how might a mental set interfere with successful problem solving

Mental set refers to a cognitive tendency or predisposition to approach problem-solving or decision-making situations in a particular way, based on previous experiences or familiar strategies. It involves a fixed mindset that influences how individuals perceive and interpret information, as well as how they apply problem-solving techniques.

Components of Mental Set

1. Fixed Patterns of Thinking: Mental set involves relying on established patterns of thinking or problem-solving techniques instead of considering alternative approaches. These patterns can be based on prior successful experiences or learned strategies.

2. Resistance to Change: Mental set can create resistance to changing one’s perspective or trying new problem-solving methods. Individuals may feel comfortable and find it difficult to deviate from their familiar mental framework, even if it may not be the most effective approach.

3. Influence of Context: Mental set is highly influenced by the specific context in which a problem or decision arises. The environment, previous experiences, and societal norms can shape an individual’s mental set and lead them to approach situations in a particular way.

Examples of Mental Set

1. Functional Fixedness: A person utilizing functional fixedness may see a household item, such as a screwdriver, only as a tool for tightening or loosening screws, without considering its potential alternative uses.

2. Expertise: Experts in a particular field often develop a mental set that allows them to quickly solve problems within their domain of knowledge. However, this expertise can also hinder their ability to think creatively or consider alternative perspectives.

3. Confirmation Bias: Confirmation bias is a type of mental set that involves seeking information or evidence that supports one’s preexisting beliefs or expectations while ignoring or dismissing contradictory information.

4. Routine Thinking: Engaging in routine thinking can become a mental set where individuals approach problems or decisions in the same way, without questioning established methods. This can limit their ability to find innovative solutions.

Overcoming Mental Set

1. Increased Awareness: Recognizing the existence of mental set and its potential limitations can help individuals be more open to trying new perspectives or problem-solving approaches.

2. Encouraging Divergent Thinking: Cultivating an environment that encourages diverse viewpoints and alternative strategies can help break free from the constraints of mental set and stimulate creative problem-solving.

3. Deconstructing Assumptions: Challenging and revisiting underlying assumptions can broaden one’s mindset and allow for a more flexible approach to problem-solving.

4. Seeking External Input: Consulting others with different perspectives or expertise can provide fresh insights and help overcome the limitations imposed by mental set.

Problem-Solving Mindset: How to Achieve It (15 Ways)

One of the most valuable skills you can have in life is a problem-solving mindset. It means that you see challenges as opportunities to learn and grow, rather than obstacles to avoid or complain about. A problem-solving mindset helps you overcome difficulties, achieve your goals, and constantly improve yourself. By developing a problem-solving mindset, you can become more confident, creative, and resilient in any situation.A well-defined problem paves the way for targeted, effective solutions. Resist the urge to jump straight into fixing things. Invest the time upfront to truly understand what needs to be solved. Starting with the end in mind will make the path to resolution that much smoother.

Sanju Pradeepa

* This Post may contain affiliate Links, and we receive an affiliate commission for any purchases made by you using such links. *

Ever feel like you’re stuck in a rut with no way out? We’ve all been there. The problems life throws at us can seem insurmountable. But the truth is, you have everything you need to overcome any challenge already within you. It’s called a problem-solving mindset. Developing the ability to see problems as puzzles to solve rather than obstacles to overcome is a game changer. With the right mindset, you can achieve amazing things.

In this article, we’ll explore what having a problem-solving mindset really means and how you can cultivate one for yourself. You’ll learn proven techniques to shift your perspective, expand your creativity, and find innovative solutions to your biggest problems. We’ll look at examples of people who have used a problem-solving mindset to accomplish extraordinary feats. By the end, you’ll have the tools and inspiration to transform how you think about and approach problems in your own life.

Table of Contents

What is a problem-solving mindset.

A problem solving mindset is all about approaching challenges in a solution-focused way. Rather than feeling defeated by obstacles, you look at them as puzzles to solve. Developing this mindset takes practice, but the rewards of increased resilience, creativity and confidence make it worth the effort.

• Identify problems, not excuses. Rather than blaming external factors, look for the issues within your control. Ask yourself, “What’s really going on here and what can I do about it?”
• Focus on solutions, not problems. Once you’ve pinpointed the issue, brainstorm options to fix it. Don’t get stuck in a negative loop. Shift your mindset to answer the question, “What are some possible solutions?”
• Look for opportunities, not obstacles. Reframe the way you view problems. See them as chances to improve and learn, rather than roadblocks stopping your progress. Ask, “What’s the opportunity or lesson here?”
• Start small and build up. Don’t feel overwhelmed by big challenges. Break them into manageable steps and celebrate small wins along the way. Solving little problems builds your confidence to tackle bigger issues.

Be patient with yourself and maintain an open and curious attitude . With regular practice, you’ll get better at seeing the solutions, rather than the obstacles. You’ll become more flexible and innovative in your thinking. And you’ll discover that you have the ability to solve problems you once thought insurmountable. That’s the power of a problem-solving mindset.

Why Developing a Problem Solving Mindset Is Important

Developing a problem-solving mindset is crucial these days. Why? Because life throws curveballs at us constantly and the only way to overcome them is through creative solutions.

Having a problem-solving mindset means you view challenges as opportunities rather than obstacles. You approach them with curiosity and optimism instead of dread. This allows you to see problems from new angles and come up with innovative solutions.

Some key characteristics of a problem-solving mindset include:

• Flexibility. You’re open to different perspectives and willing to consider alternative options.
• Creativity. You think outside the box and make unexpected connections between ideas.
• Persistence. You don’t give up easily in the face of difficulties or setbacks. You continue experimenting and adjusting your approach.
• Adaptability. You accept change and are able to quickly adjust your strategies or plans to suit new situations.
• Resourcefulness. You make the most of what you have access to and find ways to overcome limitations.

Developing a problem-solving mindset takes conscious effort and practice.

The Key Characteristics of Effective Problem Solvers

To become an effective problem solver, you need to develop certain characteristics and mindsets. Here are some of the key traits shared by great problem solvers:

1. Openness to New Ideas

Effective problem solvers have an open and curious mind. They seek out new ways of looking at problems and solutions. Rather than dismissing ideas that seem “out there,” they explore various options with an open mind.

2. Flexibility

Great problem solvers are flexible in their thinking. They can see problems from multiple perspectives and are willing to adapt their approach. If one solution isn’t working, they try another. They understand that there are many paths to solving a problem.

3. Persistence

Solving complex problems often requires persistence and determination. Effective problem solvers don’t give up easily. They continue exploring options and trying new solutions until they find one that works. They see setbacks as learning opportunities rather than failures.

Why Persistence is Important: 8 Benefits & 6 Ways to Develop

4. creativity.

Innovative problem solvers think outside the box . They make unexpected connections and come up with unconventional solutions. They utilize techniques like brainstorming, mind mapping, and lateral thinking to spark new ideas.

5. Analytical Thinking

While creativity is key, problem solvers also need to be able to evaluate solutions in a logical and analytical manner. They need to be able to determine the pros and cons, costs and benefits, and potential obstacles or issues with any solution. They rely on data, evidence, and objective reasoning to make decisions.

7 Types of Critical Thinking: A Guide to Analyzing Problems

How to cultivate a problem-solving mindset.

To cultivate a problem-solving mindset, you need to develop certain habits and ways of thinking. Here are some tips to get you started:

1. Look for Opportunities to Solve Problems

The more you practice problem solving, the better you’ll get at it. Look for opportunities in your daily life to solve small problems. This could be figuring out a better way to organize your tasks at work or coming up with a solution to traffic in your neighborhood. Start with small, low-risk problems and work your way up to more complex challenges.

