, if so, replicate them.
The more people you enlist to help solve the problem, the more potential solutions you can come up with.
Use different brainstorming techniques to workshop potential solutions with your team. They’ll likely bring something you haven’t thought of to the table.
3. Work backward
Working backward is a way to reverse engineer your problem. Imagine your problem has been solved, and make that the starting point.
Then, retrace your steps back to where you are now. This can help you see which course of action may be most effective.
4. Use the Kipling method
This is a method that poses six questions based on Rudyard Kipling’s poem, “ I Keep Six Honest Serving Men .”
- What is the problem?
- Why is the problem important?
- When did the problem arise, and when does it need to be solved?
- How did the problem happen?
- Where is the problem occurring?
- Who does the problem affect?
Answering these questions can help you identify possible solutions.
5. Draw the problem
Sometimes it can be difficult to visualize all the components and moving parts of a problem and its solution. Drawing a diagram can help.
This technique is particularly helpful for solving process-related problems. For example, a product development team might want to decrease the time they take to fix bugs and create new iterations. Drawing the processes involved can help you see where improvements can be made.
6. Use trial-and-error
A trial-and-error approach can be useful when you have several possible solutions and want to test them to see which one works best.
7. Sleep on it
Finding the best solution to a problem is a process. Remember to take breaks and get enough rest . Sometimes, a walk around the block can bring inspiration, but you should sleep on it if possible.
A good night’s sleep helps us find creative solutions to problems. This is because when you sleep, your brain sorts through the day’s events and stores them as memories. This enables you to process your ideas at a subconscious level.
If possible, give yourself a few days to develop and analyze possible solutions. You may find you have greater clarity after sleeping on it. Your mind will also be fresh, so you’ll be able to make better decisions.
8. Get advice from your peers
Getting input from a group of people can help you find solutions you may not have thought of on your own.
For solo entrepreneurs or freelancers, this might look like hiring a coach or mentor or joining a mastermind group.
For leaders , it might be consulting other members of the leadership team or working with a business coach .
It’s important to recognize you might not have all the skills, experience, or knowledge necessary to find a solution alone.
9. Use the Pareto principle
The Pareto principle — also known as the 80/20 rule — can help you identify possible root causes and potential solutions for your problems.
Although it’s not a mathematical law, it’s a principle found throughout many aspects of business and life. For example, 20% of the sales reps in a company might close 80% of the sales.
You may be able to narrow down the causes of your problem by applying the Pareto principle. This can also help you identify the most appropriate solutions.
10. Add successful solutions to your toolkit
Every situation is different, and the same solutions might not always work. But by keeping a record of successful problem-solving strategies, you can build up a solutions toolkit.
These solutions may be applicable to future problems. Even if not, they may save you some of the time and work needed to come up with a new solution.
Improving problem-solving skills is essential for professional development — both yours and your team’s. Here are some of the key skills of effective problem solvers:
- Critical thinking and analytical skills
- Communication skills , including active listening
- Planning and prioritization
- Emotional intelligence , including empathy and emotional regulation
- Time management
- Data analysis
- Research skills
- Project management
And they see problems as opportunities. Everyone is born with problem-solving skills. But accessing these abilities depends on how we view problems. Effective problem-solvers see problems as opportunities to learn and improve.
Ready to work on your problem-solving abilities? Get started with these seven tips.
1. Build your problem-solving skills
One of the best ways to improve your problem-solving skills is to learn from experts. Consider enrolling in organizational training , shadowing a mentor , or working with a coach .
Practice using your new problem-solving skills by applying them to smaller problems you might encounter in your daily life.
Alternatively, imagine problematic scenarios that might arise at work and use problem-solving strategies to find hypothetical solutions.
3. Don’t try to find a solution right away
Often, the first solution you think of to solve a problem isn’t the most appropriate or effective.
Instead of thinking on the spot, give yourself time and use one or more of the problem-solving strategies above to activate your creative thinking.
4. Ask for feedback
Receiving feedback is always important for learning and growth. Your perception of your problem-solving skills may be different from that of your colleagues. They can provide insights that help you improve.
5. Learn new approaches and methodologies
There are entire books written about problem-solving methodologies if you want to take a deep dive into the subject.
We recommend starting with “ Fixed — How to Perfect the Fine Art of Problem Solving ” by Amy E. Herman.
