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Problem-Solving Strategies and Obstacles

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

Sean is a fact-checker and researcher with experience in sociology, field research, and data analytics.

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From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.

What Is Problem-Solving?

In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.

A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.

Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.

The problem-solving process involves:

• Discovery of the problem
• Deciding to tackle the issue
• Seeking to understand the problem more fully
• Researching available options or solutions
• Taking action to resolve the issue

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

Several mental processes are at work during problem-solving. Among them are:

• Perceptually recognizing the problem
• Representing the problem in memory
• Considering relevant information that applies to the problem
• Identifying different aspects of the problem
• Labeling and describing the problem

Problem-Solving Strategies

There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.

An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.

In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.

One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.

There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.

Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.

If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.

While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.

This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.

In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.

Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .

Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.

How to Apply Problem-Solving Strategies in Real Life

If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:

• Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
• Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
• Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
• Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

Obstacles to Problem-Solving

Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:

• Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
• Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
• Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
• Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

How to Improve Your Problem-Solving Skills

In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:

• Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
• Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
• Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
• Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
• Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
• Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.

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

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9.4: Problem-Solving

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• Kelvin Seifert & Rosemary Sutton
• University of Manitoba & Cleveland State University via Global Text Project

Somewhat less open-ended than creative thinking is problem solving , the analysis and solution of tasks or situations that are complex or ambiguous and that pose difficulties or obstacles of some kind (Mayer & Wittrock, 2006). Problem solving is needed, for example, when a physician analyzes a chest X-ray: a photograph of the chest is far from clear and requires skill, experience, and resourcefulness to decide which foggy-looking blobs to ignore, and which to interpret as real physical structures (and therefore real medical concerns). Problem solving is also needed when a grocery store manager has to decide how to improve the sales of a product: should she put it on sale at a lower price, or increase publicity for it, or both? Will these actions actually increase sales enough to pay for their costs?

Problem solving in the classroom

Problem solving happens in classrooms when teachers present tasks or challenges that are deliberately complex and for which finding a solution is not straightforward or obvious. The responses of students to such problems, as well as the strategies for assisting them, show the key features of problem solving. Consider this example, and students' responses to it. We have numbered and named the paragraphs to make it easier to comment about them individually:

Scene #1: a problem to be solved

A teacher gave these instructions: "can you connect all of the dots below using only four straight lines" she drew the following display on the chalkboard:.

The problem itself and the procedure for solving it seemed very clear: simply experiment with different arrangements of four lines. But two volunteers tried doing it at the board, but were unsuccessful. Several others worked at it at their seats, but also without success.

Scene #2: coaxing students to re-frame the problem

When no one seemed to be getting it, the teacher asked, "Think about how you've set up the problem in your mind— about what you believe the problem is about. For instance, have you made any assumptions about how long the lines ought to be? Don't stay stuck on one approach if it's not working!"

Scene #3: Alicia abandons a fixed response

After the teacher said this, Alicia indeed continued to think about how she saw the problem. "The lines need to be no longer than the distance across the square," she said to herself. So she tried several more solutions, but none of them worked either.

The teacher walked by Alicia's desk and saw what Alicia was doing. She repeated her earlier comment: "Have you assumed anything about how long the lines ought to be?" Alicia stared at the teacher blankly, but then smiled and said, "Hmm! You didn't actually say that the lines could be no longer than the matrix! Why not make them longer?" Soshe experimented again using oversized lines and soon discovered a solution:

Scene #4: Willem's and Rachel's alternative strategies

Meanwhile, Willem worked on the problem. As it happened, Willem loved puzzles of all kinds, and had ample experience with them. He had not, however, seen this particular problem. "It must be a trick," he said to himself, because he knew from experience that problems posed in this way often were not what they first appeared to be. He mused to himself: "Think outside the box, they always tell you..." And that was just the hint he needed: he drew lines outside the box by making them longer than the matrix and soon came up with this solution:

When Rachel went to work, she took one look at the problem and knew the answer immediately: she had seen this problem before, though she could not remember where. She had also seen other drawing -related puzzles, and knew that their solution always depended on making the lines longer, shorter, or differently angled than first expected. After staring at the dots briefly, she drew a solution faster than Alicia or even Willem. Her solution looked exactly like Willem's.

This story illustrates two common features of problem solving: the effect of degree of structure or constraint on problem solving, and the effect of mental obstacles to solving problems. The next sections discuss each of these features, and then looks at common techniques for solving problems.

The effect of constraints: well-structured versus ill-structured problems

Problems vary in how much information they provide for solving a problem, as well as in how many rules or procedures are needed for a solution. A well-structured problem provides much of the information needed and can in principle be solved using relatively few clearly understood rules. Classic examples are the word problems often taught in math lessons or classes: everything you need to know is contained within the stated problem and the solution procedures are relatively clear and precise. An ill-structured problem has the converse qualities: the information is not necessarily within the problem, solution procedures are potentially quite numerous, and a multiple solutions are likely (Voss, 2006). Extreme examples are problems like "How can the world achieve lasting peace?" or "How can teachers insure that students learn?"

By these definitions, the nine-dot problem is relatively well-structured— though not completely. Most of the information needed for a solution is provided in Scene #1 : there are nine dots shown and instructions given to draw four lines. But not all necessary information was given: students needed to consider lines that were longer than implied in the original statement of the problem. Students had to "think outside the box", as Willem said— in this case, literally.

When a problem is well-structured, so are its solution procedures likely to be as well. A well-defined procedure for solving a particular kind of problem is often called an algorithm ; examples are the procedures for multiplying or dividing two numbers or the instructions for using a computer (Leiserson, et al., 2001). Algorithms are only effective when a problem is very well-structured and there is no question about whether the algorithm is an appropriate choice for the problem. In that situation it pretty much guarantees a correct solution. They do not work well, however, with ill-structured problems, where they are ambiguities and questions about how to proceed or even about precisely what the problem is about. In those cases it is more effective to use heuristics , which are general strategies— "rules of thumb", so to speak— that do not always work, but often do, or that provide at least partial solutions. When beginning research for a term paper, for example, a useful heuristic is to scan the library catalogue for titles that look relevant. There is no guarantee that this strategy will yield the books most needed for the paper, but the strategy works enough of the time to make it worth trying.

In the nine-dot problem, most students began in Scene #1 with a simple algorithm that can be stated like this: "Draw one line, then draw another, and another, and another". Unfortunately this simple procedure did not produce a solution, so they had to find other strategies for a solution. Three alternatives are described in Scenes #3 (for Alicia) and 4 (for Willem and Rachel). Of these, Willem's response resembled a heuristic the most: he knew from experience that a good general strategy that often worked for such problems was to suspect a deception or trick in how the problem was originally stated. So he set out to question what the teacher had meant by the word line, and came up with an acceptable solution as a result.

Common obstacles to solving problems

The example also illustrates two common problems that sometimes happen during problem solving. One of these is functional fixedness : a tendency to regard the functions of objects and ideas as fixed (German & Barrett, 2005). Over time, we get so used to one particular purpose for an object that we overlook other uses. We may think of a dictionary, for example, as necessarily something to verify spellings and definitions, but it also can function as a gift, a doorstop, or a footstool. For students working on the nine-dot matrix described in the last section, the notion of "drawing" a line was also initially fixed; they assumed it to be connecting dots but not extending lines beyond the dots. Functional fixedness sometimes is also called response set , the tendency for a person to frame or think about each problem in a series in the same way as the previous problem, even when doing so is not appropriate to later problems. In the example of the nine-dot matrix described above, students often tried one solution after another, but each solution was constrained by a set response not to extend any line beyond the matrix.

Functional fixedness and the response set are obstacles in problem representation , the way that a person understands and organizes information provided in a problem. If information is misunderstood or used inappropriately, then mistakes are likely— if indeed the problem can be solved at all. With the nine-dot matrix problem, for example, construing the instruction to draw four lines as meaning "draw four lines entirely within the matrix" means that the problem simply could not be solved. For another, consider this problem: "The number of water lilies on a lake doubles each day. Each water lily covers exactly one square foot. If it takes 100 days for the lilies to cover the lake exactly, how many days does it take for the lilies to cover exactly half of the lake?" If you think that the size of the lilies affects the solution to this problem, you have not represented the problem correctly. Information about lily size is not relevant to the solution, and only serves to distract from the truly crucial information, the fact that the lilies double their coverage each day. (The answer, incidentally, is that the lake is half covered in 99 days; can you think why?)

Strategies to assist problem solving

Just as there are cognitive obstacles to problem solving, there are also general strategies that help the process be successful, regardless of the specific content of a problem (Thagard, 2005). One helpful strategy is problem analysis — identifying the parts of the problem and working on each part separately. Analysis is especially useful when a problem is ill-structured. Consider this problem, for example: "Devise a plan to improve bicycle transportation in the city." Solving this problem is easier if you identify its parts or component subproblems, such as (1) installing bicycle lanes on busy streets, (2) educating cyclists and motorists to ride safely, (3) fixing potholes on streets used by cyclists, and (4) revising traffic laws that interfere with cycling. Each separate subproblem is more manageable than the original, general problem. The solution of each subproblem contributes the solution of the whole, though of course is not equivalent to a whole solution.

Another helpful strategy is working backward from a final solution to the originally stated problem. This approach is especially helpful when a problem is well-structured but also has elements that are distracting or misleading when approached in a forward, normal direction. The water lily problem described above is a good example: starting with the day when all the lake is covered (Day 100), ask what day would it therefore be half covered (by the terms of the problem, it would have to be the day before, or Day 99). Working backward in this case encourages reframing the extra information in the problem (i. e. the size of each water lily) as merely distracting, not as crucial to a solution.

A third helpful strategy is analogical thinking — using knowledge or experiences with similar features or structures to help solve the problem at hand (Bassok, 2003). In devising a plan to improve bicycling in the city, for example, an analogy of cars with bicycles is helpful in thinking of solutions: improving conditions for both vehicles requires many of the same measures (improving the roadways, educating drivers). Even solving simpler, more basic problems is helped by considering analogies. A first grade student can partially decode unfamiliar printed words by analogy to words he or she has learned already. If the child cannot yet read the word screen , for example, he can note that part of this word looks similar to words he may already know, such as seen or green , and from this observation derive a clue about how to read the word screen. Teachers can assist this process, as you might expect, by suggesting reasonable, helpful analogies for students to consider.

Identifying Barriers to Problem-Solving in Psychology

Problem-solving is a key aspect of psychology, essential for understanding and overcoming challenges in our daily lives. There are common barriers that can hinder our ability to effectively solve problems. From mental blocks to confirmation bias, these obstacles can impede our progress.

In this article, we will explore the various barriers to problem-solving in psychology, as well as strategies to overcome them. By addressing these challenges head-on, we can unlock the benefits of improved problem-solving skills and mental agility.

• Identifying and overcoming barriers to problem-solving in psychology can lead to more effective and efficient solutions.
• Some common barriers include mental blocks, confirmation bias, and functional fixedness, which can all limit critical thinking and creativity.
• Mindfulness techniques, seeking different perspectives, and collaborating with others can help overcome these barriers and lead to more successful problem-solving.
• 1 What Is Problem-Solving in Psychology?
• 2 Why Is Problem-Solving Important in Psychology?
• 3.1 Mental Blocks
• 3.2 Confirmation Bias
• 3.3 Functional Fixedness
• 3.4 Lack of Creativity
• 3.5 Emotional Barriers
• 3.6 Cultural Influences
• 4.1 Divergent Thinking
• 4.2 Mindfulness Techniques
• 4.3 Seeking Different Perspectives
• 4.4 Challenging Assumptions
• 4.5 Collaborating with Others
• 5 What Are the Benefits of Overcoming These Barriers?
• 6 Frequently Asked Questions

What Is Problem-Solving in Psychology?

Problem-solving in psychology refers to the cognitive processes through which individuals identify and overcome obstacles or challenges to reach a desired goal, drawing on various mental processes and strategies.

In the realm of cognitive psychology, problem-solving is a key area of study that delves into how people use algorithms and heuristics to tackle complex issues. Algorithms are systematic step-by-step procedures that guarantee a solution, whereas heuristics are mental shortcuts or rules of thumb that provide efficient solutions, albeit without certainty. Understanding these mental processes is crucial in exploring how individuals approach different types of problems and make decisions based on their problem-solving strategies.

Why Is Problem-Solving Important in Psychology?

Problem-solving holds significant importance in psychology as it facilitates the discovery of new insights, enhances understanding of complex issues, and fosters effective actions based on informed decisions.

Assumptions play a crucial role in problem-solving processes, influencing how individuals perceive and approach challenges. By challenging these assumptions, individuals can break through mental barriers and explore creative solutions.

Functional fixedness, a cognitive bias where individuals restrict the use of objects to their traditional functions, can hinder problem-solving. Overcoming functional fixedness involves reevaluating the purpose of objects, leading to innovative problem-solving strategies.

Through problem-solving, psychologists uncover underlying patterns in behavior, delve into subconscious motivations, and offer practical interventions to improve mental well-being.

What Are the Common Barriers to Problem-Solving in Psychology?

In psychology, common barriers to problem-solving include mental blocks , confirmation bias , functional fixedness, lack of creativity, emotional barriers, and cultural influences that hinder the application of knowledge and resources to overcome challenges.

Mental blocks refer to the difficulty in generating new ideas or solutions due to preconceived notions or past experiences. Confirmation bias, on the other hand, is the tendency to search for, interpret, or prioritize information that confirms existing beliefs or hypotheses, while disregarding opposing evidence.

Functional fixedness limits problem-solving by constraining individuals to view objects or concepts in their traditional uses, inhibiting creative approaches. Lack of creativity impedes the ability to think outside the box and consider unconventional solutions.

Emotional barriers such as fear, stress, or anxiety can halt progress by clouding judgment and hindering clear decision-making. Cultural influences may introduce unique perspectives or expectations that clash with effective problem-solving strategies, complicating the resolution process.

Mental Blocks

Mental blocks in problem-solving occur when individuals struggle to consider all relevant information, fall into a fixed mental set, or become fixated on irrelevant details, hindering progress and creative solutions.

For instance, irrelevant information can lead to mental blocks by distracting individuals from focusing on the key elements required to solve a problem effectively. This could involve getting caught up in minor details that have no real impact on the overall solution. A fixed mental set, formed by previous experiences or patterns, can limit one’s ability to approach a problem from new perspectives, restricting innovative thinking.

Confirmation Bias

Confirmation bias, a common barrier in problem-solving, leads individuals to seek information that confirms their existing knowledge or assumptions, potentially overlooking contradictory data and hindering objective analysis.

This cognitive bias affects decision-making and problem-solving processes by creating a tendency to favor information that aligns with one’s beliefs, rather than considering all perspectives.

• One effective method to mitigate confirmation bias is by actively challenging assumptions through critical thinking.
• By questioning the validity of existing beliefs and seeking out diverse viewpoints, individuals can counteract the tendency to only consider information that confirms their preconceptions.
• Another strategy is to promote a culture of open-mindedness and encourage constructive debate within teams to foster a more comprehensive evaluation of data.

Functional Fixedness

Functional fixedness restricts problem-solving by limiting individuals to conventional uses of objects, impeding the discovery of innovative solutions and hindering the application of insightful approaches to challenges.

For instance, when faced with a task that requires a candle to be mounted on a wall to provide lighting, someone bound by functional fixedness may struggle to see the potential solution of using the candle wax as an adhesive instead of solely perceiving the candle’s purpose as a light source.

This mental rigidity often leads individuals to overlook unconventional or creative methods, which can stifle their ability to find effective problem-solving strategies.

To combat this cognitive limitation, fostering divergent thinking, encouraging experimentation, and promoting flexibility in approaching tasks can help individuals break free from functional fixedness and unlock their creativity.

Lack of Creativity

A lack of creativity poses a significant barrier to problem-solving, limiting the potential for improvement and hindering flexible thinking required to generate novel solutions and address complex challenges.

When individuals are unable to think outside the box and explore unconventional approaches, they may find themselves stuck in repetitive patterns without breakthroughs.

Flexibility is key to overcoming this hurdle, allowing individuals to adapt their perspectives, pivot when necessary, and consider multiple viewpoints to arrive at innovative solutions.

Encouraging a culture that embraces experimentation, values diverse ideas, and fosters an environment of continuous learning can fuel creativity and push problem-solving capabilities to new heights.

Emotional Barriers

Emotional barriers, such as fear of failure, can impede problem-solving by creating anxiety, reducing risk-taking behavior, and hindering effective collaboration with others, limiting the exploration of innovative solutions.

When individuals are held back by the fear of failure, it often stems from a deep-seated worry about making mistakes or being judged negatively. This fear can lead to hesitation in decision-making processes and reluctance to explore unconventional approaches, ultimately hindering the ability to discover creative solutions. To overcome this obstacle, it is essential to cultivate a positive emotional environment that fosters trust, resilience, and open communication among team members. Encouraging a mindset that embraces failure as a stepping stone to success can enable individuals to take risks, learn from setbacks, and collaborate effectively to overcome challenges.

Cultural Influences

Cultural influences can act as barriers to problem-solving by imposing rigid norms, limiting flexibility in thinking, and hindering effective communication and collaboration among diverse individuals with varying perspectives.

When individuals from different cultural backgrounds come together to solve problems, the ingrained values and beliefs they hold can shape their approaches and methods.

For example, in some cultures, decisiveness and quick decision-making are highly valued, while in others, a consensus-building process is preferred.

Understanding and recognizing these differences is crucial for navigating through the cultural barriers that might arise during collaborative problem-solving.

How Can These Barriers Be Overcome?

These barriers to problem-solving in psychology can be overcome through various strategies such as divergent thinking, mindfulness techniques, seeking different perspectives, challenging assumptions, and collaborating with others to leverage diverse insights and foster critical thinking.

Engaging in divergent thinking , which involves generating multiple solutions or viewpoints for a single issue, can help break away from conventional problem-solving methods. By encouraging a free flow of ideas without immediate judgment, individuals can explore innovative paths that may lead to breakthrough solutions. Actively seeking diverse perspectives from individuals with varied backgrounds, experiences, and expertise can offer fresh insights that challenge existing assumptions and broaden the problem-solving scope. This diversity of viewpoints can spark creativity and unconventional approaches that enhance problem-solving outcomes.

Divergent Thinking

Divergent thinking enhances problem-solving by encouraging creative exploration of multiple solutions, breaking habitual thought patterns, and fostering flexibility in generating innovative ideas to address challenges.

When individuals engage in divergent thinking, they open up their minds to various possibilities and perspectives. Instead of being constrained by conventional norms, a person might ideate freely without limitations. This leads to out-of-the-box solutions that can revolutionize how problems are approached. Divergent thinking sparks creativity by allowing unconventional ideas to surface and flourish.

For example, imagine a team tasked with redesigning a city park. Instead of sticking to traditional layouts, they might brainstorm wild concepts like turning the park into a futuristic playground, a pop-up art gallery space, or a wildlife sanctuary. Such diverse ideas stem from divergent thinking and push boundaries beyond the ordinary.

Mindfulness Techniques

Mindfulness techniques can aid problem-solving by promoting present-moment awareness, reducing cognitive biases, and fostering a habit of continuous learning that enhances adaptability and open-mindedness in addressing challenges.

Engaging in regular mindfulness practices encourages individuals to stay grounded in the current moment, allowing them to detach from preconceived notions and biases that could cloud judgment. By cultivating a non-judgmental attitude towards thoughts and emotions, people develop the capacity to observe situations from a neutral perspective, facilitating clearer decision-making processes. Mindfulness techniques facilitate the development of a growth mindset, where one acknowledges mistakes as opportunities for learning and improvement rather than failures.