2. Ask Good Questions

One of the most important skills in problem solving is asking good questions. Questions help you gain a deeper understanding of the issue and uncover new perspectives. Ask open-ended questions like:

• What’s the real problem here?
• What are the underlying causes?
• Who does this impact and how?
• What has been tried before? What worked and what didn’t?

3. Do Your Research

Don’t go into problem solving blind. Do some research to gather relevant facts and data about the situation. The more you know, the better equipped you’ll be to come up with innovative solutions. Talk to people with different viewpoints and life experiences to gain new insights.

4. Brainstorm Many Options

When you start thinking of solutions, don’t settle for the first idea that comes to mind. Brainstorm many options to open up possibilities. The more choices you have, the more likely you are to discover an unconventional solution that really fits the needs of the situation. Think outside the box!

5. Evaluate and Decide

Once you have a list of possible solutions, evaluate each option objectively based on criteria like cost, time, and effectiveness. Get input from others if needed. Then make a decision and take action. Even if it’s not the perfect solution, you can make changes as you go based on feedback and results.

6. Question your beliefs

The beliefs and assumptions you hold can influence how you perceive and solve problems. Ask yourself:

• What beliefs or stereotypes do I have about this situation or the people involved?
• Are these beliefs grounded in facts or just my personal experiences?
• How might my beliefs be limiting my thinking?

Challenging your beliefs helps you see the problem with fresh eyes and identify new solutions.

The Ultimate Guide of Overcoming Self-Limiting Beliefs

7. seek different perspectives.

Get input from people with different backgrounds, experiences, and thought processes than your own. Their unique perspectives can reveal new insights and spark innovative ideas. Some ways to gain new perspectives include:

• Discuss the problem with colleagues from different departments or areas of expertise.
• Interview customers or clients to understand their needs and priorities.
• Consult experts in unrelated fields for an outside-the-box opinion.
• Crowdsource solutions from people of diverse ages, cultures, and socioeconomic backgrounds.

8. Look beyond the obvious

We tend to focus on the most conspicuous or straightforward solutions, but the best option isn’t always obvious. Try these techniques to stimulate unconventional thinking:

• Restate the problem in new ways. A new phrasing can reveal alternative solutions.
• Remove constraints and imagine an ideal scenario. Then work backwards to find realistic options.
• Make unexpected associations between the problem and unrelated concepts or objects. Look for parallels and analogies in different domains.
• Play with hypothetical scenarios to find combinations you may not logically deduce. Some of the wildest ideas can lead to innovative solutions!

With an open and curious mindset, you can overcome assumptions, gain new insights, and find unconventional solutions to your most complex problems. The key is looking at the situation in new ways and exploring all possibilities.

Mindset is Everything: Reprogram Your Thinking for Success

9. practice active listening.

To become an effective problem solver, you need to practice active listening. This means paying close attention to what others are saying and asking follow-up questions to gain a deeper understanding of the issues.

Listen without judgment

When someone is explaining a problem to you, listen with an open mind. Avoid interrupting or criticizing them. Your role is to understand their perspective and concerns, not pass judgment. Nod, make eye contact, and give verbal affirmations like “I see” or “go on” to show you’re engaged.

Ask clarifying questions

If something is unclear or you need more details, ask questions. Say something like, “Can you explain that in more detail?” or “What specifically do you mean by that?” The more information you have about the problem, the better equipped you’ll be to solve it. Ask open-ended questions to encourage the other person to elaborate on their points.

Paraphrase and summarize

Repeat back parts of what the speaker said in your own words to confirm you understood them correctly. Say something like, “It sounds like the main issues are…” or “To summarize, the key points you’re making are…” This also shows the other person you were paying attention and care about addressing their actual concerns.

10. Withhold suggestions initially

When someone first presents you with a problem, avoid immediately suggesting solutions. Your first task is to understand the issue thoroughly. If you start proposing solutions too soon, it can seem like you’re not really listening and are just waiting for your turn to talk. Get clarification, summarize the issues, and ask any follow up questions needed before offering your input on how to solve the problem.

Developing the patience and discipline to actively listen takes practice. But by listening without judgment, asking clarifying questions, paraphrasing, and withholding suggestions initially, you’ll gain valuable insight into problems and be better equipped to solve them. Active listening is a skill that will serve you well in all areas of life.

11. Ask Lots of Questions

To solve problems effectively, you need to ask lots of questions. Questioning helps you gain a deeper understanding of the issue, uncover hidden factors, and open your mind to new solutions.

Asking “why” helps you determine the root cause of the problem. Keep asking “why” until you reach the underlying reason. For example, if sales numbers are down, ask why. The answer may be that you lost a key client. Ask why you lost the client. The answer could be poor customer service. Ask why the customer service was poor. And so on. Getting to the root cause is key to finding the right solution.

Challenge Assumptions

We all have implicit assumptions and biases that influence our thinking. Challenge any assumptions you have about the problem by asking questions like:

• What if the opposite is true?
• What are we missing or ignoring?
• What do we think is impossible but perhaps isn’t?

Questioning your assumptions opens you up to new perspectives and innovative solutions.

12. Consider Different Viewpoints

Try to see the problem from multiple angles by asking:

• How do others see this problem?
• What solutions might employees, customers, or experts suggest?
• What would someone from a different industry or background recommend?

Getting input from people with diverse experiences and ways of thinking will lead to better solutions.

13. Brainstorm New Possibilities

Once you have a good understanding of the root problem, start generating new solutions by asking open-ended questions like:

• What if anything were possible, what solutions come to mind?
• What are some wild and crazy ideas, even if implausible?
• What solutions have we not yet thought of?

Don’t judge or evaluate ideas at this stage. Just let the questions spark new creative solutions. The more questions you ask, the more solutions you’ll discover. With an inquisitive mindset, you’ll be well on your way to solving any problem.

14. Document what you find

As you research, keep notes on key details, facts, statistics, examples, and advice that stand out as most relevant or interesting. Look for common themes and threads across the different resources. Organize your notes by topic or theme to get a better sense of the big picture. Refer back to your notes to recall important points as you evaluate options and determine next steps.

Doing thorough research arms you with the knowledge and understanding to develop effective solutions. You’ll gain a deeper appreciation for the complexity of the problem and be able to make more informed choices. Research also exposes you to new ideas you may not have considered. While it requires an investment of time, research is a crucial step for achieving an optimal solution.

15. Start With the End in Mind: Define the Problem Clearly

To solve a problem effectively, you need to first define it clearly. Without a concrete understanding of the issue at hand, you’ll waste time and energy grappling with a vague, nebulous challenge.

Identify the root cause

Ask probing questions to determine the underlying reason for the problem. Get specific by figuring out who is affected, what’s not working, where the breakdown is happening, when it started, and why it’s an issue. Look beyond the symptoms to find the source. The solution lies in resolving the root cause, not just alleviating surface-level pain points.

Gather objective data

Rely on facts, not opinions or assumptions. Observe the situation directly and collect information from multiple sources. Get input from people with different perspectives. Hard data and evidence will give you an accurate, unbiased view of the problem.

Define constraints and priorities

Determine any restrictions around time, money, resources, or policies that could impact your solution. Also identify what’s most important to solve—you can’t fix everything at once. Focus on high-priority issues and leave lower-priority problems for another time.

Frame the problem statement

With a clear understanding of the root cause, supporting data, and constraints, you can craft a concise problem statement. This articulates the issue in 1 or 2 sentences and serves as a guiding vision for developing solutions. Refer back to your problem statement regularly to ensure you stay on track.

Final Thought

Developing a problem-solving mindset is within your reach if you commit to continuous learning, looking at challenges from new angles, and not being afraid to fail. Start small by picking one problem each day to solve in a creative way. Build up your confidence and skills over time through practice.

