problem solving strategy psychology

7.3 Problem Solving

Learning objectives.

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

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

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

Problem-Solving Strategies

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

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

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

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

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

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

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

Everyday Connection

Solving puzzles.

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

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

Take a look at the “Puzzling Scales” logic puzzle below ( Figure 7.9 ). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

Pitfalls to Problem Solving

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? 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 they just need to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

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

Link to Learning

Check out this Apollo 13 scene about NASA engineers overcoming functional fixedness to learn more.

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

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

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

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

Watch this teacher-made music video about cognitive biases to learn more.

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

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Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/psychology-2e/pages/1-introduction

• Authors: Rose M. Spielman, William J. Jenkins, Marilyn D. Lovett
• Publisher/website: OpenStax
• Book title: Psychology 2e
• Publication date: Apr 22, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/psychology-2e/pages/1-introduction
• Section URL: https://openstax.org/books/psychology-2e/pages/7-3-problem-solving

© Jun 26, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

4 Main problem-solving strategies

In Psychology, you get to read about a ton of therapies. It’s mind-boggling how different theorists have looked at human nature differently and have come up with different, often somewhat contradictory, theoretical approaches.

Yet, you can’t deny the kernel of truth that’s there in all of them. All therapies, despite being different, have one thing in common- they all aim to solve people’s problems. They all aim to equip people with problem-solving strategies to help them deal with their life problems.

Problem-solving is really at the core of everything we do. Throughout our lives, we’re constantly trying to solve one problem or another. When we can’t, all sorts of psychological problems take hold. Getting good at solving problems is a fundamental life skill.

Problem-solving stages

What problem-solving does is take you from an initial state (A) where a problem exists to a final or goal state (B), where the problem no longer exists.

To move from A to B, you need to perform some actions called operators. Engaging in the right operators moves you from A to B. So, the stages of problem-solving are:

• Initial state

The problem itself can either be well-defined or ill-defined. A well-defined problem is one where you can clearly see where you are (A), where you want to go (B), and what you need to do to get there (engaging the right operators).

For example, feeling hungry and wanting to eat can be seen as a problem, albeit a simple one for many. Your initial state is hunger (A) and your final state is satisfaction or no hunger (B). Going to the kitchen and finding something to eat is using the right operator.

In contrast, ill-defined or complex problems are those where one or more of the three problem solving stages aren’t clear. For example, if your goal is to bring about world peace, what is it exactly that you want to do?

It’s been rightly said that a problem well-defined is a problem half-solved. Whenever you face an ill-defined problem, the first thing you need to do is get clear about all the three stages.

Often, people will have a decent idea of where they are (A) and where they want to be (B). What they usually get stuck on is finding the right operators.

Initial theory in problem-solving

When people first attempt to solve a problem, i.e. when they first engage their operators, they often have an initial theory of solving the problem. As I mentioned in my article on overcoming challenges for complex problems, this initial theory is often wrong.

But, at the time, it’s usually the result of the best information the individual can gather about the problem. When this initial theory fails, the problem-solver gets more data, and he refines the theory. Eventually, he finds an actual theory i.e. a theory that works. This finally allows him to engage the right operators to move from A to B.

Problem-solving strategies

These are operators that a problem solver tries to move from A to B. There are several problem-solving strategies but the main ones are:

• Trial and error

1. Algorithms

When you follow a step-by-step procedure to solve a problem or reach a goal, you’re using an algorithm. If you follow the steps exactly, you’re guaranteed to find the solution. The drawback of this strategy is that it can get cumbersome and time-consuming for large problems.

Say I hand you a 200-page book and ask you to read out to me what’s written on page 100. If you start from page 1 and keep turning the pages, you’ll eventually reach page 100. There’s no question about it. But the process is time-consuming. So instead you use what’s called a heuristic.

2. Heuristics

Heuristics are rules of thumb that people use to simplify problems. They’re often based on memories from past experiences. They cut down the number of steps needed to solve a problem, but they don’t always guarantee a solution. Heuristics save us time and effort if they work.

You know that page 100 lies in the middle of the book. Instead of starting from page one, you try to open the book in the middle. Of course, you may not hit page 100, but you can get really close with just a couple of tries.

If you open page 90, for instance, you can then algorithmically move from 90 to 100. Thus, you can use a combination of heuristics and algorithms to solve the problem. In real life, we often solve problems like this.

When police are looking for suspects in an investigation, they try to narrow down the problem similarly. Knowing the suspect is 6 feet tall isn’t enough, as there could be thousands of people out there with that height.

Knowing the suspect is 6 feet tall, male, wears glasses, and has blond hair narrows down the problem significantly.

3. Trial and error

When you have an initial theory to solve a problem, you try it out. If you fail, you refine or change your theory and try again. This is the trial-and-error process of solving problems. Behavioral and cognitive trial and error often go hand in hand, but for many problems, we start with behavioural trial and error until we’re forced to think.

Say you’re in a maze, trying to find your way out. You try one route without giving it much thought and you find it leads to nowhere. Then you try another route and fail again. This is behavioural trial and error because you aren’t putting any thought into your trials. You’re just throwing things at the wall to see what sticks.

This isn’t an ideal strategy but can be useful in situations where it’s impossible to get any information about the problem without doing some trials.

Then, when you have enough information about the problem, you shuffle that information in your mind to find a solution. This is cognitive trial and error or analytical thinking. Behavioral trial and error can take a lot of time, so using cognitive trial and error as much as possible is advisable. You got to sharpen your axe before you cut the tree.

When solving complex problems, people get frustrated after having tried several operators that didn’t work. They abandon their problem and go on with their routine activities. Suddenly, they get a flash of insight that makes them confident they can now solve the problem.

I’ve done an entire article on the underlying mechanics of insight . Long story short, when you take a step back from your problem, it helps you see things in a new light. You make use of associations that were previously unavailable to you.

You get more puzzle pieces to work with and this increases the odds of you finding a path from A to B, i.e. finding operators that work.

Pilot problem-solving

No matter what problem-solving strategy you employ, it’s all about finding out what works. Your actual theory tells you what operators will take you from A to B. Complex problems don’t reveal their actual theories easily solely because they are complex.

Therefore, the first step to solving a complex problem is getting as clear as you can about what you’re trying to accomplish- collecting as much information as you can about the problem.

This gives you enough raw materials to formulate an initial theory. We want our initial theory to be as close to an actual theory as possible. This saves time and resources.

Solving a complex problem can mean investing a lot of resources. Therefore, it is recommended you verify your initial theory if you can. I call this pilot problem-solving.

Before businesses invest in making a product, they sometimes distribute free versions to a small sample of potential customers to ensure their target audience will be receptive to the product.

Before making a series of TV episodes, TV show producers often release pilot episodes to figure out whether the show can take off.

Before conducting a large study, researchers do a pilot study to survey a small sample of the population to determine if the study is worth carrying out.

The same ‘testing the waters’ approach needs to be applied to solving any complex problem you might be facing. Is your problem worth investing a lot of resources in? In management, we’re constantly taught about Return On Investment (ROI). The ROI should justify the investment.

If the answer is yes, go ahead and formulate your initial theory based on extensive research. Find a way to verify your initial theory. You need this reassurance that you’re going in the right direction, especially for complex problems that take a long time to solve.

Getting your causal thinking right

Problem solving boils down to getting your causal thinking right. Finding solutions is all about finding out what works, i.e. finding operators that take you from A to B. To succeed, you need to be confident in your initial theory (If I do X and Y, they’ll lead me to B). You need to be sure that doing X and Y will lead you to B- doing X and Y will cause B.