Seeking Different Perspectives

Seeking different perspectives in problem-solving involves tapping into diverse resources, engaging in effective communication, and considering alternative viewpoints to broaden understanding and identify innovative solutions to complex issues.

Collaboration among individuals with various backgrounds and experiences can offer fresh insights and approaches to tackling challenges. By fostering an environment where all voices are valued and heard, teams can leverage the collective wisdom and creativity present in diverse perspectives. For example, in the tech industry, companies like Google encourage cross-functional teams to work together, harnessing diverse skill sets to develop groundbreaking technologies.

To incorporate diverse viewpoints, one can implement brainstorming sessions that involve individuals from different departments or disciplines to encourage out-of-the-box thinking. Another effective method is to conduct surveys or focus groups to gather input from a wide range of stakeholders and ensure inclusivity in decision-making processes.

Challenging Assumptions

Challenging assumptions is a key strategy in problem-solving, as it prompts individuals to critically evaluate preconceived notions, gain new insights, and expand their knowledge base to approach challenges from fresh perspectives.

By questioning established beliefs or ways of thinking, individuals open the door to innovative solutions and original perspectives. Stepping outside the boundaries of conventional wisdom enables problem solvers to see beyond limitations and explore uncharted territories. This process not only fosters creativity but also encourages a culture of continuous improvement where learning thrives. Daring to challenge assumptions can unveil hidden opportunities and untapped potential in problem-solving scenarios, leading to breakthroughs and advancements that were previously overlooked.

• One effective technique to challenge assumptions is through brainstorming sessions that encourage participants to voice unconventional ideas without judgment.
• Additionally, adopting a beginner’s mindset can help in questioning assumptions, as newcomers often bring a fresh perspective unburdened by past biases.

Collaborating with Others

Collaborating with others in problem-solving fosters flexibility, encourages open communication, and leverages collective intelligence to navigate complex challenges, drawing on diverse perspectives and expertise to generate innovative solutions.

Effective collaboration enables individuals to combine strengths and talents, pooling resources to tackle problems that may seem insurmountable when approached individually. By working together, team members can break down barriers and silos that often hinder progress, leading to more efficient problem-solving processes and better outcomes.

Collaboration also promotes a sense of shared purpose and increases overall engagement, as team members feel valued and enableed to contribute their unique perspectives. To foster successful collaboration, it is crucial to establish clear goals, roles, and communication channels, ensuring that everyone is aligned towards a common objective.

What Are the Benefits of Overcoming These Barriers?

Overcoming the barriers to problem-solving in psychology leads to significant benefits such as improved critical thinking skills, enhanced knowledge acquisition, and the ability to address complex issues with greater creativity and adaptability.

By mastering the art of problem-solving, individuals in the field of psychology can also cultivate resilience and perseverance, two essential traits that contribute to personal growth and success.

When confronting and overcoming cognitive obstacles, individuals develop a deeper understanding of their own cognitive processes and behavioral patterns, enabling them to make informed decisions and overcome challenges more effectively.

Continuous learning and adaptability play a pivotal role in problem-solving, allowing psychologists to stay updated with the latest research, techniques, and methodologies that enhance their problem-solving capabilities.

Frequently Asked Questions

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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.

The study of problem solving begins with defining problem solving, problem, and problem types. This introduction to problem solving is rounded out with an examination of cognitive processes in problem solving, the role of knowledge in problem solving, and historical approaches to the study of problem solving.

Definition of Problem Solving

Problem solving refers to cognitive processing directed at achieving a goal for which the problem solver does not initially know a solution method. This definition consists of four major elements (Mayer, 1992 ; Mayer & Wittrock, 2006 ):

Cognitive —Problem solving occurs within the problem solver’s cognitive system and can only be inferred indirectly from the problem solver’s behavior (including biological changes, introspections, and actions during problem solving). Process —Problem solving involves mental computations in which some operation is applied to a mental representation, sometimes resulting in the creation of a new mental representation. Directed —Problem solving is aimed at achieving a goal. Personal —Problem solving depends on the existing knowledge of the problem solver so that what is a problem for one problem solver may not be a problem for someone who already knows a solution method.

The definition is broad enough to include a wide array of cognitive activities such as deciding which apartment to rent, figuring out how to use a cell phone interface, playing a game of chess, making a medical diagnosis, finding the answer to an arithmetic word problem, or writing a chapter for a handbook. Problem solving is pervasive in human life and is crucial for human survival. Although this chapter focuses on problem solving in humans, problem solving also occurs in nonhuman animals and in intelligent machines.

How is problem solving related to other forms of high-level cognition processing, such as thinking and reasoning? Thinking refers to cognitive processing in individuals but includes both directed thinking (which corresponds to the definition of problem solving) and undirected thinking such as daydreaming (which does not correspond to the definition of problem solving). Thus, problem solving is a type of thinking (i.e., directed thinking).

Reasoning refers to problem solving within specific classes of problems, such as deductive reasoning or inductive reasoning. In deductive reasoning, the reasoner is given premises and must derive a conclusion by applying the rules of logic. For example, given that “A is greater than B” and “B is greater than C,” a reasoner can conclude that “A is greater than C.” In inductive reasoning, the reasoner is given (or has experienced) a collection of examples or instances and must infer a rule. For example, given that X, C, and V are in the “yes” group and x, c, and v are in the “no” group, the reasoning may conclude that B is in “yes” group because it is in uppercase format. Thus, reasoning is a type of problem solving.

Definition of Problem

A problem occurs when someone has a goal but does not know to achieve it. This definition is consistent with how the Gestalt psychologist Karl Duncker ( 1945 , p. 1) defined a problem in his classic monograph, On Problem Solving : “A problem arises when a living creature has a goal but does not know how this goal is to be reached.” However, today researchers recognize that the definition should be extended to include problem solving by intelligent machines. This definition can be clarified using an information processing approach by noting that a problem occurs when a situation is in the given state, the problem solver wants the situation to be in the goal state, and there is no obvious way to move from the given state to the goal state (Newell & Simon, 1972 ). Accordingly, the three main elements in describing a problem are the given state (i.e., the current state of the situation), the goal state (i.e., the desired state of the situation), and the set of allowable operators (i.e., the actions the problem solver is allowed to take). The definition of “problem” is broad enough to include the situation confronting a physician who wishes to make a diagnosis on the basis of preliminary tests and a patient examination, as well as a beginning physics student trying to solve a complex physics problem.

Types of Problems

It is customary in the problem-solving literature to make a distinction between routine and nonroutine problems. Routine problems are problems that are so familiar to the problem solver that the problem solver knows a solution method. For example, for most adults, “What is 365 divided by 12?” is a routine problem because they already know the procedure for long division. Nonroutine problems are so unfamiliar to the problem solver that the problem solver does not know a solution method. For example, figuring out the best way to set up a funding campaign for a nonprofit charity is a nonroutine problem for most volunteers. Technically, routine problems do not meet the definition of problem because the problem solver has a goal but knows how to achieve it. Much research on problem solving has focused on routine problems, although most interesting problems in life are nonroutine.

Another customary distinction is between well-defined and ill-defined problems. Well-defined problems have a clearly specified given state, goal state, and legal operators. Examples include arithmetic computation problems or games such as checkers or tic-tac-toe. Ill-defined problems have a poorly specified given state, goal state, or legal operators, or a combination of poorly defined features. Examples include solving the problem of global warming or finding a life partner. Although, ill-defined problems are more challenging, much research in problem solving has focused on well-defined problems.

Cognitive Processes in Problem Solving

The process of problem solving can be broken down into two main phases: problem representation , in which the problem solver builds a mental representation of the problem situation, and problem solution , in which the problem solver works to produce a solution. The major subprocess in problem representation is representing , which involves building a situation model —that is, a mental representation of the situation described in the problem. The major subprocesses in problem solution are planning , which involves devising a plan for how to solve the problem; executing , which involves carrying out the plan; and monitoring , which involves evaluating and adjusting one’s problem solving.

For example, given an arithmetic word problem such as “Alice has three marbles. Sarah has two more marbles than Alice. How many marbles does Sarah have?” the process of representing involves building a situation model in which Alice has a set of marbles, there is set of marbles for the difference between the two girls, and Sarah has a set of marbles that consists of Alice’s marbles and the difference set. In the planning process, the problem solver sets a goal of adding 3 and 2. In the executing process, the problem solver carries out the computation, yielding an answer of 5. In the monitoring process, the problem solver looks over what was done and concludes that 5 is a reasonable answer. In most complex problem-solving episodes, the four cognitive processes may not occur in linear order, but rather may interact with one another. Although some research focuses mainly on the execution process, problem solvers may tend to have more difficulty with the processes of representing, planning, and monitoring.

Knowledge for Problem Solving

An important theme in problem-solving research is that problem-solving proficiency on any task depends on the learner’s knowledge (Anderson et al., 2001 ; Mayer, 1992 ). Five kinds of knowledge are as follows:

Facts —factual knowledge about the characteristics of elements in the world, such as “Sacramento is the capital of California” Concepts —conceptual knowledge, including categories, schemas, or models, such as knowing the difference between plants and animals or knowing how a battery works Procedures —procedural knowledge of step-by-step processes, such as how to carry out long-division computations Strategies —strategic knowledge of general methods such as breaking a problem into parts or thinking of a related problem Beliefs —attitudinal knowledge about how one’s cognitive processing works such as thinking, “I’m good at this”

Although some research focuses mainly on the role of facts and procedures in problem solving, complex problem solving also depends on the problem solver’s concepts, strategies, and beliefs (Mayer, 1992 ).

Historical Approaches to Problem Solving

Psychological research on problem solving began in the early 1900s, as an outgrowth of mental philosophy (Humphrey, 1963 ; Mandler & Mandler, 1964 ). Throughout the 20th century four theoretical approaches developed: early conceptions, associationism, Gestalt psychology, and information processing.

Early Conceptions

The start of psychology as a science can be set at 1879—the year Wilhelm Wundt opened the first world’s psychology laboratory in Leipzig, Germany, and sought to train the world’s first cohort of experimental psychologists. Instead of relying solely on philosophical speculations about how the human mind works, Wundt sought to apply the methods of experimental science to issues addressed in mental philosophy. His theoretical approach became structuralism —the analysis of consciousness into its basic elements.

Wundt’s main contribution to the study of problem solving, however, was to call for its banishment. According to Wundt, complex cognitive processing was too complicated to be studied by experimental methods, so “nothing can be discovered in such experiments” (Wundt, 1911/1973 ). Despite his admonishments, however, a group of his former students began studying thinking mainly in Wurzburg, Germany. Using the method of introspection, subjects were asked to describe their thought process as they solved word association problems, such as finding the superordinate of “newspaper” (e.g., an answer is “publication”). Although the Wurzburg group—as they came to be called—did not produce a new theoretical approach, they found empirical evidence that challenged some of the key assumptions of mental philosophy. For example, Aristotle had proclaimed that all thinking involves mental imagery, but the Wurzburg group was able to find empirical evidence for imageless thought .

Associationism

The first major theoretical approach to take hold in the scientific study of problem solving was associationism —the idea that the cognitive representations in the mind consist of ideas and links between them and that cognitive processing in the mind involves following a chain of associations from one idea to the next (Mandler & Mandler, 1964 ; Mayer, 1992 ). For example, in a classic study, E. L. Thorndike ( 1911 ) placed a hungry cat in what he called a puzzle box—a wooden crate in which pulling a loop of string that hung from overhead would open a trap door to allow the cat to escape to a bowl of food outside the crate. Thorndike placed the cat in the puzzle box once a day for several weeks. On the first day, the cat engaged in many extraneous behaviors such as pouncing against the wall, pushing its paws through the slats, and meowing, but on successive days the number of extraneous behaviors tended to decrease. Overall, the time required to get out of the puzzle box decreased over the course of the experiment, indicating the cat was learning how to escape.

Thorndike’s explanation for how the cat learned to solve the puzzle box problem is based on an associationist view: The cat begins with a habit family hierarchy —a set of potential responses (e.g., pouncing, thrusting, meowing, etc.) all associated with the same stimulus (i.e., being hungry and confined) and ordered in terms of strength of association. When placed in the puzzle box, the cat executes its strongest response (e.g., perhaps pouncing against the wall), but when it fails, the strength of the association is weakened, and so on for each unsuccessful action. Eventually, the cat gets down to what was initially a weak response—waving its paw in the air—but when that response leads to accidentally pulling the string and getting out, it is strengthened. Over the course of many trials, the ineffective responses become weak and the successful response becomes strong. Thorndike refers to this process as the law of effect : Responses that lead to dissatisfaction become less associated with the situation and responses that lead to satisfaction become more associated with the situation. According to Thorndike’s associationist view, solving a problem is simply a matter of trial and error and accidental success. A major challenge to assocationist theory concerns the nature of transfer—that is, where does a problem solver find a creative solution that has never been performed before? Associationist conceptions of cognition can be seen in current research, including neural networks, connectionist models, and parallel distributed processing models (Rogers & McClelland, 2004 ).

Gestalt Psychology

The Gestalt approach to problem solving developed in the 1930s and 1940s as a counterbalance to the associationist approach. According to the Gestalt approach, cognitive representations consist of coherent structures (rather than individual associations) and the cognitive process of problem solving involves building a coherent structure (rather than strengthening and weakening of associations). For example, in a classic study, Kohler ( 1925 ) placed a hungry ape in a play yard that contained several empty shipping crates and a banana attached overhead but out of reach. Based on observing the ape in this situation, Kohler noted that the ape did not randomly try responses until one worked—as suggested by Thorndike’s associationist view. Instead, the ape stood under the banana, looked up at it, looked at the crates, and then in a flash of insight stacked the crates under the bananas as a ladder, and walked up the steps in order to reach the banana.

According to Kohler, the ape experienced a sudden visual reorganization in which the elements in the situation fit together in a way to solve the problem; that is, the crates could become a ladder that reduces the distance to the banana. Kohler referred to the underlying mechanism as insight —literally seeing into the structure of the situation. A major challenge of Gestalt theory is its lack of precision; for example, naming a process (i.e., insight) is not the same as explaining how it works. Gestalt conceptions can be seen in modern research on mental models and schemas (Gentner & Stevens, 1983 ).

Information Processing

The information processing approach to problem solving developed in the 1960s and 1970s and was based on the influence of the computer metaphor—the idea that humans are processors of information (Mayer, 2009 ). According to the information processing approach, problem solving involves a series of mental computations—each of which consists of applying a process to a mental representation (such as comparing two elements to determine whether they differ).

In their classic book, Human Problem Solving , Newell and Simon ( 1972 ) proposed that problem solving involved a problem space and search heuristics . A problem space is a mental representation of the initial state of the problem, the goal state of the problem, and all possible intervening states (based on applying allowable operators). Search heuristics are strategies for moving through the problem space from the given to the goal state. Newell and Simon focused on means-ends analysis , in which the problem solver continually sets goals and finds moves to accomplish goals.

Newell and Simon used computer simulation as a research method to test their conception of human problem solving. First, they asked human problem solvers to think aloud as they solved various problems such as logic problems, chess, and cryptarithmetic problems. Then, based on an information processing analysis, Newell and Simon created computer programs that solved these problems. In comparing the solution behavior of humans and computers, they found high similarity, suggesting that the computer programs were solving problems using the same thought processes as humans.

An important advantage of the information processing approach is that problem solving can be described with great clarity—as a computer program. An important limitation of the information processing approach is that it is most useful for describing problem solving for well-defined problems rather than ill-defined problems. The information processing conception of cognition lives on as a keystone of today’s cognitive science (Mayer, 2009 ).

Classic Issues in Problem Solving

Three classic issues in research on problem solving concern the nature of transfer (suggested by the associationist approach), the nature of insight (suggested by the Gestalt approach), and the role of problem-solving heuristics (suggested by the information processing approach).

Transfer refers to the effects of prior learning on new learning (or new problem solving). Positive transfer occurs when learning A helps someone learn B. Negative transfer occurs when learning A hinders someone from learning B. Neutral transfer occurs when learning A has no effect on learning B. Positive transfer is a central goal of education, but research shows that people often do not transfer what they learned to solving problems in new contexts (Mayer, 1992 ; Singley & Anderson, 1989 ).

Three conceptions of the mechanisms underlying transfer are specific transfer , general transfer , and specific transfer of general principles . Specific transfer refers to the idea that learning A will help someone learn B only if A and B have specific elements in common. For example, learning Spanish may help someone learn Latin because some of the vocabulary words are similar and the verb conjugation rules are similar. General transfer refers to the idea that learning A can help someone learn B even they have nothing specifically in common but A helps improve the learner’s mind in general. For example, learning Latin may help people learn “proper habits of mind” so they are better able to learn completely unrelated subjects as well. Specific transfer of general principles is the idea that learning A will help someone learn B if the same general principle or solution method is required for both even if the specific elements are different.

In a classic study, Thorndike and Woodworth ( 1901 ) found that students who learned Latin did not subsequently learn bookkeeping any better than students who had not learned Latin. They interpreted this finding as evidence for specific transfer—learning A did not transfer to learning B because A and B did not have specific elements in common. Modern research on problem-solving transfer continues to show that people often do not demonstrate general transfer (Mayer, 1992 ). However, it is possible to teach people a general strategy for solving a problem, so that when they see a new problem in a different context they are able to apply the strategy to the new problem (Judd, 1908 ; Mayer, 2008 )—so there is also research support for the idea of specific transfer of general principles.

Insight refers to a change in a problem solver’s mind from not knowing how to solve a problem to knowing how to solve it (Mayer, 1995 ; Metcalfe & Wiebe, 1987 ). In short, where does the idea for a creative solution come from? A central goal of problem-solving research is to determine the mechanisms underlying insight.

The search for insight has led to five major (but not mutually exclusive) explanatory mechanisms—insight as completing a schema, insight as suddenly reorganizing visual information, insight as reformulation of a problem, insight as removing mental blocks, and insight as finding a problem analog (Mayer, 1995 ). Completing a schema is exemplified in a study by Selz (Fridja & de Groot, 1982 ), in which people were asked to think aloud as they solved word association problems such as “What is the superordinate for newspaper?” To solve the problem, people sometimes thought of a coordinate, such as “magazine,” and then searched for a superordinate category that subsumed both terms, such as “publication.” According to Selz, finding a solution involved building a schema that consisted of a superordinate and two subordinate categories.

Reorganizing visual information is reflected in Kohler’s ( 1925 ) study described in a previous section in which a hungry ape figured out how to stack boxes as a ladder to reach a banana hanging above. According to Kohler, the ape looked around the yard and found the solution in a flash of insight by mentally seeing how the parts could be rearranged to accomplish the goal.

Reformulating a problem is reflected in a classic study by Duncker ( 1945 ) in which people are asked to think aloud as they solve the tumor problem—how can you destroy a tumor in a patient without destroying surrounding healthy tissue by using rays that at sufficient intensity will destroy any tissue in their path? In analyzing the thinking-aloud protocols—that is, transcripts of what the problem solvers said—Duncker concluded that people reformulated the goal in various ways (e.g., avoid contact with healthy tissue, immunize healthy tissue, have ray be weak in healthy tissue) until they hit upon a productive formulation that led to the solution (i.e., concentrating many weak rays on the tumor).

Removing mental blocks is reflected in classic studies by Duncker ( 1945 ) in which solving a problem involved thinking of a novel use for an object, and by Luchins ( 1942 ) in which solving a problem involved not using a procedure that had worked well on previous problems. Finding a problem analog is reflected in classic research by Wertheimer ( 1959 ) in which learning to find the area of a parallelogram is supported by the insight that one could cut off the triangle on one side and place it on the other side to form a rectangle—so a parallelogram is really a rectangle in disguise. The search for insight along each of these five lines continues in current problem-solving research.

