problem solving theory psychology

• 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

Problem-Solving Strategies and Obstacles

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

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

JGI / Jamie Grill / Getty Images

• Application
• Improvement

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

What Is Problem-Solving?

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

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

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

The problem-solving process involves:

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

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

Problem-Solving Mental Processes

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

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

Problem-Solving Strategies

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

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

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

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

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

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

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

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

Trial and Error

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

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

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

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

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

How to Apply Problem-Solving Strategies in Real Life

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

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

Obstacles to Problem-Solving

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

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

How to Improve Your Problem-Solving Skills

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

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

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

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

Dunbar K. Problem solving . A Companion to Cognitive Science . 2017. doi:10.1002/9781405164535.ch20

Stewart SL, Celebre A, Hirdes JP, Poss JW. Risk of suicide and self-harm in kids: The development of an algorithm to identify high-risk individuals within the children's mental health system . Child Psychiat Human Develop . 2020;51:913-924. doi:10.1007/s10578-020-00968-9

Rosenbusch H, Soldner F, Evans AM, Zeelenberg M. Supervised machine learning methods in psychology: A practical introduction with annotated R code . Soc Personal Psychol Compass . 2021;15(2):e12579. doi:10.1111/spc3.12579

Mishra S. Decision-making under risk: Integrating perspectives from biology, economics, and psychology . Personal Soc Psychol Rev . 2014;18(3):280-307. doi:10.1177/1088868314530517

Csikszentmihalyi M, Sawyer K. Creative insight: The social dimension of a solitary moment . In: The Systems Model of Creativity . 2015:73-98. doi:10.1007/978-94-017-9085-7_7

Chrysikou EG, Motyka K, Nigro C, Yang SI, Thompson-Schill SL. Functional fixedness in creative thinking tasks depends on stimulus modality .  Psychol Aesthet Creat Arts . 2016;10(4):425‐435. doi:10.1037/aca0000050

Huang F, Tang S, Hu Z. Unconditional perseveration of the short-term mental set in chunk decomposition .  Front Psychol . 2018;9:2568. doi:10.3389/fpsyg.2018.02568

National Alliance on Mental Illness. Warning signs and symptoms .

Mayer RE. Thinking, problem solving, cognition, 2nd ed .

Schooler JW, Ohlsson S, Brooks K. Thoughts beyond words: When language overshadows insight. J Experiment Psychol: General . 1993;122:166-183. doi:10.1037/0096-3445.2.166

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

• Subject List
• Take a Tour
• For Authors
• Subscriber Services
• Publications
• African American Studies
• African Studies
• American Literature
• Anthropology
• Architecture Planning and Preservation
• Art History
• Atlantic History
• Biblical Studies
• British and Irish Literature
• Childhood Studies
• Chinese Studies
• Cinema and Media Studies
• Communication
• Criminology
• Environmental Science
• Evolutionary Biology
• International Law
• International Relations
• Islamic Studies
• Jewish Studies
• Latin American Studies
• Latino Studies
• Linguistics
• Literary and Critical Theory
• Medieval Studies
• Military History
• Political Science
• Public Health
• Renaissance and Reformation
• Social Work
• Urban Studies
• Victorian Literature
• Browse All Subjects

How to Subscribe

• Free Trials

In This Article Expand or collapse the "in this article" section Problem Solving and Decision Making

Introduction.

• General Approaches to Problem Solving
• Representational Accounts
• Problem Space and Search
• Working Memory and Problem Solving
• Domain-Specific Problem Solving
• The Rational Approach
• Prospect Theory
• Dual-Process Theory
• Cognitive Heuristics and Biases

Related Articles Expand or collapse the "related articles" section about

About related articles close popup.

Lorem Ipsum Sit Dolor Amet

Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Aliquam ligula odio, euismod ut aliquam et, vestibulum nec risus. Nulla viverra, arcu et iaculis consequat, justo diam ornare tellus, semper ultrices tellus nunc eu tellus.

• Artificial Intelligence, Machine Learning, and Psychology
• Counterfactual Reasoning
• Critical Thinking
• Heuristics and Biases
• Protocol Analysis
• Psychology and Law

Other Subject Areas

Forthcoming articles expand or collapse the "forthcoming articles" section.

• Data Visualization
• Remote Work
• Workforce Training Evaluation
• Find more forthcoming articles...
• Export Citations
• Share This Facebook LinkedIn Twitter

Problem Solving and Decision Making by Emily G. Nielsen , John Paul Minda LAST REVIEWED: 26 June 2019 LAST MODIFIED: 26 June 2019 DOI: 10.1093/obo/9780199828340-0246

Problem solving and decision making are both examples of complex, higher-order thinking. Both involve the assessment of the environment, the involvement of working memory or short-term memory, reliance on long term memory, effects of knowledge, and the application of heuristics to complete a behavior. A problem can be defined as an impasse or gap between a current state and a desired goal state. Problem solving is the set of cognitive operations that a person engages in to change the current state, to go beyond the impasse, and achieve a desired outcome. Problem solving involves the mental representation of the problem state and the manipulation of this representation in order to move closer to the goal. Problems can vary in complexity, abstraction, and how well defined (or not) the initial state and the goal state are. Research has generally approached problem solving by examining the behaviors and cognitive processes involved, and some work has examined problem solving using computational processes as well. Decision making is the process of selecting and choosing one action or behavior out of several alternatives. Like problem solving, decision making involves the coordination of memories and executive resources. Research on decision making has paid particular attention to the cognitive biases that account for suboptimal decisions and decisions that deviate from rationality. The current bibliography first outlines some general resources on the psychology of problem solving and decision making before examining each of these topics in detail. Specifically, this review covers cognitive, neuroscientific, and computational approaches to problem solving, as well as decision making models and cognitive heuristics and biases.

General Overviews

Current research in the area of problem solving and decision making is published in both general and specialized scientific journals. Theoretical and scholarly work is often summarized and developed in full-length books and chapter. These may focus on the subfields of problem solving and decision making or the larger field of thinking and higher-order cognition.

back to top

Users without a subscription are not able to see the full content on this page. Please subscribe or login .

Oxford Bibliographies Online is available by subscription and perpetual access to institutions. For more information or to contact an Oxford Sales Representative click here .

• About Psychology »
• Meet the Editorial Board »
• Abnormal Psychology
• Academic Assessment
• Acculturation and Health
• Action Regulation Theory
• Action Research
• Addictive Behavior
• Adolescence
• Adoption, Social, Psychological, and Evolutionary Perspect...
• Advanced Theory of Mind
• Affective Forecasting
• Affirmative Action
• Ageism at Work
• Allport, Gordon
• Alzheimer’s Disease
• Ambulatory Assessment in Behavioral Science
• Analysis of Covariance (ANCOVA)
• Animal Behavior
• Animal Learning
• Anxiety Disorders
• Art and Aesthetics, Psychology of
• Assessment and Clinical Applications of Individual Differe...
• Attachment in Social and Emotional Development across the ...
• Attention-Deficit/Hyperactivity Disorder (ADHD) in Adults
• Attention-Deficit/Hyperactivity Disorder (ADHD) in Childre...
• Attitudinal Ambivalence
• Attraction in Close Relationships
• Attribution Theory
• Authoritarian Personality
• Bayesian Statistical Methods in Psychology
• Behavior Therapy, Rational Emotive
• Behavioral Economics
• Behavioral Genetics
• Belief Perseverance
• Bereavement and Grief
• Biological Psychology
• Birth Order
• Body Image in Men and Women
• Bystander Effect
• Categorical Data Analysis in Psychology
• Childhood and Adolescence, Peer Victimization and Bullying...
• Clark, Mamie Phipps
• Clinical Neuropsychology
• Clinical Psychology
• Cognitive Consistency Theories
• Cognitive Dissonance Theory
• Cognitive Neuroscience
• Communication, Nonverbal Cues and
• Comparative Psychology
• Competence to Stand Trial: Restoration Services
• Competency to Stand Trial
• Computational Psychology
• Conflict Management in the Workplace
• Conformity, Compliance, and Obedience
• Consciousness
• Coping Processes
• Correspondence Analysis in Psychology
• Counseling Psychology
• Creativity at Work
• Cross-Cultural Psychology
• Cultural Psychology
• Daily Life, Research Methods for Studying
• Data Science Methods for Psychology
• Data Sharing in Psychology
• Death and Dying
• Deceiving and Detecting Deceit
• Defensive Processes
• Depressive Disorders
• Development, Prenatal
• Developmental Psychology (Cognitive)
• Developmental Psychology (Social)
• Diagnostic and Statistical Manual of Mental Disorders (DSM...
• Discrimination
• Dissociative Disorders
• Drugs and Behavior
• Eating Disorders
• Ecological Psychology
• Educational Settings, Assessment of Thinking in
• Effect Size
• Embodiment and Embodied Cognition
• Emerging Adulthood
• Emotional Intelligence
• Empathy and Altruism
• Employee Stress and Well-Being
• Environmental Neuroscience and Environmental Psychology
• Ethics in Psychological Practice
• Event Perception
• Evolutionary Psychology
• Expansive Posture
• Experimental Existential Psychology
• Exploratory Data Analysis
• Eyewitness Testimony
• Eysenck, Hans
• Factor Analysis
• Festinger, Leon
• Five-Factor Model of Personality
• Flynn Effect, The
• Forensic Psychology
• Forgiveness
• Friendships, Children's
• Fundamental Attribution Error/Correspondence Bias
• Gambler's Fallacy
• Game Theory and Psychology
• Geropsychology, Clinical
• Global Mental Health
• Habit Formation and Behavior Change
• Health Psychology
• Health Psychology Research and Practice, Measurement in
• Heider, Fritz
• History of Psychology
• Human Factors
• Humanistic Psychology
• Implicit Association Test (IAT)
• Industrial and Organizational Psychology
• Inferential Statistics in Psychology
• Insanity Defense, The
• Intelligence
• Intelligence, Crystallized and Fluid
• Intercultural Psychology
• Intergroup Conflict
• International Classification of Diseases and Related Healt...
• International Psychology
• Interviewing in Forensic Settings
• Intimate Partner Violence, Psychological Perspectives on
• Introversion–Extraversion
• Item Response Theory
• Law, Psychology and
• Lazarus, Richard
• Learned Helplessness
• Learning Theory
• Learning versus Performance
• LGBTQ+ Romantic Relationships
• Lie Detection in a Forensic Context
• Life-Span Development
• Locus of Control
• Loneliness and Health
• Mathematical Psychology
• Meaning in Life
• Mechanisms and Processes of Peer Contagion
• Media Violence, Psychological Perspectives on
• Mediation Analysis
• Memories, Autobiographical
• Memories, Flashbulb
• Memories, Repressed and Recovered
• Memory, False
• Memory, Human
• Memory, Implicit versus Explicit
• Memory in Educational Settings
• Memory, Semantic
• Meta-Analysis
• Metacognition
• Metaphor, Psychological Perspectives on
• Microaggressions
• Military Psychology
• Mindfulness
• Mindfulness and Education
• Minnesota Multiphasic Personality Inventory (MMPI)
• Money, Psychology of
• Moral Conviction
• Moral Development
• Moral Psychology
• Moral Reasoning
• Nature versus Nurture Debate in Psychology
• Neuroscience of Associative Learning
• Nonergodicity in Psychology and Neuroscience
• Nonparametric Statistical Analysis in Psychology
• Observational (Non-Randomized) Studies
• Obsessive-Complusive Disorder (OCD)
• Occupational Health Psychology
• Olfaction, Human
• Operant Conditioning
• Optimism and Pessimism
• Organizational Justice
• Parenting Stress
• Parenting Styles
• Parents' Beliefs about Children
• Path Models
• Peace Psychology
• Perception, Person
• Performance Appraisal
• Personality and Health
• Personality Disorders
• Personality Psychology
• Person-Centered and Experiential Psychotherapies: From Car...
• Phenomenological Psychology
• Placebo Effects in Psychology
• Play Behavior
• Positive Psychological Capital (PsyCap)
• Positive Psychology
• Posttraumatic Stress Disorder (PTSD)
• Prejudice and Stereotyping
• Pretrial Publicity
• Prisoner's Dilemma
• Problem Solving and Decision Making
• Procrastination
• Prosocial Behavior
• Prosocial Spending and Well-Being
• Psycholinguistics
• Psychological Literacy
• Psychological Perspectives on Food and Eating
• Psychology, Political
• Psychoneuroimmunology
• Psychophysics, Visual
• Psychotherapy
• Psychotic Disorders
• Publication Bias in Psychology
• Reasoning, Counterfactual
• Rehabilitation Psychology
• Relationships
• Reliability–Contemporary Psychometric Conceptions
• Religion, Psychology and
• Replication Initiatives in Psychology
• Research Methods
• Risk Taking
• Role of the Expert Witness in Forensic Psychology, The
• Sample Size Planning for Statistical Power and Accurate Es...
• Schizophrenic Disorders
• School Psychology
• School Psychology, Counseling Services in
• Self, Gender and
• Self, Psychology of the
• Self-Construal
• Self-Control
• Self-Deception
• Self-Determination Theory
• Self-Efficacy
• Self-Esteem
• Self-Monitoring
• Self-Regulation in Educational Settings
• Self-Report Tests, Measures, and Inventories in Clinical P...
• Sensation Seeking
• Sex and Gender
• Sexual Minority Parenting
• Sexual Orientation
• Signal Detection Theory and its Applications
• Simpson's Paradox in Psychology
• Single People
• Single-Case Experimental Designs
• Skinner, B.F.
• Sleep and Dreaming
• Small Groups
• Social Class and Social Status
• Social Cognition
• Social Neuroscience
• Social Support
• Social Touch and Massage Therapy Research
• Somatoform Disorders
• Spatial Attention
• Sports Psychology
• Stanford Prison Experiment (SPE): Icon and Controversy
• Stereotype Threat
• Stereotypes
• Stress and Coping, Psychology of
• Student Success in College
• Subjective Wellbeing Homeostasis
• Taste, Psychological Perspectives on
• Teaching of Psychology
• Terror Management Theory
• Testing and Assessment
• The Concept of Validity in Psychological Assessment
• The Neuroscience of Emotion Regulation
• The Reasoned Action Approach and the Theories of Reasoned ...
• The Weapon Focus Effect in Eyewitness Memory
• Theory of Mind
• Therapy, Cognitive-Behavioral
• Thinking Skills in Educational Settings
• Time Perception
• Trait Perspective
• Trauma Psychology
• Twin Studies
• Type A Behavior Pattern (Coronary Prone Personality)
• Unconscious Processes
• Video Games and Violent Content
• Virtues and Character Strengths
• Women and Science, Technology, Engineering, and Math (STEM...
• Women, Psychology of
• Work Well-Being
• Wundt, Wilhelm
• Privacy Policy
• Cookie Policy
• Legal Notice
• Accessibility

Powered by:

• [66.249.64.20|109.248.223.228]
• 109.248.223.228

Cognitive Psychology

• Precursors to Cognitive Psychology
• Emergence of Cognitive Psychology
• Research Methods
• Brain and Cognition: Neurons
• Brain and Cognition: Brain Structure
• Introduction to perception
• Top-down and bottom-up theories of perception
• Problem Solving
• Problem solving and insight
• Problem solving in animals
• Welcome page
• What is a Wiki Site?
• How to edit pages?
• How to join this site?
• Site members
• Recent changes
• List all pages
• Site Manager

It seems you have no tags attached to pages. To attach a tag simply click on the tags button at the bottom of any page.

Add a new page

edit this panel

What is problem solving?

A problem arises when we need to overcome some obstacle in order to get from our current state to a desired state. Problem solving is the process that an organism implements in order to try to get from the current state to the desired state.

An historical review of approaches to problem solving

The behaviourist approach.

Behaviourist researchers argued that problem solving was a reproductive process; that is, organisms faced with a problem applied behaviour that had been successful on a previous occasion. Successful behaviour was itself believed to have been arrived at through a process of trial-and-error. In 1911 Edward Thorndike had developed his law of effect after observing cats discover how to escape from the cage into which he had placed them. This greatly influenced the behaviourist view of problem solving:

The Gestalt approach

By contrast, Gestalt psychologists argued that problem solving was a productive process. In particular, in the process of thinking about a problem individuals sometimes "restructured" their representation of the problem, leading to a flash of insight that enabled them to reach a solution. In The Mentality of Apes (1915) Wolfgang Köhler described a series of studies with apes in which the animals appeared to demonstrate insight in problem solving situations. A description of these studies, with photographs, can be found here .

The Gestalt psychologists described several aspects of thought that acted as barriers to successful problem solving. One of these was called the Einstellung effect , now more commonly referred to as mental set or entrenchment . This occurs when a problem solver becomes fixated on applying a strategy that has previously worked, but is less helpful for the current problem. Luchins (1942) reported a study in which people had to use three jugs of differing capacity (measured in cups) to measure out a required amount of water (given by the experimenter). Some people were given a series of "practice" trials prior to attempting the critical problems. These practice problems could be solved by filling Jug B, then tipping water from Jug B into Jug A until it is filled, and then twice using the remainging contents of Jug A to fill Jug C. Expressed as a formula, this is B - A - 2C. However, although this formula could be applied to the subsequent "critical" problems, these also had simpler solutions, such as A - C. People who had experienced the practice problems mostly tried to apply the more complex solution to these later problems, unlike people who had not experienced the earlier problems (who mostly found the simpler solutions).

Another barrier to problem solving is functional fixedness , whereby individuals fail to recognize that objects can be used for a purpose other than that they were designed for. Maier (1930) illustrated this with his two string problem .

For a real life example of overcoming fuctional fixedness, see: Overcoming functional fixedness: Apollo 13

Questions : What do you think of Köhler's claim that his apes had demonstrated insight? What proportion of Maier's participants spontaneously found the solution before getting any kind of hint? What did Maier do that led some people to get the correct solution? (these questions require some research)

The cognitive approach to problem solving

Problem space theory.

In 1972, Allen Newell and Herbert Simon published the book Human Problem Solving , in which they outlined their problem space theory of problem solving. In this theory, people solve problems by searching in a problem space . The problem space consists of the initial (current) state, the goal state, and all possible states in between. The actions that people take in order to move from one state to another are known as operators . Consider the eight puzzle . The problem space for the eight puzzle consists of the initial arrangement of tiles, the desired arrangement of tiles (normally 1, 2, 3….8), and all the possible arrangements that can be arrived at in between. However, problem spaces can be very large so the key issue is how people navigate their way through the possibilities, given their limited working memory capacities. In other words, how do they choose operators? For many problems we possess domain knowledge that helps us decide what to do. But for novel problems Newell and Simon proposed that operator selection is guided by cognitive short-cuts, known as heuristics . The simplest heuristic is repeat-state avoidance or backup avoidance 1 , whereby individuals prefer not to take an action that would take them back to a previous problem state. This is unhelpful when a person has taken an inappropriate action and actually needs to go back a step or more.

Another heuristic is difference reduction , or hill-climbing , whereby people take the action that leads to the biggest similarity between current state and goal state. Before reading further, see if you can solve the following problem:

In the hobbits and orcs problem the task instructions are as follows:

On one side of a river are three hobbits and three orcs. They have a boat on their side that is capable of carrying two creatures at a time across the river. The goal is to transport all six creatures across to the other side of the river. At no point on either side of the river can orcs outnumber hobbits (or the orcs would eat the outnumbered hobbits). The problem, then, is to find a method of transporting all six creatures across the river without the hobbits ever being outnumbered.

The solution to this problem, together with an explanation of how difference reduction is often applied, can be found by clicking here .