All obstacles to problem-solving or goal-accomplishing are rooted in faulty causal thinking leading to not engaging the right operators. When your causal thinking is on point, you’ll have no problem engaging the right operators.

As you can imagine, for complex problems, getting our causal thinking right isn’t easy. That’s why we need to formulate an initial theory and refine it over time.

I like to think of problem-solving as the ability to project the present into the past or into the future. When you’re solving problems, you’re basically looking at your present situation and asking yourself two questions:

“What caused this?” (Projecting present into the past)

“What will this cause?” (Projecting present into the future)

The first question is more relevant to problem-solving and the second to goal-accomplishing.

If you find yourself in a mess , you need to answer the “What caused this?” question correctly. For the operators you’re currently engaging to reach your goal, ask yourself, “What will this cause?” If you think they cannot cause B, it’s time to refine your initial theory.

Hi, I’m Hanan Parvez (MA Psychology). I’ve published over 500 articles and authored one book. My work has been featured in Forbes , Business Insider , Reader’s Digest , and Entrepreneur .

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48 Problem Solving

Department of Psychological and Brain Sciences, University of California, Santa Barbara

• Published: 03 June 2013
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Problem solving refers to cognitive processing directed at achieving a goal when the problem solver does not initially know a solution method. A problem exists when someone has a goal but does not know how to achieve it. Problems can be classified as routine or nonroutine, and as well defined or ill defined. The major cognitive processes in problem solving are representing, planning, executing, and monitoring. The major kinds of knowledge required for problem solving are facts, concepts, procedures, strategies, and beliefs. Classic theoretical approaches to the study of problem solving are associationism, Gestalt, and information processing. Current issues and suggested future issues include decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific thinking, everyday thinking, and the cognitive neuroscience of problem solving. Common themes concern the domain specificity of problem solving and a focus on problem solving in authentic contexts.

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Definition:

Problem Solving is the process of identifying, analyzing, and finding effective solutions to complex issues or challenges.

Key Steps in Problem Solving:

• Identification of the problem: Recognizing and clearly defining the issue that needs to be resolved.
• Analysis and research: Gathering relevant information, data, and facts to understand the problem in-depth.
• Formulating strategies: Developing various approaches and plans to tackle the problem effectively.
• Evaluation and selection: Assessing the viability and potential outcomes of the proposed solutions and selecting the most appropriate one.
• Implementation: Putting the chosen solution into action and executing the necessary steps to resolve the problem.
• Monitoring and feedback: Continuously evaluating the implemented solution and obtaining feedback to ensure its effectiveness.
• Adaptation and improvement: Modifying and refining the solution as needed to optimize results and prevent similar problems from arising in the future.

Skills and Qualities for Effective Problem Solving:

• Analytical thinking: The ability to break down complex problems into smaller, manageable components and analyze them thoroughly.
• Creativity: Thinking outside the box and generating innovative solutions.
• Decision making: Making logical and informed choices based on available data and critical thinking.
• Communication: Clearly conveying ideas, listening actively, and collaborating with others to solve problems as a team.
• Resilience: Maintaining a positive mindset, perseverance, and adaptability in the face of challenges.
• Resourcefulness: Utilizing available resources and seeking new approaches when confronted with obstacles.
• Time management: Effectively organizing and prioritizing tasks to optimize problem-solving efficiency.

Using Psychology

Over fifty problem-solving strategies explained — 2022.

by ahoskin4 | Oct 15, 2018 | Problem solving , Social Support | 26 comments

By John Malouff, Ph.D., J.D.

The comprehensive nature of the list of problem solving strategies allows individuals to use a checklist approach to problem solving. It also could facilitate training others in problem solving. The classification of the strategies into types may facilitate the development of new strategies that fit into a specific category. The explanations and examples given could serve as a valuable supplement to other explanations and examples available in books and on the web.

The strategies on this list are in themselves not original. The original aspects of this list are:

• putting all these specific strategies together
• organizing them into the types described below
• giving each type of strategy a fresh explanation with new examples.

Problem-solving strategies explained, with examples

Strategies to help you understand the problem.

It is easier to solve a specific problem than a vague one. So clarify the problem before you start looking for a solution. If your problem is that your spouse tells you that you are not supportive enough, find out what he or she means by supportive. If your problem is that your mother can't get the new software to work, determine what doesn't happen that she wants to happen. If your problem is a math homework question, read carefully the question (usually at the end):Is the answer supposed to be in metres or centimetres, rounded or not, square or not, etc.

 Strategies to help you simplify the task

Strategies to help you determine the cause of the problem, strategies involving the use of external aids to help you identify possible solutions, strategies involving the use of logic to help you identify possible solutions, strategies using a possible solution as a starting point to help you solve a problem, strategies to help you determine which possible solution is best, strategies using geometry for problem solving, strategies to help you function optimally while problem solving, strategies to help you solve multiple problems, sources of the list.

The strategies in this document come from a variety of sources, many of which have long since faded from my memory. Some of the ideas were previously described in the following references, which provide a wealth of examples:

D’Zurilla, T.J., & Goldfried, M.R. (1971). Problem solving and behaviour modification. Journal of Abnormal Psychology, 78, 104–126.

Fabian, J. (1990). Creative thinking & problem solving. Chelsea, MI:Lewis.

More information about Problem Solving

Harris, R. (2002).    Problem solving techniques.

McNamara, C. (1999).   Basic guidelines to problem solving and decision making.

Wikipedia (2006).   Problem solving.

About the author

John Malouff , Ph.D., J.D., earned a law degree from the University of Colorado in 1979 and a Ph.D. in clinical psychology from Arizona State University in 1984. He currently works as an associate professor of psychology at the University of New England, in Armidale, Australia. He has co-authored five books and several dozen articles in scientific journals.

26 Comments

I got a lot of in for information from this.

Great! Thanks for your comment, McKenzie. With help from a technician at the University of New England, Australia, I recently moved my public-service web sites to my blog. Now readers can comment and ask questions.

Thanks for sharing John. The examples are brief but nice and easy to read through. I had a laugh at the reference to “New VCR” in the first example. I actually still have one believe it or not.

Hi McKenzie. I too still have a VCR.

I learned a lot of information using this article!

Hi Emma. Thanks for the feedback!

Thank you John for sharing your efforts .You are very generous. Your work covers so many ways to look at problem solving. ps I was never any good at geometry !but there are plenty of other strategies .

Thanks for the positive comment, Dinah.

I am writing a book on critical thinking and evidence-based management for healthcare managers and administrators and would like your permission to include these strategies. I will provide proper attribution, including your name and link to the blog post. Thank you

Hi Frank. You may include the strategies. Best wishes for the book. John

Do you have a format or curriculum these could be used in a group structure?

Hi Erin. I do not. I assign the set of strategies in my Behavior Modification course as part of covering cognitive therapy methods. Maybe you will create something of the sort you mention.

Thank you so much. I am working on building a curriculum for a group with co-occurring disorders. And i found this information to be helpful with starting.

As always, such clear and concise instruction that can easily be applied to every day situations. Thank you

Thank you for putting this together. I found a lot of useful information here.

You’re welcome.

This resource was shared with us at our annual AISH (Academy for International School Heads) gathering. around 400 heads of schools were using this helpful resource! Thank you for posting and sharing this with us

Great! Thanks, Monique. The more people who use the methods, the better.

I learned a lot from reading this article. I realized so many things and I found many information here that is applicable in everyday situations.

Thank you so much for compiling all this information. 😀

Absolutely enjoyed reading these articles. I learned a lot of things that I never really thought about.