Heuristics are problem-solving strategies, that is, general approaches to how to solve problems. Newell and Simon ( 1972 ) suggested three general problem-solving heuristics for moving from a given state to a goal state: random trial and error , hill climbing , and means-ends analysis . Random trial and error involves randomly selecting a legal move and applying it to create a new problem state, and repeating that process until the goal state is reached. Random trial and error may work for simple problems but is not efficient for complex ones. Hill climbing involves selecting the legal move that moves the problem solver closer to the goal state. Hill climbing will not work for problems in which the problem solver must take a move that temporarily moves away from the goal as is required in many problems.

Means-ends analysis involves creating goals and seeking moves that can accomplish the goal. If a goal cannot be directly accomplished, a subgoal is created to remove one or more obstacles. Newell and Simon ( 1972 ) successfully used means-ends analysis as the search heuristic in a computer program aimed at general problem solving, that is, solving a diverse collection of problems. However, people may also use specific heuristics that are designed to work for specific problem-solving situations (Gigerenzer, Todd, & ABC Research Group, 1999 ; Kahneman & Tversky, 1984 ).

Current and Future Issues in Problem Solving

Eight current issues in problem solving involve decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific problem solving, everyday thinking, and the cognitive neuroscience of problem solving.

Decision Making

Decision making refers to the cognitive processing involved in choosing between two or more alternatives (Baron, 2000 ; Markman & Medin, 2002 ). For example, a decision-making task may involve choosing between getting $240 for sure or having a 25% change of getting $1000. According to economic theories such as expected value theory, people should chose the second option, which is worth $250 (i.e., .25 x $1000) rather than the first option, which is worth $240 (1.00 x $240), but psychological research shows that most people prefer the first option (Kahneman & Tversky, 1984 ).

Research on decision making has generated three classes of theories (Markman & Medin, 2002 ): descriptive theories, such as prospect theory (Kahneman & Tversky), which are based on the ideas that people prefer to overweight the cost of a loss and tend to overestimate small probabilities; heuristic theories, which are based on the idea that people use a collection of short-cut strategies such as the availability heuristic (Gigerenzer et al., 1999 ; Kahneman & Tversky, 2000 ); and constructive theories, such as mental accounting (Kahneman & Tversky, 2000 ), in which people build a narrative to justify their choices to themselves. Future research is needed to examine decision making in more realistic settings.

Intelligence and Creativity

Although researchers do not have complete consensus on the definition of intelligence (Sternberg, 1990 ), it is reasonable to view intelligence as the ability to learn or adapt to new situations. Fluid intelligence refers to the potential to solve problems without any relevant knowledge, whereas crystallized intelligence refers to the potential to solve problems based on relevant prior knowledge (Sternberg & Gregorenko, 2003 ). As people gain more experience in a field, their problem-solving performance depends more on crystallized intelligence (i.e., domain knowledge) than on fluid intelligence (i.e., general ability) (Sternberg & Gregorenko, 2003 ). The ability to monitor and manage one’s cognitive processing during problem solving—which can be called metacognition —is an important aspect of intelligence (Sternberg, 1990 ). Research is needed to pinpoint the knowledge that is needed to support intelligent performance on problem-solving tasks.

Creativity refers to the ability to generate ideas that are original (i.e., other people do not think of the same idea) and functional (i.e., the idea works; Sternberg, 1999 ). Creativity is often measured using tests of divergent thinking —that is, generating as many solutions as possible for a problem (Guilford, 1967 ). For example, the uses test asks people to list as many uses as they can think of for a brick. Creativity is different from intelligence, and it is at the heart of creative problem solving—generating a novel solution to a problem that the problem solver has never seen before. An important research question concerns whether creative problem solving depends on specific knowledge or creativity ability in general.

Teaching of Thinking Skills

How can people learn to be better problem solvers? Mayer ( 2008 ) proposes four questions concerning teaching of thinking skills:

What to teach —Successful programs attempt to teach small component skills (such as how to generate and evaluate hypotheses) rather than improve the mind as a single monolithic skill (Covington, Crutchfield, Davies, & Olton, 1974 ). How to teach —Successful programs focus on modeling the process of problem solving rather than solely reinforcing the product of problem solving (Bloom & Broder, 1950 ). Where to teach —Successful programs teach problem-solving skills within the specific context they will be used rather than within a general course on how to solve problems (Nickerson, 1999 ). When to teach —Successful programs teaching higher order skills early rather than waiting until lower order skills are completely mastered (Tharp & Gallimore, 1988 ).

Overall, research on teaching of thinking skills points to the domain specificity of problem solving; that is, successful problem solving depends on the problem solver having domain knowledge that is relevant to the problem-solving task.

Expert Problem Solving

Research on expertise is concerned with differences between how experts and novices solve problems (Ericsson, Feltovich, & Hoffman, 2006 ). Expertise can be defined in terms of time (e.g., 10 years of concentrated experience in a field), performance (e.g., earning a perfect score on an assessment), or recognition (e.g., receiving a Nobel Prize or becoming Grand Master in chess). For example, in classic research conducted in the 1940s, de Groot ( 1965 ) found that chess experts did not have better general memory than chess novices, but they did have better domain-specific memory for the arrangement of chess pieces on the board. Chase and Simon ( 1973 ) replicated this result in a better controlled experiment. An explanation is that experts have developed schemas that allow them to chunk collections of pieces into a single configuration.

In another landmark study, Larkin et al. ( 1980 ) compared how experts (e.g., physics professors) and novices (e.g., first-year physics students) solved textbook physics problems about motion. Experts tended to work forward from the given information to the goal, whereas novices tended to work backward from the goal to the givens using a means-ends analysis strategy. Experts tended to store their knowledge in an integrated way, whereas novices tended to store their knowledge in isolated fragments. In another study, Chi, Feltovich, and Glaser ( 1981 ) found that experts tended to focus on the underlying physics concepts (such as conservation of energy), whereas novices tended to focus on the surface features of the problem (such as inclined planes or springs). Overall, research on expertise is useful in pinpointing what experts know that is different from what novices know. An important theme is that experts rely on domain-specific knowledge rather than solely general cognitive ability.

Analogical Reasoning

Analogical reasoning occurs when people solve one problem by using their knowledge about another problem (Holyoak, 2005 ). For example, suppose a problem solver learns how to solve a problem in one context using one solution method and then is given a problem in another context that requires the same solution method. In this case, the problem solver must recognize that the new problem has structural similarity to the old problem (i.e., it may be solved by the same method), even though they do not have surface similarity (i.e., the cover stories are different). Three steps in analogical reasoning are recognizing —seeing that a new problem is similar to a previously solved problem; abstracting —finding the general method used to solve the old problem; and mapping —using that general method to solve the new problem.

Research on analogical reasoning shows that people often do not recognize that a new problem can be solved by the same method as a previously solved problem (Holyoak, 2005 ). However, research also shows that successful analogical transfer to a new problem is more likely when the problem solver has experience with two old problems that have the same underlying structural features (i.e., they are solved by the same principle) but different surface features (i.e., they have different cover stories) (Holyoak, 2005 ). This finding is consistent with the idea of specific transfer of general principles as described in the section on “Transfer.”

Mathematical and Scientific Problem Solving

Research on mathematical problem solving suggests that five kinds of knowledge are needed to solve arithmetic word problems (Mayer, 2008 ):

Factual knowledge —knowledge about the characteristics of problem elements, such as knowing that there are 100 cents in a dollar Schematic knowledge —knowledge of problem types, such as being able to recognize time-rate-distance problems Strategic knowledge —knowledge of general methods, such as how to break a problem into parts Procedural knowledge —knowledge of processes, such as how to carry our arithmetic operations Attitudinal knowledge —beliefs about one’s mathematical problem-solving ability, such as thinking, “I am good at this”

People generally possess adequate procedural knowledge but may have difficulty in solving mathematics problems because they lack factual, schematic, strategic, or attitudinal knowledge (Mayer, 2008 ). Research is needed to pinpoint the role of domain knowledge in mathematical problem solving.

Research on scientific problem solving shows that people harbor misconceptions, such as believing that a force is needed to keep an object in motion (McCloskey, 1983 ). Learning to solve science problems involves conceptual change, in which the problem solver comes to recognize that previous conceptions are wrong (Mayer, 2008 ). Students can be taught to engage in scientific reasoning such as hypothesis testing through direct instruction in how to control for variables (Chen & Klahr, 1999 ). A central theme of research on scientific problem solving concerns the role of domain knowledge.

Everyday Thinking

Everyday thinking refers to problem solving in the context of one’s life outside of school. For example, children who are street vendors tend to use different procedures for solving arithmetic problems when they are working on the streets than when they are in school (Nunes, Schlieman, & Carraher, 1993 ). This line of research highlights the role of situated cognition —the idea that thinking always is shaped by the physical and social context in which it occurs (Robbins & Aydede, 2009 ). Research is needed to determine how people solve problems in authentic contexts.

Cognitive Neuroscience of Problem Solving

The cognitive neuroscience of problem solving is concerned with the brain activity that occurs during problem solving. For example, using fMRI brain imaging methodology, Goel ( 2005 ) found that people used the language areas of the brain to solve logical reasoning problems presented in sentences (e.g., “All dogs are pets…”) and used the spatial areas of the brain to solve logical reasoning problems presented in abstract letters (e.g., “All D are P…”). Cognitive neuroscience holds the potential to make unique contributions to the study of problem solving.

Problem solving has always been a topic at the fringe of cognitive psychology—too complicated to study intensively but too important to completely ignore. Problem solving—especially in realistic environments—is messy in comparison to studying elementary processes in cognition. The field remains fragmented in the sense that topics such as decision making, reasoning, intelligence, expertise, mathematical problem solving, everyday thinking, and the like are considered to be separate topics, each with its own separate literature. Yet some recurring themes are the role of domain-specific knowledge in problem solving and the advantages of studying problem solving in authentic contexts.

Future Directions

Some important issues for future research include the three classic issues examined in this chapter—the nature of problem-solving transfer (i.e., How are people able to use what they know about previous problem solving to help them in new problem solving?), the nature of insight (e.g., What is the mechanism by which a creative solution is constructed?), and heuristics (e.g., What are some teachable strategies for problem solving?). In addition, future research in problem solving should continue to pinpoint the role of domain-specific knowledge in problem solving, the nature of cognitive ability in problem solving, how to help people develop proficiency in solving problems, and how to provide aids for problem solving.

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Further Reading

Baron, J. ( 2008 ). Thinking and deciding (4th ed). New York: Cambridge University Press.

Duncker, K. ( 1945 ). On problem solving. Psychological Monographs , 58(3) (Whole No. 270).

Holyoak, K. J. , & Morrison, R. G. ( 2005 ). The Cambridge handbook of thinking and reasoning . New York: Cambridge University Press.

Mayer, R. E. , & Wittrock, M. C. ( 2006 ). Problem solving. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (2nd ed., pp. 287–304). Mahwah, NJ: Erlbaum.

Sternberg, R. J. , & Ben-Zeev, T. ( 2001 ). Complex cognition: The psychology of human thought . New York: Oxford University Press.

Weisberg, R. W. ( 2006 ). Creativity . New York: Wiley.

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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.

The Process of Problem Solving

• Editor's Choice
• Experimental Psychology
• Problem Solving

In a 2013 article published in the Journal of Cognitive Psychology , Ngar Yin Louis Lee (Chinese University of Hong Kong) and APS William James Fellow Philip N. Johnson-Laird (Princeton University) examined the ways people develop strategies to solve related problems. In a series of three experiments, the researchers asked participants to solve series of matchstick problems.

In matchstick problems, participants are presented with an array of joined squares. Each square in the array is comprised of separate pieces. Participants are asked to remove a certain number of pieces from the array while still maintaining a specific number of intact squares. Matchstick problems are considered to be fairly sophisticated, as there is generally more than one solution, several different tactics can be used to complete the task, and the types of tactics that are appropriate can change depending on the configuration of the array.

Louis Lee and Johnson-Laird began by examining what influences the tactics people use when they are first confronted with the matchstick problem. They found that initial problem-solving tactics were constrained by perceptual features of the array, with participants solving symmetrical problems and problems with salient solutions faster. Participants frequently used tactics that involved symmetry and salience even when other solutions that did not involve these features existed.

To examine how problem solving develops over time, the researchers had participants solve a series of matchstick problems while verbalizing their problem-solving thought process. The findings from this second experiment showed that people tend to go through two different stages when solving a series of problems.

People begin their problem-solving process in a generative manner during which they explore various tactics — some successful and some not. Then they use their experience to narrow down their choices of tactics, focusing on those that are the most successful. The point at which people begin to rely on this newfound tactical knowledge to create their strategic moves indicates a shift into a more evaluative stage of problem solving.

In the third and last experiment, participants completed a set of matchstick problems that could be solved using similar tactics and then solved several problems that required the use of novel tactics.  The researchers found that participants often had trouble leaving their set of successful tactics behind and shifting to new strategies.

From the three studies, the researchers concluded that when people tackle a problem, their initial moves may be constrained by perceptual components of the problem. As they try out different tactics, they hone in and settle on the ones that are most efficient; however, this deduced knowledge can in turn come to constrain players’ generation of moves — something that can make it difficult to switch to new tactics when required.

These findings help expand our understanding of the role of reasoning and deduction in problem solving and of the processes involved in the shift from less to more effective problem-solving strategies.

Reference Louis Lee, N. Y., Johnson-Laird, P. N. (2013). Strategic changes in problem solving. Journal of Cognitive Psychology, 25 , 165–173. doi: 10.1080/20445911.2012.719021

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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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IResearchNet

Problem Solving

Problem solving, a fundamental cognitive process deeply rooted in psychology, plays a pivotal role in various aspects of human existence, especially within educational contexts. This article delves into the nature of problem solving, exploring its theoretical underpinnings, the cognitive and psychological processes that underlie it, and the application of problem-solving skills within educational settings and the broader real world. With a focus on both theory and practice, this article underscores the significance of cultivating problem-solving abilities as a cornerstone of cognitive development and innovation, shedding light on its applications in fields ranging from education to clinical psychology and beyond, thereby paving the way for future research and intervention in this critical domain of human cognition.

Introduction

Problem solving, a quintessential cognitive process deeply embedded in the domains of psychology and education, serves as a linchpin for human intellectual development and adaptation to the ever-evolving challenges of the world. The fundamental capacity to identify, analyze, and surmount obstacles is intrinsic to human nature and has been a subject of profound interest for psychologists, educators, and researchers alike. This article aims to provide a comprehensive exploration of problem solving, investigating its theoretical foundations, cognitive intricacies, and practical applications in educational contexts. With a clear understanding of its multifaceted nature, we will elucidate the pivotal role that problem solving plays in enhancing learning, fostering creativity, and promoting cognitive growth, setting the stage for a detailed examination of its significance in both psychology and education. In the continuum of psychological research and educational practice, problem solving stands as a cornerstone, enabling individuals to navigate the complexities of their world. This article’s thesis asserts that problem solving is not merely a cognitive skill but a dynamic process with profound implications for intellectual growth and application in diverse real-world contexts.

Academic Writing, Editing, Proofreading, And Problem Solving Services

Get 10% off with 24start discount code, the nature of problem solving.

Problem solving, within the realm of psychology, refers to the cognitive process through which individuals identify, analyze, and resolve challenges or obstacles to achieve a desired goal. It encompasses a range of mental activities, such as perception, memory, reasoning, and decision-making, aimed at devising effective solutions in the face of uncertainty or complexity.

Problem solving as a subject of inquiry has drawn from various theoretical perspectives, each offering unique insights into its nature. Among the seminal theories, Gestalt psychology has highlighted the role of insight and restructuring in problem solving, emphasizing that individuals often reorganize their mental representations to attain solutions. Information processing theories, inspired by computer models, emphasize the systematic and step-by-step nature of problem solving, likening it to information retrieval and manipulation. Furthermore, cognitive psychology has provided a comprehensive framework for understanding problem solving by examining the underlying cognitive processes involved, such as attention, memory, and decision-making. These theoretical foundations collectively offer a richer comprehension of how humans engage in and approach problem-solving tasks.

Problem solving is not a monolithic process but a series of interrelated stages that individuals progress through. These stages are integral to the overall problem-solving process, and they include:

• Problem Representation: At the outset, individuals must clearly define and represent the problem they face. This involves grasping the nature of the problem, identifying its constraints, and understanding the relationships between various elements.
• Goal Setting: Setting a clear and attainable goal is essential for effective problem solving. This step involves specifying the desired outcome or solution and establishing criteria for success.
• Solution Generation: In this stage, individuals generate potential solutions to the problem. This often involves brainstorming, creative thinking, and the exploration of different strategies to overcome the obstacles presented by the problem.
• Solution Evaluation: After generating potential solutions, individuals must evaluate these alternatives to determine their feasibility and effectiveness. This involves comparing solutions, considering potential consequences, and making choices based on the criteria established in the goal-setting phase.

These components collectively form the roadmap for navigating the terrain of problem solving and provide a structured approach to addressing challenges effectively. Understanding these stages is crucial for both researchers studying problem solving and educators aiming to foster problem-solving skills in learners.

Cognitive and Psychological Aspects of Problem Solving

Problem solving is intricately tied to a range of cognitive processes, each contributing to the effectiveness of the problem-solving endeavor.

• Perception: Perception serves as the initial gateway in problem solving. It involves the gathering and interpretation of sensory information from the environment. Effective perception allows individuals to identify relevant cues and patterns within a problem, aiding in problem representation and understanding.
• Memory: Memory is crucial in problem solving as it enables the retrieval of relevant information from past experiences, learned strategies, and knowledge. Working memory, in particular, helps individuals maintain and manipulate information while navigating through the various stages of problem solving.
• Reasoning: Reasoning encompasses logical and critical thinking processes that guide the generation and evaluation of potential solutions. Deductive and inductive reasoning, as well as analogical reasoning, play vital roles in identifying relationships and formulating hypotheses.

While problem solving is a universal cognitive function, individuals differ in their problem-solving skills due to various factors.

• Intelligence: Intelligence, as measured by IQ or related assessments, significantly influences problem-solving abilities. Higher levels of intelligence are often associated with better problem-solving performance, as individuals with greater cognitive resources can process information more efficiently and effectively.
• Creativity: Creativity is a crucial factor in problem solving, especially in situations that require innovative solutions. Creative individuals tend to approach problems with fresh perspectives, making novel connections and generating unconventional solutions.
• Expertise: Expertise in a specific domain enhances problem-solving abilities within that domain. Experts possess a wealth of knowledge and experience, allowing them to recognize patterns and solutions more readily. However, expertise can sometimes lead to domain-specific biases or difficulties in adapting to new problem types.

Despite the cognitive processes and individual differences that contribute to effective problem solving, individuals often encounter barriers that impede their progress. Recognizing and overcoming these barriers is crucial for successful problem solving.

• Functional Fixedness: Functional fixedness is a cognitive bias that limits problem solving by causing individuals to perceive objects or concepts only in their traditional or “fixed” roles. Overcoming functional fixedness requires the ability to see alternative uses and functions for objects or ideas.
• Confirmation Bias: Confirmation bias is the tendency to seek, interpret, and remember information that confirms preexisting beliefs or hypotheses. This bias can hinder objective evaluation of potential solutions, as individuals may favor information that aligns with their initial perspectives.
• Mental Sets: Mental sets are cognitive frameworks or problem-solving strategies that individuals habitually use. While mental sets can be helpful in certain contexts, they can also limit creativity and flexibility when faced with new problems. Recognizing and breaking out of mental sets is essential for overcoming this barrier.