A more sophisticated heuristic is means-ends analysis . Like difference reduction, the means-ends analysis heuristic looks for the action that will lead to the greatest reduction in difference between the current state and goal state, but also specifies what to do if that action cannot be taken. Means-ends analysis can be specified as follows 2 :

• Compare the current state with the goal state. If there is no difference between them, the problem is solved.
• If there is a difference between the current state and the goal state, set a goal to solve that difference. If there is more than one difference, set a goal to solve the largest difference.
• Select an operator that will solve the difference identified in Step 2.
• If the operator can be applied, apply it. If it cannot, set a new goal to reach a state that would allow the application of the operator.
• Return to Step 1 with the new goal set in Step 4.

The application of means-ends analysis can be illustrated with the Tower of Hanoi problem .

In 1957 Newell and Simon developed the General Problem Solver , a computer program that used means-ends analysis to find solutions to a range of well-defined problems - problems that have clear paths (if not easy ones) to a goal state. In their 1972 book on problem solving they reported the verbal protocols of participants engaged in problem solving, which showed a close match between the steps that they took and those taken by the General Problem Solver.

Acquiring operators

There are three ways in which operators can be acquired:

• Trial-and-error. As noted above, this formed the basis of the behaviourist account of problem solving.
• Direct instruction.
• Analogies. Analogies are examples from one domain (the source), whose elements can be used to aid problem solving in another domain (the target). However, novices often struggle to spot analogies, as described here .

Next: Problem solving and insight

• Search Menu
• Browse content in Arts and Humanities
• Browse content in Archaeology
• Anglo-Saxon and Medieval Archaeology
• Archaeological Methodology and Techniques
• Archaeology by Region
• Archaeology of Religion
• Archaeology of Trade and Exchange
• Biblical Archaeology
• Contemporary and Public Archaeology
• Environmental Archaeology
• Historical Archaeology
• History and Theory of Archaeology
• Industrial Archaeology
• Landscape Archaeology
• Mortuary Archaeology
• Prehistoric Archaeology
• Underwater Archaeology
• Urban Archaeology
• Zooarchaeology
• Browse content in Architecture
• Architectural Structure and Design
• History of Architecture
• Residential and Domestic Buildings
• Theory of Architecture
• Browse content in Art
• Art Subjects and Themes
• History of Art
• Industrial and Commercial Art
• Theory of Art
• Biographical Studies
• Byzantine Studies
• Browse content in Classical Studies
• Classical History
• Classical Philosophy
• Classical Mythology
• Classical Literature
• Classical Reception
• Classical Art and Architecture
• Classical Oratory and Rhetoric
• Greek and Roman Epigraphy
• Greek and Roman Law
• Greek and Roman Papyrology
• Greek and Roman Archaeology
• Late Antiquity
• Religion in the Ancient World
• Digital Humanities
• Browse content in History
• Colonialism and Imperialism
• Diplomatic History
• Environmental History
• Genealogy, Heraldry, Names, and Honours
• Genocide and Ethnic Cleansing
• Historical Geography
• History by Period
• History of Emotions
• History of Agriculture
• History of Education
• History of Gender and Sexuality
• Industrial History
• Intellectual History
• International History
• Labour History
• Legal and Constitutional History
• Local and Family History
• Maritime History
• Military History
• National Liberation and Post-Colonialism
• Oral History
• Political History
• Public History
• Regional and National History
• Revolutions and Rebellions
• Slavery and Abolition of Slavery
• Social and Cultural History
• Theory, Methods, and Historiography
• Urban History
• World History
• Browse content in Language Teaching and Learning
• Language Learning (Specific Skills)
• Language Teaching Theory and Methods
• Browse content in Linguistics
• Applied Linguistics
• Cognitive Linguistics
• Computational Linguistics
• Forensic Linguistics
• Grammar, Syntax and Morphology
• Historical and Diachronic Linguistics
• History of English
• Language Acquisition
• Language Evolution
• Language Reference
• Language Variation
• Language Families
• Lexicography
• Linguistic Anthropology
• Linguistic Theories
• Linguistic Typology
• Phonetics and Phonology
• Psycholinguistics
• Sociolinguistics
• Translation and Interpretation
• Writing Systems
• Browse content in Literature
• Bibliography
• Children's Literature Studies
• Literary Studies (Asian)
• Literary Studies (European)
• Literary Studies (Eco-criticism)
• Literary Studies (Romanticism)
• Literary Studies (American)
• Literary Studies (Modernism)
• Literary Studies - World
• Literary Studies (1500 to 1800)
• Literary Studies (19th Century)
• Literary Studies (20th Century onwards)
• Literary Studies (African American Literature)
• Literary Studies (British and Irish)
• Literary Studies (Early and Medieval)
• Literary Studies (Fiction, Novelists, and Prose Writers)
• Literary Studies (Gender Studies)
• Literary Studies (Graphic Novels)
• Literary Studies (History of the Book)
• Literary Studies (Plays and Playwrights)
• Literary Studies (Poetry and Poets)
• Literary Studies (Postcolonial Literature)
• Literary Studies (Queer Studies)
• Literary Studies (Science Fiction)
• Literary Studies (Travel Literature)
• Literary Studies (War Literature)
• Literary Studies (Women's Writing)
• Literary Theory and Cultural Studies
• Mythology and Folklore
• Shakespeare Studies and Criticism
• Browse content in Media Studies
• Browse content in Music
• Applied Music
• Dance and Music
• Ethics in Music
• Ethnomusicology
• Gender and Sexuality in Music
• Medicine and Music
• Music Cultures
• Music and Religion
• Music and Media
• Music and Culture
• Music Education and Pedagogy
• Music Theory and Analysis
• Musical Scores, Lyrics, and Libretti
• Musical Structures, Styles, and Techniques
• Musicology and Music History
• Performance Practice and Studies
• Race and Ethnicity in Music
• Sound Studies
• Browse content in Performing Arts
• Browse content in Philosophy
• Aesthetics and Philosophy of Art
• Epistemology
• Feminist Philosophy
• History of Western Philosophy
• Metaphysics
• Moral Philosophy
• Non-Western Philosophy
• Philosophy of Science
• Philosophy of Language
• Philosophy of Mind
• Philosophy of Perception
• Philosophy of Action
• Philosophy of Law
• Philosophy of Religion
• Philosophy of Mathematics and Logic
• Practical Ethics
• Social and Political Philosophy
• Browse content in Religion
• Biblical Studies
• Christianity
• East Asian Religions
• History of Religion
• Judaism and Jewish Studies
• Qumran Studies
• Religion and Education
• Religion and Health
• Religion and Politics
• Religion and Science
• Religion and Law
• Religion and Art, Literature, and Music
• Religious Studies
• Browse content in Society and Culture
• Cookery, Food, and Drink
• Cultural Studies
• Customs and Traditions
• Ethical Issues and Debates
• Hobbies, Games, Arts and Crafts
• Lifestyle, Home, and Garden
• Natural world, Country Life, and Pets
• Popular Beliefs and Controversial Knowledge
• Sports and Outdoor Recreation
• Technology and Society
• Travel and Holiday
• Visual Culture
• Browse content in Law
• Arbitration
• Browse content in Company and Commercial Law
• Commercial Law
• Company Law
• Browse content in Comparative Law
• Systems of Law
• Competition Law
• Browse content in Constitutional and Administrative Law
• Government Powers
• Judicial Review
• Local Government Law
• Military and Defence Law
• Parliamentary and Legislative Practice
• Construction Law
• Contract Law
• Browse content in Criminal Law
• Criminal Procedure
• Criminal Evidence Law
• Sentencing and Punishment
• Employment and Labour Law
• Environment and Energy Law
• Browse content in Financial Law
• Banking Law
• Insolvency Law
• History of Law
• Human Rights and Immigration
• Intellectual Property Law
• Browse content in International Law
• Private International Law and Conflict of Laws
• Public International Law
• IT and Communications Law
• Jurisprudence and Philosophy of Law
• Law and Politics
• Law and Society
• Browse content in Legal System and Practice
• Courts and Procedure
• Legal Skills and Practice
• Primary Sources of Law
• Regulation of Legal Profession
• Medical and Healthcare Law
• Browse content in Policing
• Criminal Investigation and Detection
• Police and Security Services
• Police Procedure and Law
• Police Regional Planning
• Browse content in Property Law
• Personal Property Law
• Study and Revision
• Terrorism and National Security Law
• Browse content in Trusts Law
• Wills and Probate or Succession
• Browse content in Medicine and Health
• Browse content in Allied Health Professions
• Arts Therapies
• Clinical Science
• Dietetics and Nutrition
• Occupational Therapy
• Operating Department Practice
• Physiotherapy
• Radiography
• Speech and Language Therapy
• Browse content in Anaesthetics
• General Anaesthesia
• Neuroanaesthesia
• Browse content in Clinical Medicine
• Acute Medicine
• Cardiovascular Medicine
• Clinical Genetics
• Clinical Pharmacology and Therapeutics
• Dermatology
• Endocrinology and Diabetes
• Gastroenterology
• Genito-urinary Medicine
• Geriatric Medicine
• Infectious Diseases
• Medical Toxicology
• Medical Oncology
• Pain Medicine
• Palliative Medicine
• Rehabilitation Medicine
• Respiratory Medicine and Pulmonology
• Rheumatology
• Sleep Medicine
• Sports and Exercise Medicine
• Clinical Neuroscience
• Community Medical Services
• Critical Care
• Emergency Medicine
• Forensic Medicine
• Haematology
• History of Medicine
• Browse content in Medical Dentistry
• Oral and Maxillofacial Surgery
• Paediatric Dentistry
• Restorative Dentistry and Orthodontics
• Surgical Dentistry
• Browse content in Medical Skills
• Clinical Skills
• Communication Skills
• Nursing Skills
• Surgical Skills
• Medical Ethics
• Medical Statistics and Methodology
• Browse content in Neurology
• Clinical Neurophysiology
• Neuropathology
• Nursing Studies
• Browse content in Obstetrics and Gynaecology
• Gynaecology
• Occupational Medicine
• Ophthalmology
• Otolaryngology (ENT)
• Browse content in Paediatrics
• Neonatology
• Browse content in Pathology
• Chemical Pathology
• Clinical Cytogenetics and Molecular Genetics
• Histopathology
• Medical Microbiology and Virology
• Patient Education and Information
• Browse content in Pharmacology
• Psychopharmacology
• Browse content in Popular Health
• Caring for Others
• Complementary and Alternative Medicine
• Self-help and Personal Development
• Browse content in Preclinical Medicine
• Cell Biology
• Molecular Biology and Genetics
• Reproduction, Growth and Development
• Primary Care
• Professional Development in Medicine
• Browse content in Psychiatry
• Addiction Medicine
• Child and Adolescent Psychiatry
• Forensic Psychiatry
• Learning Disabilities
• Old Age Psychiatry
• Psychotherapy
• Browse content in Public Health and Epidemiology
• Epidemiology
• Public Health
• Browse content in Radiology
• Clinical Radiology
• Interventional Radiology
• Nuclear Medicine
• Radiation Oncology
• Reproductive Medicine
• Browse content in Surgery
• Cardiothoracic Surgery
• Gastro-intestinal and Colorectal Surgery
• General Surgery
• Neurosurgery
• Paediatric Surgery
• Peri-operative Care
• Plastic and Reconstructive Surgery
• Surgical Oncology
• Transplant Surgery
• Trauma and Orthopaedic Surgery
• Vascular Surgery
• Browse content in Science and Mathematics
• Browse content in Biological Sciences
• Aquatic Biology
• Biochemistry
• Bioinformatics and Computational Biology
• Developmental Biology
• Ecology and Conservation
• Evolutionary Biology
• Genetics and Genomics
• Microbiology
• Molecular and Cell Biology
• Natural History
• Plant Sciences and Forestry
• Research Methods in Life Sciences
• Structural Biology
• Systems Biology
• Zoology and Animal Sciences
• Browse content in Chemistry
• Analytical Chemistry
• Computational Chemistry
• Crystallography
• Environmental Chemistry
• Industrial Chemistry
• Inorganic Chemistry
• Materials Chemistry
• Medicinal Chemistry
• Mineralogy and Gems
• Organic Chemistry
• Physical Chemistry
• Polymer Chemistry
• Study and Communication Skills in Chemistry
• Theoretical Chemistry
• Browse content in Computer Science
• Artificial Intelligence
• Computer Architecture and Logic Design
• Game Studies
• Human-Computer Interaction
• Mathematical Theory of Computation
• Programming Languages
• Software Engineering
• Systems Analysis and Design
• Virtual Reality
• Browse content in Computing
• Business Applications
• Computer Security
• Computer Games
• Computer Networking and Communications
• Digital Lifestyle
• Graphical and Digital Media Applications
• Operating Systems
• Browse content in Earth Sciences and Geography
• Atmospheric Sciences
• Environmental Geography
• Geology and the Lithosphere
• Maps and Map-making
• Meteorology and Climatology
• Oceanography and Hydrology
• Palaeontology
• Physical Geography and Topography
• Regional Geography
• Soil Science
• Urban Geography
• Browse content in Engineering and Technology
• Agriculture and Farming
• Biological Engineering
• Civil Engineering, Surveying, and Building
• Electronics and Communications Engineering
• Energy Technology
• Engineering (General)
• Environmental Science, Engineering, and Technology
• History of Engineering and Technology
• Mechanical Engineering and Materials
• Technology of Industrial Chemistry
• Transport Technology and Trades
• Browse content in Environmental Science
• Applied Ecology (Environmental Science)
• Conservation of the Environment (Environmental Science)
• Environmental Sustainability
• Environmentalist Thought and Ideology (Environmental Science)
• Management of Land and Natural Resources (Environmental Science)
• Natural Disasters (Environmental Science)
• Nuclear Issues (Environmental Science)
• Pollution and Threats to the Environment (Environmental Science)
• Social Impact of Environmental Issues (Environmental Science)
• History of Science and Technology
• Browse content in Materials Science
• Ceramics and Glasses
• Composite Materials
• Metals, Alloying, and Corrosion
• Nanotechnology
• Browse content in Mathematics
• Applied Mathematics
• Biomathematics and Statistics
• History of Mathematics
• Mathematical Education
• Mathematical Finance
• Mathematical Analysis
• Numerical and Computational Mathematics
• Probability and Statistics
• Pure Mathematics
• Browse content in Neuroscience
• Cognition and Behavioural Neuroscience
• Development of the Nervous System
• Disorders of the Nervous System
• History of Neuroscience
• Invertebrate Neurobiology
• Molecular and Cellular Systems
• Neuroendocrinology and Autonomic Nervous System
• Neuroscientific Techniques
• Sensory and Motor Systems
• Browse content in Physics
• Astronomy and Astrophysics
• Atomic, Molecular, and Optical Physics
• Biological and Medical Physics
• Classical Mechanics
• Computational Physics
• Condensed Matter Physics
• Electromagnetism, Optics, and Acoustics
• History of Physics
• Mathematical and Statistical Physics
• Measurement Science
• Nuclear Physics
• Particles and Fields
• Plasma Physics
• Quantum Physics
• Relativity and Gravitation
• Semiconductor and Mesoscopic Physics
• Browse content in Psychology
• Affective Sciences
• Clinical Psychology
• Cognitive Psychology
• Cognitive Neuroscience
• Criminal and Forensic Psychology
• Developmental Psychology
• Educational Psychology
• Evolutionary Psychology
• Health Psychology
• History and Systems in Psychology
• Music Psychology
• Neuropsychology
• Organizational Psychology
• Psychological Assessment and Testing
• Psychology of Human-Technology Interaction
• Psychology Professional Development and Training
• Research Methods in Psychology
• Social Psychology
• Browse content in Social Sciences
• Browse content in Anthropology
• Anthropology of Religion
• Human Evolution
• Medical Anthropology
• Physical Anthropology
• Regional Anthropology
• Social and Cultural Anthropology
• Theory and Practice of Anthropology
• Browse content in Business and Management
• Business Strategy
• Business Ethics
• Business History
• Business and Government
• Business and Technology
• Business and the Environment
• Comparative Management
• Corporate Governance
• Corporate Social Responsibility
• Entrepreneurship
• Health Management
• Human Resource Management
• Industrial and Employment Relations
• Industry Studies
• Information and Communication Technologies
• International Business
• Knowledge Management
• Management and Management Techniques
• Operations Management
• Organizational Theory and Behaviour
• Pensions and Pension Management
• Public and Nonprofit Management
• Strategic Management
• Supply Chain Management
• Browse content in Criminology and Criminal Justice
• Criminal Justice
• Criminology
• Forms of Crime
• International and Comparative Criminology
• Youth Violence and Juvenile Justice
• Development Studies
• Browse content in Economics
• Agricultural, Environmental, and Natural Resource Economics
• Asian Economics
• Behavioural Finance
• Behavioural Economics and Neuroeconomics
• Econometrics and Mathematical Economics
• Economic Systems
• Economic History
• Economic Methodology
• Economic Development and Growth
• Financial Markets
• Financial Institutions and Services
• General Economics and Teaching
• Health, Education, and Welfare
• History of Economic Thought
• International Economics
• Labour and Demographic Economics
• Law and Economics
• Macroeconomics and Monetary Economics
• Microeconomics
• Public Economics
• Urban, Rural, and Regional Economics
• Welfare Economics
• Browse content in Education
• Adult Education and Continuous Learning
• Care and Counselling of Students
• Early Childhood and Elementary Education
• Educational Equipment and Technology
• Educational Strategies and Policy
• Higher and Further Education
• Organization and Management of Education
• Philosophy and Theory of Education
• Schools Studies
• Secondary Education
• Teaching of a Specific Subject
• Teaching of Specific Groups and Special Educational Needs
• Teaching Skills and Techniques
• Browse content in Environment
• Applied Ecology (Social Science)
• Climate Change
• Conservation of the Environment (Social Science)
• Environmentalist Thought and Ideology (Social Science)
• Natural Disasters (Environment)
• Social Impact of Environmental Issues (Social Science)
• Browse content in Human Geography
• Cultural Geography
• Economic Geography
• Political Geography
• Browse content in Interdisciplinary Studies
• Communication Studies
• Museums, Libraries, and Information Sciences
• Browse content in Politics
• African Politics
• Asian Politics
• Chinese Politics
• Comparative Politics
• Conflict Politics
• Elections and Electoral Studies
• Environmental Politics
• European Union
• Foreign Policy
• Gender and Politics
• Human Rights and Politics
• Indian Politics
• International Relations
• International Organization (Politics)
• International Political Economy
• Irish Politics
• Latin American Politics
• Middle Eastern Politics
• Political Methodology
• Political Communication
• Political Philosophy
• Political Sociology
• Political Behaviour
• Political Economy
• Political Institutions
• Political Theory
• Politics and Law
• Public Administration
• Public Policy
• Quantitative Political Methodology
• Regional Political Studies
• Russian Politics
• Security Studies
• State and Local Government
• UK Politics
• US Politics
• Browse content in Regional and Area Studies
• African Studies
• Asian Studies
• East Asian Studies
• Japanese Studies
• Latin American Studies
• Middle Eastern Studies
• Native American Studies
• Scottish Studies
• Browse content in Research and Information
• Research Methods
• Browse content in Social Work
• Addictions and Substance Misuse
• Adoption and Fostering
• Care of the Elderly
• Child and Adolescent Social Work
• Couple and Family Social Work
• Developmental and Physical Disabilities Social Work
• Direct Practice and Clinical Social Work
• Emergency Services
• Human Behaviour and the Social Environment
• International and Global Issues in Social Work
• Mental and Behavioural Health
• Social Justice and Human Rights
• Social Policy and Advocacy
• Social Work and Crime and Justice
• Social Work Macro Practice
• Social Work Practice Settings
• Social Work Research and Evidence-based Practice
• Welfare and Benefit Systems
• Browse content in Sociology
• Childhood Studies
• Community Development
• Comparative and Historical Sociology
• Economic Sociology
• Gender and Sexuality
• Gerontology and Ageing
• Health, Illness, and Medicine
• Marriage and the Family
• Migration Studies
• Occupations, Professions, and Work
• Organizations
• Population and Demography
• Race and Ethnicity
• Social Theory
• Social Movements and Social Change
• Social Research and Statistics
• Social Stratification, Inequality, and Mobility
• Sociology of Religion
• Sociology of Education
• Sport and Leisure
• Urban and Rural Studies
• Browse content in Warfare and Defence
• Defence Strategy, Planning, and Research
• Land Forces and Warfare
• Military Administration
• Military Life and Institutions
• Naval Forces and Warfare
• Other Warfare and Defence Issues
• Peace Studies and Conflict Resolution
• Weapons and Equipment

• < Previous chapter
• Next chapter >

21 Problem Solving

Miriam Bassok, Department of Psychology, University of Washington, Seattle, WA

Laura R. Novick, Department of Psychology and Human Development, Vanderbilt University, Nashville, TN

• Published: 21 November 2012
• Cite Icon Cite
• Permissions Icon Permissions

This chapter follows the historical development of research on problem solving. It begins with a description of two research traditions that addressed different aspects of the problem-solving process: ( 1 ) research on problem representation (the Gestalt legacy) that examined how people understand the problem at hand, and ( 2 ) research on search in a problem space (the legacy of Newell and Simon) that examined how people generate the problem's solution. It then describes some developments in the field that fueled the integration of these two lines of research: work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. Next, it presents examples of recent work on problem solving in science and mathematics that highlight the impact of visual perception and background knowledge on how people represent problems and search for problem solutions. The final section considers possible directions for future research.