I have been reading how to solve problems, even before they start, once you have them and strategies to process, and this is the best I have found. Thank you for sharing to all of us!

I learned quite a bit but there was some things I struggled with

Great job! Efficient strategies and very informative.

Amazing breakdown to every example/strategies! Learned quite a bit of new ways to figure out solutions. Thank you!

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Cognitive Behavioral Therapy

Solving problems the cognitive-behavioral way, problem solving is another part of behavioral therapy..

Posted February 2, 2022 | Reviewed by Ekua Hagan

• What Is Cognitive Behavioral Therapy?
• Take our Your Mental Health Today Test
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• Problem-solving is one technique used on the behavioral side of cognitive-behavioral therapy.
• The problem-solving technique is an iterative, five-step process that requires one to identify the problem and test different solutions.
• The technique differs from ad-hoc problem-solving in its suspension of judgment and evaluation of each solution.

As I have mentioned in previous posts, cognitive behavioral therapy is more than challenging negative, automatic thoughts. There is a whole behavioral piece of this therapy that focuses on what people do and how to change their actions to support their mental health. In this post, I’ll talk about the problem-solving technique from cognitive behavioral therapy and what makes it unique.

The problem-solving technique

While there are many different variations of this technique, I am going to describe the version I typically use, and which includes the main components of the technique:

The first step is to clearly define the problem. Sometimes, this includes answering a series of questions to make sure the problem is described in detail. Sometimes, the client is able to define the problem pretty clearly on their own. Sometimes, a discussion is needed to clearly outline the problem.

The next step is generating solutions without judgment. The "without judgment" part is crucial: Often when people are solving problems on their own, they will reject each potential solution as soon as they or someone else suggests it. This can lead to feeling helpless and also discarding solutions that would work.

The third step is evaluating the advantages and disadvantages of each solution. This is the step where judgment comes back.

Fourth, the client picks the most feasible solution that is most likely to work and they try it out.

The fifth step is evaluating whether the chosen solution worked, and if not, going back to step two or three to find another option. For step five, enough time has to pass for the solution to have made a difference.

This process is iterative, meaning the client and therapist always go back to the beginning to make sure the problem is resolved and if not, identify what needs to change.

Advantages of the problem-solving technique

The problem-solving technique might differ from ad hoc problem-solving in several ways. The most obvious is the suspension of judgment when coming up with solutions. We sometimes need to withhold judgment and see the solution (or problem) from a different perspective. Deliberately deciding not to judge solutions until later can help trigger that mindset change.

Another difference is the explicit evaluation of whether the solution worked. When people usually try to solve problems, they don’t go back and check whether the solution worked. It’s only if something goes very wrong that they try again. The problem-solving technique specifically includes evaluating the solution.

Lastly, the problem-solving technique starts with a specific definition of the problem instead of just jumping to solutions. To figure out where you are going, you have to know where you are.

One benefit of the cognitive behavioral therapy approach is the behavioral side. The behavioral part of therapy is a wide umbrella that includes problem-solving techniques among other techniques. Accessing multiple techniques means one is more likely to address the client’s main concern.

Salene M. W. Jones, Ph.D., is a clinical psychologist in Washington State.

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

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

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

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

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

7.1. Different kinds of thought

7.2. Reasoning and Judgment

7.3. Problem Solving

READING WITH PURPOSE

Remember and understand.

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

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

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

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

Analyze, Evaluate, and Create

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

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

7.1. Different kinds of thought and knowledge

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

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

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

Factual and conceptual knowledge

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

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

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

Procedural knowledge

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

Metacognitive knowledge

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

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

The Dunning-Kruger Effect

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

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

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

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

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

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

Critical thinking

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

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

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

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

A Critical Thinker’s Toolkit 

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

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

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

Here are some common sources of biases:

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

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

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

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

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

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

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

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

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

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

bias : an inclination, tendency, leaning, or prejudice

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

7.2 Reasoning and Judgment

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

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

Deductive reasoning

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

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

Statement 2: You get an A on the final exam

Conclusion: You will get an A for the course

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

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

therefore q

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

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

I won’t have pizza (not p)

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

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

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

if p, then q

therefore, not p

Concrete version:

If I eat dinner, then I will have dessert

I did not have dessert

Therefore, I did not eat dinner

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

Students who like school study a lot

Students who study a lot get good grades

Jane does not like school

Therefore, Jane does not get good grades

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

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

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

You are not eleven feet tall

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

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

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

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

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

Inductive reasoning and judgment

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

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

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

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

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

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

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

Statement #1: Psychology is not my best subject

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

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

Judgment: The next exam will probably be very difficult.

Decision: I will study tonight instead of watching Netflix.

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

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

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

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

Statement #1: It is late at night.

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

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

Judgment: Albert will have no difficulty walking home.

Decision: He walks home alone.

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

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

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

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

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

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

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

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

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

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

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

Judgment: Breast cancer is the most common type.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

7.3 Problem Solving

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

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

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

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

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

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

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

Defining and Mentally Representing Problems in Order to Solve Them

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

insight :  a sudden realization of a solution to a problem

Solving Problems by Trial and Error

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

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

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

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

Solving Problems with Algorithms and Heuristics

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

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

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

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

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

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

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

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

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

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

An Effective Problem-Solving Sequence

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

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

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

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

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

a mental representation of a category of things in the world

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

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

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

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

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

an inclination, tendency, leaning, or prejudice

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

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

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

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

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

fast, automatic, and emotional thinking

slow, effortful, and logical thinking

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

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

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

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

noticing, comprehending and forming a mental conception of a problem

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

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

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

a sudden realization of a solution to a problem

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

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

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

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

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8 Effective Problem-Solving Strategies

Categories Cognition

If you need to solve a problem, there are a number of different problem-solving strategies that can help you come up with an accurate decision. Sometimes the best choice is to use a step-by-step approach that leads to the right solution, but other problems may require a trial-and-error approach. 

Some helpful problem-solving strategies include: Brainstorming Step-by-step algorithms Trial-and-error Working backward Heuristics Insight Writing it down Getting some sleep

Table of Contents

Why Use Problem-Solving Strategies

While you can always make a wild guess or pick at random, that certainly isn’t the most accurate way to come up with a solution. Using a more structured approach allows you to:

• Understand the nature of the problem
• Determine how you will solve it
• Research different options
• Take steps to solve the problem and resolve the issue

There are many tools and strategies that can be used to solve problems, and some problems may require more than one of these methods in order to come up with a solution.

Problem-Solving Strategies

The problem-solving strategy that works best depends on the nature of the problem and how much time you have available to make a choice. Here are eight different techniques that can help you solve whatever type of problem you might face.

Brainstorming

Coming up with a lot of potential solutions can be beneficial, particularly early on in the process. You might brainstorm on your own, or enlist the help of others to get input that you might not have otherwise considered.

Step-by-Step

Also known as an algorithm, this approach involves following a predetermined formula that is guaranteed to produce the correct result. While this can be useful in some situations—such as solving a math problem—it is not always practical in every situation.

On the plus side, algorithms can be very accurate and reliable. Unfortunately, they can also be time-consuming.

And in some situations, you cannot follow this approach because you simply don’t have access to all of the information you would need to do so.

Trial-and-Error

This problem-solving strategy involves trying a number of different solutions in order to figure out which one works best. This requires testing steps or more options to solve the problem or pick the right solution. 

For example, if you are trying to perfect a recipe, you might have to experiment with varying amounts of a certain ingredient before you figure out which one you prefer.