While it may feel uncomfortable at first, having an adaptable and solution-focused mindset will serve you well in all areas of life. You’ll be able to navigate obstacles and setbacks with more ease and grace. And who knows, you may even start to enjoy the problem-solving process and see problems as opportunities in disguise. The problem-solving mindset is a gift that keeps on giving. Now go out there, face your challenges head on, and solve away!

Solve It!: The Mindset and Tools of Smart Problem Solvers by  Dietmar Sternad

• Creative Problem Solving as Overcoming a Misunderstanding by Maria Bagassi  and  Laura Macchi * (Department of Psychology, University of Milano-Bicocca, Milan, Italy) ,
• Mindsets: A View From Two Eras by Carol S. Dweck 1  and  David S. Yeager 2 published in National Library of Medicine ( Perspect Psychol Sci.  Author manuscript; available in PMC 2020 May 1. Published in final edited form as: Perspect Psychol Sci. 2019 May; 14(3): 481–496. )

Call to Action

With regular practice, a problem solving mindset can become second nature. You’ll get better at seeing opportunities, asking the right questions, uncovering creative solutions, and taking action. And that will make you a highly valuable thinker in any organization or team.

Let’s boost your self-growth with Believe in Mind.

Interested in self-reflection tips, learning hacks, and knowing ways to calm down your mind? We offer you the best content which you have been looking for.

Follow Me on

You May Like Also

Leave a Comment Cancel reply

Save my name, email, and website in this browser for the next time I comment.

How to develop a problem-solving mindset

May 14, 2023 Leaders today are confronted with more problems, of greater magnitude, than ever before. In these volatile times, it’s natural to react based on what’s worked best in the past. But when you’re solving the toughest business challenges on an ongoing basis, it’s crucial to start from a place of awareness. “If you are in an uncertain situation, the most important thing you can do is calm down,” says senior partner Aaron De Smet , who coauthored Deliberate Calm  with Jacqueline Brassey  and Michiel Kruyt. “Take a breath. Take stock. ‘Is the thing I’m about to do the right thing to do?’ And in many cases, the answer is no. If you were in a truly uncertain environment, if you’re in new territory, the thing you would normally do might not be the right thing.” Practicing deliberate calm not only prepares you to deal with the toughest problems, but it enhances the quality of your decisions, makes you more productive, and enables you to be a better leader. Check out these insights to learn how to develop a problem-solving mindset—and understand why the solution to any problem starts with you.

When things get rocky, practice deliberate calm

Developing dual awareness;

How to learn and lead calmly through volatile times

Future proof: Solving the ‘adaptability paradox’ for the long term

How to demonstrate calm and optimism in a crisis

How to maintain a ‘Longpath’ mindset, even amid short-term crises

Addressing employee burnout: Are you solving the right problem?

April Rinne on finding calm and meaning in a world of flux

How spiritual health fosters human resilience

An official website of the United States government

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

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

• Publications
• Account settings

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

• Advanced Search
• Journal List
• Front Psychol

Unconditional Perseveration of the Short-Term Mental Set in Chunk Decomposition

A mental set generally refers to the brain’s tendency to stick with the most familiar solution to a problem and stubbornly ignore alternatives. This tendency is likely driven by previous knowledge (the long-term mental set) or is a temporary by-product of procedural learning (the short-term mental set). A similar problem situation is considered the factor required for perseveration of the long-term mental set, which may not be essential for the short-term mental set. To reveal the boundary conditions for perseveration of the short-term mental set, this study adopted a Chinese character decomposition task. Participants were asked to perform a practice problem that could be solved by a familiar loose chunk decomposition (loose solution) followed by a test problem, or they were asked to repeatedly perform 5–8practice problems followed by a test problem; the former is the base-set condition, and the latter is the enhanced-set condition. In Experiment 1, the test problem situation appeared to be similar to the practice problem and could be solved using the reinforced loose solution and also an unfamiliar tight chunk decomposition (tight solution) (a 2-solution problem). In Experiment 2, the test problem situation differed from the practice problem and could only be solved using an unfamiliar tight solution (a 1-solution problem). The results showed that, when comparing the enhanced-set and base-set conditions, both the accuracy rate and the response times for solving the test problem with a tight solution were worse in Experiment 1, whereas the response times were worse in Experiment 2. We concluded that perseveration of the short-term mental set was independent of the similarity between problem situations and discuss the differences in perseveration between two types of fixation.

Introduction

A mental set is also known as the Einstellung effect, which represents a form of rigidity in which an individual behaves or believes in a certain manner. In the field of psychology, this effect has typically been examined in the process of problem solving and specifically refers to the brain’s tendency to stick with the most familiar solution and to stubbornly ignore alternatives ( Schultz and Searleman , 2002 ). Both prior knowledge and a similar problem situation were considered the factors required to induce an attentional bias toward the familiar solution ( Lovett and Anderson, 1996 ). In addition, the mental set is also likely formed and strengthened by repeatedly practicing a particular solution in a short time and can be interpreted as a temporary by-product of procedural learning ( Ohlsson, 1992 ; Ollinger et al., 2008 ). However, whether a similar problem situation is an essential factor for perseveration of the short-term mental set remains largely unknown.

The mental set is likely driven by previous knowledge, particularly expertise in a domain ( Wiley, 1998 ; Ricks et al., 2007 ; Ellis and Reingold, 2014 ), which can be defined as the long-term mental set. This mental set always occurs when people are confronted with a problem situation that is similar to previously experienced problem situations. Previously acquired knowledge likely helps problem solvers to understand, interpret and solve problems quickly and also likely has a negative impact. For example, most errors that doctors make are not connected to their inadequate medical knowledge but rather to the tendency to form opinions quickly based on previous experience. Once the initial diagnosis is formed, it guides doctors in the search for supporting evidence, which in turn introduces a risk of missing important aspects unrelated to the initial diagnosis.

In a laboratory experiment, chess players were required to find a checkmate position with the fewest number of moves. If players were given a 2-solution problem that had two possible solutions, a familiar solution that took five moves and a less familiar solution that took three moves (the optimal solution), then most of the players selected the familiar but non-optimal solution and failed to notice the shorter solution ( Bilalić et al., 2008 ). Eye tracking technology revealed that the cognitive mechanism underlying this phenomenon was attentional bias, where previous knowledge likely directs attention toward relevant information and away from irrelevant information. Accordingly, players rapidly fixated on the target region that was associated with the familiar but longer solution (i.e., checkmate in five moves) and spent more time looking at these squares rather than those relevant to the shortest solution (i.e., checkmate in three moves), even when they reported that they were searching for alternative solutions in an open-minded manner ( Bilalić et al., 2008 , 2010 ; Sheridan and Reingold, 2013 ). Thus, the search for a solution became self-fulfilling as the familiar solution was consistent with previously acquired knowledge and was more likely to be utilized ( Bilalić et al., 2008 , 2010 ; citealpBR1). If a problem situation is different from previous experiences, then no cues will elicit retrieval of previously acquired knowledge and no attentional bias will occur.

In addition, the mental set is also likely strengthened by repeated practice in a short time and can be interpreted as a temporary by-product of procedural learning ( Ohlsson, 1992 ). One of the most famous examples is the so-called water jar problem, which was originally developed by Luchins ( Luchins, 1942 ; Luchins and Luchins, 1969 ). Participants are presented with three jars (A, B, and C), each of which holds a certain amount of water. The goal is to determine how the jars can be used to obtain a designated amount of water. A series of practice problems can only be solved using a complicated strategy (e.g., A – B – 2C), which participants learn quickly. Subsequently, the participants are provided a test problem (called the 2-solution problem) that could be solved using either the complicated strategy or a much easier strategy (e.g., A – C). Typically, most participants continue to use the complicated strategy instead of the simple strategy. In this case, fixation is induced by repeatedly reinforcing a small number of similar problems in people who have never experienced the task before, which can be defined as the short-term mental set.