People are confronted with problems on a daily basis, be it trying to extract a broken light bulb from a socket, finding a detour when the regular route is blocked, fixing dinner for unexpected guests, dealing with a medical emergency, or deciding what house to buy. Obviously, the problems people encounter differ in many ways, and their solutions require different types of knowledge and skills. Yet we have a sense that all the situations we classify as problems share a common core. Karl Duncker defined this core as follows: “A problem arises when a living creature has a goal but does not know how this goal is to be reached. Whenever one cannot go from the given situation to the desired situation simply by action [i.e., by the performance of obvious operations], then there has to be recourse to thinking” (Duncker, 1945 , p. 1). Consider the broken light bulb. The obvious operation—holding the glass part of the bulb with one's fingers while unscrewing the base from the socket—is prevented by the fact that the glass is broken. Thus, there must be “recourse to thinking” about possible ways to solve the problem. For example, one might try mounting half a potato on the broken bulb (we do not know the source of this creative solution, which is described on many “how to” Web sites).

The above definition and examples make it clear that what constitutes a problem for one person may not be a problem for another person, or for that same person at another point in time. For example, the second time one has to remove a broken light bulb from a socket, the solution likely can be retrieved from memory; there is no problem. Similarly, tying shoes may be considered a problem for 5-year-olds but not for readers of this chapter. And, of course, people may change their goal and either no longer have a problem (e.g., take the guests to a restaurant instead of fixing dinner) or attempt to solve a different problem (e.g., decide what restaurant to go to). Given the highly subjective nature of what constitutes a problem, researchers who study problem solving have often presented people with novel problems that they should be capable of solving and attempted to find regularities in the resulting problem-solving behavior. Despite the variety of possible problem situations, researchers have identified important regularities in the thinking processes by which people (a) represent , or understand, problem situations and (b) search for possible ways to get to their goal.

A problem representation is a model constructed by the solver that summarizes his or her understanding of the problem components—the initial state (e.g., a broken light bulb in a socket), the goal state (the light bulb extracted), and the set of possible operators one may apply to get from the initial state to the goal state (e.g., use pliers). According to Reitman ( 1965 ), problem components differ in the extent to which they are well defined . Some components leave little room for interpretation (e.g., the initial state in the broken light bulb example is relatively well defined), whereas other components may be ill defined and have to be defined by the solver (e.g., the possible actions one may take to extract the broken bulb). The solver's representation of the problem guides the search for a possible solution (e.g., possible attempts at extracting the light bulb). This search may, in turn, change the representation of the problem (e.g., finding that the goal cannot be achieved using pliers) and lead to a new search. Such a recursive process of representation and search continues until the problem is solved or until the solver decides to abort the goal.

Duncker ( 1945 , pp. 28–37) documented the interplay between representation and search based on his careful analysis of one person's solution to the “Radiation Problem” (later to be used extensively in research analogy, see Holyoak, Chapter 13 ). This problem requires using some rays to destroy a patient's stomach tumor without harming the patient. At sufficiently high intensity, the rays will destroy the tumor. However, at that intensity, they will also destroy the healthy tissue surrounding the tumor. At lower intensity, the rays will not harm the healthy tissue, but they also will not destroy the tumor. Duncker's analysis revealed that the solver's solution attempts were guided by three distinct problem representations. He depicted these solution attempts as an inverted search tree in which the three main branches correspond to the three general problem representations (Duncker, 1945 , p. 32). We reproduce this diagram in Figure 21.1 . The desired solution appears on the rightmost branch of the tree, within the general problem representation in which the solver aims to “lower the intensity of the rays on their way through healthy tissue.” The actual solution is to project multiple low-intensity rays at the tumor from several points around the patient “by use of lens.” The low-intensity rays will converge on the tumor, where their individual intensities will sum to a level sufficient to destroy the tumor.

A search-tree representation of one subject's solution to the radiation problem, reproduced from Duncker ( 1945 , p. 32).

Although there are inherent interactions between representation and search, some researchers focus their efforts on understanding the factors that affect how solvers represent problems, whereas others look for regularities in how they search for a solution within a particular representation. Based on their main focus of interest, researchers devise or select problems with solutions that mainly require either constructing a particular representation or finding the appropriate sequence of steps leading from the initial state to the goal state. In most cases, researchers who are interested in problem representation select problems in which one or more of the components are ill defined, whereas those who are interested in search select problems in which the components are well defined. The following examples illustrate, respectively, these two problem types.

The Bird-and-Trains problem (Posner, 1973 , pp. 150–151) is a mathematical word problem that tends to elicit two distinct problem representations (see Fig. 21.2a and b ):

Two train stations are 50 miles apart. At 2 p.m. one Saturday afternoon two trains start toward each other, one from each station. Just as the trains pull out of the stations, a bird springs into the air in front of the first train and flies ahead to the front of the second train. When the bird reaches the second train, it turns back and flies toward the first train. The bird continues to do this until the trains meet. If both trains travel at the rate of 25 miles per hour and the bird flies at 100 miles per hour, how many miles will the bird have flown before the trains meet? Fig. 21.2 Open in new tab Download slide Alternative representations of Posner's ( 1973 ) trains-and-bird problem. Adapted from Novick and Hmelo ( 1994 ).

Some solvers focus on the back-and-forth path of the bird (Fig. 21.2a ). This representation yields a problem that would be difficult for most people to solve (e.g., a series of differential equations). Other solvers focus on the paths of the trains (Fig. 21.2b ), a representation that yields a relatively easy distance-rate-time problem.

The Tower of Hanoi problem falls on the other end of the representation-search continuum. It leaves little room for differences in problem representations, and the primary work is to discover a solution path (or the best solution path) from the initial state to the goal state .

There are three pegs mounted on a base. On the leftmost peg, there are three disks of differing sizes. The disks are arranged in order of size with the largest disk on the bottom and the smallest disk on the top. The disks may be moved one at a time, but only the top disk on a peg may be moved, and at no time may a larger disk be placed on a smaller disk. The goal is to move the three-disk tower from the leftmost peg to the rightmost peg.

Figure 21.3 shows all the possible legal arrangements of disks on pegs. The arrows indicate transitions between states that result from moving a single disk, with the thicker gray arrows indicating the shortest path that connects the initial state to the goal state.

The division of labor between research on representation versus search has distinct historical antecedents and research traditions. In the next two sections, we review the main findings from these two historical traditions. Then, we describe some developments in the field that fueled the integration of these lines of research—work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. In the fifth section, we present some examples of recent work on problem solving in science and mathematics. This work highlights the role of visual perception and background knowledge in the way people represent problems and search for problem solutions. In the final section, we consider possible directions for future research.

Our review is by no means an exhaustive one. It follows the historical development of the field and highlights findings that pertain to a wide variety of problems. Research pertaining to specific types of problems (e.g., medical problems), specific processes that are involved in problem solving (e.g., analogical inferences), and developmental changes in problem solving due to learning and maturation may be found elsewhere in this volume (e.g., Holyoak, Chapter 13 ; Smith & Ward, Chapter 23 ; van Steenburgh et al., Chapter 24 ; Simonton, Chapter 25 ; Opfer & Siegler, Chapter 30 ; Hegarty & Stull, Chapter 31 ; Dunbar & Klahr, Chapter 35 ; Patel et al., Chapter 37 ; Lowenstein, Chapter 38 ; Koedinger & Roll, Chapter 40 ).

All possible problem states for the three-disk Tower of Hanoi problem. The thicker gray arrows show the optimum solution path connecting the initial state (State #1) to the goal state (State #27).

Problem Representation: The Gestalt Legacy

Research on problem representation has its origins in Gestalt psychology, an influential approach in European psychology during the first half of the 20th century. (Behaviorism was the dominant perspective in American psychology at this time.) Karl Duncker published a book on the topic in his native German in 1935, which was translated into English and published 10 years later as the monograph On Problem-Solving (Duncker, 1945 ). Max Wertheimer also published a book on the topic in 1945, titled Productive Thinking . An enlarged edition published posthumously includes previously unpublished material (Wertheimer, 1959 ). Interestingly, 1945 seems to have been a watershed year for problem solving, as mathematician George Polya's book, How to Solve It , also appeared then (a second edition was published 12 years later; Polya, 1957 ).

The Gestalt psychologists extended the organizational principles of visual perception to the domain of problem solving. They showed that various visual aspects of the problem, as well the solver's prior knowledge, affect how people understand problems and, therefore, generate problem solutions. The principles of visual perception (e.g., proximity, closure, grouping, good continuation) are directly relevant to problem solving when the physical layout of the problem, or a diagram that accompanies the problem description, elicits inferences that solvers include in their problem representations. Such effects are nicely illustrated by Maier's ( 1930 ) nine-dot problem: Nine dots are arrayed in a 3x3 grid, and the task is to connect all the dots by drawing four straight lines without lifting one's pencil from the paper. People have difficulty solving this problem because their initial representations generally include a constraint, inferred from the configuration of the dots, that the lines should not go outside the boundary of the imaginary square formed by the outer dots. With this constraint, the problem cannot be solved (but see Adams, 1979 ). Without this constraint, the problem may be solved as shown in Figure 21.4 (though the problem is still difficult for many people; see Weisberg & Alba, 1981 ).

The nine-dot problem is a classic insight problem (see van Steenburgh et al., Chapter 24 ). According to the Gestalt view (e.g., Duncker, 1945 ; Kohler, 1925 ; Maier, 1931 ; see Ohlsson, 1984 , for a review), the solution to an insight problem appears suddenly, accompanied by an “aha!” sensation, immediately following the sudden “restructuring” of one's understanding of the problem (i.e., a change in the problem representation): “The decisive points in thought-processes, the moments of sudden comprehension, of the ‘Aha!,’ of the new, are always at the same time moments in which such a sudden restructuring of the thought-material takes place” (Duncker, 1945 , p. 29). For the nine-dot problem, one view of the required restructuring is that the solver relaxes the constraint implied by the perceptual form of the problem and realizes that the lines may, in fact, extend past the boundary of the imaginary square. Later in the chapter, we present more recent accounts of insight.

The entities that appear in a problem also tend to evoke various inferences that people incorporate into their problem representations. A classic demonstration of this is the phenomenon of functional fixedness , introduced by Duncker ( 1945 ): If an object is habitually used for a certain purpose (e.g., a box serves as a container), it is difficult to see

A solution to the nine-dot problem.

that object as having properties that would enable it to be used for a dissimilar purpose. Duncker's basic experimental paradigm involved two conditions that varied in terms of whether the object that was crucial for solution was initially used for a function other than that required for solution.

Consider the candles problem—the best known of the five “practical problems” Duncker ( 1945 ) investigated. Three candles are to be mounted at eye height on a door. On the table, for use in completing this task, are some tacks and three boxes. The solution is to tack the three boxes to the door to serve as platforms for the candles. In the control condition, the three boxes were presented to subjects empty. In the functional-fixedness condition, they were filled with candles, tacks, and matches. Thus, in the latter condition, the boxes initially served the function of container, whereas the solution requires that they serve the function of platform. The results showed that 100% of the subjects who received empty boxes solved the candles problem, compared with only 43% of subjects who received filled boxes. Every one of the five problems in this study showed a difference favoring the control condition over the functional-fixedness condition, with average solution rates across the five problems of 97% and 58%, respectively.

The function of the objects in a problem can be also “fixed” by their most recent use. For example, Birch and Rabinowitz ( 1951 ) had subjects perform two consecutive tasks. In the first task, people had to use either a switch or a relay to form an electric circuit. After completing this task, both groups of subjects were asked to solve Maier's ( 1931 ) two-ropes problem. The solution to this problem requires tying an object to one of the ropes and making the rope swing as a pendulum. Subjects could create the pendulum using either the object from the electric-circuit task or the other object. Birch and Rabinowitz found that subjects avoided using the same object for two unrelated functions. That is, those who used the switch in the first task made the pendulum using the relay, and vice versa. The explanations subjects subsequently gave for their object choices revealed that they were unaware of the functional-fixedness constraint they imposed on themselves.

In addition to investigating people's solutions to such practical problems as irradiating a tumor, mounting candles on the wall, or tying ropes, the Gestalt psychologists examined how people understand and solve mathematical problems that require domain-specific knowledge. For example, Wertheimer ( 1959 ) observed individual differences in students' learning and subsequent application of the formula for finding the area of a parallelogram (see Fig. 21.5a ). Some students understood the logic underlying the learned formula (i.e., the fact that a parallelogram can be transformed into a rectangle by cutting off a triangle from one side and pasting it onto the other side) and exhibited “productive thinking”—using the same logic to find the area of the quadrilateral in Figure 21.5b and the irregularly shaped geometric figure in Figure 21.5c . Other students memorized the formula and exhibited “reproductive thinking”—reproducing the learned solution only to novel parallelograms that were highly similar to the original one.

The psychological study of human problem solving faded into the background after the demise of the Gestalt tradition (during World War II), and problem solving was investigated only sporadically until Allen Newell and Herbert Simon's ( 1972 ) landmark book Human Problem Solving sparked a flurry of research on this topic. Newell and Simon adopted and refined Duncker's ( 1945 ) methodology of collecting and analyzing the think-aloud protocols that accompany problem solutions and extended Duncker's conceptualization of a problem solution as a search tree. However, their initial work did not aim to extend the Gestalt findings

Finding the area of ( a ) a parallelogram, ( b ) a quadrilateral, and ( c ) an irregularly shaped geometric figure. The solid lines indicate the geometric figures whose areas are desired. The dashed lines show how to convert the given figures into rectangles (i.e., they show solutions with understanding).

pertaining to problem representation. Instead, as we explain in the next section, their objective was to identify the general-purpose strategies people use in searching for a problem solution.

Search in a Problem Space: The Legacy of Newell and Simon

Newell and Simon ( 1972 ) wrote a magnum opus detailing their theory of problem solving and the supporting research they conducted with various collaborators. This theory was grounded in the information-processing approach to cognitive psychology and guided by an analogy between human and artificial intelligence (i.e., both people and computers being “Physical Symbol Systems,” Newell & Simon, 1976 ; see Doumas & Hummel, Chapter 5 ). They conceptualized problem solving as a process of search through a problem space for a path that connects the initial state to the goal state—a metaphor that alludes to the visual or spatial nature of problem solving (Simon, 1990 ). The term problem space refers to the solver's representation of the task as presented (Simon, 1978 ). It consists of ( 1 ) a set of knowledge states (the initial state, the goal state, and all possible intermediate states), ( 2 ) a set of operators that allow movement from one knowledge state to another, ( 3 ) a set of constraints, and ( 4 ) local information about the path one is taking through the space (e.g., the current knowledge state and how one got there).

We illustrate the components of a problem space for the three-disk Tower of Hanoi problem, as depicted in Figure 21.3 . The initial state appears at the top (State #1) and the goal state at the bottom right (State #27). The remaining knowledge states in the figure are possible intermediate states. The current knowledge state is the one at which the solver is located at any given point in the solution process. For example, the current state for a solver who has made three moves along the optimum solution path would be State #9. The solver presumably would know that he or she arrived at this state from State #5. This knowledge allows the solver to recognize a move that involves backtracking. The three operators in this problem are moving each of the three disks from one peg to another. These operators are subject to the constraint that a larger disk may not be placed on a smaller disk.

Newell and Simon ( 1972 ), as well as other contemporaneous researchers (e.g., Atwood & Polson, 1976 ; Greeno, 1974 ; Thomas, 1974 ), examined how people traverse the spaces of various well-defined problems (e.g., the Tower of Hanoi, Hobbits and Orcs). They discovered that solvers' search is guided by a number of shortcut strategies, or heuristics , which are likely to get the solver to the goal state without an extensive amount of search. Heuristics are often contrasted with algorithms —methods that are guaranteed to yield the correct solution. For example, one could try every possible move in the three-disk Tower of Hanoi problem and, eventually, find the correct solution. Although such an exhaustive search is a valid algorithm for this problem, for many problems its application is very time consuming and impractical (e.g., consider the game of chess).

In their attempts to identify people's search heuristics, Newell and Simon ( 1972 ) relied on two primary methodologies: think-aloud protocols and computer simulations. Their use of think-aloud protocols brought a high degree of scientific rigor to the methodology used by Duncker ( 1945 ; see Ericsson & Simon, 1980 ). Solvers were required to say out loud everything they were thinking as they solved the problem, that is, everything that went through their verbal working memory. Subjects' verbalizations—their think-aloud protocols—were tape-recorded and then transcribed verbatim for analysis. This method is extremely time consuming (e.g., a transcript of one person's solution to the cryptarithmetic problem DONALD + GERALD = ROBERT, with D = 5, generated a 17-page transcript), but it provides a detailed record of the solver's ongoing solution process.

An important caveat to keep in mind while interpreting a subject's verbalizations is that “a protocol is relatively reliable only for what it positively contains, but not for that which it omits” (Duncker, 1945 , p. 11). Ericsson and Simon ( 1980 ) provided an in-depth discussion of the conditions under which this method is valid (but see Russo, Johnson, & Stephens, 1989 , for an alternative perspective). To test their interpretation of a subject's problem solution, inferred from the subject's verbal protocol, Newell and Simon ( 1972 ) created a computer simulation program and examined whether it solved the problem the same way the subject did. To the extent that the computer simulation provided a close approximation of the solver's step-by-step solution process, it lent credence to the researcher's interpretation of the verbal protocol.