Understanding these cognitive processes, individual differences, and common obstacles provides valuable insights into the intricacies of problem solving and offers a foundation for improving problem-solving skills and strategies in both educational and practical settings.

Problem Solving in Educational Settings

Problem solving holds a central position in educational psychology, as it is a fundamental skill that empowers students to navigate the complexities of the learning process and prepares them for real-world challenges. It goes beyond rote memorization and standardized testing, allowing students to apply critical thinking, creativity, and analytical skills to authentic problems. Problem-solving tasks in educational settings range from solving mathematical equations to tackling complex issues in subjects like science, history, and literature. These tasks not only bolster subject-specific knowledge but also cultivate transferable skills that extend beyond the classroom.

Problem-solving skills offer numerous advantages to both educators and students. For teachers, integrating problem-solving tasks into the curriculum allows for more engaging and dynamic instruction, fostering a deeper understanding of the subject matter. Additionally, it provides educators with insights into students’ thought processes and areas where additional support may be needed. Students, on the other hand, benefit from the development of critical thinking, analytical reasoning, and creativity. These skills are transferable to various life situations, enhancing students’ abilities to solve complex real-world problems and adapt to a rapidly changing society.

Teaching problem-solving skills is a dynamic process that requires effective pedagogical approaches. In K-12 education, educators often use methods such as the problem-based learning (PBL) approach, where students work on open-ended, real-world problems, fostering self-directed learning and collaboration. Higher education institutions, on the other hand, employ strategies like case-based learning, simulations, and design thinking to promote problem solving within specialized disciplines. Additionally, educators use scaffolding techniques to provide support and guidance as students develop their problem-solving abilities. In both K-12 and higher education, a key component is metacognition, which helps students become aware of their thought processes and adapt their problem-solving strategies as needed.

Assessing problem-solving abilities in educational settings involves a combination of formative and summative assessments. Formative assessments, including classroom discussions, peer evaluations, and self-assessments, provide ongoing feedback and opportunities for improvement. Summative assessments may include standardized tests designed to evaluate problem-solving skills within a particular subject area. Performance-based assessments, such as essays, projects, and presentations, offer a holistic view of students’ problem-solving capabilities. Rubrics and scoring guides are often used to ensure consistency in assessment, allowing educators to measure not only the correctness of answers but also the quality of the problem-solving process. The evolving field of educational technology has also introduced computer-based simulations and adaptive learning platforms, enabling precise measurement and tailored feedback on students’ problem-solving performance.

Understanding the pivotal role of problem solving in educational psychology, the diverse pedagogical strategies for teaching it, and the methods for assessing and measuring problem-solving abilities equips educators and students with the tools necessary to thrive in educational environments and beyond. Problem solving remains a cornerstone of 21st-century education, preparing students to meet the complex challenges of a rapidly changing world.

Applications and Practical Implications

Problem solving is not confined to the classroom; it extends its influence to various real-world contexts, showcasing its relevance and impact. In business, problem solving is the driving force behind product development, process improvement, and conflict resolution. For instance, companies often use problem-solving methodologies like Six Sigma to identify and rectify issues in manufacturing. In healthcare, medical professionals employ problem-solving skills to diagnose complex illnesses and devise treatment plans. Additionally, technology advancements frequently stem from creative problem solving, as engineers and developers tackle challenges in software, hardware, and systems design. Real-world problem solving transcends specific domains, as individuals in diverse fields address multifaceted issues by drawing upon their cognitive abilities and creative problem-solving strategies.

Clinical psychology recognizes the profound therapeutic potential of problem-solving techniques. Problem-solving therapy (PST) is an evidence-based approach that focuses on helping individuals develop effective strategies for coping with emotional and interpersonal challenges. PST equips individuals with the skills to define problems, set realistic goals, generate solutions, and evaluate their effectiveness. This approach has shown efficacy in treating conditions like depression, anxiety, and stress, emphasizing the role of problem-solving abilities in enhancing emotional well-being. Furthermore, cognitive-behavioral therapy (CBT) incorporates problem-solving elements to help individuals challenge and modify dysfunctional thought patterns, reinforcing the importance of cognitive processes in addressing psychological distress.

Problem solving is the bedrock of innovation and creativity in various fields. Innovators and creative thinkers use problem-solving skills to identify unmet needs, devise novel solutions, and overcome obstacles. Design thinking, a problem-solving approach, is instrumental in product design, architecture, and user experience design, fostering innovative solutions grounded in human needs. Moreover, creative industries like art, literature, and music rely on problem-solving abilities to transcend conventional boundaries and produce groundbreaking works. By exploring alternative perspectives, making connections, and persistently seeking solutions, creative individuals harness problem-solving processes to ignite innovation and drive progress in all facets of human endeavor.

Understanding the practical applications of problem solving in business, healthcare, technology, and its therapeutic significance in clinical psychology, as well as its indispensable role in nurturing innovation and creativity, underscores its universal value. Problem solving is not only a cognitive skill but also a dynamic force that shapes and improves the world we inhabit, enhancing the quality of life and promoting progress and discovery.

In summary, problem solving stands as an indispensable cornerstone within the domains of psychology and education. This article has explored the multifaceted nature of problem solving, from its theoretical foundations rooted in Gestalt psychology, information processing theories, and cognitive psychology to its integral components of problem representation, goal setting, solution generation, and solution evaluation. It has delved into the cognitive processes underpinning effective problem solving, including perception, memory, and reasoning, as well as the impact of individual differences such as intelligence, creativity, and expertise. Common barriers to problem solving, including functional fixedness, confirmation bias, and mental sets, have been examined in-depth.

The significance of problem solving in educational settings was elucidated, underscoring its pivotal role in fostering critical thinking, creativity, and adaptability. Pedagogical approaches and assessment methods were discussed, providing educators with insights into effective strategies for teaching and evaluating problem-solving skills in K-12 and higher education.

Furthermore, the practical implications of problem solving were demonstrated in the real world, where it serves as the driving force behind advancements in business, healthcare, and technology. In clinical psychology, problem-solving therapies offer effective interventions for emotional and psychological well-being. The symbiotic relationship between problem solving and innovation and creativity was explored, highlighting the role of this cognitive process in pushing the boundaries of human accomplishment.

As we conclude, it is evident that problem solving is not merely a skill but a dynamic process with profound implications. It enables individuals to navigate the complexities of their environment, fostering intellectual growth, adaptability, and innovation. Future research in the field of problem solving should continue to explore the intricate cognitive processes involved, individual differences that influence problem-solving abilities, and innovative teaching methods in educational settings. In practice, educators and clinicians should continue to incorporate problem-solving strategies to empower individuals with the tools necessary for success in education, personal development, and the ever-evolving challenges of the real world. Problem solving remains a steadfast ally in the pursuit of knowledge, progress, and the enhancement of human potential.

References:

• Anderson, J. R. (1995). Cognitive psychology and its implications. W. H. Freeman.
• Atkinson, R. C., & Shiffrin, R. M. (1968). Human memory: A proposed system and its control processes. In The psychology of learning and motivation (Vol. 2, pp. 89-195). Academic Press.
• Duncker, K. (1945). On problem-solving. Psychological Monographs, 58(5), i-113.
• Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive Psychology, 12(3), 306-355.
• Jonassen, D. H., & Hung, W. (2008). All problems are not equal: Implications for problem-based learning. Interdisciplinary Journal of Problem-Based Learning, 2(2), 6.
• Kitchener, K. S., & King, P. M. (1981). Reflective judgment: Concepts of justification and their relation to age and education. Journal of Applied Developmental Psychology, 2(2), 89-116.
• Luchins, A. S. (1942). Mechanization in problem solving: The effect of Einstellung. Psychological Monographs, 54(6), i-95.
• Mayer, R. E. (1992). Thinking, problem solving, cognition. W. H. Freeman.
• Newell, A., & Simon, H. A. (1972). Human problem solving (Vol. 104). Prentice-Hall Englewood Cliffs, NJ.
• Osborn, A. F. (1953). Applied imagination: Principles and procedures of creative problem solving (3rd ed.). Charles Scribner’s Sons.
• Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton University Press.
• Sternberg, R. J. (2003). Wisdom, intelligence, and creativity synthesized. Cambridge University Press.

Thinking and Intelligence

Pitfalls to Problem Solving

Learning objectives.

• Explain some common roadblocks to effective 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.

Link to Learning

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. This bias proves that first impressions do matter and that we tend to look for information to confirm our initial judgments of others.

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

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

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

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

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

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

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

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

Think It Over

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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• Modification, adaptation, and original content. Provided by : Lumen Learning. License : CC BY: Attribution

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• Problem Solving. Authored by : OpenStax College. Located at : https://openstax.org/books/psychology-2e/pages/7-3-problem-solving . License : Public Domain: No Known Copyright . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction
• More information on heuristics. Authored by : Dr. Scott Roberts, Dr. Ryan Curtis, Samantha Levy, and Dr. Dylan Selterman. Provided by : University of Maryland. Located at : http://openpsyc.blogspot.com/2014/07/heuristics.html . Project : OpenPSYC. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike

continually using an old solution to a problem without results

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

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

seeking out information that supports our stereotypes while ignoring information that is inconsistent with our stereotypes

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

faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

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

General Psychology Copyright © by OpenStax and Lumen Learning is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Facilitating Complex Thinking

Problem-Solving

Somewhat less open-ended than creative thinking is  problem-solving , the analysis and solution of tasks or situations that are complex or ambiguous and that pose difficulties or obstacles of some kind (Mayer & Wittrock, 2006). Problem-solving is needed, for example, when a physician analyzes a chest X-ray: a photograph of the chest is far from clear and requires skill, experience, and resourcefulness to decide which foggy-looking blobs to ignore, and which to interpret as real physical structures (and therefore real medical concerns). Problem-solving is also needed when a grocery store manager has to decide how to improve the sales of a product: should she put it on sale at a lower price, or increase publicity for it, or both? Will these actions actually increase sales enough to pay for their costs?

PROBLEM-SOLVING IN THE CLASSROOM

Problem-solving happens in classrooms when teachers present tasks or challenges that are deliberately complex and for which finding a solution is not straightforward or obvious. The responses of students to such problems, as well as the strategies for assisting them, show the key features of problem-solving. Consider this example and students’ responses to it. We have numbered and named the paragraphs to make it easier to comment about them individually:

Scene #1: A problem to be solved

A teacher gave these instructions: “Can you connect all of the dots below using only  four  straight lines?” She drew the following display on the chalkboard:

The problem itself and the procedure for solving it seemed very clear: simply experiment with different arrangements of four lines. But two volunteers tried doing it at the board, but were unsuccessful. Several others worked at it at their seats, but also without success.

Scene #2: Coaxing students to re-frame the problem

When no one seemed to be getting it, the teacher asked, “Think about how you’ve set up the problem in your mind—about what you believe the problem is about. For instance, have you made any assumptions about how long the lines ought to be? Don’t stay stuck on one approach if it’s not working!”

Scene #3: Alicia abandons a fixed response

After the teacher said this, Alicia indeed continued to think about how she saw the problem. “The lines need to be no longer than the distance across the square,” she said to herself. So she tried several more solutions, but none of them worked either.

The teacher walked by Alicia’s desk and saw what Alicia was doing. She repeated her earlier comment: “Have you assumed anything about how long the lines ought to be?”

Alicia stared at the teacher blankly, but then smiled and said, “Hmm! You didn’t actually  say  that the lines could be no longer than the matrix! Why not make them longer?” So she experimented again using oversized lines and soon discovered a solution:

Scene #4: Willem’s and Rachel’s alternative strategies

Meanwhile, Willem worked on the problem. As it happened, Willem loved puzzles of all kinds and had ample experience with them. He had not, however, seen this particular problem. “It  must  be a trick,” he said to himself because he knew from experience that problems posed in this way often were not what they first appeared to be. He mused to himself: “Think outside the box, they always tell you. . .” And  that  was just the hint he needed: he drew lines outside the box by making them longer than the matrix and soon came up with this solution:

When Rachel went to work, she took one look at the problem and knew the answer immediately: she had seen this problem before, though she could not remember where. She had also seen other drawing-related puzzles and knew that their solution always depended on making the lines longer, shorter, or differently angled than first expected. After staring at the dots briefly, she drew a solution faster than Alicia or even Willem. Her solution looked exactly like Willem’s.

This story illustrates two common features of problem-solving: the effect of degree of structure or constraint on problem-solving, and the effect of mental obstacles to solving problems. The next sections discuss each of these features and then look at common techniques for solving problems.

The Effect of Constraints: Well-Structured Versus Ill-Structured Problems

Problems vary in how much information they provide for solving a problem, as well as in how many rules or procedures are needed for a solution. A  well-structured problem  provides much of the information needed and can in principle be solved using relatively few clearly understood rules. Classic examples are the word problems often taught in math lessons or classes: everything you need to know is contained within the stated problem and the solution procedures are relatively clear and precise. An  ill-structured problem  has the converse qualities: the information is not necessarily within the problem, solution procedures are potentially quite numerous, and multiple solutions are likely (Voss, 2006). Extreme examples are problems like “How can the world achieve lasting peace?” or “How can teachers ensure that students learn?”

By these definitions, the nine-dot problem is relatively well-structured—though not completely. Most of the information needed for a solution is provided in Scene #1: there are nine dots shown and instructions given to draw four lines. But not  all  necessary information was given: students needed to consider lines that were longer than implied in the original statement of the problem. Students had to “think outside the box,” as Willem said—in this case, literally.

When a problem is well-structured, so are its solution procedures likely to be as well. A well-defined procedure for solving a particular kind of problem is often called an  algorithm ; examples are the procedures for multiplying or dividing two numbers or the instructions for using a computer (Leiserson, et al., 2001). Algorithms are only effective when a problem is very well-structured and there is no question about whether the algorithm is an appropriate choice for the problem. In that situation, it pretty much guarantees a correct solution. They do not work well, however, with ill-structured problems, where they are ambiguities and questions about how to proceed or even about precisely  what  the problem is about. In those cases, it is more effective to use  heuristics , which are general strategies—“rules of thumb,” so to speak—that do not always work but often do, or that provide at least partial solutions. When beginning research for a term paper, for example, a useful heuristic is to scan the library catalog for titles that look relevant. There is no guarantee that this strategy will yield the books most needed for the paper, but the strategy works enough of the time to make it worth trying.

In the nine-dot problem, most students began in Scene #1 with a simple algorithm that can be stated like this: “Draw one line, then draw another, and another, and another.” Unfortunately, this simple procedure did not produce a solution, so they had to find other strategies for a solution. Three alternatives are described in Scenes #3 (for Alicia) and 4 (for Willem and Rachel). Of these, Willem’s response resembled a heuristic the most: he knew from experience that a good  general  strategy that  often  worked for such problems was to suspect deception or trick in how the problem was originally stated. So he set out to question what the teacher had meant by the word  line  and came up with an acceptable solution as a result.

Common Obstacles to Solving Problems

The example also illustrates two common problems that sometimes happen during problem-solving. One of these is  functional fixedness : a tendency to regard the  functions  of objects and ideas as  fixed  (German & Barrett, 2005). Over time, we get so used to one particular purpose for an object that we overlook other uses. We may think of a dictionary, for example, as necessarily something to verify spellings and definitions, but it also can function as a gift, a doorstop, or a footstool. For students working on the nine-dot matrix described in the last section, the notion of “drawing” a line was also initially fixed; they assumed it to be connecting dots but not extending lines beyond the dots. Functional fixedness sometimes is also called  response set , the tendency for a person to frame or think about each problem in a series in the same way as the previous problem, even when doing so is not appropriate for later problems. In the example of the nine-dot matrix described above, students often tried one solution after another, but each solution was constrained by a set response not  to extend any line beyond the matrix.

Functional fixedness and the response set are obstacles in  problem representation , the way that a person understands and organizes information provided in a problem. If information is misunderstood or used inappropriately, then mistakes are likely—if indeed the problem can be solved at all. With the nine-dot matrix problem, for example, construing the instruction to draw four lines as meaning “draw four lines entirely within the matrix” means that the problem simply could not be solved. For another, consider this problem: “The number of water lilies on a lake doubles each day. Each water lily covers exactly one square foot. If it takes 100 days for the lilies to cover the lake exactly, how many days does it take for the lilies to cover exactly half of the lake?” If you think that the size of the lilies affects the solution to this problem, you have not represented the problem correctly. Information about lily size is  not  relevant to the solution and only serves to distract from the truly crucial information, the fact that the lilies  double  their coverage each day. (The answer, incidentally, is that the lake is half covered in 99 days; can you think why?)

Strategies to Assist Problem-Solving

Just as there are cognitive obstacles to problem-solving, there are also general strategies that help the process be successful, regardless of the specific content of a problem (Thagard, 2005). One helpful strategy is  problem analysis —identifying the parts of the problem and working on each part separately. Analysis is especially useful when a problem is ill-structured. Consider this problem, for example: “Devise a plan to improve bicycle transportation in the city.” Solving this problem is easier if you identify its parts or component subproblems, such as (1) installing bicycle lanes on busy streets, (2) educating cyclists and motorists to ride safely, (3) fixing potholes on streets used by cyclists, and (4) revising traffic laws that interfere with cycling. Each separate subproblem is more manageable than the original, general problem. The solution of each subproblem contributes to the solution of the whole, though of course is not equivalent to a whole solution.

Another helpful strategy is  working backward   from  a final solution to the originally stated problem. This approach is especially helpful when a problem is well-structured but also has elements that are distracting or misleading when approached in a forward, normal direction. The water lily problem described above is a good example: starting with the day when  all  the lake is covered (Day 100), ask what day would it, therefore, be half-covered (by the terms of the problem, it would have to be the day before, or Day 99). Working backward, in this case, encourages reframing the extra information in the problem (i. e. the size of each water lily) as merely distracting, not as crucial to a solution.

A third helpful strategy is  analogical thinking —using knowledge or experiences with similar features or structures to help solve the problem at hand (Bassok, 2003). In devising a plan to improve bicycling in the city, for example, an analogy of cars with bicycles is helpful in thinking of solutions: improving conditions for both vehicles requires many of the same measures (improving the roadways, educating drivers). Even solving simpler, more basic problems is helped by considering analogies. A first-grade student can partially decode unfamiliar printed words by analogy to words he or she has learned already. If the child cannot yet read the word screen , for example, he can note that part of this word looks similar to words he may already know, such as  seen  or  green,  and from this observation derive a clue about how to read the word  screen . Teachers can assist this process, as you might expect, by suggesting reasonable, helpful analogies for students to consider.

Video 5.4.1. Problem Solving explains strategies used for solving problems.

Many systems for problem-solving can be taught to learners (Pressley, 1995). There are problem-solving strategies to improve general problem solving (Burkell, Schneider, & Pressley, 1990; Mayer, 1987; Sternberg, 1988), scientific thinking (Kuhn, 1989), mathematical problem solving (Schoenfeld, 1989), and writing during the elementary years (Harris & Graham, 1992a) and during adolescence (Applebee, 1984; Langer & Applebee, 1987).

A problem-solving system that can be used in a variety of curriculum areas and with a variety of problems is called IDEAL (Bransford & Steen, 1984). IDEAL involves five stages of problem-solving:

• Identify the problem. Learners must know what the problem is before they can solve it. During this stage of problem-solving, learners ask themselves whether they understand what the problem is and whether they have stated it clearly.
• Define terms. During this stage, learners check whether they understand what each word in the problem statement means.
• Explore strategies. At this stage, learners compile relevant information and try out strategies to solve the problem. This can involve drawing diagrams, working backward to solve a mathematical or reading comprehension problem, or breaking complex problems into manageable units.
• Act on the strategy. Once learners have explored a variety of strategies, they select one and now use it.
• Look at the effects. During the final stage of the IDEAL method, learners ask themselves whether they have come up with an acceptable solution.