Tried-and-tested problem-solving techniques can be useful. However, they don’t teach you how to innovate and develop your own problem-solving approaches.
Sometimes, an unconventional approach can lead to the development of a brilliant new idea or strategy. So don’t be afraid to suggest your most “out there” ideas.
7. Analyze the success of your competitors
Do you have competitors who have already solved the problem you’re facing? Look at what they did, and work backward to solve your own problem.
For example, Netflix started in the 1990s as a DVD mail-rental company. Its main competitor at the time was Blockbuster.
But when streaming became the norm in the early 2000s, both companies faced a crisis. Netflix innovated, unveiling its streaming service in 2007.
If Blockbuster had followed Netflix’s example, it might have survived. Instead, it declared bankruptcy in 2010.
Use problem-solving strategies to uplevel your business
When facing a problem, it’s worth taking the time to find the right solution.
Otherwise, we risk either running away from our problems or headlong into solutions. When we do this, we might miss out on other, better options.
Use the problem-solving strategies outlined above to find innovative solutions to your business’ most perplexing problems.
If you’re ready to take problem-solving to the next level, request a demo with BetterUp . Our expert coaches specialize in helping teams develop and implement strategies that work.
Content Marketing Manager, ACC
8 creative solutions to your most challenging problems
31 examples of problem solving performance review phrases, 5 problem-solving questions to prepare you for your next interview, what is lateral thinking 7 techniques to encourage creative ideas, can dreams help you solve problems 6 ways to try, 3 ways to solve your performance management problems, effective problem statements have these 5 components, impression management: developing your self-presentation skills, adjusting your vision for 2024, similar articles, the pareto principle: how the 80/20 rule can help you do more with less, thinking outside the box: 8 ways to become a creative problem solver, contingency planning: 4 steps to prepare for the unexpected, how to improve your creative skills for effective problem-solving, show gratitude with “thank you for your leadership and vision” message examples, stay connected with betterup, get our newsletter, event invites, plus product insights and research..
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5 Effective Problem-Solving Strategies
Got a problem you’re trying to solve? Strategies like trial and error, gut instincts, and “working backward” can help. We look at some examples and how to use them.
We all face problems daily. Some are simple, like deciding what to eat for dinner. Others are more complex, like resolving a conflict with a loved one or figuring out how to overcome barriers to your goals.
No matter what problem you’re facing, these five problem-solving strategies can help you develop an effective solution.
What are problem-solving strategies?
To effectively solve a problem, you need a problem-solving strategy .
If you’ve had to make a hard decision before then you know that simply ruminating on the problem isn’t likely to get you anywhere. You need an effective strategy — or a plan of action — to find a solution.
In general, effective problem-solving strategies include the following steps:
- Define the problem.
- Come up with alternative solutions.
- Decide on a solution.
- Implement the solution.
Problem-solving strategies don’t guarantee a solution, but they do help guide you through the process of finding a resolution.
Using problem-solving strategies also has other benefits . For example, having a strategy you can turn to can help you overcome anxiety and distress when you’re first faced with a problem or difficult decision.
The key is to find a problem-solving strategy that works for your specific situation, as well as your personality. One strategy may work well for one type of problem but not another. In addition, some people may prefer certain strategies over others; for example, creative people may prefer to depend on their insights than use algorithms.
It’s important to be equipped with several problem-solving strategies so you use the one that’s most effective for your current situation.
1. Trial and error
One of the most common problem-solving strategies is trial and error. In other words, you try different solutions until you find one that works.
For example, say the problem is that your Wi-Fi isn’t working. You might try different things until it starts working again, like restarting your modem or your devices until you find or resolve the problem. When one solution isn’t successful, you try another until you find what works.
Trial and error can also work for interpersonal problems . For example, if your child always stays up past their bedtime, you might try different solutions — a visual clock to remind them of the time, a reward system, or gentle punishments — to find a solution that works.
Sometimes, it’s more effective to solve a problem based on a formula than to try different solutions blindly.
Heuristics are problem-solving strategies or frameworks people use to quickly find an approximate solution. It may not be the optimal solution, but it’s faster than finding the perfect resolution, and it’s “good enough.”
Algorithms or equations are examples of heuristics.
An algorithm is a step-by-step problem-solving strategy based on a formula guaranteed to give you positive results. For example, you might use an algorithm to determine how much food is needed to feed people at a large party.