Newell and Simon's ( 1972 ) most famous simulation was the General Problem Solver or GPS (Ernst & Newell, 1969 ). GPS successfully modeled human solutions to problems as different as the Tower of Hanoi and the construction of logic proofs using a single general-purpose heuristic: means-ends analysis . This heuristic captures people's tendency to devise a solution plan by setting subgoals that could help them achieve their final goal. It consists of the following steps: ( 1 ) Identify a difference between the current state and the goal (or subgoal ) state; ( 2 ) Find an operator that will remove (or reduce) the difference; (3a) If the operator can be directly applied, do so, or (3b) If the operator cannot be directly applied, set a subgoal to remove the obstacle that is preventing execution of the desired operator; ( 4 ) Repeat steps 1–3 until the problem is solved. Next, we illustrate the implementation of this heuristic for the Tower of Hanoi problem, using the problem space in Figure 21.3 .

As can be seen in Figure 21.3 , a key difference between the initial state and the goal state is that the large disk is on the wrong peg (step 1). To remove this difference (step 2), one needs to apply the operator “move-large-disk.” However, this operator cannot be applied because of the presence of the medium and small disks on top of the large disk. Therefore, the solver may set a subgoal to move that two-disk tower to the middle peg (step 3b), leaving the rightmost peg free for the large disk. A key difference between the initial state and this new subgoal state is that the medium disk is on the wrong peg. Because application of the move-medium-disk operator is blocked, the solver sets another subgoal to move the small disk to the right peg. This subgoal can be satisfied immediately by applying the move-small-disk operator (step 3a), generating State #3. The solver then returns to the previous subgoal—moving the tower consisting of the small and medium disks to the middle peg. The differences between the current state (#3) and the subgoal state (#9) can be removed by first applying the move-medium-disk operator (yielding State #5) and then the move-small-disk operator (yielding State #9). Finally, the move-large-disk operator is no longer blocked. Hence, the solver moves the large disk to the right peg, yielding State #11.

Notice that the subgoals are stacked up in the order in which they are generated, so that they pop up in the order of last in first out. Given the first subgoal in our example, repeated application of the means-ends analysis heuristic will yield the shortest-path solution, indicated by the large gray arrows. In general, subgoals provide direction to the search and allow solvers to plan several moves ahead. By assessing progress toward a required subgoal rather than the final goal, solvers may be able to make moves that otherwise seem unwise. To take a concrete example, consider the transition from State #1 to State #3 in Figure 21.3 . Comparing the initial state to the goal state, this move seems unwise because it places the small disk on the bottom of the right peg, whereas it ultimately needs to be at the top of the tower on that peg. But comparing the initial state to the solver-generated subgoal state of having the medium disk on the middle peg, this is exactly where the small disk needs to go.

Means-ends analysis and various other heuristics (e.g., the hill-climbing heuristic that exploits the similarity, or distance, between the state generated by the next operator and the goal state; working backward from the goal state to the initial state) are flexible strategies that people often use to successfully solve a large variety of problems. However, the generality of these heuristics comes at a cost: They are relatively weak and fallible (e.g., in the means-ends solution to the problem of fixing a hole in a bucket, “Dear Liza” leads “Dear Henry” in a loop that ends back at the initial state; the lyrics of this famous song can be readily found on the Web). Hence, although people use general-purpose heuristics when they encounter novel problems, they replace them as soon as they acquire experience with and sufficient knowledge about the particular problem space (e.g., Anzai & Simon, 1979 ).

Despite the fruitfulness of this research agenda, it soon became evident that a fundamental weakness was that it minimized the importance of people's background knowledge. Of course, Newell and Simon ( 1972 ) were aware that problem solutions require relevant knowledge (e.g., the rules of logical proofs, or rules for stacking disks). Hence, in programming GPS, they supplemented every problem they modeled with the necessary background knowledge. This practice highlighted the generality and flexibility of means-ends analysis but failed to capture how people's background knowledge affects their solutions. As we discussed in the previous section, domain knowledge is likely to affect how people represent problems and, therefore, how they generate problem solutions. Moreover, as people gain experience solving problems in a particular knowledge domain (e.g., math, physics), they change their representations of these problems (e.g., Chi, Feltovich, & Glaser, 1981 ; Haverty, Koedinger, Klahr, & Alibali, 2000 ; Schoenfeld & Herrmann, 1982 ) and learn domain-specific heuristics (e.g., Polya, 1957 ; Schoenfeld, 1979 ) that trump the general-purpose strategies.

It is perhaps inevitable that the two traditions in problem-solving research—one emphasizing representation and the other emphasizing search strategies—would eventually come together. In the next section we review developments that led to this integration.

The Two Legacies Converge

Because Newell and Simon ( 1972 ) aimed to discover the strategies people use in searching for a solution, they investigated problems that minimized the impact of factors that tend to evoke differences in problem representations, of the sort documented by the Gestalt psychologists. In subsequent work, however, Simon and his collaborators showed that such factors are highly relevant to people's solutions of well-defined problems, and Simon ( 1986 ) incorporated these findings into the theoretical framework that views problem solving as search in a problem space.

In this section, we first describe illustrative examples of this work. We then describe research on insight solutions that incorporates ideas from the two legacies described in the previous sections.

Relevance of the Gestalt Ideas to the Solution of Search Problems

In this subsection we describe two lines of research by Simon and his colleagues, and by other researchers, that document the importance of perception and of background knowledge to the way people search for a problem solution. The first line of research used variants of relatively well-defined riddle problems that had the same structure (i.e., “problem isomorphs”) and, therefore, supposedly the same problem space. It documented that people's search depended on various perceptual and conceptual inferences they tended to draw from a specific instantiation of the problem's structure. The second line of research documented that people's search strategies crucially depend on their domain knowledge and on their prior experience with related problems.

Problem Isomorphs

Hayes and Simon ( 1977 ) used two variants of the Tower of Hanoi problem that, instead of disks and pegs, involved monsters and globes that differed in size (small, medium, and large). In both variants, the initial state had the small monster holding the large globe, the medium-sized monster holding the small globe, and the large monster holding the medium-sized globe. Moreover, in both variants the goal was for each monster to hold a globe proportionate to its own size. The only difference between the problems concerned the description of the operators. In one variant (“transfer”), subjects were told that the monsters could transfer the globes from one to another as long as they followed a set of rules, adapted from the rules in the original Tower of Hanoi problem (e.g., only one globe may be transferred at a time). In the other variant (“change”), subjects were told that the monsters could shrink and expand themselves according to a set of rules, which corresponded to the rules in the transfer version of the problem (e.g., only one monster may change its size at a time). Despite the isomorphism of the two variants, subjects conducted their search in two qualitatively different problem spaces, which led to solution times for the change variant being almost twice as long as those for the transfer variant. This difference arose because subjects could more readily envision and track an object that was changing its location with every move than one that was changing its size.

Recent work by Patsenko and Altmann ( 2010 ) found that, even in the standard Tower of Hanoi problem, people's solutions involve object-bound routines that depend on perception and selective attention. The subjects in their study solved various Tower of Hanoi problems on a computer. During the solution of a particular “critical” problem, the computer screen changed at various points without subjects' awareness (e.g., a disk was added, such that a subject who started with a five-disc tower ended with a six-disc tower). Patsenko and Altmann found that subjects' moves were guided by the configurations of the objects on the screen rather than by solution plans they had stored in memory (e.g., the next subgoal).

The Gestalt psychologists highlighted the role of perceptual factors in the formation of problem representations (e.g., Maier's, 1930 , nine-dot problem) but were generally silent about the corresponding implications for how the problem was solved (although they did note effects on solution accuracy). An important contribution of the work on people's solutions of the Tower of Hanoi problem and its variants was to show the relevance of perceptual factors to the application of various operators during search for a problem solution—that is, to the how of problem solving. In the next section, we describe recent work that documents the involvement of perceptual factors in how people understand and use equations and diagrams in the context of solving math and science problems.

Kotovsky, Hayes, and Simon ( 1985 ) further investigated factors that affect people's representation and search in isomorphs of the Tower of Hanoi problem. In one of their isomorphs, three disks were stacked on top of each other to form an inverted pyramid, with the smallest disc on the bottom and the largest on top. Subjects' solutions of the inverted pyramid version were similar to their solutions of the standard version that has the largest disc on the bottom and the smallest on top. However, the two versions were solved very differently when subjects were told that the discs represent acrobats. Subjects readily solved the version in which they had to place a small acrobat on the shoulders of a large one, but they refrained from letting a large acrobat stand on the shoulders of a small one. In other words, object-based inferences that draw on people's semantic knowledge affected the solution of search problems, much as they affect the solution of the ill-defined problems investigated by the Gestalt psychologists (e.g., Duncker's, 1945 , candles problem). In the next section, we describe more recent work that shows similar effects in people's solutions to mathematical word problems.

The work on differences in the representation and solution of problem isomorphs is highly relevant to research on analogical problem solving (or analogical transfer), which examines when and how people realize that two problems that differ in their cover stories have a similar structure (or a similar problem space) and, therefore, can be solved in a similar way. This research shows that minor differences between example problems, such as the use of X-rays versus ultrasound waves to fuse a broken filament of a light bulb, can elicit different problem representations that significantly affect the likelihood of subsequent transfer to novel problem analogs (Holyoak & Koh, 1987 ). Analogical transfer has played a central role in research on human problem solving, in part because it can shed light on people's understanding of a given problem and its solution and in part because it is believed to provide a window onto understanding and investigating creativity (see Smith & Ward, Chapter 23 ). We briefly mention some findings from the analogy literature in the next subsection on expertise, but we do not discuss analogical transfer in detail because this topic is covered elsewhere in this volume (Holyoak, Chapter 13 ).

Expertise and Its Development

In another line of research, Simon and his colleagues examined how people solve ecologically valid problems from various rule-governed and knowledge-rich domains. They found that people's level of expertise in such domains, be it in chess (Chase & Simon, 1973 ; Gobet & Simon, 1996 ), mathematics (Hinsley, Hayes, & Simon, 1977 ; Paige & Simon, 1966 ), or physics (Larkin, McDermott, Simon, & Simon, 1980 ; Simon & Simon, 1978 ), plays a crucial role in how they represent problems and search for solutions. This work, and the work of numerous other researchers, led to the discovery (and rediscovery, see Duncker, 1945 ) of important differences between experts and novices, and between “good” and “poor” students.

One difference between experts and novices pertains to pattern recognition. Experts' attention is quickly captured by familiar configurations within a problem situation (e.g., a familiar configuration of pieces in a chess game). In contrast, novices' attention is focused on isolated components of the problem (e.g., individual chess pieces). This difference, which has been found in numerous domains, indicates that experts have stored in memory many meaningful groups (chunks) of information: for example, chess (Chase & Simon, 1973 ), circuit diagrams (Egan & Schwartz, 1979 ), computer programs (McKeithen, Reitman, Rueter, & Hirtle, 1981 ), medicine (Coughlin & Patel, 1987 ; Myles-Worsley, Johnston, & Simons, 1988 ), basketball and field hockey (Allard & Starkes, 1991 ), and figure skating (Deakin & Allard, 1991 ).

The perceptual configurations that domain experts readily recognize are associated with stored solution plans and/or compiled procedures (Anderson, 1982 ). As a result, experts' solutions are much faster than, and often qualitatively different from, the piecemeal solutions that novice solvers tend to construct (e.g., Larkin et al., 1980 ). In effect, experts often see the solutions that novices have yet to compute (e.g., Chase & Simon, 1973 ; Novick & Sherman, 2003 , 2008 ). These findings have led to the design of various successful instructional interventions (e.g., Catrambone, 1998 ; Kellman et al., 2008 ). For example, Catrambone ( 1998 ) perceptually isolated the subgoals of a statistics problem. This perceptual chunking of meaningful components of the problem prompted novice students to self-explain the meaning of the chunks, leading to a conceptual understanding of the learned solution. In the next section, we describe some recent work that shows the beneficial effects of perceptual pattern recognition on the solution of familiar mathematics problems, as well as the potentially detrimental effects of familiar perceptual chunks to understanding and reasoning with diagrams depicting evolutionary relationships among taxa.

Another difference between experts and novices pertains to their understanding of the solution-relevant problem structure. Experts' knowledge is highly organized around domain principles, and their problem representations tend to reflect this principled understanding. In particular, they can extract the solution-relevant structure of the problems they encounter (e.g., meaningful causal relations among the objects in the problem; see Cheng & Buehner, Chapter 12 ). In contrast, novices' representations tend to be bound to surface features of the problems that may be irrelevant to solution (e.g., the particular objects in a problem). For example, Chi, Feltovich, and Glaser ( 1981 ) examined how students with different levels of physics expertise group mechanics word problems. They found that advanced graduate students grouped the problems based on the physics principles relevant to the problems' solutions (e.g., conservation of energy, Newton's second law). In contrast, undergraduates who had successfully completed an introductory course in mechanics grouped the problems based on the specific objects involved (e.g., pulley problems, inclined plane problems). Other researchers have found similar results in the domains of biology, chemistry, computer programming, and math (Adelson, 1981 ; Kindfield, 1993 / 1994 ; Kozma & Russell, 1997 ; McKeithen et al., 1981 ; Silver, 1979 , 1981 ; Weiser & Shertz, 1983 ).

The level of domain expertise and the corresponding representational differences are, of course, a matter of degree. With increasing expertise, there is a gradual change in people's focus of attention from aspects that are not relevant to solution to those that are (e.g., Deakin & Allard, 1991 ; Hardiman, Dufresne, & Mestre, 1989 ; McKeithen et al., 1981 ; Myles-Worsley et al., 1988 ; Schoenfeld & Herrmann, 1982 ; Silver, 1981 ). Interestingly, Chi, Bassok, Lewis, Reimann, and Glaser ( 1989 ) found similar differences in focus on structural versus surface features among a group of novices who studied worked-out examples of mechanics problems. These differences, which echo Wertheimer's ( 1959 ) observations of individual differences in students' learning about the area of parallelograms, suggest that individual differences in people's interests and natural abilities may affect whether, or how quickly, they acquire domain expertise.

An important benefit of experts' ability to focus their attention on solution-relevant aspects of problems is that they are more likely than novices to recognize analogous problems that involve different objects and cover stories (e.g., Chi et al., 1989 ; Novick, 1988 ; Novick & Holyoak, 1991 ; Wertheimer, 1959 ) or that come from other knowledge domains (e.g., Bassok & Holyoak, 1989 ; Dunbar, 2001 ; Goldstone & Sakamoto, 2003 ). For example, Bassok and Holyoak ( 1989 ) found that, after learning to solve arithmetic-progression problems in algebra, subjects spontaneously applied these algebraic solutions to analogous physics problems that dealt with constantly accelerated motion. Note, however, that experts and good students do not simply ignore the surface features of problems. Rather, as was the case in the problem isomorphs we described earlier (Kotovsky et al., 1985 ), they tend to use such features to infer what the problem's structure could be (e.g., Alibali, Bassok, Solomon, Syc, & Goldin-Meadow, 1999 ; Blessing & Ross, 1996 ). For example, Hinsley et al. ( 1977 ) found that, after reading no more than the first few words of an algebra word problem, expert solvers classified the problem into a likely problem category (e.g., a work problem, a distance problem) and could predict what questions they might be asked and the equations they likely would need to use.

Surface-based problem categorization has a heuristic value (Medin & Ross, 1989 ): It does not ensure a correct categorization (Blessing & Ross, 1996 ), but it does allow solvers to retrieve potentially appropriate solutions from memory and to use them, possibly with some adaptation, to solve a variety of novel problems. Indeed, although experts exploit surface-structure correlations to save cognitive effort, they have the capability to realize that a particular surface cue is misleading (Hegarty, Mayer, & Green, 1992 ; Lewis & Mayer, 1987 ; Martin & Bassok, 2005 ; Novick 1988 , 1995 ; Novick & Holyoak, 1991 ). It is not surprising, therefore, that experts may revert to novice-like heuristic methods when solving problems under pressure (e.g., Beilock, 2008 ) or in subdomains in which they have general but not specific expertise (e.g., Patel, Groen, & Arocha, 1990 ).

Relevance of Search to Insight Solutions

We introduced the notion of insight in our discussion of the nine-dot problem in the section on the Gestalt tradition. The Gestalt view (e.g., Duncker, 1945 ; Maier, 1931 ; see Ohlsson, 1984 , for a review) was that insight problem solving is characterized by an initial work period during which no progress toward solution is made (i.e., an impasse), a sudden restructuring of one's problem representation to a more suitable form, followed immediately by the sudden appearance of the solution. Thus, solving problems by insight was believed to be all about representation, with essentially no role for a step-by-step solution process (i.e., search). Subsequent and contemporary researchers have generally concurred with the Gestalt view that getting the right representation is crucial. However, research has shown that insight solutions do not necessarily arise suddenly or full blown after restructuring (e.g., Weisberg & Alba, 1981 ); and even when they do, the underlying solution process (in this case outside of awareness) may reflect incremental progress toward the goal (Bowden & Jung-Beeman, 2003 ; Durso, Rea, & Dayton, 1994 ; Novick & Sherman, 2003 ).

“Demystifying insight,” to borrow a phrase from Bowden, Jung-Beeman, Fleck, and Kounios ( 2005 ), requires explaining ( 1 ) why solvers initially reach an impasse in solving a problem for which they have the necessary knowledge to generate the solution, ( 2 ) how the restructuring occurred, and ( 3 ) how it led to the solution. A detailed discussion of these topics appears elsewhere in this volume (van Steenburgh et al., Chapter 24 ). Here, we describe briefly three recent theories that have attempted to account for various aspects of these phenomena: Knoblich, Ohlsson, Haider, and Rhenius's ( 1999 ) representational change theory, MacGregor, Ormerod, and Chronicle's ( 2001 ) progress monitoring theory, and Bowden et al.'s ( 2005 ) neurological model. We then propose the need for an integrated approach to demystifying insight that considers both representation and search.

According to Knoblich et al.'s ( 1999 ) representational change theory, problems that are solved with insight are highly likely to evoke initial representations in which solvers place inappropriate constraints on their solution attempts, leading to an impasse. An impasse can be resolved by revising one's representation of the problem. Knoblich and his colleagues tested this theory using Roman numeral matchstick arithmetic problems in which solvers must move one stick to a new location to change a false numerical statement (e.g., I = II + II ) into a statement that is true. According to representational change theory, re-representation may occur through either constraint relaxation or chunk decomposition. (The solution to the example problem is to change II + to III – , which requires both methods of re-representation, yielding I = III – II ). Good support for this theory has been found based on measures of solution rate, solution time, and eye fixation (Knoblich et al., 1999 ; Knoblich, Ohlsson, & Raney, 2001 ; Öllinger, Jones, & Knoblich, 2008 ).

Progress monitoring theory (MacGregor et al., 2001 ) was proposed to account for subjects' difficulty in solving the nine-dot problem, which has traditionally been classified as an insight problem. According to this theory, solvers use the hill-climbing search heuristic to solve this problem, just as they do for traditional search problems (e.g., Hobbits and Orcs). In particular, solvers are hypothesized to monitor their progress toward solution using a criterion generated from the problem's current state. If solvers reach criterion failure, they seek alternative solutions by trying to relax one or more problem constraints. MacGregor et al. found support for this theory using several variants of the nine-dot problem (also see Ormerod, MacGregor, & Chronicle, 2002 ). Jones ( 2003 ) suggested that progress monitoring theory provides an account of the solution process up to the point an impasse is reached and representational change is sought, at which point representational change theory picks up and explains how insight may be achieved. Hence, it appears that a complete account of insight may require an integration of concepts from the Gestalt (representation) and Newell and Simon's (search) legacies.