Video 5.4.2. The Problem Solving Model explains the process involved in solving problems. These steps can be explicitly taught to enhance problem-solving skills.

Candela Citations

• Problem-Solving. Authored by : Nicole Arduini-Van Hoose. Provided by : Hudson Valley Community College. Retrieved from : https://courses.lumenlearning.com/edpsy/chapter/problemsolving. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
• Educational Psychology. Authored by : Kelvin Seifert and Rosemary Sutton. Provided by : The Saylor Foundation. Retrieved from : https://courses.lumenlearning.com/educationalpsychology. License : CC BY: Attribution
• Educational Psychology. Authored by : Bohlin. License : CC BY: Attribution
• Problem Solving. Authored by : Carole Yue. Provided by : Khan Academy. Retrieved from : https://youtu.be/J3GGx9wy07w. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
• The Problem Solving Model. Provided by : Gregg Learning. Retrieved from : https://youtu.be/CDk_BD1LXiI. License : All Rights Reserved

Educational Psychology Copyright © 2020 by Nicole Arduini-Van Hoose is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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The Stages of the Problem Solving Cycle in Cognitive Psychology – Understanding, Planning, Execution, Evaluation, and Reflection

• Post author By bicycle-u
• Post date 08.12.2023

Problem solving is a fundamental aspect of human cognition. It involves the ability to identify and define a problem, generate potential solutions, evaluate those solutions, and select the most appropriate one. The problem solving cycle is a key concept in cognitive psychology that helps us understand how individuals approach and solve problems.

In the problem solving cycle , individuals first must recognize and define the problem they are facing. This involves identifying the specific issue or obstacle that needs to be overcome. Once the problem is clearly defined, individuals can then move on to the next stage of the cycle.

Next, individuals engage in the process of generating potential solutions . This may involve brainstorming ideas, seeking out information or advice, or experimenting with different approaches. The goal is to come up with as many possible solutions as possible, without judgment or evaluation.

Once a range of potential solutions has been generated, individuals then evaluate these solutions based on their feasibility and effectiveness . This involves assessing the advantages and disadvantages of each solution and considering the potential outcomes of implementing them. It may also involve consulting others or seeking additional information to inform the evaluation process.

Finally, individuals select the most appropriate solution from the evaluated options. This decision-making process takes into account various factors such as the individual’s goals, resources, and constraints. Once a solution has been selected, individuals can then implement and evaluate its effectiveness, closing the problem solving cycle.

The problem solving cycle is a dynamic and iterative process that can be applied to a wide range of problems and situations. It provides a framework for understanding how individuals approach and solve problems, and it can be useful in both personal and professional settings. By understanding the various stages of the problem solving cycle, individuals can become more effective problem solvers and make better decisions.

Understanding the Problem Solving Process

In cognitive psychology, the problem solving process is a key concept in understanding how individuals navigate and overcome challenges. Problem solving is a cyclical process that involves identifying a problem, developing a strategy to solve it, implementing the strategy, and then evaluating the results.

Identifying the problem: The first step in the problem solving cycle is identifying the problem at hand. This may involve defining the problem, gathering information and relevant data, and understanding the desired outcome.

Developing a strategy: Once the problem is identified, individuals must develop a strategy or plan of action to solve it. This may involve brainstorming ideas, evaluating potential solutions, and selecting the best approach.

Implementing the strategy: After a strategy is developed, it must be put into action. This may involve executing specific steps, utilizing resources, and adjusting the strategy as needed.

Evaluating the results: The final step in the problem solving cycle is evaluating the results of the implemented strategy. This may involve assessing the effectiveness of the solution, determining if the desired outcome was achieved, and making any necessary adjustments or improvements.

The Role of Cognitive Psychology

Cognitive psychology plays a crucial role in understanding the problem solving process. It focuses on how individuals perceive, think, and reason about problems, as well as the various strategies and mental processes involved in solving them.

Research in cognitive psychology has shown that problem solving is not purely a linear process, but rather a dynamic and iterative cycle. Individuals may iterate through the different stages of the problem solving cycle multiple times as they encounter new information or face unexpected challenges.

The study of problem solving in cognitive psychology has led to the development of various theories and models, such as the Gestalt theory, which emphasizes the importance of insight and reorganizing information, and the information processing model, which highlights the role of attention, memory, and decision-making in problem solving.

The Importance of Problem Solving Skills

Problem solving is a key concept in cognitive psychology. It is a process that involves identifying, analyzing, and coming up with solutions to problems. Problem solving skills are essential in various aspects of life, including personal and professional contexts.

Mastering problem solving skills enables individuals to tackle challenges and overcome obstacles effectively. It helps in critical thinking, decision making, and finding innovative solutions. Problem solving skills are also important in the field of psychology, as they are often used to understand and address complex psychological issues.

Enhancing Cognitive Abilities

Problem solving activities stimulate and enhance cognitive abilities. They require individuals to think critically, analyze information, and use logical reasoning. By engaging in problem solving, individuals improve their cognitive processes, such as memory, attention, and problem representation.

Building Resilience

Developing problem solving skills also helps in building resilience. It teaches individuals to approach challenges with a proactive mindset and seek solutions rather than giving up. This resilience can be applied in various aspects of life, including personal relationships, work, and education.

In conclusion, problem solving skills play a crucial role in cognitive psychology and various aspects of life. They enhance cognitive abilities, promote critical thinking, and build resilience. Developing and honing problem solving skills is essential for personal growth and success in today’s complex world.

The Four Stages of Problem Solving

Problem solving is a cognitive process that involves the use of mental processes to find a solution to a problem. It is a cycle that is often studied in cognitive psychology. The problem solving cycle consists of four stages, which are:

1. Understanding the Problem

In this stage, the individual must first understand and define the problem. This involves gathering information, analyzing the problem, and identifying the key elements that need to be addressed. It is important to have a clear understanding of the problem before moving on to the next stage.

2. Generating Potential Solutions

Once the problem is understood, the next stage involves generating potential solutions. This requires using both logical and creative thinking to come up with possible ways to solve the problem. It is important to consider different perspectives and explore a variety of options.

3. Evaluating and Selecting Solutions

After generating potential solutions, the individual must evaluate and select the most appropriate solution. This involves weighing the pros and cons of each potential solution and considering factors such as feasibility, effectiveness, and practicality. The goal is to select a solution that is likely to lead to the desired outcome.

4. Implementing and Evaluating the Solution

Once a solution has been selected, the final stage involves implementing the solution and evaluating its effectiveness. This may involve taking action, making changes, and monitoring the results. It is important to assess whether the solution has solved the problem and to make adjustments if needed.

In conclusion, problem solving is a cognitive process that involves four stages: understanding the problem, generating potential solutions, evaluating and selecting solutions, and implementing and evaluating the solution. By following this problem solving cycle, individuals can effectively approach and solve a wide range of problems.

Identifying the Problem

The first step in the problem solving cycle is identifying the problem. In cognitive psychology, this step involves recognizing that there is a problem to be solved and understanding what it entails.

When identifying a problem, it is important to clearly define and articulate what the issue is. This can involve breaking the problem down into smaller components or examining the factors that contribute to the problem.

Factors to consider when identifying a problem:

• What is the desired outcome or goal?
• What are the obstacles or challenges that need to be overcome?
• What are the potential causes or explanations for the problem?

Identifying the problem involves gathering information and analyzing it to gain a better understanding of the situation. This can include conducting research, gathering data, or seeking input from others who may have expertise or experience in the area.

Once the problem has been clearly identified, it can then be approached using the problem solving cycle. By breaking down the problem into smaller steps and systematically working through each one, individuals can increase their chances of finding an effective solution.

Defining the Problem

Defining the problem is a crucial step in the problem-solving cycle. In the context of cognitive psychology, a problem can be defined as a situation or task that requires a solution. This could be a complex mathematical equation, a riddle, or a real-life challenge. The process of defining the problem involves clarifying the specific requirements or constraints of the situation and understanding what needs to be solved. By clearly defining the problem, it becomes easier to identify potential strategies and solutions.

When defining a problem, it is important to consider both the immediate and underlying issues. Often, the surface-level problem may not be the root cause, and addressing only the symptoms may not lead to a satisfactory solution. Therefore, it is essential to dig deeper and identify the underlying factors that contribute to the problem.

Clarifying the requirements

One aspect of defining the problem is clarifying the specific requirements or constraints that need to be considered. These requirements can include the desired outcome, the available resources, the time frame, and any limitations or restrictions. By understanding these requirements, it becomes easier to focus on finding a solution that meets the given criteria.

Understanding the problem space

Another important aspect of defining the problem is understanding the problem space. The problem space refers to the set of all possible solutions and strategies that can be explored to solve the problem. By understanding the problem space, individuals can develop a clearer understanding of the scope of the problem and the potential avenues for finding a solution.

Generating Solution Options

In cognitive psychology, problem solving is a key concept that explores how individuals go about finding solutions to problems. One important aspect of the problem solving cycle is generating solution options.

When faced with a problem, individuals engage in cognitive processes to come up with potential solutions. This often involves brainstorming, where individuals generate a list of possible options.

There are various strategies that individuals can use to generate solution options. One common approach is divergent thinking, which involves thinking creatively and generating a large number of potential solutions. This can be done by considering different perspectives, exploring alternative possibilities, and challenging assumptions.

Another strategy is convergent thinking, which involves evaluating and narrowing down the potential solutions. This can be done by considering the feasibility and practicality of each option, as well as weighing the potential risks and benefits.

It is important for individuals to consider a wide range of solution options, as this increases the likelihood of finding an effective solution. This can be achieved by using techniques such as mind mapping, where individuals visually organize their thoughts and ideas to generate new connections and possibilities.

By generating a variety of solution options, individuals can increase their chances of finding the most suitable and effective solution to a problem. This stage of the problem solving cycle is crucial in the overall problem solving process.

Evaluating and Selecting the Best Solution

Once you have gone through the problem solving cycle and generated potential solutions, the next step is to evaluate and select the best solution. This is an essential part of the problem solving process, as it involves critically analyzing each potential solution and determining which one is the most effective and feasible.

When evaluating potential solutions, it is important to consider various factors. One key factor is the effectiveness of each solution in actually solving the problem at hand. Will the solution address the root cause of the problem, or just temporarily alleviate the symptoms?

In addition to effectiveness, it is also important to consider the feasibility of each solution. Is the solution realistic and practical to implement? Does it require significant resources or time that may not be available? These are all important considerations to take into account when evaluating potential solutions.

Furthermore, it is important to consider the potential consequences of each solution. Will the solution create any new problems or unintended side effects? Will it have any negative impacts on other areas or stakeholders? These potential consequences must be carefully considered before making a final decision.

Finally, it is important to approach the evaluation process with an open and flexible mindset. It is not uncommon for new information or perspectives to emerge during the evaluation process, which may alter the assessment of potential solutions. Remaining open to new information and being willing to adapt the evaluation criteria is crucial in selecting the best solution.

By carefully evaluating each potential solution and considering factors such as effectiveness, feasibility, and potential consequences, you can effectively select the best solution to the problem at hand. This is an essential step in the problem solving cycle, as it moves you closer to a successful resolution.

Implementing the Solution

Once the problem-solving cycle has been completed in cognitive psychology, the next step is to implement the solution. This phase involves taking the proposed solution and putting it into action.

Before implementation, it is crucial to evaluate the solution thoroughly. This evaluation helps ensure that the proposed solution is practical and feasible.

Evaluating the Solution

The evaluation process involves considering possible obstacles and risks that could hinder the successful implementation of the solution. By identifying these potential challenges, steps can be taken to mitigate them.

In addition, evaluating the solution also involves conducting a cost-benefit analysis. This analysis takes into account the potential costs and benefits associated with implementing the solution. It helps determine whether the solution is worth pursuing.

Putting the Solution into Action

Once the solution has been thoroughly evaluated, it is time to put it into action. This requires careful planning and coordination.

During the implementation phase, it is important to closely monitor the progress and make any necessary adjustments. This ensures that the solution is effectively addressing the problem at hand.

Furthermore, clear communication is vital during implementation. All relevant stakeholders should be informed and involved in the process to ensure everyone is working towards a common goal.

By implementing the solution effectively, the problem-solving cycle in cognitive psychology can come to a successful conclusion.

Monitoring and Evaluating the Outcome

Monitoring and evaluating the outcome is a crucial step in the problem-solving process in cognitive psychology. After identifying and implementing a solution, it is important to assess whether the problem has been effectively solved and whether the desired outcome has been achieved.

Evaluating the Effectiveness of the Solution

One way to monitor and evaluate the outcome is to assess the effectiveness of the solution. This involves determining whether the chosen solution has successfully addressed the problem and whether it has led to the desired result. Cognitive psychologists often use various measures and metrics to evaluate the effectiveness of problem-solving strategies. These may include objective measures such as test scores or subjective measures such as self-report questionnaires.

By evaluating the effectiveness of the solution, cognitive psychologists can determine whether further adjustments or modifications are necessary. If the outcome is not satisfactory, they can go back to the problem-solving cycle and repeat the steps to find a more suitable solution.

Reflecting on the Process

In addition to evaluating the effectiveness of the solution, it is also important to reflect on the problem-solving process itself. This involves considering the strategies and techniques used, as well as identifying any obstacles or challenges encountered. By reflecting on the process, cognitive psychologists can gain valuable insights into how they approached the problem and how they can improve their problem-solving skills in the future.

Reflection can be done through self-reflection or by seeking feedback from others, such as colleagues or experts in the field. This feedback can provide alternative perspectives and help identify areas for improvement.

In conclusion, monitoring and evaluating the outcome is a critical aspect of the problem-solving cycle in cognitive psychology. By assessing the effectiveness of the solution and reflecting on the process, cognitive psychologists can continually improve their problem-solving skills and contribute to the development of this field.

The Role of Cognitive Processes in Problem Solving

In the field of cognitive psychology, problem solving is a fundamental aspect of human thinking. It involves the use of various cognitive processes to analyze a problem, develop possible solutions, and determine the best course of action.

One key cognitive process involved in problem solving is perception. This process allows individuals to perceive and understand the problem at hand, by gathering information from the environment and organizing it into meaningful patterns. Perception helps identify the relevant aspects of a problem and guides the problem-solving process.

Another important cognitive process in problem solving is reasoning. Reasoning involves logical thinking and the ability to draw conclusions based on available information. It helps individuals make sense of the problem and generate possible solutions. Reasoning also helps evaluate the potential outcomes of each solution and select the most appropriate one.

Memory plays a crucial role in problem solving as well. It allows individuals to recall relevant information from past experiences and apply it to the current problem. Memory aids in recognizing patterns, generating hypotheses, and retrieving information necessary for problem solving. Without memory, it would be challenging to solve problems efficiently.

Moreover, attention and concentration are essential cognitive processes in problem solving. They help individuals focus on the relevant aspects of a problem and block out distractions. Attention allows individuals to allocate cognitive resources effectively and process information in a systematic manner. Concentration enables individuals to stay engaged in problem solving and persevere until a solution is found.

The role of cognitive processes in problem solving is vital as they provide the framework for effective problem-solving strategies. Understanding how perception, reasoning, memory, attention, and concentration contribute to problem solving helps researchers and practitioners develop interventions and techniques to improve problem-solving skills.

In conclusion, cognitive processes are crucial in problem solving. Perception, reasoning, memory, attention, and concentration work together to help individuals analyze problems, generate solutions, and make informed decisions. By studying and understanding these cognitive processes, researchers can enhance problem-solving abilities, ultimately leading to more effective problem-solving strategies in various fields of study and practice.

How Cognitive Biases can Impact Problem Solving

Cognitive biases are inherent tendencies in human thinking that can lead to errors or deviations from rationality. These biases can have a significant impact on problem solving, as they can influence the way individuals perceive, interpret, and evaluate information.

Confirmation Bias

One common cognitive bias that can affect problem solving is confirmation bias. This bias leads individuals to favor information that confirms their existing beliefs or hypotheses while disregarding or downplaying information that contradicts them. In problem-solving scenarios, confirmation bias can prevent individuals from considering alternative solutions or exploring different perspectives, potentially leading to a less effective problem-solving process.

Availability Heuristic

The availability heuristic is another cognitive bias that can impact problem solving. This bias involves relying on easily accessible information or examples when making judgments or decisions. In problem-solving situations, this bias can lead individuals to overlook less accessible information or fail to consider all relevant factors. This can limit the effectiveness of problem solving by restricting the range of potential solutions or failing to consider alternative approaches.

• Overcoming cognitive biases in problem solving

Recognizing and overcoming cognitive biases is crucial for effective problem solving. Strategies such as actively seeking out diverse perspectives, questioning assumptions, and considering alternative explanations can help mitigate the impact of cognitive biases. Additionally, fostering an environment that encourages open-mindedness, critical thinking, and intellectual humility can also support more effective problem-solving processes.

By understanding how cognitive biases can impact problem solving, psychologists and individuals alike can work towards improving their problem-solving skills and decision-making processes. By recognizing and addressing these biases, individuals can enhance their ability to approach problems with greater objectivity, flexibility, and creativity.

The Relationship Between Problem Solving and Decision Making

Problem solving and decision making are closely interconnected in cognitive psychology. When faced with a problem, individuals engage in a cognitive process known as problem solving, which involves identifying and evaluating possible solutions in order to reach a desired goal or outcome. Decision making, on the other hand, refers to the act of choosing one particular solution from the options generated during the problem-solving process.

The problem-solving cycle, a key concept in cognitive psychology, highlights the iterative nature of problem solving and decision making. This cycle consists of several steps, including problem identification, problem analysis, solution generation, solution evaluation, and solution implementation. During the problem identification phase, individuals recognize and define the problem they are facing. Problem analysis involves gathering information and analyzing the underlying causes and factors contributing to the problem. Once a thorough analysis is conducted, individuals can generate potential solutions through creative thinking and brainstorming.

After generating potential solutions, individuals must evaluate the effectiveness and feasibility of each option. This involves considering the potential consequences and weighing the pros and cons of each alternative. By carefully assessing each solution, individuals can make an informed decision and choose the most suitable course of action. Finally, the chosen solution is implemented, and individuals monitor the outcomes to determine whether the problem has been effectively resolved.

It is important to note that problem solving and decision making are not linear processes, but rather they involve feedback loops and revisions as new information becomes available or as the initial solution proves to be ineffective. Successful problem solving and decision making require flexibility, critical thinking, and adaptability to changing circumstances.

In summary, problem solving and decision making are intertwined cognitive processes within the problem-solving cycle. Problem solving involves identifying and evaluating possible solutions, while decision making involves choosing the most appropriate solution. By understanding the relationship between problem solving and decision making, individuals can enhance their problem-solving skills and make more effective decisions in various aspects of life and work.

The Effect of Expertise on Problem Solving

In the cognitive psychology field, the problem solving cycle is a key concept that involves several stages: understanding the problem, devising a plan, executing the plan, and evaluating the solution. An important factor that can influence problem solving abilities is expertise.

Experts, who have extensive knowledge and experience in a specific domain, often exhibit superior problem solving skills compared to novices. This is because experts have a large mental database of problem-solving strategies and a deep understanding of the underlying concepts. They can quickly recognize patterns and make accurate decisions based on their knowledge.

Research has shown that experts are able to solve problems more efficiently and effectively than novices. They are able to quickly identify the relevant information and ignore irrelevant details, which allows them to focus on the core of the problem. Experts also have a better ability to generate and evaluate multiple potential solutions, leading to more creative problem solving.