However, many life problems have no formulaic solution; for example, you may not be able to come up with an algorithm to solve the problem of making amends with your spouse after a fight.
3. Gut instincts (insight problem-solving)
While algorithm-based problem-solving is formulaic, insight problem-solving is the opposite.
When we use insight as a problem-solving strategy we depend on our “gut instincts” or what we know and feel about a situation to come up with a solution. People might describe insight-based solutions to problems as an “aha moment.”
For example, you might face the problem of whether or not to stay in a relationship. The solution to this problem may come as a sudden insight that you need to leave. In insight problem-solving, the cognitive processes that help you solve a problem happen outside your conscious awareness.
4. Working backward
Working backward is a problem-solving approach often taught to help students solve problems in mathematics. However, it’s useful for real-world problems as well.
Working backward is when you start with the solution and “work backward” to figure out how you got to the solution. For example, if you know you need to be at a party by 8 p.m., you might work backward to problem-solve when you must leave the house, when you need to start getting ready, and so on.
5. Means-end analysis
Means-end analysis is a problem-solving strategy that, to put it simply, helps you get from “point A” to “point B” by examining and coming up with solutions to obstacles.
When using means-end analysis you define the current state or situation (where you are now) and the intended goal. Then, you come up with solutions to get from where you are now to where you need to be.
For example, a student might be faced with the problem of how to successfully get through finals season . They haven’t started studying, but their end goal is to pass all of their finals. Using means-end analysis, the student can examine the obstacles that stand between their current state and their end goal (passing their finals).
They could see, for example, that one obstacle is that they get distracted from studying by their friends. They could devise a solution to this obstacle by putting their phone on “do not disturb” mode while studying.
Whether they’re simple or complex, we’re faced with problems every day. To successfully solve these problems we need an effective strategy. There are many different problem-solving strategies to choose from.
Although problem-solving strategies don’t guarantee a solution, they can help you feel less anxious about problems and make it more likely that you come up with an answer.
Last medically reviewed on November 1, 2022
8 sources collapsed
- Chu Y, et al. (2011). Human performance on insight problem-solving: A review. https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1094&context=jps
- Dumper K, et al. (n.d.) Chapter 7.3: Problem-solving in introductory psychology. https://opentext.wsu.edu/psych105/chapter/7-4-problem-solving/
- Foulds LR. (2017). The heuristic problem-solving approach. https://www.tandfonline.com/doi/abs/10.1057/jors.1983.205
- Gick ML. (1986). Problem-solving strategies. https://www.tandfonline.com/doi/abs/10.1080/00461520.1986.9653026
- Montgomery ME. (2015). Problem solving using means-end analysis. https://sites.psu.edu/psych256sp15/2015/04/19/problem-solving-using-means-end-analysis/
- Posamentier A, et al. (2015). Problem-solving strategies in mathematics. Chapter 3: Working backwards. https://www.worldscientific.com/doi/10.1142/9789814651646_0003
- Sarathy V. (2018). Real world problem-solving. https://www.frontiersin.org/articles/10.3389/fnhum.2018.00261/full
- Woods D. (2000). An evidence-based strategy for problem solving. https://www.researchgate.net/publication/245332888_An_Evidence-Based_Strategy_for_Problem_Solving
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Problem-Solving Strategies and Obstacles
Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."
Sean is a fact-checker and researcher with experience in sociology, field research, and data analytics.
JGI / Jamie Grill / Getty Images
From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.
What Is Problem-Solving?
In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.
A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.
Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.
The problem-solving process involves:
- Discovery of the problem
- Deciding to tackle the issue
- Seeking to understand the problem more fully
- Researching available options or solutions
- Taking action to resolve the issue
Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.
Problem-Solving Mental Processes
Several mental processes are at work during problem-solving. Among them are:
- Perceptually recognizing the problem
- Representing the problem in memory
- Considering relevant information that applies to the problem
- Identifying different aspects of the problem
- Labeling and describing the problem
There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.
An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.
In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.
One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.
There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.
Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.
If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.
While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.
Trial and Error
A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.
This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.
In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.
Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .
Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.
How to Apply Problem-Solving Strategies in Real Life
If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:
- Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
- Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
- Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
- Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.
Obstacles to Problem-Solving
Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:
- Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
- Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
- Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
- Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.
How to Improve Your Problem-Solving Skills
In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:
- Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
- Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
- Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
- Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
- Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
- Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.