Bowden et al.'s ( 2005 ) neurological model emphasizes the overlap between problem solving and language comprehension, and it hinges on differential processing in the right and left hemispheres. They proposed that an impasse is reached because initial processing of the problem produces strong activation of information irrelevant to solution in the left hemisphere. At the same time, weak semantic activation of alternative semantic interpretations, critical for solution, occurs in the right hemisphere. Insight arises when the weakly activated concepts reinforce each other, eventually rising above the threshold required for conscious awareness. Several studies of problem solving using compound remote associates problems, involving both behavioral and neuroimaging data, have found support for this model (Bowden & Jung-Beeman, 1998 , 2003 ; Jung-Beeman & Bowden, 2000 ; Jung-Beeman et al., 2004 ; also see Moss, Kotovsky, & Cagan, 2011 ).

Note that these three views of insight have received support using three quite distinct types of problems (Roman numeral matchstick arithmetic problems, the nine-dot problem, and compound remote associates problems, respectively). It remains to be established, therefore, whether these accounts can be generalized across problems. Kershaw and Ohlsson ( 2004 ) argued that insight problems are difficult because the key behavior required for solution may be hindered by perceptual factors (the Gestalt view), background knowledge (so expertise may be important; e.g., see Novick & Sherman, 2003 , 2008 ), and/or process factors (e.g., those affecting search). From this perspective, solving visual problems (e.g., the nine-dot problem) with insight may call upon more general visual processes, whereas solving verbal problems (e.g., anagrams, compound remote associates) with insight may call upon general verbal/semantic processes.

The work we reviewed in this section shows the relevance of problem representation (the Gestalt legacy) to the way people search the problem space (the legacy of Newell and Simon), and the relevance of search to the solution of insight problems that require a representational change. In addition to this inevitable integration of the two legacies, the work we described here underscores the fact that problem solving crucially depends on perceptual factors and on the solvers' background knowledge. In the next section, we describe some recent work that shows the involvement of these factors in the solution of problems in math and science.

Effects of Perception and Knowledge in Problem Solving in Academic Disciplines

Although the use of puzzle problems continues in research on problem solving, especially in investigations of insight, many contemporary researchers tackle problem solving in knowledge-rich domains, often in academic disciplines (e.g., mathematics, biology, physics, chemistry, meteorology). In this section, we provide a sampling of this research that highlights the importance of visual perception and background knowledge for successful problem solving.

The Role of Visual Perception

We stated at the outset that a problem representation (e.g., the problem space) is a model of the problem constructed by solvers to summarize their understanding of the problem's essential nature. This informal definition refers to the internal representations people construct and hold in working memory. Of course, people may also construct various external representations (Markman, 1999 ) and even manipulate those representations to aid in solution (see Hegarty & Stull, Chapter 31 ). For example, solvers often use paper and pencil to write notes or draw diagrams, especially when solving problems from formal domains (e.g., Cox, 1999 ; Kindfield, 1993 / 1994 ; S. Schwartz, 1971 ). In problems that provide solvers with external representation, such as the Tower of Hanoi problem, people's planning and memory of the current state is guided by the actual configurations of disks on pegs (Garber & Goldin-Meadow, 2002 ) or by the displays they see on a computer screen (Chen & Holyoak, 2010 ; Patsenko & Altmann, 2010 ).

In STEM (science, technology, engineering, and mathematics) disciplines, it is common for problems to be accompanied by diagrams or other external representations (e.g., equations) to be used in determining the solution. Larkin and Simon ( 1987 ) examined whether isomorphic sentential and diagrammatic representations are interchangeable in terms of facilitating solution. They argued that although the two formats may be equivalent in the sense that all of the information in each format can be inferred from the other format (informational equivalence), the ease or speed of making inferences from the two formats might differ (lack of computational equivalence). Based on their analysis of several problems in physics and math, Larkin and Simon further argued for the general superiority of diagrammatic representations (but see Mayer & Gallini, 1990 , for constraints on this general conclusion).

Novick and Hurley ( 2001 , p. 221) succinctly summarized the reasons for the general superiority of diagrams (especially abstract or schematic diagrams) over verbal representations: They “(a) simplify complex situations by discarding unnecessary details (e.g., Lynch, 1990 ; Winn, 1989 ), (b) make abstract concepts more concrete by mapping them onto spatial layouts with familiar interpretational conventions (e.g., Winn, 1989 ), and (c) substitute easier perceptual inferences for more computationally intensive search processes and sentential deductive inferences (Barwise & Etchemendy, 1991 ; Larkin & Simon, 1987 ).” Despite these benefits of diagrammatic representations, there is an important caveat, noted by Larkin and Simon ( 1987 , p. 99) at the very end of their paper: “Although every diagram supports some easy perceptual inferences, nothing ensures that these inferences must be useful in the problem-solving process.” We will see evidence of this in several of the studies reviewed in this section.

Next we describe recent work on perceptual factors that are involved in people's use of two types of external representations that are provided as part of the problem in two STEM disciplines: equations in algebra and diagrams in evolutionary biology. Although we focus here on effects of perceptual factors per se, it is important to note that such factors only influence performance when subjects have background knowledge that supports differential interpretation of the alternative diagrammatic depictions presented (Hegarty, Canham, & Fabricant, 2010 ).

In the previous section, we described the work of Patsenko and Altmann ( 2010 ) that shows direct involvement of visual attention and perception in the sequential application of move operators during the solution of the Tower of Hanoi problem. A related body of work documents similar effects in tasks that require the interpretation and use of mathematical equations (Goldstone, Landy, & Son, 2010 ; Landy & Goldstone, 2007a , b). For example, Landy and Goldstone ( 2007b ) varied the spatial proximity of arguments to the addition (+) and multiplication (*) operators in algebraic equations, such that the spatial layout of the equation was either consistent or inconsistent with the order-of-operations rule that multiplication precedes addition. In consistent equations , the space was narrower around multiplication than around addition (e.g., g*m + r*w = m*g + w*r ), whereas in inconsistent equations this relative spacing was reversed (e.g., s * n+e * c = n * s+c * e ). Subjects' judgments of the validity of such equations (i.e., whether the expressions on the two sides of the equal sign are equivalent) were significantly faster and more accurate for consistent than inconsistent equations.

In discussing these findings and related work with other external representations, Goldstone et al. ( 2010 ) proposed that experience with solving domain-specific problems leads people to “rig up” their perceptual system such that it allows them to look at the problem in a way that is consistent with the correct rules. Similar logic guides the Perceptual Learning Modules developed by Kellman and his collaborators to help students interpret and use algebraic equations and graphs (Kellman et al., 2008 ; Kellman, Massey, & Son, 2009 ). These authors argued and showed that, consistent with the previously reviewed work on expertise, perceptual training with particular external representations supports the development of perceptual fluency. This fluency, in turn, supports students' subsequent use of these external representations for problem solving.

This research suggests that extensive experience with particular equations or graphs may lead to perceptual fluency that could replace the more mindful application of domain-specific rules. Fisher, Borchert, and Bassok ( 2011 ) reported results from algebraic-modeling tasks that are consistent with this hypothesis. For example, college students were asked to represent verbal statements with algebraic equations, a task that typically elicits systematic errors (e.g., Clement, Lochhead, & Monk, 1981 ). Fisher et al. found that such errors were very common when subjects were asked to construct “standard form” equations ( y = ax ), which support fluent left-to-right translation of words to equations, but were relatively rare when subjects were asked to construct nonstandard division-format equations (x = y/a) that do not afford such translation fluency.

In part because of the left-to-right order in which people process equations, which mirrors the linear order in which they process text, equations have traditionally been viewed as sentential representations. However, Landy and Goldstone ( 2007a ) have proposed that equations also share some properties with diagrammatic displays and that, in fact, in some ways they are processed like diagrams. That is, spatial information is used to represent and to support inferences about syntactic structure. This hypothesis received support from Landy and Goldstone's ( 2007b ) results, described earlier, in which subjects' judgments of the validity of equations were affected by the Gestalt principle of grouping: Subjects did better when the grouping was consistent rather than inconsistent with the underlying structure of the problem (order of operations). Moreover, Landy and Goldstone ( 2007a ) found that when subjects wrote their own equations they grouped numbers and operators (+, *, =) in a way that reflected the hierarchical structure imposed by the order-of-operations rule.

In a recent line of research, Novick and Catley ( 2007 ; Novick, Catley, & Funk, 2010 ; Novick, Shade, & Catley, 2011 ) have examined effects of the spatial layout of diagrams depicting the evolutionary history of a set of taxa on people's ability to reason about patterns of relationship among those taxa. We consider here their work that investigates the role of another Gestalt perceptual principle—good continuation—in guiding students' reasoning. According to this principle, a continuous line is perceived as a single entity (Kellman, 2000 ). Consider the diagrams shown in Figure 21.6 . Each is a cladogram, a diagram that depicts nested sets of taxa that are related in terms of levels of most recent common ancestry. For example, chimpanzees and starfish are more closely related to each other than either is to spiders. The supporting evidence for their close relationship is their most recent common ancestor, which evolved the novel character of having radial cleavage. Spiders do not share this ancestor and thus do not have this character.

Cladograms are typically drawn in two isomorphic formats, which Novick and Catley ( 2007 ) referred to as trees and ladders. Although these formats are informationally equivalent (Larkin & Simon, 1987 ), Novick and Catley's ( 2007 ) research shows that they are not computationally equivalent (Larkin & Simon, 1987 ). Imagine that you are given evolutionary relationships in the ladder format, such as in Figure 21.6a (but without the four characters—hydrostatic skeleton, bilateral symmetry, radial cleavage, and trocophore larvae—and associated short lines indicating their locations on the cladogram), and your task is to translate that diagram to the tree format. A correct translation is shown in Figure 21.6b . Novick and Catley ( 2007 ) found that college students were much more likely to get such problems correct when the presented cladogram was in the nested circles (e.g., Figure 21.6d ) rather than the ladder format. Because the Gestalt principle of good continuation makes the long slanted line at the base of the ladder appear to represent a single hierarchical level, a common translation error for the ladder to tree problems was to draw a diagram such as that shown in Figure 21.6c .

The difficulty that good continuation presents for interpreting relationships depicted in the ladder format extends to answering reasoning questions as well. Novick and Catley (unpublished data) asked comparable questions about relationships depicted in the ladder and tree formats. For example, using the cladograms depicted in Figures 21.6a and 21.6b , consider the following questions: (a) Which taxon—jellyfish or earthworm—is the closest evolutionary relation to starfish, and what evidence supports your answer? (b) Do the bracketed taxa comprise a clade (a set of taxa consisting of the most recent common ancestor and all of its descendants), and what evidence supports your answer? For both such questions, students had higher accuracy and evidence quality composite scores when the relationships were depicted in the tree than the ladder format.

Four cladograms depicting evolutionary relationships among six animal taxa. Cladogram ( a ) is in the ladder format, cladograms ( b ) and ( c ) are in the tree format, and cladogram ( d ) is in the nested circles format. Cladograms ( a ), ( b ), and ( d ) are isomorphic.

If the difficulty in extracting the hierarchical structure of the ladder format is due to good continuation (which leads problem solvers to interpret continuous lines that depict multiple hierarchical levels as depicting only a single level), then a manipulation that breaks good continuation at the points where a new hierarchical level occurs should improve understanding. Novick et al. ( 2010 ) tested this hypothesis using a translation task by manipulating whether characters that are the markers for the most recent common ancestor of each nested set of taxa were included on the ladders. Figure 21.6a shows a ladder with such characters. As predicted, translation accuracy increased dramatically simply by adding these characters to the ladders, despite the additional information subjects had to account for in their translations.

The Role of Background Knowledge

As we mentioned earlier, the specific entities in the problems people encounter evoke inferences that affect how people represent these problems (e.g., the candle problem; Duncker, 1945 ) and how they apply the operators in searching for the solution (e.g., the disks vs. acrobats versions of the Tower of Hanoi problem; Kotovsky et al., 1985 ). Such object-based inferences draw on people's knowledge about the properties of the objects (e.g., a box is a container, an acrobat is a person who can be hurt). Here, we describe the work of Bassok and her colleagues, who found that similar inferences affect how people select mathematical procedures to solve problems in various formal domains. This work shows that the objects in the texts of mathematical word problems affect how people represent the problem situation (i.e., the situation model they construct; Kintsch & Greeno, 1985 ) and, in turn, lead them to select mathematical models that have a corresponding structure. To illustrate, a word problem that describes constant change in the rate at which ice is melting off a glacier evokes a model of continuous change, whereas a word problem that describes constant change in the rate at which ice is delivered to a restaurant evokes a model of discrete change. These distinct situation models lead subjects to select corresponding visual representations (e.g., Bassok & Olseth, 1995 ) and solutions methods, such as calculating the average change over time versus adding the consecutive changes (e.g., Alibali et al., 1999 ).

In a similar manner, people draw on their general knowledge to infer how the objects in a given problem are related to each other and construct mathematical solutions that correspond to these inferred object relations. For example, a word problem that involves doctors from two hospitals elicits a situation model in which the two sets of doctors play symmetric roles (e.g., work with each other), whereas a mathematically isomorphic problem that involves mechanics and cars elicits a situation model in which the sets play asymmetric roles (e.g., mechanics fix cars). The mathematical solutions people construct to such problems reflect this difference in symmetry (Bassok, Wu, & Olseth, 1995 ). In general, people tend to add objects that belong to the same taxonomic category (e.g., doctors + doctors) but divide functionally related objects (e.g., cars ÷ mechanics). People establish this correspondence by a process of analogical alignment between semantic and arithmetic relations, which Bassok and her colleagues refer to as “semantic alignment” (Bassok, Chase, & Martin, 1998 ; Doumas, Bassok, Guthormsen, & Hummel, 2006 ; Fisher, Bassok, & Osterhout, 2010 ).

Semantic alignment occurs very early in the solution process and can prime arithmetic facts that are potentially relevant to the problem solution (Bassok, Pedigo, & Oskarsson, 2008 ). Although such alignments can lead to erroneous solutions, they have a high heuristic value because, in most textbook problems, object relations indeed correspond to analogous mathematical relations (Bassok et al., 1998 ). Interestingly, unlike in the case of reliance on specific surface-structure correlations (e.g., the keyword “more” typically appears in word problems that require addition; Lewis & Mayer, 1987 ), people are more likely to exploit semantic alignment when they have more, rather than less modeling experience. For example, Martin and Bassok ( 2005 ) found very strong semantic-alignment effects when subjects solved simple division word problems, but not when they constructed algebraic equations to represent the relational statements that appeared in the problems. Of course, these subjects had significantly more experience with solving numerical word problems than with constructing algebraic models of relational statements. In a subsequent study, Fisher and Bassok ( 2009 ) found semantic-alignment effects for subjects who constructed correct algebraic models, but not for those who committed modeling errors.

Conclusions and Future Directions

In this chapter, we examined two broad components of the problem-solving process: representation (the Gestalt legacy) and search (the legacy of Newell and Simon). Although many researchers choose to focus their investigation on one or the other of these components, both Duncker ( 1945 ) and Simon ( 1986 ) underscored the necessity to investigate their interaction, as the representation one constructs for a problem determines (or at least constrains) how one goes about trying to generate a solution, and searching the problem space may lead to a change in problem representation. Indeed, Duncker's ( 1945 ) initial account of one subject's solution to the radiation problem was followed up by extensive and experimentally sophisticated work by Simon and his colleagues and by other researchers, documenting the involvement of visual perception and background knowledge in how people represent problems and search for problem solutions.

The relevance of perception and background knowledge to problem solving illustrates the fact that, when people attempt to find or devise ways to reach their goals, they draw on a variety of cognitive resources and engage in a host of cognitive activities. According to Duncker ( 1945 ), such goal-directed activities may include (a) placing objects into categories and making inferences based on category membership, (b) making inductive inferences from multiple instances, (c) reasoning by analogy, (d) identifying the causes of events, (e) deducing logical implications of given information, (f) making legal judgments, and (g) diagnosing medical conditions from historical and laboratory data. As this list suggests, many of the chapters in the present volume describe research that is highly relevant to the understanding of problem-solving behavior. We believe that important advancements in problem-solving research would emerge by integrating it with research in other areas of thinking and reasoning, and that research in these other areas could be similarly advanced by incorporating the insights gained from research on what has more traditionally been identified as problem solving.

As we have described in this chapter, many of the important findings in the field have been established by a careful investigation of various riddle problems. Although there are good methodological reasons for using such problems, many researchers choose to investigate problem solving using ecologically valid educational materials. This choice, which is increasingly common in contemporary research, provides researchers with the opportunity to apply their basic understanding of problem solving to benefit the design of instruction and, at the same time, allows them to gain a better understanding of the processes by which domain knowledge and educational conventions affect the solution process. We believe that the trend of conducting educationally relevant research is likely to continue, and we expect a significant expansion of research on people's understanding and use of dynamic and technologically rich external representations (e.g., Kellman et al., 2008 ; Mayer, Griffith, Jurkowitz, & Rothman, 2008 ; Richland & McDonough, 2010 ; Son & Goldstone, 2009 ). Such investigations are likely to yield both practical and theoretical payoffs.

Adams, J. L. ( 1979 ). Conceptual blockbusting: A guide to better ideas (2nd ed.). New York: Norton.

Google Scholar

Google Preview

Adelson, B. ( 1981 ). Problem solving and the development of abstract categories in programming languages.   Memory and Cognition , 9 , 422–433.

Alibali, M. W., Bassok, M., Solomon, K. O., Syc, S. E., & Goldin-Meadow, S. ( 1999 ). Illuminating mental representations through speech and gesture.   Psychological Science , 10 , 327–333.

Allard, F., & Starkes, J. L. ( 1991 ). Motor-skill experts in sports, dance, and other domains. In K. A. Ericsson & J. Smith (Eds.), Toward a general theory of expertise: Prospects and limits (pp. 126–152). New York: Cambridge University Press.

Anderson, J. R. ( 1982 ). Acquisition of cognitive skill.   Psychological Review , 89 , 369–406.

Anzai, Y., & Simon, H. A. ( 1979 ). The theory of learning by doing.   Psychological Review , 86 , 124–140.

Atwood, M. E, & Polson, P.G. ( 1976 ). A process model for water jug problems.   Cognitive Psychology , 8 , 191–216.

Barwise, J., & Etchemendy, J. ( 1991 ). Visual information and valid reasoning. In W. Zimmermann & S. Cunningham (Eds.), Visualization in teaching and learning mathematics (pp. 9–24). Washington, DC: Mathematical Association of America.

Bassok, M., Chase, V. M., & Martin, S. A. ( 1998 ). Adding apples and oranges: Alignment of semantic and formal knowledge.   Cognitive Psychology , 35 , 99–134.

Bassok, M., & Holyoak, K. J. ( 1989 ). Interdomain transfer between isomorphic topics in algebra and physics.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 15 , 153–166.

Bassok, M., & Olseth, K. L. ( 1995 ). Object-based representations: Transfer between cases of continuous and discrete models of change.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 21 , 1522–1538.

Bassok, M., Pedigo, S. F., & Oskarsson, A. T. ( 2008 ). Priming addition facts with semantic relations.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 34 , 343–352.

Bassok, M., Wu, L., & Olseth, L. K. ( 1995 ). Judging a book by its cover: Interpretative effects of content on problem solving transfer.   Memory and Cognition , 23 , 354–367.

Beilock, S. L. ( 2008 ). Math performance in stressful situations.   Current Directions in Psychological Science , 17 , 339–343.

Birch, H. G. & Rabinowitz, H. S. ( 1951 ). The negative effect of previous experience on productive thinking.   Journal of Experimental Psychology , 41 , 122–126.