In previous studies, the short-term mental effect has been demonstrated in both the laboratory and real-life settings using a range of different problem-solving tasks ( Schultz and Searleman, 2002 ). However, the neurocognitive mechanism underlying this effect and its boundary conditions remain largely unknown. One possibility is that the reinforced solution gradually realizes mechanization, which likely becomes automatically activated during the next problem when the problem situation is similar to the former practice problems. Accordingly, problem solvers progressively require less time to solve problems with a reinforced solution but also experience greater difficulties in searching for alternative solutions ( Neroni et al., 2017 ). Meanwhile, mechanization of a particular solution likely implies that people’s brains lost flexibility to manage novel stimuli or tasks. Therefore, although the next problem situation was different from the former practice problems, negative influences of the short-term mental set likely remained. More generally, regardless of whether the next problem is similar to the former practice problems, problem solving will be hindered when people try to use alternative solutions rather than the reinforced solution.

To reveal the boundary conditions of perseveration of the short-term mental set, a chunk decomposition task was adopted in this study. As a possible means to solve insight problems, chunk decomposition refers to decomposing familiar patterns into their components such that they can be regrouped in a different and meaningful manner ( Knoblich et al., 1999 ). Based on whether the components of the chunks to be decomposed are themselves meaningful perceptual patterns, chunk decomposition can be divided into loose and tight levels. Decomposing the numeral “VI” into “V” and “I” is an example of loose chunk decomposition, and decomposing ‘X’ into “/” and “∖” is an example of tight chunk decomposition because ‘VI’ is composed of meaningful small chunks (‘V’ and ‘I’), whereas ‘X’ is composed of meaningless small chunks (“/” and “∖”) ( Knoblich et al., 1999 ). Generally, participants are more familiar with loose chunk decomposition rather than tight chunk decomposition due to previous knowledge about chunks ( Knoblich et al., 1999 ; Wu et al., 2013 ; Huang et al., 2015 ), but the latter strategy is critical to solving insight problems. Moreover, previous studies have demonstrated that performance in solving mathematical problems with loose chunk decomposition (a loose solution) was improved by repeated practice in the set ( Knoblich et al., 2001 ; Chi and Snyder, 2011 ), i.e., the short-term mental set of chunk decomposition was formed and strengthened by intense practice. After repeatedly solving 5∼8 practice mathematical problems using a loose solution, participants were asked to solve a test mathematical problem, which was different from the practice problem and could only be solved by tight chunk decomposition (a tight solution), in the experimental condition; or else participants were asked to perform a test mathematical problem after repeatedly solving several anagrams in the control condition ( Ollinger et al., 2008 ). Results showed no significant difference in the performance of the test problem between two conditions. Researchers believe that the short-term mental set did not perseverate in the test problem since it was insightful ( Ollinger et al., 2008 ) and different from the practice problem situation. However, another possibility is that perseveration of the short-term mental set was independent on the problem situation similarity, and was happened in both the experimental condition and the control condition; or the short-term mental set likely perseverate in a totally different problem situation.

To further reveal the boundary condition of the short-term mental set, we selectively adopted the design of Ollinger et al. (2008) in this study. Participants were asked to repeatedly perform 5–8 practice problems that could be solved using a loose solution, followed by a test problem, or they were asked to perform a single practice problem followed by a test problem; the former is the enhanced-set condition, and the latter is the base-set condition. In Experiment 1, the test problem situation appeared to be similar to the practice problem and could be solved by the reinforced loose solution and also an unfamiliar tight solution (a 2-solution problem). In Experiment 2, the test problem situation was different from the practice problem and could only be solved by an unfamiliar tight solution (a 1-solution problem). By comparing the success probability and response time of solving the test problem with an unfamiliar tight solution between the enhanced- and base-set conditions, the influences of the short-term mental set on the unfamiliar tight solution were revealed, allowing examination of whether perseveration of the short-term mental set was independent of the situation similarity between the practice problems and the test problem.

We assumed that the short-term mental set would be formed and strengthened after repeatedly solving several similar practice problems using the loose solution and would negatively influence solving of the test problem with an unfamiliar tight solution. The accuracy rates and response times associated with the tight solution for the test problem would be worse in the enhanced-set condition versus the base-set condition regardless of whether the test problem situation was similar to the practice problems.

Experiment 1

Participants.

Thirty-two paid participants (18 males between the ages of 18 and 22 years; mean age 20.11 ± 1.31 years) recruited from the Jiangxi Normal University participated in the task as paid volunteers. They were all native Chinese speakers and had normal or corrected-to-normal vision. Before the experiment, all participants signed the informed consent form approved by the institutional review board of the Jiangxi Normal University.

Tasks, Design, and Procedure

Example of the Chinese character decomposition task in this study.

Two conditions were created in this study, namely, the base-set and enhanced-set conditions, and their presentation sequences were random. In the base-set condition, the participants were asked to perform a practice problem that could be solved only by a loose solution (decompose and remove radicals), followed by a test problem that could be solved by a loose solution and also a tight solution (decompose and remove strokes). In the enhanced-set condition, the participants were asked to continuously perform 5∼8 similar practice problems, followed by one test problem; the range was designed to prevent participants from anticipating. In both conditions, the test problem situation was similar to the practice problems in which the character to be decomposed had a radical element that was closely associated with the loose solution. In total, 24 practice problems and 24 test problems were included in the base-set condition, and 156 practice problems and 24 test problems were included in the enhanced-set condition. Each problem was a Chinese character that was highly familiar to the participants, who were native Chinese speakers.

The time course of each trial is shown below (see Figure ​ Figure2). 2 ). After a period of 500∼800 ms that was designed to reduce expectation, the character to be decomposed appeared in the center of the screen for up to 3,000 ms. During this period, the participants were instructed to consider the answers one by one and to press a response key with the right index finger as soon as they determined an answer. Then, an input box appeared on the screen, and the participants were given an unlimited period of time to enter their answers using a keyboard and then press the “Enter” key to complete the task. Subsequently, the same character again appeared in the center of the screen for up to 10,000 ms minus the reaction time for the first encounter, and the participants were given an unlimited amount of time to enter their answers using a keyboard, or the participants could press the “Space” key to end the trial if they believed that no other answer was possible. Thus, both the character to be decomposed and the answer input box appeared twice since two answers were required for the test problem, and the same procedure was applied to the practice problem for coherence. After the participants finished a practice problem and a test problem or 5∼8 practice problems and a test problem in the set, a 3∼5-s interval was included as a break. The random length was designed to reduce the impact of expectation and preparation.

Example of the experimental trial timeline in Experiment 1.

To demonstrate the influences of the short-term mental set on chunk decomposition, we compared the response times and accuracy rates of the loose solution for both the practice and test problems and the tight solution for the test problem between the enhanced-set condition and the base-set condition.

For the accuracy rate, a 2 (condition: base-set, enhanced-set) × 2 (solution: loose, tight) repeated-measures analysis of variance (ANOVA) revealed significant effects of the condition [ F (1,31) = 6.58, p = 0.015, η 2 = 0.18], the solution [ F (1,31) = 940.16, p < 0.001, η 2 = 0.97], and the interaction effect [ F (1,31) = 11.00, p = 0.002, η 2 = 0.26]. The participants achieved fewer correct responses for the tight solution in the test task in the enhanced-set condition than in the base-set condition [ t (31) = 9.42, p = 0.004], but no significant differences emerged between the enhanced-set condition and the base-set condition for the loose solution [ t (31) = 0.24, p = 0.63] (Figure ​ (Figure3 3 ).