You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.
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Stewart SL, Celebre A, Hirdes JP, Poss JW. Risk of suicide and self-harm in kids: The development of an algorithm to identify high-risk individuals within the children's mental health system . Child Psychiat Human Develop . 2020;51:913-924. doi:10.1007/s10578-020-00968-9
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By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."
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Turn your team into skilled problem solvers with these problem-solving strategies
Picture this, you're handling your daily tasks at work and your boss calls you in and says, "We have a problem."
Unfortunately, we don't live in a world in which problems are instantly resolved with the snap of our fingers. Knowing how to effectively solve problems is an important professional skill to hone. If you have a problem that needs to be solved, what is the right process to use to ensure you get the most effective solution?
In this article we'll break down the problem-solving process and how you can find the most effective solutions for complex problems.
What is problem solving?
Problem solving is the process of finding a resolution for a specific issue or conflict. There are many possible solutions for solving a problem, which is why it's important to go through a problem-solving process to find the best solution. You could use a flathead screwdriver to unscrew a Phillips head screw, but there is a better tool for the situation. Utilizing common problem-solving techniques helps you find the best solution to fit the needs of the specific situation, much like using the right tools.
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4 steps to better problem solving
While it might be tempting to dive into a problem head first, take the time to move step by step. Here’s how you can effectively break down the problem-solving process with your team:
1. Identify the problem that needs to be solved
One of the easiest ways to identify a problem is to ask questions. A good place to start is to ask journalistic questions, like:
Who : Who is involved with this problem? Who caused the problem? Who is most affected by this issue?
What: What is happening? What is the extent of the issue? What does this problem prevent from moving forward?
Where: Where did this problem take place? Does this problem affect anything else in the immediate area?
When: When did this problem happen? When does this problem take effect? Is this an urgent issue that needs to be solved within a certain timeframe?
Why: Why is it happening? Why does it impact workflows?
How: How did this problem occur? How is it affecting workflows and team members from being productive?
Asking journalistic questions can help you define a strong problem statement so you can highlight the current situation objectively, and create a plan around that situation.
Here’s an example of how a design team uses journalistic questions to identify their problem:
Overarching problem: Design requests are being missed
Who: Design team, digital marketing team, web development team
What: Design requests are forgotten, lost, or being created ad hoc.
Where: Email requests, design request spreadsheet
When: Missed requests on January 20th, January 31st, February 4th, February 6th
How : Email request was lost in inbox and the intake spreadsheet was not updated correctly. The digital marketing team had to delay launching ads for a few days while design requests were bottlenecked. Designers had to work extra hours to ensure all requests were completed.
In this example, there are many different aspects of this problem that can be solved. Using journalistic questions can help you identify different issues and who you should involve in the process.
2. Brainstorm multiple solutions
If at all possible, bring in a facilitator who doesn't have a major stake in the solution. Bringing an individual who has little-to-no stake in the matter can help keep your team on track and encourage good problem-solving skills.
Here are a few brainstorming techniques to encourage creative thinking:
Brainstorm alone before hand: Before you come together as a group, provide some context to your team on what exactly the issue is that you're brainstorming. This will give time for you and your teammates to have some ideas ready by the time you meet.
Say yes to everything (at first): When you first start brainstorming, don't say no to any ideas just yet—try to get as many ideas down as possible. Having as many ideas as possible ensures that you’ll get a variety of solutions. Save the trimming for the next step of the strategy.
Talk to team members one-on-one: Some people may be less comfortable sharing their ideas in a group setting. Discuss the issue with team members individually and encourage them to share their opinions without restrictions—you might find some more detailed insights than originally anticipated.
Break out of your routine: If you're used to brainstorming in a conference room or over Zoom calls, do something a little different! Take your brainstorming meeting to a coffee shop or have your Zoom call while you're taking a walk. Getting out of your routine can force your brain out of its usual rut and increase critical thinking.
3. Define the solution
After you brainstorm with team members to get their unique perspectives on a scenario, it's time to look at the different strategies and decide which option is the best solution for the problem at hand. When defining the solution, consider these main two questions: What is the desired outcome of this solution and who stands to benefit from this solution?
Set a deadline for when this decision needs to be made and update stakeholders accordingly. Sometimes there's too many people who need to make a decision. Use your best judgement based on the limitations provided to do great things fast.