Blessing, S. B., & Ross, B. H. ( 1996 ). Content effects in problem categorization and problem solving.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 22 , 792–810.

Bowden, E. M., & Jung-Beeman, M. ( 1998 ). Getting the right idea: Semantic activation in the right hemisphere may help solve insight problems.   Psychological Science , 6 , 435–440.

Bowden, E. M., & Jung-Beeman, M. ( 2003 ). Aha! Insight experience correlates with solution activation in the right hemisphere.   Psychonomic Bulletin and Review , 10 , 730–737.

Bowden, E. M., Jung-Beeman, M., Fleck, J., & Kounios, J. ( 2005 ). New approaches to demystifying insight.   Trends in Cognitive Sciences , 9 , 322–328.

Catrambone, R. ( 1998 ). The subgoal-learning model: Creating better examples so that students can solve novel problems.   Journal of Experimental Psychology: General , 127 , 355–376.

Chase, W. G., & Simon, H. A. ( 1973 ). Perception in chess.   Cognitive Psychology , 4 , 55–81.

Chen, D., & Holyoak, K. J. ( 2010 ). Enhancing acquisition of intuition versus planning in problem solving. In S. Ohlsson & R. Catrambone (Eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society (pp. 1875–1880). Austin, TX: Cognitive Science Society.

Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. ( 1989 ). Self-explanations: How students study and use examples in learning to solve problems.   Cognitive Science , 13 , 145–182.

Chi, M. T. H., Feltovich, P. J., & Glaser, R. ( 1981 ). Categorization and representation of physics problems by experts and novices.   Cognitive Science , 5 , 121–152.

Clement, J., Lochhead, J., & Monk, G. S. ( 1981 ). Translation difficulties in learning mathematics.   The American Mathematical Monthly , 88 , 286–290.

Coughlin, L. D., & Patel, V. L. ( 1987 ). Processing of critical information by physicians and medical students.   Journal of Medical Education , 62 , 818–828.

Cox, R. ( 1999 ). Representation construction, externalised cognition and individual differences.   Learning and Instruction , 9 , 343–363.

Deakin, J. M., & Allard, F. ( 1991 ). Skilled memory in expert figure skaters.   Memory and Cognition , 19 , 79–86.

Doumas, L. A. A., Bassok, M., Guthormsen, A., & Hummel, J. E. ( 2006 ). Theory of reflexive relational generalization. In R. Sun & N. Miyake (Eds.), Proceedings of the 28th Annual Conference of the Cognitive Science Society (pp. 1246–1250). Mahwah, NJ: Erlbaum.

Dunbar, K. ( 2001 ). The analogical paradox: Why analogy is so easy in naturalistic settings, yet so difficult in the psychological laboratory. In D. Gentner, K. J. Holyoak, & B. Kokinov (Eds.), Analogy: Perspectives from cognitive science (pp. 313–362). Cambridge, MA: MIT Press.

Duncker, K. ( 1945 ). On problem-solving (L. S. Lees, Trans.). Psychological Monographs , 58 (Whole No. 270). (Original work published 1935).

Durso, F. T., Rea, C. B., & Dayton, T. ( 1994 ). Graph-theoretic confirmation of restructuring during insight.   Psychological Science , 5 , 94–98.

Egan, D. E., & Schwartz, B. J. ( 1979 ). Chunking in the recall of symbolic drawings.   Memory and Cognition , 7 , 149–158.

Ericsson, K. A., & Simon, H. A. ( 1980 ). Verbal reports as data.   Psychological Review , 87 , 215–251.

Ernst, G. W., & Newell, A. ( 1969 ). GPS: A case study in generality and problem solving . New York: Academic Press.

Fisher, K. J., & Bassok, M. ( 2009 ). Analogical alignments in algebraic modeling. In B. Kokinov, D. Gentner, & K. J. Holyoak (Eds.), Proceedings of the 2nd International Analogy Conference (pp. 137–144). Sofia, Bulgaria: New Bulgarian University Press.

Fisher, K. J., Bassok, M., & Osterhout, L. ( 2010 ). When two plus two does not equal four: Event-related potential responses to semantically incongruous arithmetic word problems. In S. Ohlsson & R. Catrambone (Eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society (pp. 1571–1576). Austin, TX: Cognitive Science Society.

Fisher, K. J., Borchert, K., & Bassok, M. ( 2011 ). Following the standard form: Effects of equation format on algebraic modeling.   Memory and Cognition , 39 , 502–515.

Garber, P., & Goldin-Meadow, S. ( 2002 ). Gesture offers insight into problem solving in adults and children.   Cognitive Science , 26 , 817–831.

Gobet, F., & Simon, H. ( 1996 ). Recall of rapidly presented random chess positions is a function of skill.   Psychonomic Bulletin and Review , 3 , 159–163.

Goldstone, R. L., Landy, D. H., & Son, J. Y. ( 2010 ). The education of perception.   Topics in Cognitive Science , 2 , 265–284.

Goldstone, R. L., & Sakamoto, J. Y. ( 2003 ). The transfer of abstract principles governing complex adaptive systems.   Cognitive Psychology , 46 , 414–466.

Greeno, J. G. ( 1974 ). Hobbits and orcs: Acquisition of a sequential concept.   Cognitive Psychology , 6 , 270–292.

Hardiman, P. T., Dufresne, R., & Mestre, J. P. ( 1989 ). The relation between problem categorization and problem solving among experts and novices.   Memory and Cognition , 17 , 627–638.

Haverty, L. A., Koedinger, K. R., Klahr, D., & Alibali, M. W. ( 2000 ). Solving induction problems in mathematics: Not-so-trivial Pursuit.   Cognitive Science , 24 , 249–298.

Hayes, J. R., & Simon, H. A. ( 1977 ). Psychological differences among problem isomorphs. In N. J. Castellan, D. B. Pisoni, & G. R. Potts (Eds.), Cognitive theory (Vol. 2, pp. 21–44). Hillsdale, NJ: Erlbaum.

Hegarty, M., Canham, M. S., & Fabricant, S. I. ( 2010 ). Thinking about the weather: How display salience and knowledge affect performance in a graphic inference task.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 36 , 37–53.

Hegarty, M., Mayer, R. E., & Green, C. E. ( 1992 ). Comprehension of arithmetic word problems: Evidence from students' eye fixations.   Journal of Educational Psychology , 84 , 76–84.

Hinsley, D. A., Hayes, J. R., & Simon, H. A. ( 1977 ). From words to equations: Meaning and representation in algebra word problems. In D. Hinsley, M. Just., & P. Carpenter (Eds.), Cognitive processes in comprehension (pp. 89–106). Hillsdale, NJ: Erlbaum.

Holyoak, K. J., & Koh, K. ( 1987 ). Surface and structural similarity in analogical transfer.   Memory and Cognition , 15 , 332–340.

Jones, G. ( 2003 ). Testing two cognitive theories of insight.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 29 , 1017–1027.

Jung-Beeman, M., & Bowden, E. M. ( 2000 ). The right hemisphere maintains solution-related activation for yet-to-be solved insight problems.   Memory and Cognition , 28 , 1231–1241.

Jung-Beeman, M., Bowden, E. M., Haberman, J., Frymiare, J. L., Arambel-Liu, S., Greenblatt, R., … Kounios, J. ( 2004 ). Neural activity when people solve verbal problems with insight.   PLOS Biology , 2 , 500–510.

Kellman, P. J. ( 2000 ). An update on Gestalt psychology. In B. Landau, J. Sabini, J. Jonides, & E. Newport (Eds.), Perception, cognition, and language: Essays in honor of Henry and Lila Gleitman (pp. 157–190). Cambridge, MA: MIT Press.

Kellman, P. J., Massey, C. M., & Son, J. Y ( 2009 ). Perceptual learning modules in mathematics: Enhancing students' pattern recognition, structure extraction, and fluency.   Topics in Cognitive Science , 1 , 1–21.

Kellman, P. J., Massey, C., Roth, Z., Burke, T., Zucker, J., Saw, A., … Wise, J. A. ( 2008 ). Perceptual learning and the technology of expertise.   Pragmatics and Cognition , 16 , 356–405.

Kershaw, T. C., & Ohlsson, S. ( 2004 ). Multiple causes of difficulty in insight: The case of the nine-dot problem.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 30 , 3–13.

Kindfield, A. C. H. ( 1993 /1994). Biology diagrams: Tools to think with.   Journal of the Learning Sciences , 3 , 1–36.

Kintsch, W., & Greeno, J. G. ( 1985 ). Understanding and solving word arithmetic problems.   Psychological Review , 92 , 109–129.

Knoblich, G., Ohlsson, S., Haider, H., & Rhenius, D. ( 1999 ). Constraint relaxation and chunk decomposition in insight problem solving.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 25 , 1534–1555.

Knoblich, G., Ohlsson, S., & Raney, G. E. ( 2001 ). An eye movement study of insight problem solving.   Memory and Cognition , 29 , 1000–1009.

Kohler, W. ( 1925 ). The mentality of apes . New York: Harcourt Brace.

Kotovsky, K., Hayes, J. R., & Simon, H. A. ( 1985 ). Why are some problems hard? Evidence from Tower of Hanoi.   Cognitive Psychology , 17 , 248–294.

Kozma, R. B., & Russell, J. ( 1997 ). Multimedia and understanding: Expert and novice responses to different representations of chemical phenomena.   Journal of Research in Science Teaching , 34 , 949–968.

Landy, D., & Goldstone, R. L. ( 2007 a). Formal notations are diagrams: Evidence from a production task.   Memory and Cognition , 35, 2033–2040.

Landy, D., & Goldstone, R. L. ( 2007 b). How abstract is symbolic thought?   Journal of Experimental Psychology: Learning, Memory, and Cognition , 33, 720–733.

Larkin, J. H., McDermott, J., Simon, D. P., & Simon, H. A. ( 1980 ). Models of competence in solving physics problems.   Cognitive Science , 4 , 317–345.

Larkin, J. H., & Simon, H. A. ( 1987 ). Why a diagram is (sometimes) worth ten thousand words.   Cognitive Science , 11 , 65–99.

Lewis, A. B., & Mayer, R. E. ( 1987 ). students' miscomprehension of relational statements in arithmetic word problems.   Journal of Educational Psychology , 79 , 363–371.

Lynch, M. ( 1990 ). The externalized retina: Selection and mathematization in the visual documentation of objects in the life sciences. In M. Lynch & S. Woolgar (Eds.), Representation in scientific practice (pp. 153–186). Cambridge, MA: MIT Press.

MacGregor, J. N., Ormerod, T. C., & Chronicle, E. P. ( 2001 ). Information processing and insight: A process model of performance on the nine-dot and related problems.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 27 , 176–201.

Maier, N. ( 1930 ). Reasoning in humans. I. On direction.   Journal of Comparative Psychology , 10 , 15–43.

Maier, N. ( 1931 ). Reasoning in humans. II. The solution of a problem and its appearance in consciousness.   Journal of Comparative Psychology , 12 , 181–194.

Markman, A. B. ( 1999 ). Knowledge representation . Mahwah, NJ: Erlbaum.

Martin, S. A., & Bassok, M. ( 2005 ). Effects of semantic cues on mathematical modeling: Evidence from word-problem solving and equation construction tasks.   Memory and Cognition , 33 , 471–478.

Mayer, R. E., & Gallini, J. K. ( 1990 ). When is an illustration worth ten thousand words?   Journal of Educational Psychology , 82 , 715–726.

Mayer, R. E., Griffith, E., Jurkowitz, I. T. N., & Rothman, D. ( 2008 ). Increased interestingness of extraneous details in a multimedia science presentation leads to decreased learning.   Journal of Experimental Psychology: Applied , 14 , 329–339.

McKeithen, K. B., Reitman, J. S., Rueter, H. H., & Hirtle, S. C. ( 1981 ). Knowledge organization and skill differences in computer programmers.   Cognitive Psychology , 13 , 307–325.

Medin, D. L., & Ross, B. H. ( 1989 ). The specific character of abstract thought: Categorization, problem solving, and induction. In R. J. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 5, pp. 189–223). Hillsdale, NJ: Erlbaum.

Moss, J., Kotovsky, K., & Cagan, J. ( 2011 ). The effect of incidental hints when problems are suspended before, during, and after an impasse.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 37 , 140–148.

Myles-Worsley, M., Johnston, W. A., & Simons, M. A ( 1988 ). The influence of expertise on X-ray image processing.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 14 , 553–557.

Newell, A., & Simon, H. A. ( 1972 ). Human problem solving . Englewood Cliffs, NJ: Prentice-Hall.

Newell, A., & Simon, H. A. ( 1976 ). Computer science as empirical enquiry: Symbols and search.   Communications of the ACM , 19 , 113–126.

Novick, L. R. ( 1988 ). Analogical transfer, problem similarity, and expertise.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 14 , 510–520.

Novick, L. R. ( 1995 ). Some determinants of successful analogical transfer in the solution of algebra word problems.   Thinking and Reasoning , 1 , 5–30.

Novick, L. R., & Catley, K. M. ( 2007 ). Understanding phylogenies in biology: The influence of a Gestalt perceptual principle.   Journal of Experimental Psychology: Applied , 13 , 197–223.

Novick, L. R., Catley, K. M., & Funk, D. J. ( 2010 ). Characters are key: The effect of synapomorphies on cladogram comprehension.   Evolution: Education and Outreach , 3 , 539–547.

Novick, L. R., & Hmelo, C. E. ( 1994 ). Transferring symbolic representations across non-isomorphic problems.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 20 , 1296–1321.

Novick, L. R., & Holyoak, K. J. ( 1991 ). Mathematical problem solving by analogy.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 17 , 398–415.

Novick, L. R., & Hurley, S. M. ( 2001 ). To matrix, network, or hierarchy: That is the question.   Cognitive Psychology , 42 , 158–216.

Novick, L. R., Shade, C. K., & Catley, K. M. ( 2011 ). Linear versus branching depictions of evolutionary history: Implications for diagram design.   Topics in Cognitive Science , 3 (3), 536–559.

Novick, L. R., & Sherman, S. J. ( 2003 ). On the nature of insight solutions: Evidence from skill differences in anagram solution.   The Quarterly Journal of Experimental Psychology , 56A , 351–382.

Novick, L. R., & Sherman, S. J. ( 2008 ). The effects of superficial and structural information on on-line problem solving for good versus poor anagram solvers.   The Quarterly Journal of Experimental Psychology , 61 , 1098–1120.

Ohlsson, S. ( 1984 ). Restructuring revisited I. Summary and critique of the Gestalt theory of problem solving.   Scandinavian Journal of Psychology , 25 , 65–78.

Öllinger, M., Jones, G., & Knoblich, G. ( 2008 ). Investigating the effect of mental set on insight problem solving.   Experimental Psychology , 55 , 269–282.

Ormerod, T. C., MacGregor, J. N., & Chronicle, E. P. ( 2002 ). Dynamics and constraints in insight problem solving.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 28 , 791–799.

Paige, J. M., & Simon, H. A. ( 1966 ). Cognitive processes in solving algebra word problems. In B. Kleinmuntz (Ed.), Problem solving: Research, method, and theory (pp. 51–119). New York: Wiley

Patel, V. L., Groen, G. J., & Arocha, J. F. ( 1990 ). Medical expertise as a function of task difficulty.   Memory and Cognition , 18 , 394–406.

Patsenko, E. G., & Altmann, E. M. ( 2010 ). How planful is routine behavior? A selective attention model of performance in the Tower of Hanoi.   Journal of Experimental Psychology: General , 139 , 95–116.

Polya, G. ( 1957 ). How to solve it (2nd ed.). Princeton, NJ: Princeton University Press.

Posner, M. I. ( 1973 ). Cognition: An introduction . Glenview, IL: Scott, Foresman and Company.

Reitman, W. R. ( 1965 ). Cognition and thought . New York: Wiley.

Richland, L. E., & McDonough, I. M. ( 2010 ), Learning by analogy: Discriminating between potential analogs.   Contemporary Educational Psychology , 35 , 28–43.

Russo, J. E., Johnson, E. J., & Stephens, D. L. ( 1989 ). The validity of verbal protocols.   Memory and Cognition , 17 , 759–769.

Schoenfeld, A. H. ( 1979 ). Explicit heuristic training as a variable in problem-solving performance.   Journal for Research in Mathematics Education , 10 , 173–187.

Schoenfeld, A. H., & Herrmann, D. J. ( 1982 ). Problem perception and knowledge structure in expert and novice mathematical problem solvers.   Journal of Experimental Psychology: Learning, Memory, and Cognition , 8 , 484–494.

Schwartz, S. H. ( 1971 ). Modes of representation and problem solving: Well evolved is half solved.   Journal of Experimental Psychology , 91 , 347–350.

Silver, E. A. ( 1979 ). Student perceptions of relatedness among mathematical verbal problems.   Journal for Research in Mathematics Education , 10 , 195–210.

Silver, E. A. ( 1981 ). Recall of mathematical problem information: Solving related problems.   Journal for Research in Mathematics Education , 12 , 54–64.

Simon, D. P., & Simon, H. A. ( 1978 ). Individual differences in solving physics problems. In R. Siegler (Ed.), Children's thinking: What develops? (pp. 325–348). Hillsdale, NJ: Erlbaum.

Simon, H. A. ( 1978 ). Information-processing theory of human problem solving. In W. K. Estes (Ed.), Handbook of learning and cognitive processes (Vol. 5, pp. 271–295). Hillsdale, NJ: Erlbaum.

Simon, H. A. ( 1986 ). The information processing explanation of Gestalt Phenomena.   Computers in Human Behavior , 2 , 241–255.

Simon, H. A. ( 1990 ). Invariants of human behavior.   Annual Review of Psychology , 41 , 1–19.

Son, J. Y., & Goldstone, R. L. ( 2009 ). Fostering general transfer with specific simulations.   Pragmatics and Cognition , 17 , 1–42.

Thomas, J. C., Jr., ( 1974 ). An analysis of behavior in the hobbits-orcs problem.   Cognitive Psychology , 6 , 257–269.

Weisberg, R. W., & Alba, J. W. ( 1981 ). An examination of the alleged role of “fixation” in the solution of several “insight” problems.   Journal of Experimental Psychology: General , 110 , 169–192.

Weiser, M., & Shertz, J. ( 1983 ). Programming problem representation in novice and expert programmers.   International Journal of Man-Machine Studies , 19 , 391–398.

Wertheimer, M. ( 1959 ). Productive thinking (Rev. ed.). Chicago, IL: University of Chicago Press.

Winn, W. ( 1989 ). The design and use of instructional graphics. In H. Mandl & J. R. Levin (Eds.), Knowledge acquisition from text and pictures (pp. 125–144). Amsterdam, Netherlands: Elsevier

• About Oxford Academic
• Publish journals with us
• University press partners
• What we publish
• New features  
• Open access
• Institutional account management
• Rights and permissions
• Get help with access
• Accessibility
• Advertising
• Media enquiries
• Oxford University Press
• Oxford Languages
• University of Oxford

Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide

• Copyright © 2024 Oxford University Press
• Cookie settings
• Cookie policy
• Privacy policy
• Legal notice

This Feature Is Available To Subscribers Only

Sign In or Create an Account

This PDF is available to Subscribers Only

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.

• Skip to main content
• Skip to primary sidebar

IResearchNet

Problem Solving

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

Introduction

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

The Nature of Problem Solving

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

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

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

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

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

Cognitive and Psychological Aspects of Problem Solving

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

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

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

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

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

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

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

Problem Solving in Educational Settings

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

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

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

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

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

Applications and Practical Implications

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

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

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

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

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

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

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

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

References:

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

Thinking and Intelligence

Introduction to Thinking and Problem-Solving

What you’ll learn to do: describe cognition and problem-solving strategies.