The panel shows the mean accuracy rate and the mean response times for loose and tight solutions for character decomposition in both the base-set and enhanced-set conditions in Experiment 1. Error bars represent the 95% confidence interval. The asterisks indicate significant differences between conditions ( ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001).

For the mean response times, a 2 (condition: base-set, enhanced-set) × 2 (solution: loose, tight) repeated-measures ANOVA showed significant effects of the condition [ F (1,31) = 7.75, p = 0.009, η 2 = 0.20], the solution [ F (1,31) = 203.25, p < 0.001, η 2 = 0.87] and the interaction effect [ F (1,31) = 5.67, p = 0.024, η 2 = 0.16]. The reaction times of the tight-level solution for the test task were longer in the enhanced-set condition than those in the base-set condition [ t (31) = 6.87, p = 0.013], but no difference in response time for the loose solution for both tasks was found in either condition [ t (31) = 0.74, p = 0.40] (Figure ​ (Figure3 3 ).

Experiment 2

Twenty-eight participants (20 males between the ages of 18 and 22 years; mean age 19.93 ± 1.36 years) recruited from the Jiangxi Normal University participated in the task as paid volunteers. They were all native Chinese speakers and had normal or corrected-to-normal vision. Before the experiment, all participants signed the informed consent forms approved by the institutional review board of the Jiangxi Normal University.

The time course for each trial was as follows (see Figure ​ Figure4). 4 ). After 500∼800 ms, the character to be decomposed appeared in the center of the screen for up to 10,000 ms. During this period, the participants were asked to press a response key with the right index finger as soon as they determined an answer. Subsequently, an input box appeared on the screen, and the participants were given an unlimited amount of time to enter their answers using a keyboard and press the “Enter” key to complete the task. After the participants finished a practice problem and a test problem or 5∼8 practice problems and a test problem in the set, a 3∼5-s interval was provided as a break.

Example of the experimental trial timeline in Experiment 2.

To demonstrate the influences of the short-term mental set on chunk decomposition, we compared the response times and accuracy rates of the loose solution for all practice problems and the tight solution for the test problem between the enhanced-set condition and the base-set condition.

For the accuracy rate, a 2 (condition: base-set, enhanced-set) × 2 (solution: loose, tight) repeated-measures ANOVA revealed significant effects of the solution [ F (1,27) = 107.41, p < 0.001, η 2 = 0.80], indicating that the participants had fewer correct responses for the tight solution versus the loose solution, whereas the main effects of the condition [ F (1,27) = 0.02, p = 0.89, η 2 = 0.001] and the interaction effect [ F (1,27) = 0.06, p = 0.81, η 2 = 0.002] were not significant (Figure ​ (Figure5 5 ).

The panel shows the mean accuracy rate and the mean response times for the practice and test problems in both the base-set and enhanced-set conditions in Experiment 2. Error bars represent the 95% confidence interval. The asterisks indicate significant differences between conditions ( ∗∗∗ p < 0.001).

For the mean response times, a 2 (condition: base-set, enhanced-set) × 2 (solution: loose, tight) repeated-measures ANOVA showed the significant effects of the condition [ F (1,27) = 16.12, p < 0.001, η 2 = 0.37], the solution [ F (1,27) = 371.25, p < 0.001, η 2 = 0.93] and the interaction effect [ F (1,27) = 29.50, p < 0.001, η 2 = 0.52]. The reaction times of the tight solution were longer in the enhanced-set condition than those in the base-set condition [ t (27) = 23.85, p < 0.001], but no difference in response time for the loose solution was found between the two conditions [ t (27) = 1.18, p = 0.29] (Figure ​ (Figure5 5 ).

To reveal the boundary conditions of perseveration of the short-term mental set, this study adopted a Chinese character decomposition task. Participants were asked to perform a practice problem that could be solved by a familiar loose solution followed by a test problem, or they were asked to repeatedly perform 5–8 practice problems followed by a test problem; the former task is the base-set condition, and the latter task is the enhanced-set condition. The test problem situation was similar to the practice problem, which included a character with a radical structure, and could be solved by the reinforced loose solution and also an unfamiliar tight solution (Experiment 1), or the situation was different from the practice problem, which included a character without a radical structure, and could only be solved using an unfamiliar tight solution (Experiment 2). The results showed that the participants’ performance in solving the test problems with the unfamiliar tight solution was worse in the enhanced-set condition than in the base-set condition regardless of whether the test problem situation was similar to the practice problems.

For the 2-solution test problem in both the base- and enhanced-set conditions of Experiment 1, all of the participants selected the loose solution as their first choice even though no cue toward a loose or tight solution was provided in the experimental instructions, and the probability of using the loose solution was much higher than that of using the tight solution. This result was consistent with the chunk decomposition hypothesis that chunk decomposition begins with loose chunks, and that the probability that a chunk will be decomposed is inversely proportional to the tightness of the chunk ( Knoblich et al., 1999 ). The processing tendency toward loose chunk decomposition likely reflected the long-term mental set, which originated from previous knowledge about chunks. In particular, Chinese characters are composed of radicals, which are composed of strokes. Because radicals are meaningful elements and can be viewed as independent units, people likely consider removing radicals as the first choice in the process of chunk decomposition when a radical structure is present in the characters ( Luo and Knoblich, 2007 ; Luo et al., 2008 ). In other words, previous knowledge biased attention toward the radical structure and the corresponding loose solution, which was likely prioritized first when performing the Chinese characters decomposition task.

Compared with the base-set condition of Experiment 1, the participants had a lower probability of identifying and required more time to search for the tight solution for the test problem in the enhanced-set condition, reflecting the negative influence of the short-term mental set. As a temporary by-product of procedural learning, the short-term mental set was formed and strengthened with repeated practice of a particular solution. The solution that was satisfactory for all of the practice problems resulted in gradual realization of mechanization, which was likely automatically activated in the problem situation that was similar with prior practice problems ( Lovett and Anderson, 1996 ). Accordingly, problem solvers become faster at solving similar consecutive problems ( Ollinger et al., 2008 ). In this study, performance in solving the practice problem did not increase in the enhanced-set condition compared with the base-set condition, likely because of a ceiling effect. More importantly, performance in solving the test problem by the unfamiliar tight solution was decreased in the enhanced-set condition versus the base-set condition. Two possible mechanisms may underlie this phenomenon. First, reinforced practice enhanced the attentional bias toward the loose solution since a radical structure was present in the test problem situation and in the practice problems. Second, a particular solution realizing mechanization indicates that cognitive and neural adaptation occurred, and the participants may have lost the flexibility to shift their attention to search for other solutions.

For the 1-solution test problem in both conditions of Experiment 2, no radical element was present for retrieval of the loose solution, and the loose solution did not interfere with the tight solution. Therefore, the accuracy rate of solving the test problem with an unfamiliar tight solution was relatively high. Compared with the base-set condition, the participants showed poorer performance in solving the test problem by the tight solution after repeatedly solving the practice problems by the loose solution. This result revealed that the short-term mental set persisted in a different problem situation even though no attentional bias toward the radical structure and its corresponding loose solution likely occurred. The only possible explanation is that mechanization of a particular solution decreased cognitive flexibility, which likely increased the switching costs from the practiced problems to a totally different problem. Therefore, perseveration of the short-term mental set was independent of the similarity between the problem situations. Regardless of whether the next problem situation is similar to the previously practiced problems, problem solving will be hindered when people try to explore alternative solutions rather than using the repeatedly reinforced solution.