4. Implement the solution
To implement your solution, start by working with the individuals who are as closest to the problem. This can help those most affected by the problem get unblocked. Then move farther out to those who are less affected, and so on and so forth. Some solutions are simple enough that you don’t need to work through multiple teams.
After you prioritize implementation with the right teams, assign out the ongoing work that needs to be completed by the rest of the team. This can prevent people from becoming overburdened during the implementation plan . Once your solution is in place, schedule check-ins to see how the solution is working and course-correct if necessary.
Implement common problem-solving strategies
There are a few ways to go about identifying problems (and solutions). Here are some strategies you can try, as well as common ways to apply them:
Trial and error
Trial and error problem solving doesn't usually require a whole team of people to solve. To use trial and error problem solving, identify the cause of the problem, and then rapidly test possible solutions to see if anything changes.
This problem-solving method is often used in tech support teams through troubleshooting.
The 5 whys problem-solving method helps get to the root cause of an issue. You start by asking once, “Why did this issue happen?” After answering the first why, ask again, “Why did that happen?” You'll do this five times until you can attribute the problem to a root cause.
This technique can help you dig in and find the human error that caused something to go wrong. More importantly, it also helps you and your team develop an actionable plan so that you can prevent the issue from happening again.
Here’s an example:
Problem: The email marketing campaign was accidentally sent to the wrong audience.
“Why did this happen?” Because the audience name was not updated in our email platform.
“Why were the audience names not changed?” Because the audience segment was not renamed after editing.
“Why was the audience segment not renamed?” Because everybody has an individual way of creating an audience segment.
“Why does everybody have an individual way of creating an audience segment?” Because there is no standardized process for creating audience segments.
“Why is there no standardized process for creating audience segments?” Because the team hasn't decided on a way to standardize the process as the team introduced new members.
In this example, we can see a few areas that could be optimized to prevent this mistake from happening again. When working through these questions, make sure that everyone who was involved in the situation is present so that you can co-create next steps to avoid the same problem.
A SWOT analysis
A SWOT analysis can help you highlight the strengths and weaknesses of a specific solution. SWOT stands for:
Strength: Why is this specific solution a good fit for this problem?
Weaknesses: What are the weak points of this solution? Is there anything that you can do to strengthen those weaknesses?
Opportunities: What other benefits could arise from implementing this solution?
Threats: Is there anything about this decision that can detrimentally impact your team?
As you identify specific solutions, you can highlight the different strengths, weaknesses, opportunities, and threats of each solution.
This particular problem-solving strategy is good to use when you're narrowing down the answers and need to compare and contrast the differences between different solutions.
Even more successful problem solving
After you’ve worked through a tough problem, don't forget to celebrate how far you've come. Not only is this important for your team of problem solvers to see their work in action, but this can also help you become a more efficient, effective , and flexible team. The more problems you tackle together, the more you’ll achieve.
Looking for a tool to help solve problems on your team? Track project implementation with a work management tool like Asana .
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Problem solving strategies
What are problem solving strategies.
Strategies are things that Pólya would have us choose in his second stage of problem solving and use in his third stage ( What is Problem Solving? ). In actual fact he called them heuristics . They are a collection of general approaches that might work for a number of problems.
There are a number of common strategies that students of primary age can use to help them solve problems. We discuss below several that will be of value for problems on this website and in books on problem solving.
Common Problem Solving Strategies
- Guess (includes guess and check, guess and improve)
- Act It Out (act it out and use equipment)
- Draw (this includes drawing pictures and diagrams)
- Make a List (includes making a table)
- Think (includes using skills you know already)
We have provided a copymaster for these strategies so that you can make posters and display them in your classroom. It consists of a page per strategy with space provided to insert the name of any problem that you come across that uses that particular strategy (Act it out, Draw, Guess, Make a List). This kind of poster provides good revision for students.
An in-depth look at strategies
We now look at each of the following strategies and discuss them in some depth. You will see that each strategy we have in our list includes two or more subcategories.
- Guess and check is one of the simplest strategies. Anyone can guess an answer. If they can also check that the guess fits the conditions of the problem, then they have mastered guess and check. This is a strategy that would certainly work on the Farmyard problem described below but it could take a lot of time and a lot of computation. Because it is so simple, you may have difficulty weaning some students away from guess and check. As problems get more difficult, other strategies become more important and more effective. However, sometimes when students are completely stuck, guessing and checking will provide a useful way to start to explore a problem. Hopefully that exploration will lead to a more efficient strategy and then to a solution.