On the plus side, trial-and-error can be a great problem-solving strategy in situations that require an individualized solution. However, this approach can be very time-consuming and costly.

Working Backward

This problem-solving strategy involves looking at the end result and working your way back through the chain of events. It can be a useful tool when you are trying to figure out what might have led to a particular outcome.

It can also be a beneficial way to play out how you will complete a task. For example, if you know you need to have a project done by a certain date, working backward can help you figure out the steps you’ll need to complete in order to successfully finish the project.

Heuristics are mental shortcuts that allow you to come up with solutions quite quickly. They are often based on past experiences that are then applied to other situations. They are, essentially, a handy rule of thumb.

For example, imagine a student is trying to pick classes for the next term. While they aren’t sure which classes they’ll enjoy the most, they know that they tend to prefer subjects that involve a lot of creativity. They utilize this heuristic to pick classes that involve art and creative writing.

The benefit of a heuristic is that it is a fast way to make fairly accurate decisions. The trade-off is that you give up some accuracy in order to gain speed and efficiency.

Sometimes, the solution to a problem seems to come out of nowhere. You might suddenly envision a solution after struggling with the problem for a while. Or you might abruptly recognize the correct solution that you hadn’t seen before. 

No matter the source, insight-based problem-solving relies on following your gut instincts. While this may not be as objective or accurate as some other problem-solving strategies, it can be a great way to come up with creative, novel solutions.

Write It Down

Sometimes putting the problem and possible solutions down in paper can be a useful way to visualize solutions. Jot down whatever might help you envision your options. Draw a picture, create a mind map, or just write some notes to clarify your thoughts.

Get Some Sleep

If you’re facing a big problem or trying to make an important decision, try getting a good night’s sleep before making a choice. Sleep plays an essential role in memory consolidation, so getting some rest may help you access the information or insight you need to make the best choice.

Other Considerations

Even with an arsenal of problem-solving strategies at your disposal, coming up with solutions isn’t always easy. Certain challenges can make the process more difficult. A few issues that might emerge include:

• Mental set : When people form a mental set, they only rely on things that have worked in the last. Sometimes this can be useful, but in other cases, it can severely hinder the problem-solving process.
• Cognitive biases : Unconscious cognitive biases can make it difficult to see situations clearly and objectively. As a result, you may not consider all of your options or ignore relevant information.
• Misinformation : Poorly sourced clues and irrelevant details can add more complications. Being able to sort out what’s relevant and what’s not is essential for solving problems accurately.
• Functional fixedness : Functional fixedness happens when people only think of customary solutions to problems. It can hinder out-of-the-box thinking and prevents insightful, creative solutions.

Important Problem-Solving Skills

Becoming a good problem solver can be useful in a variety of domains, from school to work to interpersonal relationships. Important problem-solving skills encompass being able to identify problems, coming up with effective solutions, and then implementing these solutions.

According to a 2023 survey by the National Association of Colleges and Employers, 61.4% of employers look for problem-solving skills on applicant resumes.

Some essential problem-solving skills include:

• Research skills
• Analytical abilities
• Decision-making skills
• Critical thinking
• Communication
• Time management 
• Emotional intelligence

Solving a problem is complex and requires the ability to recognize the issue, collect and analyze relevant data, and make decisions about the best course of action. It can also involve asking others for input, communicating goals, and providing direction to others.

How to Become a Better Problem-Solver

If you’re ready to strengthen your problem-solving abilities, here are some steps you can take:

Identify the Problem

Before you can practice your problem-solving skills, you need to be able to recognize that there is a problem. When you spot a potential issue, ask questions about when it started and what caused it.

Do Your Research

Instead of jumping right in to finding solutions, do research to make sure you fully understand the problem and have all the background information you need. This helps ensure you don’t miss important details.

Hone Your Skills

Consider signing up for a class or workshop focused on problem-solving skill development. There are also books that focus on different methods and approaches.

The best way to strengthen problem-solving strategies is to give yourself plenty of opportunities to practice. Look for new challenges that allow you to think critically, analytically, and creatively.

Final Thoughts

If you have a problem to solve, there are plenty of strategies that can help you make the right choice. The key is to pick the right one, but also stay flexible and willing to shift gears.

In many cases, you might find that you need more than one strategy to make the choices that are right for your life.

Brunet, J. F., McNeil, J., Doucet, É., & Forest, G. (2020). The association between REM sleep and decision-making: Supporting evidences. Physiology & Behavior , 225, 113109. https://doi.org/10.1016/j.physbeh.2020.113109

Chrysikou, E. G, Motyka, K., Nigro, C., Yang, S. I. , & Thompson-Schill, S. L. (2016). Functional fixedness in creative thinking tasks depends on stimulus modality. Psychol Aesthet Creat Arts , 10(4):425‐435. https://doi.org/10.1037/aca0000050

Sarathy, V. (2018). Real world problem-solving. Front Hum Neurosci , 12:261. https://doi.org/10.3389/fnhum.2018.00261

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

Thinking and Intelligence

Problem Solving

OpenStaxCollege

[latexpage]

Learning Objectives

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

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

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

PROBLEM-SOLVING STRATEGIES

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

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

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

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

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

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

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

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

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

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

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.

Check out this Apollo 13 scene where the group of NASA engineers are given the task of overcoming functional fixedness.

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

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

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

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

Please visit this site to see a clever music video that a high school teacher made to explain these and other cognitive biases to his AP psychology students.

Were you able to determine how many marbles are needed to balance the scales in [link] ? You need nine. Were you able to solve the problems in [link] and [link] ? Here are the answers ( [link] ).

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

Review Questions

A specific formula for solving a problem is called ________.

• an algorithm
• a heuristic
• a mental set
• trial and error

A mental shortcut in the form of a general problem-solving framework is called ________.

Which type of bias involves becoming fixated on a single trait of a problem?

• anchoring bias
• confirmation bias
• representative bias
• availability bias

Which type of bias involves relying on a false stereotype to make a decision?

Critical Thinking Questions

What is functional fixedness and how can overcoming it help you solve problems?

Functional fixedness occurs when you cannot see a use for an object other than the use for which it was intended. For example, if you need something to hold up a tarp in the rain, but only have a pitchfork, you must overcome your expectation that a pitchfork can only be used for garden chores before you realize that you could stick it in the ground and drape the tarp on top of it to hold it up.

How does an algorithm save you time and energy when solving a problem?

An algorithm is a proven formula for achieving a desired outcome. It saves time because if you follow it exactly, you will solve the problem without having to figure out how to solve the problem. It is a bit like not reinventing the wheel.

Personal Application Question

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

Problem Solving Copyright © 2014 by OpenStaxCollege is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

Problem Solving Strategies

Problem solving is something that we go through on a daily basis. As problems never end, the need to solve them is also everlasting. From managing your books properly on a shelf to deciding the next step for your career, the problems can be small or big but they need to be solved on daily basis.

Study in cognitive psychology , has definitely made our lives easier to some extent. There are concrete psychological steps involved in problem solving, which if properly followed, can help us tackle every sort of problems.

[ Learn more : Psychological steps involved in problem solving ]

One of the important aspects of solving a problem is forming a good strategy. A strategy might be well thought of, rigorous and a sure winner but might not be viable given the resources available in hand.

Below given are the core strategies involved in solving every problem.

Problem-Solving Strategies

The step-by-step procedure involved in figuring out the correct answer to any problem is called algorithm. The step by step procedure involved in solving a mathematical problem using math formula is a perfect example of a problem-solving algorithm. Algorithm is the strategy that results in accurate answer; however, it’s not always practical. The strategy is highly time consuming, and involves taking lots of steps.