Furthermore, experts are more likely to use metacognitive strategies, such as self-monitoring and self-regulation, during the problem solving process. They are able to reflect on their own thinking and adjust their strategies as needed. This metacognitive awareness helps experts to overcome obstacles and adapt their problem solving approach as necessary.

However, it is important to note that expertise is domain-specific. An individual may be an expert in one area but not in another. For example, a chess grandmaster may struggle with solving complex math problems. Therefore, expertise does not guarantee proficiency in all problem-solving domains.

In conclusion, expertise plays a significant role in problem solving. Experts have a deeper understanding of the problem domain, possess a larger repertoire of strategies, and exhibit metacognitive awareness. These factors contribute to their more efficient and effective problem solving abilities compared to novices.

Developing Problem Solving Skills through Practice

In the field of psychology, problem solving is considered an essential cognitive skill that helps individuals navigate through various challenges and obstacles. The problem solving cycle, a key concept in cognitive psychology, emphasizes the importance of practice in developing and honing problem solving skills.

Practice plays a crucial role in problem solving as it helps individuals familiarize themselves with different problem-solving techniques and strategies. By engaging in regular practice, individuals can strengthen their analytical thinking, creative problem solving, and decision-making abilities.

Through practice, individuals learn to approach problems systematically, breaking down complex tasks into smaller, more manageable steps. This systematic approach allows individuals to identify the root causes of a problem, generate potential solutions, and evaluate the effectiveness of each solution.

In addition to improving analytical thinking, practice also helps individuals develop their creative problem solving skills. By repeatedly facing various problems, individuals become more comfortable with thinking outside the box and exploring unconventional solutions. This creative thinking enables individuals to come up with innovative and effective solutions to complex problems.

Moreover, practice enhances individuals’ decision-making abilities. As individuals engage in problem solving practice, they become more skilled at assessing different options, weighing the pros and cons, and making informed decisions. This ability to make sound decisions is crucial in both personal and professional contexts.

In conclusion, developing problem solving skills requires consistent practice. By engaging in regular problem solving practice, individuals can improve their analytical thinking, creative problem solving, and decision-making abilities. The problem solving cycle emphasizes the importance of practice in developing these skills, and individuals who actively engage in practice are more likely to become adept problem solvers.

Teaching Problem Solving Skills in Education

Problem solving skills are an essential component of education, as they enable students to analyze and tackle complex issues across various subject areas. By teaching problem solving skills, educators help students develop critical thinking abilities and cognitive strategies that can be applied in real-life situations.

The Problem Solving Cycle

One effective approach to teaching problem solving skills is through the use of the problem solving cycle. The problem solving cycle is a key concept in cognitive psychology, which involves a systematic approach to identifying, analyzing, and resolving problems.

First, students are introduced to a problem or a question that requires analysis and solution. They are encouraged to define the problem clearly and understand its scope. This initial step helps students develop problem awareness and identify potential barriers or constraints that may affect the problem-solving process.

Next, students engage in information gathering and analysis. They gather relevant data, facts, and evidence, and apply critical thinking skills to evaluate and interpret the information. This step helps students develop analytical skills and generate possible solutions.

Once students have gathered and analyzed the information, they move on to the generation of potential solutions. This involves brainstorming and exploring different approaches to the problem, encouraging creativity and flexibility in thinking. Students are encouraged to think outside the box and consider multiple perspectives.

After generating potential solutions, students evaluate each option based on effectiveness, feasibility, and potential consequences. They consider the advantages and disadvantages of each solution, weighing the pros and cons. This step helps students develop decision-making skills and enhances their ability to critically evaluate potential solutions.

Finally, students select the most appropriate solution and implement it. They develop an action plan, outlining the steps needed to solve the problem. This requires effective communication skills, as students may need to collaborate and communicate their ideas with others.

Benefits of Teaching Problem Solving Skills

Teaching problem solving skills in education offers numerous benefits to students. Firstly, it enhances their cognitive abilities, allowing them to think critically and logically. This helps students become more independent learners and problem solvers.

Additionally, teaching problem solving skills improves students’ creativity and innovation. By encouraging them to think outside the box and explore different solutions, educators foster a mindset of curiosity and exploration.

Moreover, problem solving skills are transferable to various contexts, both within and outside of the classroom. Students can apply these skills to academic subjects, as well as to real-life situations, such as social issues, personal challenges, and future career paths.

In conclusion, teaching problem solving skills in education is crucial for students’ cognitive development and future success. By implementing the problem solving cycle and fostering critical thinking abilities, educators empower students with the skills necessary to navigate complex challenges and become lifelong learners.

Real-World Applications of the Problem Solving Cycle

The problem solving cycle is a fundamental concept in cognitive psychology that has numerous applications in real-world situations. This cycle involves a series of steps that individuals go through in order to identify, analyze, and solve problems.

1. Business

In the business world, problem solving is essential for success. From identifying market trends and determining customer needs to finding solutions to production issues or administrative challenges, the problem solving cycle is used to tackle a variety of business-related problems.

2. Education

The problem solving cycle is also highly applicable in education. Teachers often use this approach to help students develop critical thinking skills and solve complex problems. By following this cycle, students learn to break down problems, gather relevant information, analyze various options, and come up with effective solutions.

3. Medicine

Medical professionals frequently employ the problem solving cycle when diagnosing and treating patients. By systematically gathering patient history, evaluating symptoms, conducting tests, and analyzing data, doctors are able to identify the underlying problem and develop appropriate treatment plans.

4. Engineering

In the field of engineering, the problem solving cycle is crucial for designing and implementing solutions. Engineers use this approach to identify and address technical challenges, improve existing systems, and develop innovative technologies. By following this cycle, engineers can efficiently solve complex problems and ensure the success of their projects.

5. Everyday Life

Lastly, the problem solving cycle is applicable to everyday life. Whether it’s figuring out the best route to work, resolving conflicts in relationships, or making important decisions, individuals use this cycle to identify issues, explore possible solutions, and make informed choices.

The problem solving cycle is a versatile concept that finds widespread applications in various domains. From business and education to medicine and engineering, this approach facilitates effective problem solving and decision making. By following the steps of the cycle, individuals and organizations can overcome challenges and achieve their goals.

The Future of Problem Solving Research

In the field of cognitive psychology, research on problem solving is an ongoing and dynamic area of study. As technology continues to advance and our understanding of the cognitive processes involved in problem solving deepens, the future of problem solving research looks promising.

Advancements in Technology

Advancements in technology have already had a significant impact on problem solving research. The use of computer simulations and virtual environments has allowed researchers to create realistic problem-solving scenarios and collect data in a controlled environment. This technology has also allowed for the development of intelligent tutoring systems that can provide personalized feedback and guidance to individuals as they work through various problem-solving tasks.

In the future, we can expect even more sophisticated technologies to be developed, which will enhance our ability to study problem solving. For example, virtual reality technology may allow researchers to create immersive problem-solving environments that closely mimic real-life situations. This could provide researchers with valuable insights into how individuals approach and solve complex problems in a realistic setting.

Integration of Cognitive Processes

As our understanding of cognitive processes continues to grow, future research on problem solving will likely focus on the integration of various cognitive processes. Problem solving is a complex task that involves numerous cognitive processes, such as attention, memory, decision-making, and reasoning. Understanding how these processes interact and influence problem-solving performance will be crucial in developing effective strategies for problem solving.

Researchers may also explore the role of emotions in problem solving. Emotions can have a significant impact on cognitive processes and decision-making. Understanding how emotions influence problem-solving performance may provide valuable insights into how individuals can improve their problem-solving abilities.

Collaborative Problem Solving

Collaborative problem solving, or problem solving in a group setting, is another area that holds great potential for future research. Many real-world problems require collaboration and teamwork to solve effectively. Research on collaborative problem solving can provide valuable insights into how individuals interact and communicate with each other during problem-solving tasks, and how team dynamics impact problem-solving performance.

Furthermore, advancements in communication technology have made it easier than ever for individuals to collaborate remotely. Studying how individuals solve problems in virtual teams or online communities can provide valuable insights into the dynamics of collaborative problem solving in today’s interconnected world.

Continued Development of the Problem Solving Cycle

The problem solving cycle, which involves the stages of problem identification, solution generation, solution implementation, and solution evaluation, will continue to be a key concept in problem solving research. Researchers will seek to understand how individuals move through these stages, the strategies they employ at each stage, and how their problem-solving performance can be optimized.

By understanding the cognitive processes involved in each stage of the problem solving cycle, researchers can develop interventions and strategies to help individuals become more effective problem solvers.

In conclusion, the future of problem solving research in cognitive psychology looks promising. Advancements in technology, a deeper understanding of cognitive processes, the study of collaborative problem solving, and the continued development of the problem solving cycle will all contribute to our understanding of problem solving and help individuals become more effective in solving complex problems.

Questions and answers:

What is the problem-solving cycle.

The problem-solving cycle is a key concept in cognitive psychology that refers to the sequence of steps or processes involved in solving a problem.

What are the stages of the problem-solving cycle?

The problem-solving cycle typically consists of four stages: problem identification, problem definition, strategy selection, and solution implementation.

How does problem identification occur in the problem-solving cycle?

Problem identification involves recognizing that there is a problem or a discrepancy between a desired state and the current state.

What is problem definition in the problem-solving cycle?

Problem definition involves clearly specifying or defining the problem in a way that allows for a focused approach to finding a solution.

What is strategy selection in the problem-solving cycle?

Strategy selection involves choosing an appropriate approach or method to solve the problem, such as using a specific algorithm or heuristic.

What is the problem-solving cycle in cognitive psychology?

The problem-solving cycle is a concept in cognitive psychology that outlines the steps individuals go through when tackling a problem. It involves identifying the problem, gathering information, generating possible solutions, evaluating the solutions, and implementing the best one.

How does the problem-solving cycle help in problem-solving?

The problem-solving cycle provides a structured approach to problem-solving by breaking it down into manageable steps. By following this cycle, individuals can better understand the problem, explore various solutions, evaluate their effectiveness, and ultimately make an informed decision on how to solve the problem.

Related posts:

• A Comprehensive Guide to the Problem Solving Cycle in Psychology – Strategies, Techniques, and Applications
• The Importance of Implementing the Problem Solving Cycle in Education to Foster Critical Thinking and Problem-Solving Skills in Students
• The Step-by-Step Problem Solving Cycle for Effective Solutions
• The Comprehensive Guide to the Problem Solving Cycle in PDF Format
• The Importance of the Problem Solving Cycle in Business Studies – Strategies for Success
• A Comprehensive Guide on the Problem Solving Cycle – Step-by-Step Approach with Real-Life Example
• The Seven Essential Steps of the Problem Solving Cycle
• Exploring the Problem Solving Cycle in Computer Science – Strategies, Techniques, and Tools

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Worry Impairs the Problem-Solving Process: Results from an Experimental Study

Sandra j. llera.

a Department of Psychology, Towson University, 8000 York Road, Towson, MD 21252.

Michelle G. Newman

b Department of Psychology, The Pennsylvania State University, 140 Moore Building, University Park, PA 16801.

Associated Data

Introduction:.

Many individuals believe that worry helps solve real-life problems. Some researchers also purport that nonpathological worry can aid problem solving. However, this is in contrast to evidence that worry impairs cognitive functioning.

This was the first study to empirically test the effects of a laboratory-based worry induction on problem-solving abilities.

Both high ( n = 96) and low ( n = 89) trait worriers described a current problem in their lives. They were then randomly assigned to contemplate their problem in a worrisome ( n = 60) or objective ( n = 63) manner or to engage in a diaphragmatic breathing task ( n = 62). All participants subsequently generated solutions and then selected their most effective solution. Next, they rated their confidence in the solution’s effectiveness, their likelihood to implement the solution, and their current anxiety/worry. Experimenters uninformed of condition also rated solution effectiveness.

The worry induction led to lower reported confidence in solutions for high trait worry participants, and lower experimenter-rated effectiveness of solutions for all participants, relative to objective thinking. Further, state worry predicted less reported intention to implement solutions, while controlling for trait worry. Finally, worrying about the problem led to more elevated worry and anxiety after solving the problem compared to the other two conditions.

CONCLUSIONS:

Overall, the worry induction impaired problem solving on multiple levels, and this was true for both high and low trait worriers.

Worry is the defining feature of generalized anxiety disorder (GAD; American Psychiatric Association, 2013 ), but it is also a common experience for most individuals. Though many report the belief that worry has benefits for coping with potential threats ( Borkovec & Roemer, 1995 ; Hebert, Dugas, Tulloch, & Holowka, 2014 ), a wide literature documents its negative impact on cognitive, emotional, and behavioral levels. Despite being extensively researched, the effects of worry on some aspects of cognitive functioning and behavioral motivation remain understudied and require further exploration.

Several theories suggest that worry negatively affects cognitive functioning. The Attentional Control Theory ( Eysenck, Derakshan, Santos, & Calvo, 2007 ), posits that worry demands attentional resources that could be allocated to other cognitive capacities and thus creates cognitive impairment. Similarly, Affective Neuroscience theories propose that worry increases cognitive load and interferes with the capacity to ignore task-irrelevant matters ( Beaudreau, MacKay-Brandt, & Reynolds, 2013 ). These theories further posit that because worrisome thoughts are attentionally demanding, additional resources are required to inhibit worry in order to focus attention elsewhere. Thus, worry may interfere with tasks that compete for executive functioning resources.

This perspective has garnered empirical support. High trait worriers performed slower than controls on a number of cognitive and decision-making tasks, in both clinical ( LaFreniere & Newman, 2019 ; Stefanopoulou, Hirsch, Hayes, Adlam, & Coker, 2014 ) and non-clinical ( Tallis, Eysenck, & Mathews, 1991 ) samples. In a meta-analysis of 94 studies, recurrent negative thinking, including trait worry, was associated with impaired ability to discard irrelevant information from working memory ( Zetsche, Bürkner, & Schulze, 2018 ). Additionally, impaired cognitive functioning, such as difficulty concentrating, slowed learning, and delayed decision-making, has been associated with GAD status in both undergraduate ( LaFreniere & Newman, 2019 ; Pawluk & Koerner, 2013 ) and community GAD samples ( Hallion, Steinman, & Kusmierski, 2018 ). Similar to trait-level worry, experimentally manipulated state worry has also been found to reduce working memory ( Rapee, 1993 ; Trezise & Reeve, 2016 ) and attentional control ( Hayes, Hirsch, & Mathews, 2008 ; Stefanopoulou et al., 2014 ). Further, efforts to inhibit state worry depleted working memory and performance on cognitive tasks ( Hallion, Ruscio, & Jha, 2014 ). Thus, both trait and state worry independently have been associated with cognitive impairment.

Similar to evidence of the association between trait/state worry and impaired cognitive functioning, there have been questions as to whether worry impacts problem-solving abilities. D’Zurilla and Goldfried (1971) suggest that effective problem-solving requires five major components. These include: 1) problem orientation (i.e., confidence in and perceived control over the problem-solving process), 2) problem definition and goal identification, 3) generating solutions, 4) decision making, and 5) implementation/verification. Accordingly, impairment at any one of these levels would hinder one’s ability to resolve problems.

On the one hand, many individuals, especially those with GAD symptoms, believe that worry is helpful when solving problems. In fact, such beliefs predicted worry severity levels ( Hebert et al., 2014 ), and were able to distinguish those with GAD from controls ( Borkovec & Roemer, 1995 ). Further, beliefs that worry was helpful in the face of problems, or that persistent thinking was required in order to find the best solution, both predicted trait worry levels ( Kelly & Kelly, 2007 ; Sugiura, 2007 ). In fact, when tested on their ability to solve hypothetical problems in a laboratory setting, anxious participants performed no differently than controls ( Anderson, Goddard, & Powell, 2009 ), and in an unselected student sample these abilities were uncorrelated with trait worry ( Davey, 1994 ).

On the other hand, however, there is reason to believe that the act of worrying and/or trait worry might be associated with impairment in the real world. Negative effects of worry on problem-solving could happen in several ways. Worrying about a problem could increase cognitive load ( Beaudreau, MacKay-Brandt, & Reynolds, 2013 ), interfering with one’s ability to focus on effective solution generation. This could induce lower confidence in one’s abilities to generate effective solutions, leading individuals to stall or avoid decision-making ( D’Zurilla & Goldfried, 1971 ) or to prematurely dismiss possible solutions as likely to be ineffective. Additionally, worry could provoke repetitive rehearsal of the problem and/or focus on potential negative outcomes ( Mathews, 1990 ), thereby interfering with effective solution generation and implementation. Trait worry could also have negative effects. These could include difficulty tolerating the uncertainty inherent in the problem-solving process ( Dugas, Gagnon, Ladouceur, & Freeston, 1998 ), which might be linked to the higher “evidence requirements” seen in chronic worriers when making decisions ( Tallis et al., 1991 ). This, in addition to heightened attentional bias toward threat ( Goodwin, Yiend and Hirsch, 2017 ), could serve to prolong indecision in the face of real-life problems while the worrier attempts to gather more information. Finally, the Contrast Avoidance model of GAD ( Newman & Llera, 2011 ) would suggest that for chronic worriers, reluctance to implement solutions could be due to a fear of getting one’s hopes up only to be confronted with failure (i.e., emotional contrast). In fact, it is possible that multiple factors could work together to impair problem-solving abilities.

In support of impairment related to chronic worry, Davey, Hampton, Farrell, and Davidson (1992) identified a link between harboring a negative attitude toward problems, termed negative problem orientation (NPO), and high trait worry. Since then, NPO has been linked with anxiety and trait worry in both clinical ( Dugas et al., 1998 ; Fergus, Valentiner, Wu, & McGrath, 2015 ; Ladouceur, Blais, Freeston, & Dugas, 1998 ) and non-clinical samples ( Anderson et al., 2009 ; Robichaud & Dugas, 2005 ). Notably, NPO was more robustly associated with trait worry over other anxiety, mood, and obsessive symptoms in a mixed-clinical sample ( Fergus et al., 2015 ). Additional studies found trait worry to be associated with impairment in other aspects of the problem-solving process, such as skills and/or knowledge base. For example, Borkovec (1985) observed that whereas chronic worriers were very good at defining their problems and identifying possible negative outcomes, they often had difficulty implementing solutions. Further, when assessing real-life problem solving based on daily diary and recall data, a mixed anxious-depressed group demonstrated fewer functional cognitions and behaviors, and less effective solutions, than did controls ( Anderson et al., 2009 ).

Although such research on the nature of chronic worriers tends to converge, the extent to which the act of worrying itself impairs problem solving represents a point of contention within the field. Some researchers have argued that worry interferes with successful problem resolution across the board, whereas others contend that this may only apply to pathological worriers (i.e., those for whom worry is excessive and uncontrollable). Mathews (1990) adopted the first stance, arguing that although worry may begin as attempted problem solving, it predominantly leads to the cognitive rehearsal of danger for everyone. Taking the second stance, Davey and colleagues ( Davey, 1994 ; Davey et al., 1992 ) proposed that worry may actually enhance problem solving for many individuals, but that this process can become thwarted for those with high levels of trait worry. The latter argument was based in part on evidence that trait worry was associated with some active coping styles (e.g., information seeking) when controlling for trait anxiety in unselected student samples ( Davey et al., 1992 ). Therefore, Davey and colleagues concluded that for some individuals worry might be an adaptive or constructive approach when confronting a problem.