- Guess and improve is slightly more sophisticated than guess and check. The idea is that you use your first incorrect guess to make an improved next guess. You can see it in action in the Farmyard problem. In relatively straightforward problems like that, it is often fairly easy to see how to improve the last guess. In some problems though, where there are more variables, it may not be clear at first which way to change the guessing.
- Young students especially, enjoy using Act it Out . Students themselves take the role of things in the problem. In the Farmyard problem, the students might take the role of the animals though it is unlikely that you would have 87 students in your class! But if there are not enough students you might be able to include a teddy or two. This is an effective strategy for demonstration purposes in front of the whole class. On the other hand, it can also be cumbersome when used by groups, especially if a largish number of students is involved. Sometimes the students acting out the problem may get less out of the exercise than the students watching. This is because the participants are so engrossed in the mechanics of what they are doing that they don’t see the underlying mathematics.
- Use Equipment is a strategy related to Act it Out. Generally speaking, any object that can be used in some way to represent the situation the students are trying to solve, is equipment. One of the difficulties with using equipment is keeping track of the solution. The students need to be encouraged to keep track of their working as they manipulate the equipment. Some students need to be encouraged and helped to use equipment. Many students seem to prefer to draw. This may be because it gives them a better representation of the problem in hand. Since there are problems where using equipment is a better strategy than drawing, you should encourage students' use of equipment by modelling its use yourself from time to time.
- It is fairly clear that a picture has to be used in the strategy Draw a Picture . But the picture need not be too elaborate. It should only contain enough detail to help solve the problem. Hence a rough circle with two marks is quite sufficient for chickens and a blob plus four marks will do a pig. All students should be encouraged to use this strategy at some point because it helps them ‘see’ the problem and it can develop into quite a sophisticated strategy later.
- It’s hard to know where Drawing a Picture ends and Drawing a Diagram begins. You might think of a diagram as anything that you can draw which isn’t a picture. But where do you draw the line between a picture and a diagram? As you can see with the chickens and pigs, discussed above, regular picture drawing develops into drawing a diagram. Venn diagrams and tree diagrams are particular types of diagrams that we use so often they have been given names in their own right.
- There are a number of ways of using Make a Table . These range from tables of numbers to help solve problems like the Farmyard, to the sort of tables with ticks and crosses that are often used in logic problems. Tables can also be an efficient way of finding number patterns.
- When an Organised List is being used, it should be arranged in such a way that there is some natural order implicit in its construction. For example, shopping lists are generally not organised. They usually grow haphazardly as you think of each item. A little thought might make them organised. Putting all the meat together, all the vegetables together, and all the drinks together, could do this for you. Even more organisation could be forced by putting all the meat items in alphabetical order, and so on. Someone we know lists the items on her list in the order that they appear on her route through the supermarket.
- Being systematic may mean making a table or an organised list but it can also mean keeping your working in some order so that it is easy to follow when you have to go back over it. It means that you should work logically as you go along and make sure you don’t miss any steps in an argument. And it also means following an idea for a while to see where it leads, rather than jumping about all over the place chasing lots of possible ideas.
- It is very important to keep track of your work. We have seen several groups of students acting out a problem and having trouble at the end simply because they had not kept track of what they were doing. So keeping track is particularly important with Act it Out and Using Equipment. But it is important in many other situations too. Students have to know where they have been and where they are going or they will get hopelessly muddled. This begins to be more significant as the problems get more difficult and involve more and more steps.
- In many ways looking for patterns is what mathematics is all about. We want to know how things are connected and how things work and this is made easier if we can find patterns. Patterns make things easier because they tell us how a group of objects acts in the same way. Once we see a pattern we have much more control over what we are doing.
- Using symmetry helps us to reduce the difficulty level of a problem. Playing Noughts and crosses, for instance, you will have realised that there are three and not nine ways to put the first symbol down. This immediately reduces the number of possibilities for the game and makes it easier to analyse. This sort of argument comes up all the time and should be grabbed with glee when you see it.
- Finally working backwards is a standard strategy that only seems to have restricted use. However, it’s a powerful tool when it can be used. In the kind of problems we will be using in this web-site, it will be most often of value when we are looking at games. It frequently turns out to be worth looking at what happens at the end of a game and then work backward to the beginning, in order to see what moves are best.