Although the formation mechanisms of the long-term mental set and the short-term mental set are completely different, these two kinds of fixation likely occur at the same time. In particular, the short-term mental set can be formed and strengthened on the basis of the long-term mental set. As in this study, the short-term mental set of chunk decomposition was formed and strengthened after the participants repeatedly solved several practice problems with the loose solution, which was driven by the long-term mental set originating from previous knowledge about Chinese character chunks. Then, when the next problem situation was similar to the previously practiced problems, influences from both the long-term mental set and also the short-term mental set manifested. The former set likely decreased the accuracy rate of solving the test problem with the tight solution due to an attentional bias toward the familiar loose solution, whereas the latter set likely increased the response times of solving the test problem with the tight solution since cognitive flexibility was lost after a particular process realizing mechanization. Therefore, both the accuracy and the response time in solving the test problem with an alternative solution were worse in the enhanced-set condition than those in the base-set condition (in Experiment 1). If the next problem situation was not similar to the previously practiced situation, then the influence from the short-term mental set leads to cognitive inflexibility, which likely affected performance on the switching task. Consequently, the participants spent considerably more time searching for and executing the solution in the enhanced-set condition versus the base-set condition (in Experiment 2). The different influences of the test problem on performance in the two experiments also demonstrated the differences in perseveration of the long-term mental set and the short-term mental set.

In sum, the short-term mental set that was formed and strengthened by repeated reinforcement of a particular solution to solve a set of similar practice problems not only likely increased the attentional bias toward the familiar solution when the test problem situation was similar to the practice problems but also likely decreased cognitive flexibility and increased the switching costs from the practice problems to a totally different test problem. Perseveration of the short-term mental set was independent of the similarity between problem situations. Therefore, the short-term mental set was different from the long-term mental set since the latter can only be induced when a similar situation activates previous knowledge. This study largely broadens our general understanding of the mental set and not only distinguished two types of mental sets on the basis of the forming processes but also revealed the differences in the necessary conditions for perseveration. In future research, the neurocognitive mechanism underlying the two types of fixation should be further investigated.

Ethics Statement

This study was carried out in accordance with the recommendations of Norms for human behavior experiments in Jiangxi Normal University with written informed consent from all subjects. All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the institutional review board of the Jiangxi Normal University.

Author Contributions

FH and ST designed the experiments. ST collected and analyzed the data. FH, ST, and ZH wrote the manuscript.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Funding. This work was supported by funding programs from the National Natural Science Foundation of China (Grant Nos. 31700956 and 31860278), a project funded by the China Postdoctoral Science Foundation (Grant Nos. 2018M632598 and 2018T110657), the Natural Science Foundation of Jiangxi, China (Grant No. 20181BAB214010), and the Science and Technology Research Project of the Educational Department in Jiangxi Province, China (Grant No. GJJ160343).

• Bilalić M., McLeod P. (2014). Why good thoughts block better ones. Sci. Am. 310 74–79. 10.1038/scientificamerican0314-74 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Bilalić M., McLeod P., Gobet F. (2008). Why good thoughts block better ones: the mechanism of the pernicious Einstellung (set) effect. Cognition 108 652–661. 10.1016/j.cognition.2008.05.005 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Bilalić M., McLeod P., Gobet F. (2010). The mechanism of the Einstellung (set) effect: a pervasive source of cognitive bias. Curr. Dir. Psychol. Sci. 19 111–115. 10.1177/0963721410363571 [ CrossRef ] [ Google Scholar ]
• Chi R. P., Snyder A. W. (2011). Facilitate insight by non-invasive brain stimulation. PLoS One 6 : e16655 . 10.1371/journal.pone.0016655 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Ellis J. J., Reingold E. M. (2014). The einstellung effect in anagram problem solving: evidence from eye movements. Front. Psychol. 5 : 679 . 10.3389/fpsyg.2014.00679 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Huang F., Fan J., Luo J. (2015). Neural basis of novelty and appropriateness in processing of creative chunk decomposition. Neuroimage 113 122–132. 10.1016/j.neuroimage.2015.03.030 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Knoblich G., Ohlsson S., Haider H., Rhenius D. (1999). Constraint relaxation and chunk decomposition in insight problem solving. J. Exp. Psychol. 25 1534–1555. 10.1037/0278-7393.25.6.1534 [ CrossRef ] [ Google Scholar ]
• Knoblich G., Ohlsson S., Raney G. E. (2001). An eye movement study of insight problem solving. Mem. Cogn. 29 1000–1009. 10.1016/j.actpsy.2008.08.008 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Lovett M. C., Anderson J. R. (1996). History of success and current context in problem solving: combined influences on operator selection. Cognit. Psychol. 31 168–217. 10.1006/cogp.1996.0016 [ CrossRef ] [ Google Scholar ]
• Luchins A. S. (1942). Mechanization in problem solving – The effect of Einstellung. Psychol. Monogr. 54 i–95. 10.1037/h0093502 [ CrossRef ] [ Google Scholar ]
• Luchins A. S., Luchins E. H. (1969). Einstellung effect and group problem solving. J. Soc. Psychol. 77 79–89. 10.1080/00224545.1969.9919848 [ CrossRef ] [ Google Scholar ]
• Luo J., Knoblich G. (2007). Studying insight problem solving with neuroscientific methods. Methods 42 77–86. 10.1016/j.ymeth.2006.12.005 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Luo J., Knoblich G., Lin C. (2008). “ Neural correlates of insight phenomena ,” in Neural Correlates of Thinking , eds Kraft E., Guly B.ás, and E. Pöppel (New York, NY: Springer-Verlag), 253–267. [ Google Scholar ]
• Neroni M. A., Vasconcelos L. A., Crilly N. (2017). Computer-based ’mental set’ tasks: an alternative approach to studying design fixation. J. Mech. Design 139 : 071102 10.1115/1.4036562 [ CrossRef ] [ Google Scholar ]
• Ohlsson S. (1992). Information-Processing Explanations of Insight and Related Phenomena. Advances in the Psychology of Thinking. London: Harvester Wheatsheaf. [ Google Scholar ]
• Ollinger M., Jones G., Knoblich G. (2008). Investigating the effect of mental set on insight problem solving. Exp. Psychol. 55 270–282. 10.1027/1618-3169.55.4.269 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Ricks T. R., Turleyames K. J., Wiley J. (2007). Effects of working memory capacity on mental set due to domain knowledge. Mem. Cogn. 35 1456–1462. 10.3758/BF03193615 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Schultz P., Searleman A. (2002). Rigidity of thought and behavior: 100 years of research. Genet. Soc. Gen. Psychol. Monogr. 128 165–207. [ PubMed ] [ Google Scholar ]
• Sheridan H., Reingold E. M. (2013). The mechanisms and boundary conditions of the einstellung effect in chess: evidence from eye movements. PLoS One 8 : e75796 . 10.1371/journal.pone.0075796 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Tang X., Pang J., Nie Q. Y., Conci M., Luo J., Luo J. (2016). Probing the cognitive mechanism of mental representational change during chunk decomposition: a parametric fmri study. Cereb. Cortex 26 2991–2999. 10.1093/cercor/bhv113 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Wiley J. (1998). Expertise as mental set: the effects of domain knowledge in creative problem solving. Mem. Cogn. 26 716–730. 10.3758/BF03211392 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Wu L., Knoblich G., Luo J. (2013). The role of chunk tightness and chunk familiarity in problem solving: evidence from ERPs and fMRI. Hum. Brain Mapp. 34 1173–1186. 10.1002/hbm.21501 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Wu X., He M., Zhou Y., Xiao J., Luo J. (2017). Decomposing a chunk into its elements and reorganizing them as a new chunk: the two different sub-processes underlying insightful chunk decomposition. Front. Psychol. 8 : 2001 . 10.3389/fpsyg.2017.02001 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Zhang Z., Yang K., Warren C. M., Zhao G., Li P., Lei Y., et al. (2015). The influence of element type and crossed relation on the difficulty of chunk decomposition. Front. Psychol. 6 : 1025 . 10.3389/fpsyg.2015.01025 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]

Breaking the Barrier: How to Overcome Mental Set and Unlock Creative Problem Solving

Mental set is a cognitive bias that occurs when individuals approach a problem or situation with a preconceived notion or rigid way of thinking that limits their ability to see alternative solutions. Mental set can be referred to as the tendency to approach a particular problem or task in the same way as one has previously done, failing to consider new or creative ways to approach the problem.