Imagine all of your thoughts as if they were physical entities, swirling rapidly inside your mind. How is it possible that the brain is able to move from one thought to the next in an organized, orderly fashion? The brain is endlessly perceiving, processing, planning, organizing, and remembering—it is always active. Yet, you don’t notice most of your brain’s activity as you move throughout your daily routine. This is only one facet of the complex processes involved in cognition. Simply put, cognition is thinking, and it encompasses the processes associated with perception, knowledge, problem solving, judgment, language, and memory. Scientists who study cognition are searching for ways to understand how we integrate, organize, and utilize our conscious cognitive experiences without being aware of all of the unconscious work that our brains are doing (for example, Kahneman, 2011).

Learning Objectives

• Distinguish between concepts and prototypes
• Explain the difference between natural and artificial concepts
• Describe problem solving strategies, including algorithms and heuristics
• Explain some common roadblocks to effective problem solving

CC licensed content, Original

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

CC licensed content, Shared previously

• What Is Cognition?. Authored by : OpenStax College. Located at : https://openstax.org/books/psychology-2e/pages/7-1-what-is-cognition . License : CC BY: Attribution . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction
• A Thinking Man Image. Authored by : Wesley Nitsckie. Located at : https://www.flickr.com/photos/nitsckie/5507777269 . License : CC BY-SA: Attribution-ShareAlike

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

Problem-Solving Theory: The Task-Centred Model

• Living reference work entry
• First Online: 12 April 2022
• Cite this living reference work entry

• Blanca M. Ramos 5 &
• Randall L. Stetson 6  

Part of the book series: Social Work ((SOWO))

462 Accesses

This chapter examines the task-centred model to illustrate the application of problem-solving theory for social work intervention. First, it provides a brief description of the problem-solving model. Its historical development and key principles and concepts are presented. Next, the chapter offers a general overview of the crisis intervention model. The task-centred model and crisis intervention share principles and methods drawn from problem-solving theory. The remainder of the chapter focuses on the task-centred model. It reviews its historical background, viability as a framework for social work generalist practice, as well as its applicability with diverse client populations and across cultural settings. The structured steps that guide task-centred implementation throughout the helping process are described. A brief critical review of the model’s strengths and limitations is provided. The chapter concludes with a brief summary and some closing thoughts.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Brieland D (1977) Historical overview. Soc Work 22(5):341–346. http://www.jstor.org.libezproxy2.syr.edu/stable/23712810

Google Scholar  

Coady N, Lehmann P (2016) The problem-solving model: a framework for integrating the science and art of practice. In: Lehmann P, Coady N (eds) Theoretical perspectives for direct social work practice: a generalist-eclectic approach, 3rd edn. Springer

Chapter   Google Scholar  

D’Zurilla TJ, Goldfried MR (1971) Problem solving and behavior modification. J Abnorm Psychol 78(1):107–126. https://doi.org/10.1037/h0031360

Article   Google Scholar  

Dattilio F (1998) Cognitive behavioral therapy. In: Dattilio M (ed) Case studies in couple and family therapy: systems and cognitive perspectives. Guilford, New York, pp 62–82

Dohert W (1981) Cognitive processes in intimate conflicts: extending attribution theory. Am J Fam Ther 9:3–12

Duckword G (1967) A project in crisis intervention. Soc Casework 48(4):227–231

Fortune AE (2012) Development of the task-centered model. In: Rzepnicki TL, McCracken SG, Briggs HE (eds) From task-centered social work to evidence-based and integrative practice: reflections on history and implementation. Oxford University Press, pp 15–39

Fortune AE, Reid WJ (2011) Task-centered social work. In: Turner F (ed) Social work treatment: interlocking theoretical approaches, 6th edn. Oxford University Press, New York, pp 513–532

Fortune AE, McCallion P, Briar-Lawson K (Eds.) (2010) Social work practice research for the 21st century. New York: Columbia University Press

Fortune AE, Ramos BM, Reid WJ (2022) Task-Centered practice. In: Lisa Rapp-McCall, Kevin Corcoran & Albert R. Roberts, (eds.), Social workers’ desk reference, 4th edn Oxford University Press, New York

Fortune AE, Ramos BM, Reid WJ (2022) Task-Centered Practice. In: Lisa Rapp-McCall, Kevin Corcoran, Albert R Roberts, (Eds.). Social Workers’ Desk Reference, 4th edition. New York: Oxford University Press

Garfield SL (1994) Research on client variables in psychotherapy. In: Bergin A, Garfield S (eds) Handbook of psychotherapy and behavior change, 4th edn. Wiley, New York, pp 190–228

Golan N, Carey H, Hyttinnen E (1969) The emerging role of the social worker in the psychiatric emergency service. Community Ment Health J 5(1):55–61

Gorey KM, Thyer BA, Pawfuck DE (1998) Differential effectiveness of prevalent social work practice models: a meta-analysis. Soc Work 43:269–278

Hollis F (1970) The psychosocial approach to the practice of casework. In: Theories of social casework. University of Chicago Press, pp 33–75

Hoyt MF (2000) Some stories are better than others: doing what works in brief therapy and managed care. Brunner/Mazel, Philadelphia

Hubble M, Duncan B, Miller S (1999) Introduction. In: Hubble M, Duncan B, Miller S (eds) The heart and soul of change: what works in therapy. American Psychological Association, Washington, DC

Huh NS, Koh YS (2010) Task-centered practice in South Korea. In: Fortune AE, McCallion P, Briar-Lawson K (eds) Social work practice research for the 21st century. Columbia University Press, New York, pp 235–239

Jagt N, Jagt L (2010) Task-centered practice in the Netherlands. In: Fortune AE, McCallion P, Briar-Lawson K (eds) Social work practice research for the 21st century. Columbia University Press, New York, pp 208–212

Lo TW (2010) Task-centered practice in Hong Kong. In: Fortune AE, McCallion P, Briar-Lawson K (eds) Social work practice research for the 21st century. Columbia University Press, New York, pp 240–244

Malouff JM, Thorsteinsson EB, Schutte NS (2007) The efficacy of problem-solving therapy in reducing mental and physical health problems: a meta-analysis. Clin Psychol Rev 27(1):46–57

Marsh P (2010) Task-centered practice in Great Britain. In: Fortune AE, McCallion P, Briar-Lawson K (eds) Social work practice research for the 21st century. Columbia University Press, New York, pp 203–2007

Marsh P, Doel M (2005) The task-centred book. Routledge, Abingdon/New York

Book   Google Scholar  

Miley K, O’Melia M, DuBois (2017) Generalist social work practice: an empowering approach. Allyn & Bacon, Boston

Morris B (1968) Crisis intervention in a public welfare agency. Soc Casework 49(10):612–617

Naleppa M (2010) Task-centered practice in Germany. In: Fortune AE, McCallion P, Briar-Lawson K (eds) Social work practice research for the 21st century. Columbia University Press, New York, pp 213–216

Nezu AM, Nezu CM, D’Zurilla T (2012) Problem-solving therapy: a treatment manual. Springer

Nichols M, Schwartz R (2001) Family therapy. Allyn and Bacon, Needham Heights

Parad HJ (1958) Ego psychology and dynamic casework. Family Association of America, New York

Parad H (1965) Preventive casework: problems and implications. In: Parad H (ed) Crisis intervention: selected readings. Family Service Association of America, New York

Parad H (1966) The use of time-limited crisis interventions in community mental health programming. Soc Serv Rev 40(3):275–282

Parad H, Capland G (1960) A framework for studying families in crisis. Soc Work 5(3):3–15

Parad H, Parad G (1968) A study of crisis oriented planned short-term treatment. Soc Casework 49(6):346–355

Payne M (2014) Modern social work theory, 3rd edn. Palgrave Macmillan, Basingstoke

Perlman HH (1957) Social casework: a problem-solving process. University of Chicago Press, Chicago

Poal P (1990) Introduction to the theory and practice of crisis intervention. Quadernos Psicol 10:121–140

Ramos BM, Garvin C (2003) Task centered treatment with culturally diverse populations. In: Tolson E, Reid W, Garvin C (eds) Generalist practice: a task centered approach, pp. Columbia University Press, New York, pp 441–463

Ramos B, Tolson E (2016) The task-centered model. In: Lehmann P, Coady N (eds) Theoretical perspectives for direct social work practice: a generalist-eclectic approach, 3rd edn. Springer

Regehr C (2017) Crisis theory and social work treatment. In: Turner F (ed) Social work treatment: interlocking theoretical approaches. Oxford University Press

Reid WJ (1992) Task strategies: an empirical approach to social work practice. Columbia University Press, New York

Reid WJ, Epstein L (eds) (1972) Task-centered casework. Columbia University Press, New York

Reid W, Ramos B (2002) Intervención “Centrada en la Tarea”, un Modelo de Práctica de Trabajo Social. Rev Treball Soc 168:6–22

Reid WJ, Shyne AW (1969) Brief and extended casework. Columbia University Press, New York

Roberts A (2005) Bridging the past and present to the future of crisis intervention and case management. In: Roberts A (ed) Crisis intervention handbook: assessment, treatment, and research, 3rd edn. Oxford University Press

Rooney RH (2010) Task-centered practice in the United States. In: Fortune AE, McCallion P, Briar-Lawson K (eds) Social work practice research for the 21st century. Columbia University Press, New York, pp 195–202

Ruben D (1998) Social exchange theory: dynamics of a system governing the dysfunctional family and guide to assessment. J Contemp Psychother 8(3):307–325

Schatz MS, Jenkins LE, Sheafor BW (1990) Milford redefined: a model of initial and advanced generalist social work [Article]. J Soc Work Educ 26(3):217–231. https://doi.org/10.1080/10437797.1990.10672154

Strean HS (1968) Some reactions of case workers to the war on poverty. J Contemp Psychother 1:43–48

Strickler M (1965) Applying crisis theory in a community clinic. Soc Casework 46:150–154

Studt E (1968) Social work theory and implication for the practice of methods. Soc Work Educ Report 16:22–46

Tolson R, Reid W, Garvin C (2003) Generalist practice: a task-centered approach, 2nd edn. Columbia University Press, New York

Trotter C (2010) Task-centred practice in Australia. In Fortune AE, McCallion P, Briar-Lawson K (Eds.), Social work practice research for the 21st century, 235–239. New York: Columbia University Press

Watzlawick P, Bervin J, Jackson D (1967) Pragmatics of human communication. W.W. Norton, New York

Download references

Author information

Authors and affiliations.

State University of New York at Albany, Albany, NY, USA

Blanca M. Ramos

State University of New York at Oswego, Oswego, NY, USA

Randall L. Stetson

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Blanca M. Ramos .

Editor information

Editors and affiliations.

School of Human Services and Social Work, Griffith University, Meadowbrook, QLD, Australia

Dorothee Hölscher

School of Social Sciences, UNSW Sydney, Sydney, NSW, Australia

Richard Hugman

Donna McAuliffe

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Singapore Pte Ltd.

About this entry

Cite this entry.

Ramos, B.M., Stetson, R.L. (2022). Problem-Solving Theory: The Task-Centred Model. In: Hölscher, D., Hugman, R., McAuliffe, D. (eds) Social Work Theory and Ethics. Social Work. Springer, Singapore. https://doi.org/10.1007/978-981-16-3059-0_9-1

Download citation

DOI : https://doi.org/10.1007/978-981-16-3059-0_9-1

Received : 24 December 2021

Accepted : 25 January 2022

Published : 12 April 2022

Publisher Name : Springer, Singapore

Print ISBN : 978-981-16-3059-0

Online ISBN : 978-981-16-3059-0

eBook Packages : Social Sciences Reference Module Humanities and Social Sciences Reference Module Business, Economics and Social Sciences

• Publish with us

Policies and ethics

• Find a journal
• Track your research

Insight Learning Theory: Definition, Stages, and Examples

Categories Learning

Insight learning theory is all about those “lightbulb moments” we experience when we suddenly understand something. Instead of slowly figuring things out through trial and error, insight theory says we can suddenly see the solution to a problem in our minds. 

This theory is super important because it helps us understand how our brains work when we learn and solve problems. It can help teachers find better ways to teach and improve our problem-solving skills and creativity. It’s not just useful in school—insight theory also greatly impacts science, technology, and business.

Table of Contents

What Is Insight Learning?

Insight learning is like having a lightbulb moment in your brain. It’s when you suddenly understand something without needing to go through a step-by-step process. Instead of slowly figuring things out by trial and error, insight learning happens in a flash. One moment, you’re stuck, and the next, you have the solution. 

This type of learning is all about those “aha” experiences that feel like magic. The key principles of insight learning involve recognizing patterns, making connections, and restructuring our thoughts. It’s as if our brains suddenly rearrange the pieces of a puzzle, revealing the big picture. So, next time you have a brilliant idea pop into your head out of nowhere, you might just be experiencing insight learning in action!

Three Components of Insight Learning Theory

Insight learning, a concept rooted in psychology, comprises three distinct properties that characterize its unique nature:

1. Sudden Realization

Unlike gradual problem-solving methods, insight learning involves sudden and profound understanding. Individuals may be stuck on a problem for a while, but then, seemingly out of nowhere, the solution becomes clear. This sudden “aha” moment marks the culmination of mental processes that have been working behind the scenes to reorganize information and generate a new perspective .

2. Restructuring of Problem-Solving Strategies

Insight learning often involves a restructuring of mental representations or problem-solving strategies . Instead of simply trying different approaches until stumbling upon the correct one, individuals experience a shift in how they perceive and approach the problem. This restructuring allows for a more efficient and direct path to the solution once insight occurs.

3. Aha Moments

A hallmark of insight learning is the experience of “aha” moments. These moments are characterized by a sudden sense of clarity and understanding, often accompanied by a feeling of satisfaction or excitement. It’s as if a mental lightbulb turns on, illuminating the solution to a previously perplexing problem. 

These moments of insight can be deeply rewarding and serve as powerful motivators for further learning and problem-solving endeavors.

Four Stages of Insight Learning Theory

Insight learning unfolds in a series of distinct stages, each contributing to the journey from problem recognition to the sudden realization of a solution. These stages are as follows:

1. Problem Recognition

The first stage of insight learning involves recognizing and defining the problem at hand. This may entail identifying obstacles, discrepancies, or gaps in understanding that need to be addressed. Problem recognition sets the stage for the subsequent stages of insight learning by framing the problem and guiding the individual’s cognitive processes toward finding a solution.

2. Incubation

After recognizing the problem, individuals often enter a period of incubation where the mind continues to work on the problem unconsciously. During this stage, the brain engages in background processing, making connections, and reorganizing information without the individual’s conscious awareness. 

While it may seem like a period of inactivity on the surface, incubation is a crucial phase where ideas gestate, and creative solutions take shape beneath the surface of conscious thought.

3. Illumination

The illumination stage marks the sudden emergence of insight or understanding. It is characterized by a moment of clarity and realization, where the solution to the problem becomes apparent in a flash of insight. 

This “aha” moment often feels spontaneous and surprising, as if the solution has been waiting just below the surface of conscious awareness to be revealed. Illumination is the culmination of the cognitive processes initiated during problem recognition and incubation, resulting in a breakthrough in understanding.

4. Verification

Following the illumination stage, individuals verify the validity and feasibility of their insights by testing the proposed solution. This may involve applying the solution in practice, checking it against existing knowledge or expertise, or seeking feedback from others. 

Verification serves to confirm the efficacy of the newfound understanding and ensure its practical applicability in solving the problem at hand. It also provides an opportunity to refine and iterate on the solution based on real-world feedback and experience.

Famous Examples of Insight Learning

Examples of insight learning can be observed in various contexts, ranging from everyday problem-solving to scientific discoveries and creative breakthroughs. Some well-known examples of how insight learning theory works include the following:

Archimedes’ Principle

According to legend, the ancient Greek mathematician Archimedes experienced a moment of insight while taking a bath. He noticed that the water level rose as he immersed his body, leading him to realize that the volume of water displaced was equal to the volume of the submerged object. This insight led to the formulation of Archimedes’ principle, a fundamental concept in fluid mechanics.

Köhler’s Chimpanzee Experiments

In Wolfgang Köhler’s experiments with chimpanzees on Tenerife in the 1920s, the primates demonstrated insight learning in solving novel problems. One famous example involved a chimpanzee named Sultan, who used sticks to reach bananas placed outside his cage. After unsuccessful attempts at using a single stick, Sultan suddenly combined two sticks to create a longer tool, demonstrating insight into the problem and the ability to use tools creatively.

Eureka Moments in Science

Many scientific discoveries are the result of insight learning. For instance, the famed naturalist Charles Darwin had many eureka moments where he gained sudden insights that led to the formation of his influential theories.

Everyday Examples of Insight Learning Theory

You can probably think of some good examples of the role that insight learning theory plays in your everyday life. A few common real-life examples include:

• Finding a lost item : You might spend a lot of time searching for a lost item, like your keys or phone, but suddenly remember exactly where you left them when you’re doing something completely unrelated. This sudden recollection is an example of insight learning.
• Untangling knots : When trying to untangle a particularly tricky knot, you might struggle with it for a while without making progress. Then, suddenly, you realize a new approach or see a pattern that helps you quickly unravel the knot.
• Cooking improvisation : If you’re cooking and run out of a particular ingredient, you might suddenly come up with a creative substitution or alteration to the recipe that works surprisingly well. This moment of improvisation demonstrates insight learning in action.
• Solving riddles or brain teasers : You might initially be stumped when trying to solve a riddle or a brain teaser. However, after some time pondering the problem, you suddenly grasp the solution in a moment of insight.
• Learning a new skill : Learning to ride a bike or play a musical instrument often involves moments of insight. You might struggle with a certain technique or concept but then suddenly “get it” and experience a significant improvement in your performance.
• Navigating a maze : While navigating through a maze, you might encounter dead ends and wrong turns. However, after some exploration, you suddenly realize the correct path to take and reach the exit efficiently.
• Remembering information : When studying for a test, you might find yourself unable to recall a particular piece of information. Then, when you least expect it, the answer suddenly comes to you in a moment of insight.

These everyday examples illustrate how insight learning is a common and natural part of problem-solving and learning in our daily lives.

Exploring the Uses of Insight Learning

Insight learning isn’t an interesting explanation for how we suddenly come up with a solution to a problem—it also has many practical applications. Here are just a few ways that people can use insight learning in real life:

Problem-Solving

Insight learning helps us solve all sorts of problems, from finding lost items to untangling knots. When we’re stuck, our brains might suddenly come up with a genius idea or a new approach that saves the day. It’s like having a mental superhero swoop in to rescue us when we least expect it!

Ever had a brilliant idea pop into your head out of nowhere? That’s insight learning at work! Whether you’re writing a story, composing music, or designing something new, insight can spark creativity and help you come up with fresh, innovative ideas.

Learning New Skills

Learning isn’t always about memorizing facts or following step-by-step instructions. Sometimes, it’s about having those “aha” moments that make everything click into place. Insight learning can help us grasp tricky concepts, master difficult skills, and become better learners overall.

Insight learning isn’t just for individuals—it’s also crucial for innovation and progress in society. Scientists, inventors, and entrepreneurs rely on insight to make groundbreaking discoveries and develop new technologies that improve our lives. Who knows? The next big invention could start with someone having a brilliant idea in the shower!