Nonetheless, an abundance of data shows that worry increases state negative affect and arousal for all individuals (see Newman & Llera, 2011 ; Newman et al., 2019 ; Ottaviani et al., 2016 ), which itself may impact the problem-solving process. For instance, a negative mood induction increased perseveration and catastrophizing on a high-responsibility task ( Startup & Davey, 2003 ), which could have negative implications for problem solving. Furthermore, daily diary studies have found that the intensity of state worry was associated with more anticipation of negative outcomes, greater negative evaluation of solutions to problems, more self-blame, and lower rates of solution selection during worry episodes, in samples including both high and low trait worriers ( Szabó & Lovibond, 2002 , 2006 ). Additionally, state levels of anxious thinking, including worry, were associated with lower problem-solving effectiveness in a community GAD sample ( Pawluk, Koerner, Tallon, & Antony, 2017 ).

In summary, although there is strong evidence to suggest that worry is associated with impairment in problem solving, none of the studies reviewed above experimentally manipulated worry when testing problem-solving abilities. Therefore, it is impossible to determine the extent to which worry itself causally impacted the problem-solving process, as opposed to other characteristics associated with state or trait worry. Interestingly, depressive rumination (a close conceptual relative to worry) has been shown to impact both mood and the problem-solving process across several studies. For example, experimentally induced rumination (versus distraction) led to lower mood in a non-clinical dysphoric sample, and resulted in generating less effective solutions for hypothetical problems, as well as reduced likelihood of implementing solutions for a personal problem ( Lyubomirsky & Nolen-Hoeksema, 1995 ; Lyubomirsky, Tucker, Caldwell, & Berg, 1999 ). The absence of similar research on the effect of worry represents a critical gap in our understanding of this phenomenon.

In this study, we sought to address this gap by testing the effects of experimentally manipulated worry on problem solving using a sample of individuals with both high and low trait worry. In this way, we were able to test whether inducing state worry would hinder problem solving for all participants, thereby supporting Matthews’ (1990) perspective, or if it would enhance problem-solving in low trait worriers and only become problematic at high trait levels, thus supporting Davey and colleagues’ perspective ( Davey, 1994 ; Davey et al., 1992 ). We chose to observe the effects of worrying about a real-life problem, as opposed to a hypothetical problem, in order to increase external validity. As a comparison condition, we chose the problem definition stage of problem solving as outlined in D’Zurilla and Goldfried (1971) . This allowed us to equalize the amount of time spent contemplating the problem, but to channel thinking into styles typical of a worry episode versus thinking in a more objective, emotionally neutral manner. As an additional control condition, a third group engaged in a diaphragmatic breathing task. Immediately afterward, all groups were instructed to brainstorm solutions to their problem and choose the solution they thought would be most successful. We tested a variety of outcomes related to problem solving, including the number of solutions generated, self-reported and experimenter-rated effectiveness of solutions, as well as participant ratings of intention to implement solutions. Further, we assessed state levels of anxiety and worry following the solution-generation phase, to determine the extent to which participants felt calmer once a solution had been identified.

We hypothesized that relative to objective thinking or diaphragmatic breathing instructions, worrying about a problem would lead to 1) generating fewer solutions during brainstorming, 2) generating less effective solutions (based on both participants’ and judge’s ratings), and 3) lower intention to implement solutions. Further, we hypothesized that 4) worrying would lead to lingering anxiety and worry following solution generation, relative to other conditions. We also hypothesized that these effects would be observed for both high and low trait worriers alike.

Research Design and Method

Overall design.

A 2 (Group: High vs. Low Trait Worry) X 3 (Condition: Worry, Think Objectively, Diaphragmatic Breathing) block design was used to determine the effects of worrying about a problem on various outcomes related to problem-solving.

Participants and Measures

The current study recruited 185 volunteers from psychology courses in a public university. Students received class credit as compensation. Participants were largely young adult (M = 20.06 years, SD = 6.47) females (76.8%), with 57.8% identifying as White, 24.3% African American, 7.6% Asian, 6.2% Hispanic/Latinx, 1% American Indian/Pacific Islander, and 8.6% other (e.g., “mixed race”).

Participants were selected based on their scores on the Penn State Worry Questionnaire (PSWQ; Meyer, Miller, Metzger, & Borkovec, 1990 ), a 16-item self-report measure designed to assess the frequency, intensity, and uncontrollability characteristics of trait worry. The PSWQ demonstrates strong internal consistency (Chronbach’s α = .91; Meyer et al., 1990 ) and retest reliability (.74 – .93; Molina & Borkovec, 1994 ). Internal consistency for the current sample was high (α = .95). Participants also completed the Generalized Anxiety Disorder Questionnaire (GAD-Q-IV; Newman et al., 2002 ) to assess for clinical-level GAD symptoms. The GAD-Q-IV is a 9-item self-report questionnaire based on diagnostic criteria for GAD. It demonstrates strong internal consistency (α = .94) and good retest reliability. A cut-score of 5.7 leads to 83% sensitivity and 89% specificity relative to a structured diagnostic interview ( Newman et al., 2002 ). Internal consistency for the current sample was high (α = .91).

Participants were included in the High Trait Worry group (N = 96) if they scored in the upper range on the PSWQ (≥ 60) during a pre-screen. On the day of testing, the High Trait Worry PSWQ score mean was comparable to that found in GAD patient samples (M = 66.68, SD = 9.47; see Startup & Erickson, 2006 ). The High Trait Worry mean on the GAD-Q-IV was also well above the clinical cut-score (M = 8.58, SD = 2.35). Participants were included in the Low Trait Worry group (N = 89) if they scored in the mid-low range on the PSWQ (≤ 45). On the day of testing, scores in this group were comparable to those of nonanxious samples from other studies (M = 41.02, SD = 11.93; see Startup & Erickson, 2006 ). Further, the Low Trait Worry group scored well below the cut-score on the GAD-Q-IV (M = 3.66, SD = 2.82).

This study was approved by the university IRB. Participants were each tested alone in a private room equipped with a computer. All instructions and tasks were completed using the Qualtrics survey platform (Qualtrics, Provo, UT). Participants first provided informed consent, and then completed demographic questions along with the PSWQ and GAD-Q-IV. Next, they completed baseline state measures, comprised of 4 items: worry , anxiety , relaxation , and mood . They were instructed to rate each item based on how they felt right now . The first 3 items were rated on a scale of 0 ( not at all ) to 100 ( extremely ). Mood was rated from 0 ( very negative ) to 100 ( very positive ).

Participants were next instructed to identify a current, real-life problem; specifically, one that was affecting them right now, and for which they had some control over the outcome. The latter requirement was to assist in identifying a problem for which there were possible solutions, as opposed to an uncontrollable issue (e.g., a loved one’s terminal illness). They were then asked to briefly describe their problem by typing it out on the computer.

Next, participants were randomly assigned to either a Worry (WOR; N = 60) or Think Objectively (T-OBJ; N = 63) task, with the remaining third assigned to a Diaphragmatic Breathing (DB; N = 62) task. The primary distinction between WOR and T-OBJ conditions was that participants either worried or did not worry over their problem. To that end, instructions for the WOR task were based on the definition of worry as negatively valanced cognitive activity focused on a threat, along with consideration of potential negative outcomes (i.e., negative emotional and catastrophic thinking; Borkovec, 1985 ; Borkovec, Robinson, Pruzinsky, & DePree, 1983 ). Those in the WOR task were therefore instructed to worry about their problem, with an emphasis on their concerns along with possible negative outcomes and implications (see supplement for full instructions ). To control for the amount of time spent contemplating the problem, but to do so in a non-emotional, non-catastrophic manner, instructions for the T-OBJ task were based on the problem definition stage of problem solving ( D’Zurilla & Goldfried, 1971 ). Participants in the T-OBJ task were instructed to attempt to focus on their problem in a more objective, emotionally neutral manner, such as by breaking it down into smaller components and coming up with ultimate goals. If they found themselves focusing on negative thoughts, participants were instructed to refocus their attention back on the problem itself.

After receiving these instructions, participants in the WOR and T-OBJ conditions were asked to think about their problem for 2 minutes in the specified manner. Those in the DB task were given instructions to engage in diaphragmatic breathing for 2 minutes.

Following this task, and to determine whether the manipulations had their intended effects, all participants again completed state measures of worry , anxiety , relaxation , and mood . This was to ensure that conditions led to three distinct groups: one that had engaged in emotional/catastrophic thinking (WOR), one that had engaged in non-emotional, non-catastrophic thinking (T-OBJ), and one that had engaged in a relaxation-inducing breathing task (DB). As such, distinctions on state levels of worry , anxiety , relaxation , and mood between conditions served as compliance checks for adherence to the manipulations.

Immediately afterward, all participants were asked to generate as many solutions to their problem as they could for 2 minutes, representing the brainstorming stage of problem solving. Solutions were typed out on the computer. Next, they were instructed to reflect on these ideas and choose their “best, most effective” solution, representing the decision-making stage. Once finished, they ranked how confident they felt that this solution would be effective, as well as how likely they were to actually carry it out, on a scale of 0 ( not at all confident/likely ) to 100 ( very confident/likely ). They then provided final ratings of current state worry and anxiety and were debriefed about the study.

Once data collection was complete, a judge uninformed of condition rated participants’ self-identified “best” solutions for their effectiveness on a 7-point scale (1 = not at all effective , to 7 = extremely effective ), identical to that used in similar studies ( Lyubomirsky & Nolen-Hoeksema, 1995 ; Lyubomirsky et al., 1999 ). To determine this score, they rated the likelihood that participants’ solutions would lead to successful resolution of the problem (i.e., maximize positive consequences and minimize negative ones, and not create additional problems; D’Zurilla & Goldfried, 1971 ). For example, if participants listed a solution that would likely improve or resolve the situation (e.g., behavior that would directly enhance their performance in a class, etc.), that was rated as more effective. If their solution was unlikely to improve or resolve the situation, or could potentially exacerbate the issue (e.g., distraction from or avoidance of the problem, etc.), it would be rated as less effective. A second independent judge who was also uninformed of condition rated a random selection of 25% of responses, with evidence of sufficient interrater reliability (ICC = .7). (See Supplemental Materials for an overview of the process used to ensure reliability of judges’ ratings.)

Data Analytic Plan

We first tested whether there were any differences at baseline on measures of state worry , anxiety , relaxation , and mood , using a 2 (Group: High/Low Trait Worry) X 3 (Condition: WOR, T-OBJ, DB) MANOVA. Next, to test that WOR, T-OBJ, and DB tasks had the intended effects, we ran a similar MANOVA but with ratings of state measures of worry , anxiety , relaxation , and mood immediately following the induction as manipulation checks.

To test the 4 main hypotheses, we ran a series of factorial ANOVAs, using Group and Condition as predictors. Outcome variables included 1) the number of solutions participants generated during the brainstorming phase, 2) participant and judge’s ratings of effectiveness of solutions, and 3) ratings of intention to implement solutions. Finally, to determine the presence of any lingering anxiety and worry after participants chose their best solution (4), we ran a MANOVA with Group and Condition as predictors, and state worry and anxiety levels after identifying “best” solutions as outcomes.

In the case of nonsignificant findings, we ran exploratory secondary analyses in the form of hierarchical linear regression models to test if reported state worry levels following the WOR/T-OBJ/DB tasks could predict problem-solving outcomes, while controlling for trait worry. The purpose of these analyses was to determine if the extent to which participants reported actually worrying during the induction would be a better predictor than their assigned condition, while also controlling for the possible influence of trait worry on these outcomes. To do so, we entered PSWQ in the first block of the model, followed by state worry levels in the second block. To address any issues of non-normality, bootstrapping using 1000 samples was applied to all ANOVAs and regressions.

Baseline Measures and Manipulation Check

At baseline, there was a main effect of Group, F (4, 176) = 15.92, p < .001, η 2 p = .27. As expected, the High Trait Worry group reported more baseline worry and anxiety than did the Low Trait Worry group. Further, the Low Trait Worry group reported more baseline relaxation and better mood than did the High Trait Worry group (see Table 1 for means and standard deviations). There was no main effect of Condition; F (8, 354) = 1.55, p = .139, η 2 p = .03; and no Group X Condition interaction; F (8, 354) = 1.07, p = .385, η 2 p = .02; suggesting no significant baseline differences between conditions.

State Measures at Baseline and Post Problem-Thinking Task

Note . Reported raw means with standard deviations in parentheses. WOR/W = worry task, T-OBJ/O = think objectively task, DB = diaphragmatic breathing task, ns = non-significant.

Following the WOR, T-OBJ, and DB tasks, our manipulation check measures showed a main effect of Group, F (4, 176) = 15.07, p < .001, η 2 p = .26. The High Trait Worry group reported significantly more worry and anxiety , lower relaxation , and worse mood than the Low Trait Worry group, regardless of their assigned task. More importantly, however, there was a main effect of Condition; F (8, 354) = 8.75, p < .001, η 2 p = .17; such that WOR led to significantly higher ratings of worry and anxiety than T-OBJ and DB, and T-OBJ led to higher ratings than DB. WOR also led to significantly worse mood than both T-OBJ and DB, which were not significantly different from one-another. Finally, DB led to significantly higher relaxation than both T-OBJ and WOR, and T-OBJ was higher than WOR (see Table 1 ). There was no significant Group X Condition interaction, F (8, 354) = .93, p = .494, η 2 p = .02. As such, data suggest that these tasks operated in the intended way for both High and Low Trait Worry groups.

Main Hypotheses

Number of solutions..

Contrary to predictions, there were no main effects of Group; F (1, 178) = .67, p = .414, η 2 p = .00; or Condition; F (2, 178) = 2.61, p = .076, η 2 p = .03; and no interaction; F (2, 178) = .87, p = .419, η 2 p = .01; on number of solutions generated during the brainstorming period. In a follow-up regression, the first block of the model, consisting of the PSWQ, was not significant; F (1,181) = .17, p = .685; and accounted for only 0.1% of the total variance. Adding state worry levels to the model did not significantly increase predictive value; F (1,180) = 1.52, p = .221; and only accounted for an additional 1.6% of the variance.

Effectiveness of solutions.

In terms of participants’ own ratings of their confidence in solution effectiveness, there was a main effect of Group; F (1, 178) = 9.13, p = .003, η 2 p = .05. Overall, High Trait Worriers reported less confidence in the effectiveness of their solutions (M = 66.73, SD = 22.31) than did Low Trait Worriers (M = 76.25, SD = 23.57), regardless of condition. There was no main effect of Condition; F (2, 178) = 1.01, p = .367, η 2 p = .01; but there was a significant Group X Condition interaction; F (2, 178) = 4.54, p = .012, η 2 p = .05. When divided by Group, High Trait Worriers in the WOR condition rated confidence in their selected solution as significantly lower (M = 57.77, SD = 29.46) than those in T-OBJ (M = 72.97, SD = 15.0; p = .017), and marginally lower than those in DB (M = 68.97, SD = 18.06; p = .076), but this did not reach significance. There were no significant differences between T-OBJ and DB ( p = .347; see Figure 1 ). Low Trait Worriers did not demonstrate significant differences by condition (all p ’s > .05).

Participant Ratings of Confidence in Effectiveness of Solutions for the High Trait Worry Group

Note. WOR = worry task, T-OBJ = think objectively task, DB = diaphragmatic breathing task, * p < .05.

In terms of judge’s ratings, there was a main effect of Condition; F (2, 177) = 5.08, p = .007, η 2 p = .05. Those in the T-OBJ condition were judged to have generated significantly more effective solutions (M = 5.77, SD = .93) than those in WOR (M = 5.18, SD = 1.19, p = .004) and DB (M = 5.21, SD = 1.38, p = .009), which were not significantly different from each other ( p = .938). Observed differences were modest, but nonetheless significant (see Figure 2 ). There was neither a main effect of Group; F (1, 177) = .14, p = .711, η 2 p = .001; nor an interaction; F (2, 177) = 1.85, p = .161, η 2 p = .02.

Judge’s Ratings of Effectiveness of Solutions across High and Low Trait Worry Groups

Note. WOR = worry task, T-OBJ = think objectively task, DB = diaphragmatic breathing task, ** p < .01.

Intention to implement solutions.

Contrary to predictions, there were no main effects of Group; F (1, 178) = 3.00, p = .085, η 2 p = .02; Condition; F (2, 178) = .21, p = .814, η 2 p = .00; or an interaction; F (2, 178) = 2.34, p = .10, η 2 p = .03; on participants’ ratings of intention to implement their solutions. A follow-up regression indicated that trait and state worry together significantly predicted intention, accounting for 5.5% of the total variance. When entered first, the PSWQ was a negative predictor of intention ( β = −.158, p = .032), such that higher trait worry predicted less reported intention. Upon adding state worry levels, the model’s predictive value significantly increased (Δ R 2 = .03, p = .017). Higher state worry also predicted less reported intention to implement solutions ( β = −.212, p = .020), but importantly, trait worry was no longer a significant predictor in the full model (see Table 2 ).

Trait and State Worry Predicting Intention to Implement Solutions

Note. Confidence intervals and standard errors are based on 1000 bootstrapped samples. PSWQ = Penn State Worry Questionnaire, Worry = self-reported state worry levels post problem-thinking task,

Worry and anxiety levels after choosing a solution.

There was a main effect of Group; F (2, 178) = 18.17, p < .001, η 2 p = .17. On average, High Trait Worriers reported greater worry (M = 40.53, SD = 26.04) and anxiety (M = 42.80, SD = 25.97) than did Low Trait Worriers (M = 21.91, SD = 26.59; M = 21.12, SD = 25.11, respectively) after generating their solutions, regardless of condition. Consistent with hypotheses, there was also a main effect of Condition; F (4, 358) = 4.27, p = .002, η 2 p = .05. All participants in the WOR condition reported significantly greater worry (M = 40.82, SD = 29.68) and anxiety (M = 41.90, SD = 29.40) following solution generation compared to those in T-OBJ (M = 31.10, SD = 25.55, p = .047; M = 32.11, SD = 27.69, p = .030; respectively) and DB (M = 23.11, SD = 25.80, p = .002; M = 23.42, SD = 23.01, p < .001; respectively). Those in the T-OBJ condition also reported greater anxiety than those in DB ( p = .042), but not greater worry ( p = .071; see Figure 3 ). There was no Group X Condition interaction; F (4, 358) = .87, p = .484, η 2 p = .01.

Post-Solution Generation State Levels

Note. WOR = worry task, T-OBJ = think objectively task, DB = diaphragmatic breathing task, * p < .05, ** p < .01

Research has long suggested the possibility of a connection between worry and impaired problem solving; yet no prior study has experimentally manipulated worry to test for a causal link. In this study we tested the effects of a controlled worry manipulation on several factors related to the problem-solving process, using both high and low trait worriers. Ultimately, we found that worrying about a real-life problem, relative to attempting to think about the problem objectively or diaphragmatic breathing, led to interference at multiple levels of problem solving. These findings held true at least in part for both high and low trait worriers alike.

Several findings emerged in terms of the effects of trait or state worry on aspects of the problem solving process. Contrary to our expectations, we found no differences for Group or Condition on the number of solutions participants generated when asked to brainstorm ways to solve their problems. This is not to say that all solutions were of equal quality. For example, some participants listed ideas such as, “ignore it until later”, “get some sushi”, and “do nothing”, alongside more effective ideas (e.g., “join a study group”, “make a budget and stick to it”). Listing as many ideas as possible without judgment while in the brainstorming phase is considered beneficial for problem solving ( D’Zurilla & Goldfried, 1971 ). Our data suggested that both trait worry status and condition type neither significantly helped nor hindered brainstorming performance, and that specific negative effects of worry only emerged later in the problem-solving process.