For example, if an individual is used to solving a particular type of math problem using a specific formula, they might apply the same formula on a different type of problem where it is not applicable, resulting in incorrect solutions. This approach might lead them to overlook other, more effective solutions.

Overcoming mental set requires individuals to challenge their assumptions, which can be achieved by thinking creatively about a problem or task. Individuals should try to approach a problem from a fresh perspective, experiment with different approaches, and remove themselves from their comfort zones by trying out new things. Taking breaks and allowing oneself to reflect, visualize, or discuss with others can also help in identifying new strategies that might help yield a better outcome.

More Answers:

Recent posts, ramses ii a prominent pharaoh and legacy of ancient egypt.

Ramses II (c. 1279–1213 BCE) Ramses II, also known as Ramses the Great, was one of the most prominent and powerful pharaohs of ancient Egypt.

Formula for cyclic adenosine monophosphate & Its Significance

Is the formula of cyclic adenosine monophosphate (cAMP) $ce{C_{10}H_{11}N_{5}O_{6}P}$ or $ce{C_{10}H_{12}N_{5}O_{6}P}$? Does it matter? The correct formula for cyclic adenosine monophosphate (cAMP) is $ce{C_{10}H_{11}N_{5}O_{6}P}$. The

Development of a Turtle Inside its Egg

How does a turtle develop inside its egg? The development of a turtle inside its egg is a fascinating process that involves several stages and

The Essential Molecule in Photosynthesis for Energy and Biomass

Why does photosynthesis specifically produce glucose? Photosynthesis is the biological process by which plants, algae, and some bacteria convert sunlight, carbon dioxide (CO2), and water

How the Human Body Recycles its Energy Currency

Source for “The human body recycles its body weight of ATP each day”? The statement that “the human body recycles its body weight of ATP

Don't Miss Out! Sign Up Now!

Sign up now to get started for free!

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?

CC licensed content, Original

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

CC licensed content, Shared previously

• 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.

Share This Book

• Bipolar Disorder
• Therapy Center
• When To See a Therapist
• Types of Therapy
• Best Online Therapy
• Best Couples Therapy
• Best Family Therapy
• Managing Stress
• Sleep and Dreaming
• Understanding Emotions
• Self-Improvement
• Healthy Relationships
• Student Resources
• Personality Types
• Guided Meditations
• Verywell Mind Insights
• 2024 Verywell Mind 25
• Mental Health in the Classroom
• Editorial Process
• Meet Our Review Board
• Crisis Support

Overview of the Problem-Solving Mental Process

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

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

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

Frequently Asked Questions

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

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

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

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

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

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

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

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

2. Defining the Problem

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

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

3. Forming a Strategy

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

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

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

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

4. Organizing Information

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

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

5. Allocating Resources

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

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

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

6. Monitoring Progress

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

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

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

7. Evaluating the Results

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

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

A Word From Verywell​

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

Get Advice From The Verywell Mind Podcast

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

Follow Now : Apple Podcasts / Spotify / Google Podcasts

You can become a better problem solving by:

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

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

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

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

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

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

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

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons

Margin Size

• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

6.8: Blocks to Problem Solving

• Last updated
• Save as PDF
• Page ID 54768

• Mehgan Andrade and Neil Walker
• College of the Canyons

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\id}{\mathrm{id}}\)

\( \newcommand{\kernel}{\mathrm{null}\,}\)

\( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\)

\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\)

\( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vectorC}[1]{\textbf{#1}} \)

\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

Sometimes, previous experience or familiarity can even make problem solving more difficult. This is the case whenever habitual directions get in the way of finding new directions – an effect called fixation.

Functional Fixedness

Functional fixedness concerns the solution of object-use problems. The basic idea is that when the usual way of using an object is emphasised, it will be far more difficult for a person to use that object in a novel manner. An example for this effect is the candle problem : Imagine you are given a box of matches, some candles and tacks. On the wall of the room there is a cork- board. Your task is to fix the candle to the cork-board in such a way that no wax will drop on the floor when the candle is lit. – Got an idea?

Explanation: The clue is just the following: when people are confronted with a problem

and given certain objects to solve it, it is difficult for them to figure out that they could use them in a different (not so familiar or obvious) way. In this example the box has to be recognized as a support rather than as a container.

A further example is the two-string problem: Knut is left in a room with a chair and a pair of pliers given the task to bind two strings together that are hanging from the ceiling. The problem he faces is that he can never reach both strings at a time because they are just too far away from each other. What can Knut do?

Solution: Knut has to recognize he can use the pliers in a novel function – as weight for a pendulum. He can bind them to one of the strings, push it away, hold the other string and just wait for the first one moving towards him. If necessary, Knut can even climb on the chair, but he is not that small, we suppose…

Mental Fixedness

Functional fixedness as involved in the examples above illustrates a mental set - a person’s tendency to respond to a given task in a manner based on past experience. Because Knut maps an object to a particular function he has difficulties to vary the way of use (pliers as pendulum's weight). One approach to studying fixation was to study wrong-answer verbal insight problems. It was shown that people tend to give rather an incorrect answer when failing to solve a problem than to give no answer at all.

A typical example: People are told that on a lake the area covered by water lilies doubles every 24 hours and that it takes 60 days to cover the whole lake. Then they are asked how many days it takes to cover half the lake. The typical response is '30 days' (whereas 59 days is correct).

These wrong solutions are due to an inaccurate interpretation, hence representation, of the problem. This can happen because of sloppiness (a quick shallow reading of the problemand/or weak monitoring of their efforts made to come to a solution). In this case error feedback should help people to reconsider the problem features, note the inadequacy of their first answer, and find the correct solution. If, however, people are truly fixated on their incorrect representation, being told the answer is wrong does not help. In a study made by P.I. Dallop and R.L. Dominowski in 1992 these two possibilities were contrasted. In approximately one third of the cases error feedback led to right answers, so only approximately one third of the wrong answers were due to inadequate monitoring. [6] Another approach is the study of examples with and without a preceding analogous task. In cases such like the water-jug task analogous thinking indeed leads to a correct solution, but to take a different way might make the case much simpler:

Imagine Knut again, this time he is given three jugs with different capacities and is asked to measure the required amount of water. Of course he is not allowed to use anything despite the jugs and as much water as he likes. In the first case the sizes are 127 litres, 21 litres and 3 litres while 100 litres are desired. In the second case Knut is asked to measure 18 litres from jugs of 39, 15 and three litres size.

In fact participants faced with the 100 litre task first choose a complicate way in order tosolve the second one. Others on the contrary who did not know about that complex task solved the 18 litre case by just adding three litres to 15.

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 non-industrialized cultures (German & Barrett, 2005).

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?)

Thinking and Intelligence

Solving problems, learning objectives.

• Describe problem solving strategies, including algorithms and heuristics

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

Problem-Solving Strategies

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

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

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

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

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

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

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

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

Everyday Connections: Solving Puzzles

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

Figure 1 . 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 that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Figure 2 . Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

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

Figure 3 . The puzzle reads, “Since the scales now balance…and balance when arranged this way, then how many marbles will it require to balance with that top?