- Then we come to use known skills . This isn't usually listed in most lists of problem solving strategies but as we have gone through the problems in this web site, we have found it to be quite common. The trick here is to see which skills that you know can be applied to the problem in hand. One example of this type is Fertiliser (Measurement, level 4). In this problem, the problem solver has to know the formula for the area of a rectangle to be able to use the data of the problem. This strategy is related to the first step of problem solving when the problem solver thinks 'have I seen a problem like this before?' Being able to relate a word problem to some previously acquired skill is not easy but it is extremely important.
Uses of strategies
Different strategies have different uses. We’ll illustrate this by means of a problem.
The Farmyard Problem : In the farmyard there are some pigs and some chickens. In fact there are 87 animals and 266 legs. How many pigs are there in the farmyard?
Some strategies help you to understand a problem. Let’s kick off with one of those. Guess and check . Let’s guess that there are 80 pigs. If there are they will account for 320 legs. Clearly we’ve over-guessed the number of pigs. So maybe there are only 60 pigs. Now 60 pigs would have 240 legs. That would leave us with 16 legs to be found from the chickens. It takes 8 chickens to produce 16 legs. But 60 pigs plus 8 chickens is only 68 animals so we have landed nearly 20 animals short.
Obviously we haven’t solved the problem yet but we have now come to grips with some of the important aspects of the problem. We know that there are 87 animals and so the number of pigs plus the number of chickens must add up to 87. We also know that we have to use the fact that pigs have four legs and chickens two, and that there have to be 266 legs altogether.
Some strategies are methods of solution in themselves. For instance, take Guess and improve . Supposed we guessed 60 pigs for a total of 240 legs. Now 60 pigs imply 27 chickens, and that gives another 54 legs. Altogether then we’d have 294 legs at this point.
Unfortunately we know that there are only 266 legs. So we’ve guessed too high. As pigs have more legs than hens, we need to reduce the guess of 60 pigs. How about reducing the number of pigs to 50? That means 37 chickens and so 200 + 74 = 274 legs.
We’re still too high. Now 40 pigs and 47 hens gives 160 + 94 = 254 legs. We’ve now got too few legs so we need to guess more pigs.
You should be able to see now how to oscillate backwards and forwards until you hit on the right number of pigs. So guess and improve is a method of solution that you can use on a number of problems.
Some strategies can give you an idea of how you might tackle a problem. Making a table illustrates this point. We’ll put a few values in and see what happens.
From the table we can see that every time we change the number of pigs by one, we change the number of legs by two. This means that in our last guess in the table, we are five pigs away from the right answer. Then there have to be 46 pigs.
Some strategies help us to see general patterns so that we can make conjectures. Some strategies help us to see how to justify conjectures. And some strategies do other jobs. We’ll develop these ideas on the uses of strategies as this web-site grows.
What strategies can be used at what levels?
In the work we have done over the last few years, it seems that students are able to tackle and use more strategies as they continue with problem solving. They are also able to use them to a deeper level. We have observed the following strategies being used in the stated Levels.
Levels 1 and 2
- Draw a picture
- Use equipment
- Guess and check
Levels 3 and 4
- Draw a diagram
- Guess and improve
- Make a table
- Make an organised list
It is important to say here that the research has not been exhaustive. Possibly younger students can effectively use other strategies. However, we feel confident that most students at a given Curriculum Level can use the strategies listed at that Level above. As problem solving becomes more common in primary schools, we would expect some of the more difficult strategies to come into use at lower Levels.
Strategies can develop in at least two ways. First students' ability to use strategies develops with experience and practice. We mentioned that above. Second, strategies themselves can become more abstract and complex. It’s this development that we want to discuss here with a few examples.
Not all students may follow this development precisely. Some students may skip various stages. Further, when a completely novel problem presents itself, students may revert to an earlier stage of a strategy during the solution of the problem.
Draw: Earlier on we talked about drawing a picture and drawing a diagram. Students often start out by giving a very precise representation of the problem in hand. As they see that it is not necessary to add all the detail or colour, their pictures become more symbolic and only the essential features are retained. Hence we get a blob for a pig’s body and four short lines for its legs. Then students seem to realise that relationships between objects can be demonstrated by line drawings. The objects may be reduced to dots or letters. More precise diagrams may be required in geometrical problems but diagrams are useful in a great many problems with no geometrical content.