For instance , attempting to open a door lock using algorithm to find out the possible number combinations would take a really long time.

Heuristics refers to mental strategy based on rule-of thumb. There is no guarantee that it will always work out to produce the best solution. However, the rule of thumb strategy does help to simplify complex problems by narrowing the possible solutions. It makes it easier to reach the correct solution using other strategies.

Heuristic strategy of problem solving can also be referred to as the mental shortcut. For instance , you need to reach the other part of the city in a limited amount of time. You’ll obviously seek for the shortest route and means of transportation. The rule of thumb allows you to make up your mind about the fastest route depending on your past commutes. You might choose subway instead of hiring a cab.

Trial-and-Error

Trial and error strategy is the approach that deals with trying a number of different solutions and ruling out the ones that do not work. Approaching this strategy as the first method in an attempt to solve any problem can be highly time-consuming. So, it’s best to use this strategy as a follow up to figure out the best possible solution, after you have narrowed down the possible number of solutions using other techniques.

For instance , you’re trying to open a lock. Trying to enter every possible combination directly onto the lock for Trial-and-Error method can be highly time-consuming. Instead, if you’ve narrowed down the possible combinations to 20, you’ll have a much easier time solving the particular problem.

Insight is something that just occurs suddenly. Researchers suggest that insight can occur if you’ve dealt with similar problems in the past. For instance , Knowing that you’ve solved a particular algebra question in the past will make it much easier for you to solve the similar questions at present. However, it’s not always necessary that the mental processes be related with past problems. In fact, most cases of mental processes leading to insight happen outside of consciousness.

Every strategy you build for solving a specific problem, be it for buying groceries or deciding your career, can be narrowed down into one of the above strategy techniques. Some strategies are a combination of Algorithms and Heuristics while others are based on trial-and-error. Choose wisely analyzing your resources, collecting information and monitoring progress.

What are other people reading?

Convergent Vs Divergent Thinking

Convergent Thinking

Divergent Thinking

42 Problem Solving

[latexpage]

Learning Objectives

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

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

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

PROBLEM-SOLVING STRATEGIES

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

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

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

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

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

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

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

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

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

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

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.

Check out this Apollo 13 scene where the group of NASA engineers are given the task of overcoming functional fixedness.

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

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

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

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

Please visit this site to see a clever music video that a high school teacher made to explain these and other cognitive biases to his AP psychology students.

Were you able to determine how many marbles are needed to balance the scales in [link] ? You need nine. Were you able to solve the problems in [link] and [link] ? Here are the answers ( [link] ).

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

Review Questions

A specific formula for solving a problem is called ________.

• an algorithm
• a heuristic
• a mental set
• trial and error

A mental shortcut in the form of a general problem-solving framework is called ________.

Which type of bias involves becoming fixated on a single trait of a problem?

• anchoring bias
• confirmation bias
• representative bias
• availability bias

Which type of bias involves relying on a false stereotype to make a decision?

Critical Thinking Questions

What is functional fixedness and how can overcoming it help you solve problems?

Functional fixedness occurs when you cannot see a use for an object other than the use for which it was intended. For example, if you need something to hold up a tarp in the rain, but only have a pitchfork, you must overcome your expectation that a pitchfork can only be used for garden chores before you realize that you could stick it in the ground and drape the tarp on top of it to hold it up.

How does an algorithm save you time and energy when solving a problem?

An algorithm is a proven formula for achieving a desired outcome. It saves time because if you follow it exactly, you will solve the problem without having to figure out how to solve the problem. It is a bit like not reinventing the wheel.

Personal Application Question

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

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April 7, 2021

Our Brain Typically Overlooks This Brilliant Problem-Solving Strategy

People often limit their creativity by continually adding new features to a design rather than removing existing ones

By Diana Kwon

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For generations, the standard way to learn how to ride a bicycle was with training wheels or a tricycle. But in recent years, many parents have opted to train their kids with balance bikes , pedalless two-wheelers that enable children to develop the coordination needed for bicycling—a skill that is not as easily acquired with an extra set of wheels.

Given the benefits of balance bikes, why did it take so long for them to replace training wheels? There are plenty of other examples in which overlooked solutions that involve subtraction turn out to be better alternatives. In some European cities, for example, urban planners have gotten rid of traffic lights and road signs to make streets safer—an idea that runs counter to conventional traffic design.

Leidy Klotz , an engineer at the University of Virginia, noticed that minimalist designs, in which elements are removed from an existing model, were uncommon. So he reached out to Gabrielle Adams , a social psychologist at the university, to try to figure out why this was the case. The two researchers hypothesized that there might be a psychological explanation: when faced with a problem, people tend to select solutions that involve adding new elements rather than taking existing components away.

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Adams, Klotz and their colleagues set out to test if their hunch was correct. “We wanted to investigate whether, and to what extent, people actually overlooked subtraction when they’re tasked with changing things,” Adams says. Their investigation “wasn’t literature driven, because there’s [no academic] literature on this phenomenon. It was really just us putting our heads together to think up why this might be the case.”

The researchers first carried out a set of observational studies, assessments without a control group, to see whether this bias existed at all. In one, they asked 91 participants to make a pattern symmetrical by either adding or removing colored boxes. Only 18 people (20 percent) used subtraction. In another, the team scanned through an archive of ideas for improvement submitted to an incoming university president and found that only 11 percent of 651 proposals involved eliminating an existing regulation, practice or program. Similar results emerged across tasks that involved modifying structures, essays and itineraries—in each case, the vast majority of people chose to augment rather than remove.

To determine why people tended to choose additive solutions, the team dug deeper by conducting a series of eight experiments with more than 1,500 individuals recruited either from a university campus or through Amazon Mechanical Turk, a crowdsourcing Web site. In one experiment, people were asked to stabilize the roof of a Lego structure held up by a single block that rested atop a cube-shaped base. The reward for completing the task was $1, and participants could add new blocks for 10 cents apiece or get rid of blocks for free. The researchers wrote that one group was provided a cue about potential subtractive solutions by being told, “Each piece that you add costs ten cents but removing pieces is free,” while another group was just told, “Each piece that you add costs ten cents.” Almost two thirds of people in the cued group ended up choosing to eliminate the single block rather than adding new ones, compared with 41 percent of those who had not received the prompt.

The researchers also observed that people were more likely to remove features when they were given more opportunities to consider alternative ways to address a problem: when participants were asked to create a symmetrical pattern by adding or eliminating colored blocks, they opted for removal more often if they were given practice trials than if they had just one chance to tackle the problem. On the other hand, having to simultaneously juggle another task—such as keeping track of numbers on a screen—made individuals less likely to subtract elements to solve the same problem, suggesting that it requires more effort to think up subtractive solutions than additive ones. (In both of these experiments, removing blocks was the more efficient solution.)

These findings, which were published today in Nature, suggest that “additive solutions have sort of a privileged status—they tend to come to mind quickly and easily,” says Benjamin Converse , a social psychologist at the University of Virginia and a co-author of the study. “Subtractive solutions are not necessarily harder to consider, but they take more effort to find.”

The authors “convincingly demonstrate that we tend to not consider subtractive solutions as much as additive ones,” says Tom Meyvis , a consumer psychologist at New York University, who was not directly involved in the study but reviewed it and co-authored  a commentary about it in Nature. While the propensity for businesses and organizations to opt for complexity rather than simplification was previously known, the novelty of this paper is that it shows that people tend toward adding new features, “even when subtracting would clearly be better,” he adds. Meyvis also notes that other reasons for this effect may be a greater likelihood that additive solutions will be appreciated or the so-called sunk-cost bias, in which people continue investing in things for which time, money or effort has already been spent.