After choosing the “best” of these solutions, however, high trait worriers reported lower confidence in the effectiveness of their chosen solution compared to low trait worriers, regardless of condition. Also, high trait worriers who worried before generating solutions reported significantly lower confidence in their chosen solution than did those instructed to think about their problems more objectively. They also reported marginally lower confidence than those who engaged in a diaphragmatic breathing exercise, though this did not reach significance. This is consistent with prior findings that chronic worriers reported lower confidence in their ability to solve problems relative to nonanxious controls (e.g., Anderson et al., 2009 ; Ladouceur et al., 1998 ); however, this is the first study to demonstrate that in high trait worriers, the specific act of worrying reduced problem-solving confidence. In low trait worriers, on the other hand, worry (vs other conditions) did not lead to a significantly different impact on confidence in their solutions’ effectiveness.

The fact that a prior worry induction only reduced confidence for chronic worriers is more in line with the perspective articulated by Davey and colleagues ( Davey, 1994 ; Davey et al., 1992 ), who argued that factors such as low problem-solving confidence would impair problem solving, but only for pathological worriers. Notably, high trait worriers who were instructed to think objectively reported mean confidence scores that were significantly higher than those instructed to worry. These results imply that instructing chronic worriers to think about their problems in a more objective manner, and to refrain from negative thinking, may counteract such pessimistic beliefs and enhance confidence levels. However, contrary to Davey’s theory, there was no significant benefit of worry on confidence in low trait worriers. Thus, whereas the worry induction impaired confidence in high trait worriers, it neither helped nor hindered confidence in low trait worriers.

As opposed to participants’ subjective ratings of confidence in their solutions’ effectiveness, ratings made by an independent judge reflected our attempts to objectively rate whether the solution would be effective. In this case, a main effect of condition emerged across all participants. According to these ratings, attempting to think objectively about a problem led to a small but significant advantage in coming up with more effective solutions relative to both worrying and diaphragmatic breathing, which were not significantly different. As such, this finding does not represent a unique impairment effect of worry per se , but rather points to the benefits of attempting to contemplate problems in an objective, emotionally-neutral manner. It also indicates that although worrying did not reduce low trait worriers’ confidence in their solution effectiveness, such confidence was not matched by an independent judge.

To further unpack this finding, as a non-worry comparison individuals in the T-OBJ condition were instructed to think about their problem in a less emotional, more constructive way (i.e., breaking it down, focusing on their goals), without falling into negative or catastrophic thinking. We cannot rule out that this may have fueled more solution-focused thinking than worrying. In fact, the very act of focusing on a problem (whether it be catastrophically or objectively), likely made it difficult for participants not to consider various possible solutions during this manipulation period. If, however, those in the T-OBJ condition tended to naturally spend more time generating better solutions, this still supports the conclusion that worry detracts from problem solving, as it suggests that the negative and catastrophic thinking characteristic of worry interferes with more constructive processes and ultimately detracts from coming up with good solutions. It also suggests this can happen for both high and low trait worriers.

Regarding the lack of differences between WOR and DB on experimenter-rated effectiveness, it is important to note that those randomly assigned to the DB condition were not instructed to contemplate their problem at all prior to brainstorming solutions, but rather were instructed to focus attention on their breathing. That they were then able to generate impromptu solutions rated as not different from solutions of those who had actively worried over their problem beforehand, is a notable finding. This suggests that worrying about a problem offered no greater advantage in this context than did a diaphragmatic breathing exercise. It also contradicts the beliefs of many individuals, and especially those of chronic worriers, that worrying is necessary in order to find the best solution to a problem (e.g., Borkovec & Roemer, 1995 ; Hebert et al., 2014 ). Taken together, these findings are more consistent with Mathews’ (1990) proposition that for all individuals, the act of worrying is not actually helpful in terms of finding adequate solutions to problems.

In terms of participants’ reported intention to implement their solutions, there were no significant effects of Group or Condition. A follow-up exploratory regression analysis identified that the extent to which participants worried during their assigned task (irrespective of what that task was) predicted lower reported intention to engage in proactive action. This effect was not simply driven by those with higher trait worry, as state worry predicted ratings of intention when controlling for trait worry, and trait worry was no longer a significant predictor once state worry was entered in the model. This finding provides more clear support for Mathews’ (1990) stance on worry thwarting the problem-solving process, regardless of whether it is experienced at chronic levels or not. This also dovetails with the finding that depressive rumination reduced participants’ reported likelihood to implement solutions to their problems ( Lyubomirsky et al., 1999 ), suggesting that both forms of repetitive negative thinking may discourage engaging in such proactive behaviors. However, it should be noted that this analysis was simply a secondary, and more correlational, exploration of our data, and as such does not allow for more robust causal interpretations.

Finally, we found that for both high and low trait worriers, worrying about one’s problem led to significantly higher reported worry and anxiety levels even after having identified a solution, as compared to thinking objectively about the problem or relaxing. This is consistent with research showing that the negative effects of worry linger over time (e.g., Newman et al., 2019 ; Pieper, Brosschot, van der Leeden, & Thayer, 2010 ), and appears to hold true even after making a decision about the best course of action to ameliorate a problem. Thus, rather than feel a sense of resolution about the issue, with corresponding decreases in worry and anxiety, worrying before choosing a solution may instead lead to lingering feelings of doubt.

Overall, these results provide evidence that engaging in worry is detrimental to problem solving on multiple levels, which apart from reducing confidence in the process, appears to affect both high and low trait worriers alike. One explanation for these findings may be that, consistent with Attentional Control Theory ( Eysenck et al., 2007 ), worrying about a personal problem focused participants’ attention on threatening aspects of the situation (e.g., potential negative outcomes). As such, shifting from worrying into generating and evaluating solutions to the problem, (i.e., threat-related versus goal-directed attention) demanded additional cognitive resources. Attempting to think about the problem objectively, however, is more consistent with goal-directed attention and thus would not have required inhibition. In this way, attempting to think objectively may have allowed for greater access to cognitive resources while problem solving, and possibly more time spent contemplating solutions, relative to worrying. However, we did not measure these effects directly, other than to show that objective thinking facilitated generating more highly rated solution effectiveness than either worry or a breathing exercise.

Another explanation may be that the worry induction both increased cognitive load, and led to greater anxiety and worse mood, and these factors interacted to undermine the problem-solving process. According to Gray’s (1990) neuropsychology theory of emotions, anxiety triggers the behavioral inhibition system, promoting harm-avoidance over approach strategies in the face of a problem. This dovetails with the affect-as-information perspective, which states that affect influences judgment and decision-making ( Clore & Huntsinger, 2007 ). As such, in the context of problem solving, a negative mood may focus attention on potential obstacles to goals or unwanted outcomes, thus leading to pessimistic appraisals of one’s performance (see Schwarz & Skurnik, 2003 ). Our data support this trajectory based on the fact that worry 1) created greater negative affect in the moment, 2) led to sustained worry and anxiety levels even after participants had chosen a solution, 3) decreased confidence in effectiveness of solutions for the high worry group, 4) led to lower judge’s ratings of effectiveness, and 5) predicted less intention to implement solutions for all participants, while controlling for trait worry (though this latter finding was more correlational than causal). In sum, this suggests that worry led to negative cognitive and emotional effects, impairing problem solving at several stages of the process.

Overall, although the worry induction reduced problem-solving confidence only for high trait worriers, it led to a number of additional negative outcomes for all participants. As such, these data provide initial evidence that state worry hinders proactive problem solving across high and low trait worry levels. Moreover, despite the fact that low trait worriers reported a non-significant impact of worry on their confidence in solutions, it still predicted lower judge’s ratings of the solution effectiveness and less willingness to enact them. Therefore, results of this study provide more robust support for Mathews’ (1990) theory, suggesting that worry is a problematic strategy for all persons interested in resolving their problems.

This study has some notable limitations. Because high trait worry participants were not treatment-seeking, this limits our ability to generalize findings to clinically worried individuals. However, previous studies have identified impairment associated with worry in unselected samples (e.g., Hallion et al., 2014 ), as well as in samples of participants diagnosed with GAD (e.g., Pawluk et al., 2017 ). Furthermore, we hypothesized that the worry induction would impair problem solving even at low levels of trait worry, thus it was important to demonstrate that findings were not exclusive to a sample with clinically high levels of trait worry. Future studies should seek to replicate findings in clinical populations before such generalizations can be made. Moreover, because our study population consisted of college students, we cannot generalize findings to non-college student samples. As such these findings merit replication in other samples. On the other hand, our college student sample included adequate representation of racial diversity, with about 42% reflecting non-white groups.

Finally, because we asked participants to think about problems in their own lives, this may have led to some lack of uniformity in the complexity or severity level of problems participants were attempting to solve. For example, pathological worriers may be more likely than nonworriers to worry about even minor things. For this reason, we ensured that there was an equal balance of high and low trait worriers randomly assigned across conditions. Our procedure also directed participants to choose a problem for which they had some control over the outcome (i.e., we directed them to avoid problems for which there were no solutions). This may have also helped to prevent one group from selecting more intractable problems than another. Nonetheless, we cannot rule out the possibility that problem severity varied systematically across conditions leading to the effects we found. Considering that studies of problem solving in real-life settings have been better able to detect worry-related impairment (e.g., Szabó & Lovibond, 2006 ) relative to those using hypothetical problems in an laboratory setting (e.g., Davey, 1994 ), we strove to create a task that was both externally valid and experimentally rigorous. However, future studies may wish to increase uniformity of this variable, while attempting to maintain external validity (such as by balancing participants by the types of problems they report or by ratings of problem severity).

In sum, this was the first study to experimentally manipulate worry immediately prior to problem solving in a controlled laboratory setting, and provides initial evidence that the worry process is detrimental to problem solving in this context. Although many individuals are prone to worry in the face of problems, believe that this is a helpful approach to confronting problems, and often conflate worry with active problem solving (e.g., Kelly & Kelly, 2007 ; Sugiura, 2013 ; Szabó & Lovibond, 2002 ), our findings suggest otherwise. We argue that worry is distinct from adaptive problem solving. Whereas it does direct attention to potential threats, worrying about a problem inhibits the ability to proactively address threats in an optimal way, and instead may repeatedly cycle people through their worst-case scenario fears. Data from this study argue that attempting to take a more objective stance when evaluating a problem, and refraining from catastrophic thinking, represent the most effective problem-solving strategies for both high and low trait worry individuals alike.

• Worrying about a personal problem lowered confidence in solutions for high trait worriers.
• Thinking objectively about a problem led to more effective solutions than worrying or focused breathing.
• State worry predicted less intention to implement solutions, while controlling for trait worry.
• Worrying beforehand led to elevated worry and anxiety after solving a personal problem.

Supplementary Material

Acknowledgments.

This study was partially supported by NIMH 1R01MH115128-01A1 to Michelle Newman.

Declarations of interest: none

Sandra Llera: Conceptualization, Methodology, Formal Analysis, Investigation, Writing - Original draft preparation. Michelle G. Newman: Conceptualization, Methodology, Formal Analysis, Writing - Review and editing.

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Problem Solving

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Introduction & Theoretical Background

Problem Solving is a helpful intervention whenever clients present with difficulties, dilemmas, and conundrums, or when they experience repetitive thought such as rumination or worry. Effective problem solving is an essential life skill and this Problem Solving worksheet is designed to guide adults through steps which will help them to generate solutions to ‘stuck’ situations in their lives. It follows the qualities of effective problem solving outlined by Nezu, Nezu & D’Zurilla (2013), namely: clearly defining a problem; generation of alternative solutions; deliberative decision making; and the implementation of the chosen solution.

The therapist’s stance during problem solving should be one of collaborative curiosity. It is not for the therapist to pass judgment or to impose their preferred solution. Instead it is the clinician’s role to sit alongside clients and to help them examine the advantages and disadvantages of their options and, if the client is ‘stuck’ in rumination or worry, to help motivate them to take action to become unstuck – constructive rumination asks “How can I…?” questions instead of “Why…?” questions.

In their description of problem solving therapy Nezu, Nezu & D’Zurilla (2013) describe how it is helpful to elicit a positive orientation towards the problem which involves: being willing to appraise problems as challenges; remain optimistic that problems are solvable; remember that successful problem solving involves time and effort.

Therapist Guidance

• What is the nature of the problem?
• What are my goals?
• What is getting the way of me reaching my goals?
• “Can you think of any ways that you could make this problem not be a problem any more?”
• “What’s keeping this problem as a problem? What could you do to target that part of the problem?”
• “If your friend was bothered by a problem like this what might be something that you recommend they try?”
• “What would be some of the worst ways of solving a problem like this? And the best?”
• “How would Batman solve a problem like this?”
• Consider short term and long-term implications of each strategy
• Implications may relate to: emotional well-being, choices & opportunities, relationships, self-growth
• The next step is to consider which of the available options is the best solution. If you do not feel positive about any solutions, the choice becomes “Which is the least-worst?”. Remember that “even not-making-a-choice is a form of choice”.  
• The last step of problem solving is putting a plan into action. Rumination, worry, and being in the horns of a dilemma are ‘stuck’ states which require a behavioral ‘nudge’ to become unstuck. Once you have put your plan into action it is important to monitor the outcome and to evaluate whether the actual outcome was consistent with the anticipated outcome.

References And Further Reading

• Beck, A.T., Rush, A.J., Shaw, B.F., & Emery, G. (1979). Cognitive therapy of depression . New York: Guilford. Nezu, A. M., Nezu, C. M., D’Zurilla, T. J. (2013). Problem-solving therapy: a treatment manual . New York: Springer.
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7. Thinking and Intelligence

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

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.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

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

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

Take a look at the “Puzzling Scales” logic puzzle below ( [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.

Link to Learning

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.

Self Check Questions

Critical thinking questions.

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

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

Personal Application Question

3. 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?

1. 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.

2. 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.

• Psychology. Authored by : OpenStax College. Located at : http://cnx.org/contents/[email protected]:1/Psychology . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/content/col11629/latest/.

A Crash Course in Critical Thinking

What you need to know—and read—about one of the essential skills needed today..

Posted April 8, 2024 | Reviewed by Michelle Quirk

• In research for "A More Beautiful Question," I did a deep dive into the current crisis in critical thinking.
• Many people may think of themselves as critical thinkers, but they actually are not.
• Here is a series of questions you can ask yourself to try to ensure that you are thinking critically.

Conspiracy theories. Inability to distinguish facts from falsehoods. Widespread confusion about who and what to believe.

These are some of the hallmarks of the current crisis in critical thinking—which just might be the issue of our times. Because if people aren’t willing or able to think critically as they choose potential leaders, they’re apt to choose bad ones. And if they can’t judge whether the information they’re receiving is sound, they may follow faulty advice while ignoring recommendations that are science-based and solid (and perhaps life-saving).

Moreover, as a society, if we can’t think critically about the many serious challenges we face, it becomes more difficult to agree on what those challenges are—much less solve them.

On a personal level, critical thinking can enable you to make better everyday decisions. It can help you make sense of an increasingly complex and confusing world.

In the new expanded edition of my book A More Beautiful Question ( AMBQ ), I took a deep dive into critical thinking. Here are a few key things I learned.

First off, before you can get better at critical thinking, you should understand what it is. It’s not just about being a skeptic. When thinking critically, we are thoughtfully reasoning, evaluating, and making decisions based on evidence and logic. And—perhaps most important—while doing this, a critical thinker always strives to be open-minded and fair-minded . That’s not easy: It demands that you constantly question your assumptions and biases and that you always remain open to considering opposing views.

In today’s polarized environment, many people think of themselves as critical thinkers simply because they ask skeptical questions—often directed at, say, certain government policies or ideas espoused by those on the “other side” of the political divide. The problem is, they may not be asking these questions with an open mind or a willingness to fairly consider opposing views.

When people do this, they’re engaging in “weak-sense critical thinking”—a term popularized by the late Richard Paul, a co-founder of The Foundation for Critical Thinking . “Weak-sense critical thinking” means applying the tools and practices of critical thinking—questioning, investigating, evaluating—but with the sole purpose of confirming one’s own bias or serving an agenda.

In AMBQ , I lay out a series of questions you can ask yourself to try to ensure that you’re thinking critically. Here are some of the questions to consider:

• Why do I believe what I believe?
• Are my views based on evidence?
• Have I fairly and thoughtfully considered differing viewpoints?
• Am I truly open to changing my mind?

Of course, becoming a better critical thinker is not as simple as just asking yourself a few questions. Critical thinking is a habit of mind that must be developed and strengthened over time. In effect, you must train yourself to think in a manner that is more effortful, aware, grounded, and balanced.

For those interested in giving themselves a crash course in critical thinking—something I did myself, as I was working on my book—I thought it might be helpful to share a list of some of the books that have shaped my own thinking on this subject. As a self-interested author, I naturally would suggest that you start with the new 10th-anniversary edition of A More Beautiful Question , but beyond that, here are the top eight critical-thinking books I’d recommend.

The Demon-Haunted World: Science as a Candle in the Dark , by Carl Sagan

This book simply must top the list, because the late scientist and author Carl Sagan continues to be such a bright shining light in the critical thinking universe. Chapter 12 includes the details on Sagan’s famous “baloney detection kit,” a collection of lessons and tips on how to deal with bogus arguments and logical fallacies.

Clear Thinking: Turning Ordinary Moments Into Extraordinary Results , by Shane Parrish

The creator of the Farnham Street website and host of the “Knowledge Project” podcast explains how to contend with biases and unconscious reactions so you can make better everyday decisions. It contains insights from many of the brilliant thinkers Shane has studied.

Good Thinking: Why Flawed Logic Puts Us All at Risk and How Critical Thinking Can Save the World , by David Robert Grimes

A brilliant, comprehensive 2021 book on critical thinking that, to my mind, hasn’t received nearly enough attention . The scientist Grimes dissects bad thinking, shows why it persists, and offers the tools to defeat it.

Think Again: The Power of Knowing What You Don't Know , by Adam Grant

Intellectual humility—being willing to admit that you might be wrong—is what this book is primarily about. But Adam, the renowned Wharton psychology professor and bestselling author, takes the reader on a mind-opening journey with colorful stories and characters.

Think Like a Detective: A Kid's Guide to Critical Thinking , by David Pakman

The popular YouTuber and podcast host Pakman—normally known for talking politics —has written a terrific primer on critical thinking for children. The illustrated book presents critical thinking as a “superpower” that enables kids to unlock mysteries and dig for truth. (I also recommend Pakman’s second kids’ book called Think Like a Scientist .)

Rationality: What It Is, Why It Seems Scarce, Why It Matters , by Steven Pinker

The Harvard psychology professor Pinker tackles conspiracy theories head-on but also explores concepts involving risk/reward, probability and randomness, and correlation/causation. And if that strikes you as daunting, be assured that Pinker makes it lively and accessible.

How Minds Change: The Surprising Science of Belief, Opinion and Persuasion , by David McRaney

David is a science writer who hosts the popular podcast “You Are Not So Smart” (and his ideas are featured in A More Beautiful Question ). His well-written book looks at ways you can actually get through to people who see the world very differently than you (hint: bludgeoning them with facts definitely won’t work).

A Healthy Democracy's Best Hope: Building the Critical Thinking Habit , by M Neil Browne and Chelsea Kulhanek

Neil Browne, author of the seminal Asking the Right Questions: A Guide to Critical Thinking, has been a pioneer in presenting critical thinking as a question-based approach to making sense of the world around us. His newest book, co-authored with Chelsea Kulhanek, breaks down critical thinking into “11 explosive questions”—including the “priors question” (which challenges us to question assumptions), the “evidence question” (focusing on how to evaluate and weigh evidence), and the “humility question” (which reminds us that a critical thinker must be humble enough to consider the possibility of being wrong).

Warren Berger is a longtime journalist and author of A More Beautiful Question .

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