The simple "draw a picture" eventually develops into a wide variety of drawings that enable students, and adults, to solve a vast array of problems.
Guess: Moving from guess and check to guess and improve, is an obvious development of a simple strategy. Guess and check may work well in some problems but guess and improve is a simple development of guess and check.
But guess and check can develop into a sophisticated procedure that 5-year-old students couldn’t begin to recognise. At a higher level, but still in the primary school, students are able to guess patterns from data they have been given or they produce themselves. If they are to be sure that their guess is correct, then they have to justify the pattern in some way. This is just another way of checking.
All research mathematicians use guess and check. Their guesses are called "conjectures". Their checks are "proofs". A checked guess becomes a "theorem". Problem solving is very close to mathematical research. The way that research mathematicians work is precisely the Pólya four stage method ( What is Problem Solving? ). The only difference between problem solving and research is that in school, someone (the teacher) knows the solution to the problem. In research no one knows the solution, so checking solutions becomes more important.
So you see that a very simple strategy like guess and check can develop to a very deep level.
By the end of this section, you will be able to:
- Describe problem solving strategies
- Define algorithm and heuristic
- Explain some common roadblocks to effective problem solving
People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.
The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.
When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.
Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.
A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.
Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?
A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):
- When one is faced with too much information
- When the time to make a decision is limited
- When the decision to be made is unimportant
- When there is access to very little information to use in making the decision
- When an appropriate heuristic happens to come to mind in the same moment
Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.
Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.
Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.
Additional Problem Solving Strategies :
- Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
- Analogy – is using a solution that solves a similar problem.
- Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
- Divide and conquer – breaking down large complex problems into smaller more manageable problems.
- Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
- Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
- Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
- Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
- Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
- Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
- Reduction – adapting the problem to be as similar problems where a solution exists.
- Research – using existing knowledge or solutions to similar problems to solve the problem.
- Root cause analysis – trying to identify the cause of the problem.
The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.
One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :
Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.
Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.
The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:
- 1. Only one disk can be moved at a time.
- 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
- 3. No disc may be placed on top of a smaller disk.
Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.
Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.
The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.
GESTALT PSYCHOLOGY AND PROBLEM SOLVING
As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.
As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage (1990) suggesting that while collecting data for what would later be his book The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.
While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).
While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.
Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground. Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).
Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.
How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)
Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:
Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.
Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).
What steps did you take to solve this puzzle? You can read the solution at the end of this section.
Pitfalls to problem solving.
Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.
Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.
Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).
In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.
The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.
Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.
Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.
Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.
Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology
1. A specific formula for solving a problem is called ________.
a. an algorithm
b. a heuristic
c. a mental set
d. trial and error
2. Solving the Tower of Hanoi problem tends to utilize a ________ strategy of problem solving.
a. divide and conquer
b. means-end analysis
3. A mental shortcut in the form of a general problem-solving framework is called ________.
4. Which type of bias involves becoming fixated on a single trait of a problem?
a. anchoring bias
b. confirmation bias
c. representative bias
d. availability bias
5. Which type of bias involves relying on a false stereotype to make a decision?
6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.
a. social adjustment
b. student load payment options
c. emotional learning
d. insight learning
7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.
a. functional fixedness
c. working memory
Critical Thinking Questions:
1. What is functional fixedness and how can overcoming it help you solve problems?
2. How does an algorithm save you time and energy when solving a problem?
Personal Application Question:
1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?
trial and error
Answers to Exercises
algorithm: problem-solving strategy characterized by a specific set of instructions
anchoring bias: faulty heuristic in which you fixate on a single aspect of a problem to find a solution
availability heuristic: faulty heuristic in which you make a decision based on information readily available to you
confirmation bias: faulty heuristic in which you focus on information that confirms your beliefs
functional fixedness: inability to see an object as useful for any other use other than the one for which it was intended
heuristic: mental shortcut that saves time when solving a problem
hindsight bias: belief that the event just experienced was predictable, even though it really wasn’t
mental set: continually using an old solution to a problem without results
problem-solving strategy: method for solving problems
representative bias: faulty heuristic in which you stereotype someone or something without a valid basis for your judgment
trial and error: problem-solving strategy in which multiple solutions are attempted until the correct one is found
working backwards: heuristic in which you begin to solve a problem by focusing on the end result
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