A number of open questions remain, such as whether the bias against subtractive solutions generalizes across cultures and if it exists in childhood or develops over time. For now the team hopes that these findings will encourage people across various fields, whether they be engineering, architecture or medicine, to think about subtractive options—such as balance bikes—that might be typically be overlooked. “The hope is that, just by getting people to think about this more, that maybe it will help inspire some other neglected subtractions,” Converse says.

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What Is Problem-Solving Therapy?

Verywell / Madelyn Goodnight

Problem-Solving Therapy Techniques

How effective is problem-solving therapy, things to consider, how to get started.

Problem-solving therapy is a brief intervention that provides people with the tools they need to identify and solve problems that arise from big and small life stressors. It aims to improve your overall quality of life and reduce the negative impact of psychological and physical illness.

Problem-solving therapy can be used to treat depression , among other conditions. It can be administered by a doctor or mental health professional and may be combined with other treatment approaches.

At a Glance

Problem-solving therapy is a short-term treatment used to help people who are experiencing depression, stress, PTSD, self-harm, suicidal ideation, and other mental health problems develop the tools they need to deal with challenges. This approach teaches people to identify problems, generate solutions, and implement those solutions. Let's take a closer look at how problem-solving therapy can help people be more resilient and adaptive in the face of stress.

Problem-solving therapy is based on a model that takes into account the importance of real-life problem-solving. In other words, the key to managing the impact of stressful life events is to know how to address issues as they arise. Problem-solving therapy is very practical in its approach and is only concerned with the present, rather than delving into your past.

This form of therapy can take place one-on-one or in a group format and may be offered in person or online via telehealth . Sessions can be anywhere from 30 minutes to two hours long. 

Key Components

There are two major components that make up the problem-solving therapy framework:

• Applying a positive problem-solving orientation to your life
• Using problem-solving skills

A positive problem-solving orientation means viewing things in an optimistic light, embracing self-efficacy , and accepting the idea that problems are a normal part of life. Problem-solving skills are behaviors that you can rely on to help you navigate conflict, even during times of stress. This includes skills like:

• Knowing how to identify a problem
• Defining the problem in a helpful way
• Trying to understand the problem more deeply
• Setting goals related to the problem
• Generating alternative, creative solutions to the problem
• Choosing the best course of action
• Implementing the choice you have made
• Evaluating the outcome to determine next steps

Problem-solving therapy is all about training you to become adaptive in your life so that you will start to see problems as challenges to be solved instead of insurmountable obstacles. It also means that you will recognize the action that is required to engage in effective problem-solving techniques.

Planful Problem-Solving

One problem-solving technique, called planful problem-solving, involves following a series of steps to fix issues in a healthy, constructive way:

• Problem definition and formulation : This step involves identifying the real-life problem that needs to be solved and formulating it in a way that allows you to generate potential solutions.
• Generation of alternative solutions : This stage involves coming up with various potential solutions to the problem at hand. The goal in this step is to brainstorm options to creatively address the life stressor in ways that you may not have previously considered.
• Decision-making strategies : This stage involves discussing different strategies for making decisions as well as identifying obstacles that may get in the way of solving the problem at hand.
• Solution implementation and verification : This stage involves implementing a chosen solution and then verifying whether it was effective in addressing the problem.

Other Techniques

Other techniques your therapist may go over include:

• Problem-solving multitasking , which helps you learn to think clearly and solve problems effectively even during times of stress
• Stop, slow down, think, and act (SSTA) , which is meant to encourage you to become more emotionally mindful when faced with conflict
• Healthy thinking and imagery , which teaches you how to embrace more positive self-talk while problem-solving

What Problem-Solving Therapy Can Help With

Problem-solving therapy addresses life stress issues and focuses on helping you find solutions to concrete issues. This approach can be applied to problems associated with various psychological and physiological symptoms.

Mental Health Issues

Problem-solving therapy may help address mental health issues, like:

• Chronic stress due to accumulating minor issues
• Complications associated with traumatic brain injury (TBI)
• Emotional distress
• Post-traumatic stress disorder (PTSD)
• Problems associated with a chronic disease like cancer, heart disease, or diabetes
• Self-harm and feelings of hopelessness
• Substance use
• Suicidal ideation

Specific Life Challenges

This form of therapy is also helpful for dealing with specific life problems, such as:

• Death of a loved one
• Dissatisfaction at work
• Everyday life stressors
• Family problems
• Financial difficulties
• Relationship conflicts

Your doctor or mental healthcare professional will be able to advise whether problem-solving therapy could be helpful for your particular issue. In general, if you are struggling with specific, concrete problems that you are having trouble finding solutions for, problem-solving therapy could be helpful for you.

Benefits of Problem-Solving Therapy

The skills learned in problem-solving therapy can be helpful for managing all areas of your life. These can include:

• Being able to identify which stressors trigger your negative emotions (e.g., sadness, anger)
• Confidence that you can handle problems that you face
• Having a systematic approach on how to deal with life's problems
• Having a toolbox of strategies to solve the issues you face
• Increased confidence to find creative solutions
• Knowing how to identify which barriers will impede your progress
• Knowing how to manage emotions when they arise
• Reduced avoidance and increased action-taking
• The ability to accept life problems that can't be solved
• The ability to make effective decisions
• The development of patience (realizing that not all problems have a "quick fix")

Problem-solving therapy can help people feel more empowered to deal with the problems they face in their lives. Rather than feeling overwhelmed when stressors begin to take a toll, this therapy introduces new coping skills that can boost self-efficacy and resilience .

Other Types of Therapy

Other similar types of therapy include cognitive-behavioral therapy (CBT) and solution-focused brief therapy (SFBT) . While these therapies work to change thinking and behaviors, they work a bit differently. Both CBT and SFBT are less structured than problem-solving therapy and may focus on broader issues. CBT focuses on identifying and changing maladaptive thoughts, and SFBT works to help people look for solutions and build self-efficacy based on strengths.

This form of therapy was initially developed to help people combat stress through effective problem-solving, and it was later adapted to address clinical depression specifically. Today, much of the research on problem-solving therapy deals with its effectiveness in treating depression.

Problem-solving therapy has been shown to help depression in: 

• Older adults
• People coping with serious illnesses like cancer

Problem-solving therapy also appears to be effective as a brief treatment for depression, offering benefits in as little as six to eight sessions with a therapist or another healthcare professional. This may make it a good option for someone unable to commit to a lengthier treatment for depression.

Problem-solving therapy is not a good fit for everyone. It may not be effective at addressing issues that don't have clear solutions, like seeking meaning or purpose in life. Problem-solving therapy is also intended to treat specific problems, not general habits or thought patterns .

In general, it's also important to remember that problem-solving therapy is not a primary treatment for mental disorders. If you are living with the symptoms of a serious mental illness such as bipolar disorder or schizophrenia , you may need additional treatment with evidence-based approaches for your particular concern.

Problem-solving therapy is best aimed at someone who has a mental or physical issue that is being treated separately, but who also has life issues that go along with that problem that has yet to be addressed.

For example, it could help if you can't clean your house or pay your bills because of your depression, or if a cancer diagnosis is interfering with your quality of life.

Your doctor may be able to recommend therapists in your area who utilize this approach, or they may offer it themselves as part of their practice. You can also search for a problem-solving therapist with help from the American Psychological Association’s (APA) Society of Clinical Psychology .