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

• Modification and adaptation. Provided by : Lumen Learning. License : CC BY: Attribution
• Problem-Solving. Authored by : OpenStax College. Located at : https://openstax.org/books/psychology-2e/pages/7-3-problem-solving . License : CC BY: Attribution . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction
• Can you solve Einsteinu2019s Riddle? . Authored by : Dan Van der Vieren. Provided by : Ted-Ed. Located at : https://www.youtube.com/watch?v=1rDVz_Fb6HQ&index=3&list=PLUmyCeox8XCwB8FrEfDQtQZmCc2qYMS5a . License : Other . License Terms : Standard YouTube License

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

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

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

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

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

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

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

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

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

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

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

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

• Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
• Analogy – is using a solution that solves a similar problem.
• Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
• Divide and conquer – breaking down large complex problems into smaller more manageable problems.
• Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
• Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
• Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
• Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
• Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
• Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
• Reduction – adapting the problem to be as similar problems where a solution exists.
• Research – using existing knowledge or solutions to similar problems to solve the problem.
• Root cause analysis – trying to identify the cause of the problem.

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

• 1. Only one disk can be moved at a time.
• 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
• 3. No disc may be placed on top of a smaller disk.

  Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage  (1990) suggesting that while collecting data for what would later be his book  The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as  insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground.  Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

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 (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

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

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

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

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

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

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

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

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

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

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

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

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

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

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

a. an algorithm

b. a heuristic

c. a mental set

d. trial and error

2. Solving the Tower of Hanoi problem tends to utilize a  ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

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

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

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

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

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

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

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

Personal Application Question:

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

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm:  problem-solving strategy characterized by a specific set of instructions

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

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

confirmation bias:  faulty heuristic in which you focus on information that confirms your beliefs

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

heuristic:  mental shortcut that saves time when solving a problem

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

mental set:  continually using an old solution to a problem without results

problem-solving strategy:  method for solving problems

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

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

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

Share This Book

• Increase Font Size

Please log in to save materials. Log in

• Anchoring Bias
• Availability Heuristic
• Confirmation Bias
• Functional Fixedness
• Hindsight Bias
• Problem-solving Strategy
• Representative Bias
• Trial and Error
• Working Backwards

Problem Solving

• 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 ( Table ). 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.

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 ) 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 ) 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 ). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

PITFALLS TO PROBLEM SOLVING

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

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

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

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

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

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

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

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 Figure ? You need nine. Were you able to solve the problems in Figure and Figure ? Here are the answers ( Figure ).

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

Review Questions

A specific formula for solving a problem is called ________.

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

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

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

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

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

Critical Thinking Questions

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

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

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

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

Personal Application Question

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

Self-Esteem

It’s ok you can’t solve every problem, trying to “fix" everything can leave you feeling like a failure..

Updated May 10, 2024 | Reviewed by Ray Parker

• What Is Self-Esteem?
• Find counselling near me
• Your intrinsic value is more than what you can do for other people.

You are still worthwhile and can be successful, even if you don’t have all the solutions.

• Consider which decision will make you feel you’ve stayed true to your values.

In coaching others, I often discuss problem-solving strategies to help individuals think creatively and consider many options when they are faced with challenging situations.

Problem solving 1-2 includes the following:

• Define the problem, identify obstacles, and set realistic goals .
• Generate a variety of alternative solutions to overcome obstacles identified.
• Choose which idea has the highest likelihood to achieve the goal.
• Try out the solution in real-life and see if it worked or not.

Problem-solving strategies can be helpful in many situations. Thinking creatively and testing out different potential solutions can help you come up with alternative ways of solving your problems.

While many problems can be solved, there are also situations in which there is no “perfect” solution or in which what seems to be the best solution still leaves you feeling unsatisfied or like you’re not doing enough.

I encourage you to increase your comfort around the following three truths:

1. You can’t always solve everyone else’s problems.

2. You can’t always solve all of your own problems.

3. You are not a failure if you can’t solve every problem.

You can’t always solve everyone else’s problems.

When someone around you needs help, do you feel compelled to find solutions to their problem?

Are you seen as the problem solver at your job or in your close relationships?

Does it feel uncomfortable for you to listen to someone tell you about a problem and not offer solutions?

There are times when others come to you because they know you can help them solve a problem. There are also times when the other person is coming to you not for a solution to their problem, but for support, empathy, and a listening ear.

Your relationships may be negatively impacted if others feel that you don’t fully listen and only try to “fix” everything for them. While this may feel like a noble act, it may lead the other person to feel like they have failed or that you think they are unable to solve their own problems.

Consider approaching such situations with curiosity by saying to the other person:

• As you share this information with me, tell me how I can best support you.
• What would be most helpful right now? Are you looking for an empathetic ear or want to brainstorm potential next steps?
• I want to be sure I am as helpful as I can be right now; what are you hoping to get out of our conversation?

You can’t always solve all of your own problems.

We are taught from a young age that problems have a solution. For example, while solving word problems in math class may not have been your favorite thing to do, you knew there was ultimately a “right” answer. Many times, the real world is much more complex, and many of the problems that you face do not have clear or “right” answers.

You may often be faced with finding solutions that do the most good for the most amount of people, but you know that others may still be left out or feel unsatisfied with the result.

Your beliefs about yourself, other people, and the world can sometimes help you make decisions in such circumstances. You may ask for help from others. Some may consider their faith or spirituality for guidance. While others may consider philosophical theories.

Knowing that there often isn’t a “perfect” solution, you may consider asking yourself some of the following questions:

• What’s the healthiest decision I can make? The healthiest decision for yourself and for those who will be impacted.
• Imagine yourself 10 years in the future, looking back on the situation: What do you think the future-you would encourage you to do?
• What would a wise person do?
• What decision will allow you to feel like you’ve stayed true to your values?

You are not a failure if you can’t solve all of the problems.

If you have internalized feeling like you need to be able to solve every problem that comes across your path, you may feel like a failure each time you don’t.

It’s impossible to solve every problem.

Your intrinsic value is more than what you can do for other people. You have value because you are you.

Consider creating more realistic and adaptive thoughts around your ability to help others and solve problems.

Some examples include:

• I am capable, even without solving all of the problems.
• I am worthwhile, even if I’m not perfect.
• What I do for others does not define my worth.
• In living my values, I know I’ve done my best.

I hope you utilize the information above to consider how you can coach yourself the next time you:

• Start to solve someone else’s problem without being asked.
• Feel stuck in deciding the best next steps.
• Judge yourself negatively.

1. D'zurilla, T. J., & Goldfried, M. R. (1971). Problem solving and behavior modification. Journal of abnormal psychology, 78(1), 107.

2. D’Zurilla, T. J., & Nezu, A. M. (2010). Problem-solving therapy. Handbook of cognitive-behavioral therapies, 3(1), 197-225.

Julie Radico, Psy.D. ABPP, is a board-certified clinical psychologist and coauthor of You Will Get Through This: A Mental Health First-Aid Kit.

• Find a Therapist
• Find a Treatment Center
• Find a Psychiatrist
• Find a Support Group
• Find Online Therapy
• International
• New Zealand
• South Africa
• Switzerland
• Asperger's
• Bipolar Disorder
• Chronic Pain
• Eating Disorders
• Passive Aggression
• Personality
• Goal Setting
• Positive Psychology
• Stopping Smoking
• Low Sexual Desire
• Relationships
• Child Development
• Self Tests NEW
• Therapy Center
• Diagnosis Dictionary
• Types of Therapy

At any moment, someone’s aggravating behavior or our own bad luck can set us off on an emotional spiral that threatens to derail our entire day. Here’s how we can face our triggers with less reactivity so that we can get on with our lives.

• Emotional Intelligence
• Gaslighting
• Affective Forecasting
• Neuroscience

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 ).

As an Amazon Associate we earn from qualifying purchases.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

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

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

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

© Jan 6, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.