If receiving problem-solving therapy from a doctor or mental healthcare professional is not an option for you, you could also consider implementing it as a self-help strategy using a workbook designed to help you learn problem-solving skills on your own.

During your first session, your therapist may spend some time explaining their process and approach. They may ask you to identify the problem you’re currently facing, and they’ll likely discuss your goals for therapy .

Keep In Mind

Problem-solving therapy may be a short-term intervention that's focused on solving a specific issue in your life. If you need further help with something more pervasive, it can also become a longer-term treatment option.

Get Help Now

We've tried, tested, and written unbiased reviews of the best online therapy programs including Talkspace, BetterHelp, and ReGain. Find out which option is the best for you.

Shang P, Cao X, You S, Feng X, Li N, Jia Y. Problem-solving therapy for major depressive disorders in older adults: an updated systematic review and meta-analysis of randomized controlled trials .  Aging Clin Exp Res . 2021;33(6):1465-1475. doi:10.1007/s40520-020-01672-3

Cuijpers P, Wit L de, Kleiboer A, Karyotaki E, Ebert DD. Problem-solving therapy for adult depression: An updated meta-analysis . Eur Psychiatry . 2018;48(1):27-37. doi:10.1016/j.eurpsy.2017.11.006

Nezu AM, Nezu CM, D'Zurilla TJ. Problem-Solving Therapy: A Treatment Manual . New York; 2013. doi:10.1891/9780826109415.0001

Owens D, Wright-Hughes A, Graham L, et al. Problem-solving therapy rather than treatment as usual for adults after self-harm: a pragmatic, feasibility, randomised controlled trial (the MIDSHIPS trial) .  Pilot Feasibility Stud . 2020;6:119. doi:10.1186/s40814-020-00668-0

Sorsdahl K, Stein DJ, Corrigall J, et al. The efficacy of a blended motivational interviewing and problem solving therapy intervention to reduce substance use among patients presenting for emergency services in South Africa: A randomized controlled trial . Subst Abuse Treat Prev Policy . 2015;10(1):46. doi:doi.org/10.1186/s13011-015-0042-1

Margolis SA, Osborne P, Gonzalez JS. Problem solving . In: Gellman MD, ed. Encyclopedia of Behavioral Medicine . Springer International Publishing; 2020:1745-1747. doi:10.1007/978-3-030-39903-0_208

Kirkham JG, Choi N, Seitz DP. Meta-analysis of problem solving therapy for the treatment of major depressive disorder in older adults . Int J Geriatr Psychiatry . 2016;31(5):526-535. doi:10.1002/gps.4358

Garand L, Rinaldo DE, Alberth MM, et al. Effects of problem solving therapy on mental health outcomes in family caregivers of persons with a new diagnosis of mild cognitive impairment or early dementia: A randomized controlled trial . Am J Geriatr Psychiatry . 2014;22(8):771-781. doi:10.1016/j.jagp.2013.07.007

Noyes K, Zapf AL, Depner RM, et al. Problem-solving skills training in adult cancer survivors: Bright IDEAS-AC pilot study .  Cancer Treat Res Commun . 2022;31:100552. doi:10.1016/j.ctarc.2022.100552

Albert SM, King J, Anderson S, et al. Depression agency-based collaborative: effect of problem-solving therapy on risk of common mental disorders in older adults with home care needs . The American Journal of Geriatric Psychiatry . 2019;27(6):619-624. doi:10.1016/j.jagp.2019.01.002

By Arlin Cuncic, MA Arlin Cuncic, MA, is the author of The Anxiety Workbook and founder of the website About Social Anxiety. She has a Master's degree in clinical psychology.

Heuristics: Definition, Examples, And How They Work

Benjamin Frimodig

Science Expert

B.A., History and Science, Harvard University

Ben Frimodig is a 2021 graduate of Harvard College, where he studied the History of Science.

Learn about our Editorial Process

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

On This Page:

Every day our brains must process and respond to thousands of problems, both large and small, at a moment’s notice. It might even be overwhelming to consider the sheer volume of complex problems we regularly face in need of a quick solution.

While one might wish there was time to methodically and thoughtfully evaluate the fine details of our everyday tasks, the cognitive demands of daily life often make such processing logistically impossible.

Therefore, the brain must develop reliable shortcuts to keep up with the stimulus-rich environments we inhabit. Psychologists refer to these efficient problem-solving techniques as heuristics.

Heuristics can be thought of as general cognitive frameworks humans rely on regularly to reach a solution quickly.

For example, if a student needs to decide what subject she will study at university, her intuition will likely be drawn toward the path that she envisions as most satisfying, practical, and interesting.

She may also think back on her strengths and weaknesses in secondary school or perhaps even write out a pros and cons list to facilitate her choice.

It’s important to note that these heuristics broadly apply to everyday problems, produce sound solutions, and helps simplify otherwise complicated mental tasks. These are the three defining features of a heuristic.

While the concept of heuristics dates back to Ancient Greece (the term is derived from the Greek word for “to discover”), most of the information known today on the subject comes from prominent twentieth-century social scientists.

Herbert Simon’s study of a notion he called “bounded rationality” focused on decision-making under restrictive cognitive conditions, such as limited time and information.

This concept of optimizing an inherently imperfect analysis frames the contemporary study of heuristics and leads many to credit Simon as a foundational figure in the field.

Kahneman’s Theory of Decision Making

The immense contributions of psychologist Daniel Kahneman to our understanding of cognitive problem-solving deserve special attention.

As context for his theory, Kahneman put forward the estimate that an individual makes around 35,000 decisions each day! To reach these resolutions, the mind relies on either “fast” or “slow” thinking.

The fast thinking pathway (system 1) operates mostly unconsciously and aims to reach reliable decisions with as minimal cognitive strain as possible.

While system 1 relies on broad observations and quick evaluative techniques (heuristics!), system 2 (slow thinking) requires conscious, continuous attention to carefully assess the details of a given problem and logically reach a solution.

Given the sheer volume of daily decisions, it’s no surprise that around 98% of problem-solving uses system 1.

Thus, it is crucial that the human mind develops a toolbox of effective, efficient heuristics to support this fast-thinking pathway.

Heuristics vs. Algorithms

Those who’ve studied the psychology of decision-making might notice similarities between heuristics and algorithms. However, remember that these are two distinct modes of cognition.

Heuristics are methods or strategies which often lead to problem solutions but are not guaranteed to succeed.

They can be distinguished from algorithms, which are methods or procedures that will always produce a solution sooner or later.

An algorithm is a step-by-step procedure that can be reliably used to solve a specific problem. While the concept of an algorithm is most commonly used in reference to technology and mathematics, our brains rely on algorithms every day to resolve issues (Kahneman, 2011).

The important thing to remember is that algorithms are a set of mental instructions unique to specific situations, while heuristics are general rules of thumb that can help the mind process and overcome various obstacles.

For example, if you are thoughtfully reading every line of this article, you are using an algorithm.

On the other hand, if you are quickly skimming each section for important information or perhaps focusing only on sections you don’t already understand, you are using a heuristic!

Why Heuristics Are Used

Heuristics usually 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 at the same moment

When studying heuristics, keep in mind both the benefits and unavoidable drawbacks of their application. The ubiquity of these techniques in human society makes such weaknesses especially worthy of evaluation.

More specifically, in expediting decision-making processes, heuristics also predispose us to a number of cognitive biases .

A cognitive bias is an incorrect but pervasive judgment derived from an illogical pattern of cognition. In simple terms, a cognitive bias occurs when one internalizes a subjective perception as a reliable and objective truth.

Heuristics are reliable but imperfect; In the application of broad decision-making “shortcuts” to guide one’s response to specific situations, occasional errors are both inevitable and have the potential to catalyze persistent mistakes.

For example, consider the risks of faulty applications of the representative heuristic discussed above. While the technique encourages one to assign situations into broad categories based on superficial characteristics and one’s past experiences for the sake of cognitive expediency, such thinking is also the basis of stereotypes and discrimination.

In practice, these errors result in the disproportionate favoring of one group and/or the oppression of other groups within a given society.

Indeed, the most impactful research relating to heuristics often centers on the connection between them and systematic discrimination.

The tradeoff between thoughtful rationality and cognitive efficiency encompasses both the benefits and pitfalls of heuristics and represents a foundational concept in psychological research.

When learning about heuristics, keep in mind their relevance to all areas of human interaction. After all, the study of social psychology is intrinsically interdisciplinary.

Many of the most important studies on heuristics relate to flawed decision-making processes in high-stakes fields like law, medicine, and politics.

Researchers often draw on a distinct set of already established heuristics in their analysis. While dozens of unique heuristics have been observed, brief descriptions of those most central to the field are included below:

Availability Heuristic

The availability heuristic describes the tendency to make choices based on information that comes to mind readily.

For example, children of divorced parents are more likely to have pessimistic views towards marriage as adults.

Of important note, this heuristic can also involve assigning more importance to more recently learned information, largely due to the easier recall of such information.

Representativeness Heuristic

This technique allows one to quickly assign probabilities to and predict the outcome of new scenarios using psychological prototypes derived from past experiences.

For example, juries are less likely to convict individuals who are well-groomed and wearing formal attire (under the assumption that stylish, well-kempt individuals typically do not commit crimes).

This is one of the most studied heuristics by social psychologists for its relevance to the development of stereotypes.

Scarcity Heuristic

This method of decision-making is predicated on the perception of less abundant, rarer items as inherently more valuable than more abundant items.

We rely on the scarcity heuristic when we must make a fast selection with incomplete information. For example, a student deciding between two universities may be drawn toward the option with the lower acceptance rate, assuming that this exclusivity indicates a more desirable experience.

The concept of scarcity is central to behavioral economists’ study of consumer behavior (a field that evaluates economics through the lens of human psychology).

Trial and Error

This is the most basic and perhaps frequently cited heuristic. Trial and error can be used to solve a problem that possesses a discrete number of possible solutions and involves simply attempting each possible option until the correct solution is identified.

For example, if an individual was putting together a jigsaw puzzle, he or she would try multiple pieces until locating a proper fit.

This technique is commonly taught in introductory psychology courses due to its simple representation of the central purpose of heuristics: the use of reliable problem-solving frameworks to reduce cognitive load.

Anchoring and Adjustment Heuristic

Anchoring refers to the tendency to formulate expectations relating to new scenarios relative to an already ingrained piece of information.

Put simply, this anchoring one to form reasonable estimations around uncertainties. For example, if asked to estimate the number of days in a year on Mars, many people would first call to mind the fact the Earth’s year is 365 days (the “anchor”) and adjust accordingly.

This tendency can also help explain the observation that ingrained information often hinders the learning of new information, a concept known as retroactive inhibition.

Familiarity Heuristic

This technique can be used to guide actions in cognitively demanding situations by simply reverting to previous behaviors successfully utilized under similar circumstances.

The familiarity heuristic is most useful in unfamiliar, stressful environments.

For example, a job seeker might recall behavioral standards in other high-stakes situations from her past (perhaps an important presentation at university) to guide her behavior in a job interview.

Many psychologists interpret this technique as a slightly more specific variation of the availability heuristic.

How to Make Better Decisions

Heuristics are ingrained cognitive processes utilized by all humans and can lead to various biases.

Both of these statements are established facts. However, this does not mean that the biases that heuristics produce are unavoidable. As the wide-ranging impacts of such biases on societal institutions have become a popular research topic, psychologists have emphasized techniques for reaching more sound, thoughtful and fair decisions in our daily lives.

Ironically, many of these techniques are themselves heuristics!

To focus on the key details of a given problem, one might create a mental list of explicit goals and values. To clearly identify the impacts of choice, one should imagine its impacts one year in the future and from the perspective of all parties involved.

Most importantly, one must gain a mindful understanding of the problem-solving techniques used by our minds and the common mistakes that result. Mindfulness of these flawed yet persistent pathways allows one to quickly identify and remedy the biases (or otherwise flawed thinking) they tend to create!

Further Information

• Shah, A. K., & Oppenheimer, D. M. (2008). Heuristics made easy: an effort-reduction framework. Psychological bulletin, 134(2), 207.
• Marewski, J. N., & Gigerenzer, G. (2012). Heuristic decision making in medicine. Dialogues in clinical neuroscience, 14(1), 77.
• Del Campo, C., Pauser, S., Steiner, E., & Vetschera, R. (2016). Decision making styles and the use of heuristics in decision making. Journal of Business Economics, 86(4), 389-412.

What is a heuristic in psychology?

A heuristic in psychology is a mental shortcut or rule of thumb that simplifies decision-making and problem-solving. Heuristics often speed up the process of finding a satisfactory solution, but they can also lead to cognitive biases.

Bobadilla-Suarez, S., & Love, B. C. (2017, May 29). Fast or Frugal, but Not Both: Decision Heuristics Under Time Pressure. Journal of Experimental Psychology: Learning, Memory, and Cognition .

Bowes, S. M., Ammirati, R. J., Costello, T. H., Basterfield, C., & Lilienfeld, S. O. (2020). Cognitive biases, heuristics, and logical fallacies in clinical practice: A brief field guide for practicing clinicians and supervisors. Professional Psychology: Research and Practice, 51 (5), 435–445.

Dietrich, C. (2010). “Decision Making: Factors that Influence Decision Making, Heuristics Used, and Decision Outcomes.” Inquiries Journal/Student Pulse, 2(02).

Groenewegen, A. (2021, September 1). Kahneman Fast and slow thinking: System 1 and 2 explained by Sue. SUE Behavioral Design. Retrieved March 26, 2022, from https://suebehaviouraldesign.com/kahneman-fast-slow-thinking/

Kahneman, D., Lovallo, D., & Sibony, O. (2011). Before you make that big decision .

Kahneman, D. (2011). Thinking, fast and slow . Macmillan.

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

Simon, H.A., 1956. Rational choice and the structure of the environment. Psychological Review .

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

Thinking and Intelligence

Solving Problems

Learning objectives.

• Describe problem solving strategies, including algorithms and heuristics

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

Problem-Solving Strategies

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

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

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

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

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

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

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

https://youtube.com/watch?v=1rDVz_Fb6HQ%3Flist%3DPLUmyCeox8XCwB8FrEfDQtQZmCc2qYMS5a

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

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

Everyday Connections: Solving Puzzles

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (Figure 1) 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.

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

Take a look at the “Puzzling Scales” logic puzzle below (Figure 3). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

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

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• Can you solve Einsteinu2019s Riddle? . Authored by : Dan Van der Vieren. Provided by : Ted-Ed. Located at : https://www.youtube.com/watch?v=1rDVz_Fb6HQ&index=3&list=PLUmyCeox8XCwB8FrEfDQtQZmCc2qYMS5a . License : Other . License Terms : Standard YouTube License

method for solving problems

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

problem-solving strategy characterized by a specific set of instructions

mental shortcut that saves time when solving a problem

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

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