Overcoming Challenges

Life is full of challenges, but insight learning can help us tackle them with confidence. Whether it’s navigating a maze, solving a puzzle, or facing a tough decision, insight can provide the clarity and creativity we need to overcome obstacles and achieve our goals.

The next time you’re feeling stuck or uninspired, remember: the solution might be just one “aha” moment away!

Alternatives to Insight Learning Theory

While insight learning theory emphasizes sudden understanding and restructuring of problem-solving strategies, several alternative theories offer different perspectives on how learning and problem-solving occur. Here are some of the key alternative theories:

Behaviorism

Behaviorism is a theory that focuses on observable, overt behaviors and the external factors that influence them. According to behaviorists like B.F. Skinner, learning is a result of conditioning, where behaviors are reinforced or punished based on their consequences. 

In contrast to insight learning theory, behaviorism suggests that learning occurs gradually through repeated associations between stimuli and responses rather than sudden insights or realizations.

Cognitive Learning Theory

Cognitive learning theory, influenced by psychologists such as Jean Piaget and Lev Vygotsky , emphasizes the role of mental processes in learning. This theory suggests that individuals actively construct knowledge and understanding through processes like perception, memory, and problem-solving. 

Cognitive learning theory acknowledges the importance of insight and problem-solving strategies but places greater emphasis on cognitive structures and processes underlying learning.

Gestalt Psychology

Gestalt psychology, which influenced insight learning theory, proposes that learning and problem-solving involve the organization of perceptions into meaningful wholes or “gestalts.” 

Gestalt psychologists like Max Wertheimer emphasized the role of insight and restructuring in problem-solving, but their theories also consider other factors, such as perceptual organization, pattern recognition, and the influence of context.

Information Processing Theory

Information processing theory views the mind as a computer-like system that processes information through various stages, including input, processing, storage, and output. This theory emphasizes the role of attention, memory, and problem-solving strategies in learning and problem-solving. 

While insight learning theory focuses on sudden insights and restructuring, information processing theory considers how individuals encode, manipulate, and retrieve information to solve problems.

Kizilirmak, J. M., Fischer, L., Krause, J., Soch, J., Richter, A., & Schott, B. H. (2021). Learning by insight-like sudden comprehension as a potential strategy to improve memory encoding in older adults .  Frontiers in Aging Neuroscience ,  13 , 661346. https://doi.org/10.3389/fnagi.2021.661346

Lind, J., Enquist, M. (2012). Insight learning and shaping . In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning . Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_851

Osuna-Mascaró, A. J., & Auersperg, A. M. I. (2021). Current understanding of the “insight” phenomenon across disciplines . Frontiers in Psychology , 12, 791398. https://doi.org/10.3389/fpsyg.2021.791398

Salmon-Mordekovich, N., & Leikin, M. (2023). Insight problem solving is not that special, but business is not quite ‘as usual’: typical versus exceptional problem-solving strategies .  Psychological Research ,  87 (6), 1995–2009. https://doi.org/10.1007/s00426-022-01786-5

Facilitating Complex Thinking

Problem-Solving

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

PROBLEM-SOLVING IN THE CLASSROOM

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

Scene #1: A problem to be solved

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

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

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

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

Scene #3: Alicia abandons a fixed response

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

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

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

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

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

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

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

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

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

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

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

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

Common Obstacles to Solving Problems

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

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

Strategies to Assist Problem-Solving

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

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

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

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

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

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

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

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

Candela Citations

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

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

Share This Book

What Is the Cognitive Psychology Approach? 12 Key Theories

Maintaining focus on the oncoming traffic is paramount, yet I am barely aware of the seagulls flying overhead.

These noisy birds only receive attention when I am safely walking up the other side of the road, their cries reminding me of childhood seaside vacations.

Cognitive psychology focuses on the internal mental processes needed to make sense of the environment and decide on the next appropriate action (Eysenck & Keane, 2015).

This article explores the cognitive psychology approach, its origins, and several theories and models involved in cognition.

Before you continue, we thought you might like to download our three Positive Psychology Exercises for free . These science-based exercises explore fundamental aspects of positive psychology, including strengths, values, and self-compassion, and will give you the tools to enhance the wellbeing of your clients, students, or employees.

This Article Contains:

What is the cognitive psychology approach, a brief history of cognitive psychology, cognitive psychology vs behaviorism, 12 key theories, concepts, and models, fascinating research experiments, a look at positive cognitive psychology, interesting resources from positivepsychology.com, a take-home message.

The upsurge of research into the mysteries of the human brain and mind has been considerable in recent decades, with recognition of the importance of cognitive process in clinical psychology and social psychology  (Eysenck & Keane, 2015).

As a result, cognitive psychology has profoundly affected the field of psychology and our understanding of what it is to be human.

Perhaps more surprisingly, it has had such an effect without clear boundaries, an integrated set of assumptions and concepts, or a recognizable spokesperson (Gross, 2020).

So, what exactly is the cognitive psychology approach?

Cognitive psychology attempts to understand human cognition by focusing on what appear to be cognitive tasks that require little effort (Goldstein, 2011).

Let’s return to our example of walking down the road. Imagine now that we are also taking a call. We’re now combining several concurrent cognitive tasks:

• Perceiving the environment Distinguishing cars from traffic signals and discerning their direction and speed on the road as well as the people ahead standing, talking, and blocking the sidewalk.
• Paying attention Attending to what our partner is asking us on the phone, above the traffic noise.
• Visualizing Forming a mental image of items in the house, responding to the question, “Where did you leave your car keys?”
• Comprehending and producing language Understanding the real question (“I need to take the car. Where are your keys?”) from what is said and formulating a suitable reply.
• Problem-solving Working out how to get to the next appointment without the car.
• Decision-making Concluding that the timing of one meeting will not work and choosing to push it to another day.

While cognitive psychologists initially focused firmly on an analogy comparing the mind to a computer, their understanding has moved on.

There are currently four approaches, often overlapping and frequently combined, that science uses to understand human cognition (Eysenck & Keane, 2015):

• Cognitive psychology The attempt to “understand human cognition by using behavioral evidence” (Eysenck & Keane, 2015, p. 2).
• Cognitive neuropsychology Understanding ‘normal’ cognition through the study of patients living with a brain injury.
• Cognitive neuroscience Combining evidence from the brain with behavior to form a more complete picture of cognition.
• Computational cognitive science Using computational models to understand and test our understanding of human cognition.

Cognitive psychology plays a massive and essential role in understanding human cognition and is stronger because of its close relationships and interdependencies with other academic disciplines (Eysenck & Keane, 2015).

In 1868, a Dutch physiologist, Franciscus Donders, began to measure reaction time – something we would now see as an experiment in cognitive psychology (Goldstein, 2011).

Donders recognized that mental responses could not be measured directly but could be inferred from behavior. Not long after, Hermann Ebbinghaus began examining the nature and inner workings of human memory using nonsense syllables (Goldstein, 2011).

By the late 1800s, Wilhelm Wundt had set up the first laboratory dedicated to studying the mind scientifically. His approach became known as structuralism . His bold aim was to build a periodic table of the mind , containing all the sensations involved in creating any experience (Goldstein, 2011).

However, the use of analytical introspection to uncover hidden mental processes was gradually dropped when John Watson proposed a new psychological approach that became known as behaviorism (Goldstein, 2011).

Watson rejected the introspective approach and instead focused on observable behavior. His idea of classical conditioning – the connection of a new stimulus with a previously neutral one – was later surpassed by B. F. Skinner’s idea of operant conditioning , which focused on positive reinforcement (Goldstein, 2011).

Both theories sought to understand the relationship between stimulus and response rather than the mind’s inner workings (Goldstein, 2011).

Prompted by a scathing attack by linguist and cognitive scientist Noam Chomsky, by the 1950s behaviorism as the dominant psychological discipline was in decline. The introduction of the digital computer led to the information-processing approach , inspiring psychologists to think of the mind in terms of a sequence of processing stages (Goldstein, 2011).

Download 3 Free Positive Psychology Exercises (PDF)

Enhance wellbeing with these free, science-based exercises that draw on the latest insights from positive psychology.

Download 3 Free Positive Psychology Tools Pack (PDF)

By filling out your name and email address below.

Moore (1996) recognized the tensions of the paradigm shift from behaviorism to cognitive psychology.

While research into cognitive psychology, cognitive neuropsychology, cognitive neuroscience , and computational cognitive science is now widely accepted as the driving force behind understanding mental processes (such as memory, perception, problem-solving, and attention), this was not always the case (Gross, 2020).

Moore (1996) highlighted the relationship between behaviorism and the relatively new field of cognitive psychology, and the sometimes mistaken assumptions regarding the nature of the former approach:

• Behaviorism is typically only associated with studying publicly observable behavior. Unlike behaviorism, cognitive psychology is viewed as free of the restrictions of logical positivism, which rely on verification through observation.

Since then, modern cognitive psychology has incorporated findings from many other disciplines, including evolutionary psychology , computer science, artificial intelligence , and neuroscience (Eysenck & Keane, 2015).

• Unlike behaviorism, cognitive psychology is theoretical and explanatory. Behaviorism is often considered merely descriptive, while cognitive psychology is seen as being able to explain what is behind behavior.

Particular ongoing advances in cognitive psychology include perception, language comprehension and production, and problem-solving (Eysenck & Keane, 2015).

• Behaviorism cannot incorporate theoretical terms. While challenged by some behaviorists at the time, it was argued that behaviorism could not incorporate theoretical terms unless related to directly observable behavior.

At the time, cognitive psychologists also argued that it was wrong of behaviorists to interpret mental states in terms of brain states.

Neuroscience advances, such as new imaging techniques like functional MRI, continue to offer fresh insights into the relationship between the brain and mental states (Eysenck & Keane, 2015).

Clearly, the relationship between behaviorism and the developing field of cognitive psychology has been complex. However, cognitive psychology has grown into a school of thought that has led to significant advances in understanding cognition, especially when teamed up with other developments in computing and neuroscience.

This may not have been possible without the shift in the dominant schools of thought in psychology (Gross, 2020; Goldstein, 2011; Eysenck & Keane, 2015).

And while it is beyond the scope of this article to cover the full breadth or depth of the areas of research, we list several of the most important and fascinating specialties and theories below.

It is hardly possible to imagine a world in which attention doesn’t play an essential role in how we interact with the environment, and yet, we rarely give it a thought.

According to cognitive psychology, attention is most active when driven by an individual’s expectations or goals, known as top-down processing . On the other hand, it is more passive when controlled by external stimuli, such as a loud noise, referred to as bottom-up processing (Eysenck & Keane, 2015).

A further distinction exists between focused attention (selective) and divided attention . Research into the former explores how we are able to focus on one item (noise, image, etc.) when there are several. In contrast, the latter looks at how we can maintain attention on two or more stimuli simultaneously.

Donald Broadbent proposed the bottleneck model to explain how we can attend to just one message when several are presented, for example, in dichotic listening experiments, where different auditory stimuli are presented to each ear. Broadbent’s model suggests multiple processing stages, each one progressively restricting the information flow (Goldstein, 2011).

As with all other areas of cognition, perception is far more complicated than we might first imagine. Take, for example, vision. While a great deal of research has “involved presenting a visual stimulus and assessing aspects of its processing,” there is also the time aspect to consider (Eysenck & Keane, 2015, p. 121).

We need to not only perceive objects, but also make sense of their movement and detect changes in the visual environment over time (Eysenck & Keane, 2015).

Research suggests perception, like attention, combines bottom-up and top-down processing. Bottom-up processing involves neurons that fire in response to specific elements of an image – perhaps aspects of a face, nose, eyebrows, jawline, etc. Top-down processing considers how the knowledge someone brings with them affects their perception.

Bottom-down processing helps explain why two people, presented with the same stimuli, experience different perceptions as a result of their expectations and prior knowledge (Goldstein, 2011).

Combining bottom-up and top-down processing also enables the individual to make sense of both static and moving images when limited information is available; we can track a person walking through a crowd or a plane disappearing in and out of clouds (Eysenck & Keane, 2015).

The mirror neuron system is incredibly fascinating and is proving valuable in our attempts to understand biological motion. Observing actions activates similar areas of the brain as performing them. The model appears to explain how we can imitate the actions of another person – crucial to learning (Eysenck & Keane, 2015).

Language comprehension

Whether written or spoken, understanding language involves a high degree of multi-level processing (Eysenck & Keane, 2015).

Comprehension begins with an initial analysis of sentence structure (larger language units require additional processing). Beyond processing syntax (the rules for building and analyzing sentences), analysis of sentence meaning ( semantics ) is necessary to understand if the interpretation should be literal or involve irony, metaphor, or sarcasm (Eysenck & Keane, 2015).

Pragmatics examines intended meaning. For example, shouting, “That’s the doorbell!” is not likely to be a simple observation, but rather a request to answer the door (Eysenck & Keane, 2015).

Several models have been proposed to understand the analysis and comprehension of sentences, known as parsing , including (Eysenck & Keane, 2015):

• Garden-path model This model attempts to explain why some sentences are ambiguous (such as, “The horse raced past the barn fell.”). It suggests they are challenging to comprehend because the analysis is performed on each individual unit of the sentence with little feedback, and correction is inhibited.
• Constraint-based model The interpretations of a sentence may be limited by several constraints, including syntactic, semantic, and general world knowledge.
• Unrestricted race model This model combines the garden-path and constraint-based model, and suggests all sources of information inform syntactic structure. One such interpretation is selected until it is discarded, with good reason, for another.
• Good-enough representation This model proposes that parsing provides a ‘good-enough’ interpretation rather than something detailed, accurate, and complete.

The research and theories above hint at the vast complexity of human cognition and explain why so many models and concepts attempt to answer what happens when it works and, equally important, when it doesn’t.

A level of psychology: the cognitive approach – Atomi

There are many research experiments in cognitive psychology that highlight the successes and failings of human cognition. Each of the following three offers insight into the mental processes behind our thinking and behavior.

Cocktail party phenomenon

Selective attention – or in this case, selective listening – is often exemplified by what has become known as the cocktail party phenomenon  (Eysenck & Keane, 2015).

Even in a busy room and possibly mid-conversation, we can often hear if someone else mentions our name. It seems we can filter out surrounding noise by combining bottom-up and top-down processing to create a “winner takes it all” situation where the processing of one high-value auditory input suppresses the brain activity of all others (Goldstein, 2011).

While people may believe that the speed of hand movement allows magicians to trick us, research suggests the main factor is misdirection (Eysenck & Keane, 2015).

A 2010 study of a trick involving the disappearance of a lighter identified that when the lighter was dropped (to hide it from a later hand-opening finale), it was masked by directing attention from the fixation point – known as covert attention – with surprising effectiveness.

However, subjects were able to identify the drop when their attention was directed to the fixation point – known as overt attention (Kuhn & Findlay, 2010).

In a thought-provoking study exploring freewill, participants were asked to consciously decide whether to move their finger left or right while a functional MRI scanner monitored their prefrontal cortex and parietal cortex (Soon, Brass, Heinze, & Haynes, 2008).

Brain activity predicted the direction of movement a full seven seconds before they consciously became aware of their decision. While follow-up research has challenged some of the findings, it appears that brain activity may come before conscious thinking (Eysenck & Keane, 2015).

Associations have been found between positive emotions, creative thinking, and overall wellbeing, suggesting environmental changes that may benefit staff productivity and innovation in the workplace (Yuan, 2015).

Factors explored include creating climates geared toward creativity, boosting challenge, trust, freedom, risk taking, low conflict, and even the beneficial effects of humor.

Undoubtedly, further innovation will be seen from marrying the two powerful and compelling new fields of positive psychology and cognitive psychology.

17 Top-Rated Positive Psychology Exercises for Practitioners

Expand your arsenal and impact with these 17 Positive Psychology Exercises [PDF] , scientifically designed to promote human flourishing, meaning, and wellbeing.

Created by Experts. 100% Science-based.

We have many tools, worksheets, and exercises to explore and improve attention, problem-solving, and the ability to regulate emotions.

Why not download our free emotional intelligence pack and try out the powerful tools contained within?

• Building Emotional Awareness In this exercise, we foster emotional intelligence by mindfully attending to existing emotional states.
• Identifying False Beliefs About Emotions Our beliefs often operate outside of conscious awareness. This exercise addresses clients’ basic and often unconscious assumptions about their emotions.

Other free resources include:

• Skills for Regulating Emotion We can learn to manage our emotions by focusing on more positive experiences than negative ones.
• Emotional Repetition and Attention Remodeling Identifying phrases used to describe ourselves can help desensitize negative feelings .

More extensive versions of the following tools are available with a subscription to the Positive Psychology Toolkit© , but here is a brief overview:

• Creating Savoring Rituals It’s possible to increase positive emotions by sharpening our sensory perceptions via savoring.

Learning to focus can help.

Step one – Identify everyday activities that bring you pleasure. Step two – Focus on experiencing pleasure as it happens when doing these activities.

At the end of the week, take some time to record your reflections on creating savoring rituals.

• Extracting Strengths From Problems Surprisingly, using our strengths too much can harm our problem-solving ability.

In this exercise, we examine an existing issue in a client’s life:

Step one – Describe a current problem. Step two – Identify the problematic context or life domain. Step three – Identify the problematic behavior in yourself. Step four – Recognize your underlying strength. Step five – Identify what you can do to remedy the problem.

If you’re looking for more science-based ways to help others enhance their wellbeing, check out this signature collection of 17 validated positive psychology tools for practitioners. Use them to help others flourish and thrive.

Cognitive psychology is crucial in our search for understanding how we interact with and make sense of a constantly changing and potentially harmful environment.

Not only that, it offers insight into what happens when things go wrong and the likely impact on our wellbeing and ability to cope with life events.

Cognitive psychology’s strength is its willingness to embrace research findings from many other disciplines, combining them with existing psychological theory to create new models of cognition.

The tasks we appear to carry out unconsciously are a great deal more complex than they might first appear. Perception, attention, problem-solving, language comprehension and production, and decision-making often happen without intentional thought and yet have enormous consequences on our lives.

Use this article as a starting point to explore the many and diverse aspects of cognitive psychology. Consider their relationships with associated research fields and reflect on the importance of understanding cognition in helping clients overcome complex events or circumstances.

We hope you enjoyed reading this article. Don’t forget to download our three Positive Psychology Exercises for free .

• Eysenck, M. W., & Keane, M. T. (2015). Cognitive psychology: A student’s handbook . Psychology Press.
• Goldstein, E. B. (2011). Cognitive psychology . Wadsworth, Cengage Learning.
• Gross, R. D. (2020). Psychology: The science of mind and behaviour . Hodder and Stoughton.
• Kuhn, G., & Findlay, J. M. (2010). Misdirection, attention and awareness: Inattentional blindness reveals temporal relationship between eye movements and visual awareness. The Quarterly Journal of Experimental Psychology , 63 (1), 136–146.
• Moore, J. (1996). On the relation between behaviorism and cognitive psychology. Journal of Mind and Behavior , 17 (4), 345–367
• Soon, C. S., Brass, M., Heinze, H., & Haynes, J. (2008). Unconscious determinants of free decisions in the human brain. Nature Neuroscience , 11 (5), 543–545.
• Yuan, L. (2015). The happier one is, the more creative one becomes: An investigation on inspirational positive emotions from both subjective well-being and satisfaction at work. Psychology , 6 , 201–209.

Share this article:

Article feedback

What our readers think.

As a widowed Mother and Grandmother, whom was recently told by an adult child that maybe I should have “cognitive” testing done, I found this article to be very informative and refreshing. Having the ability to read and and learn about cognitive psychology is interesting as their are so many ways our brains are affected from the time we are born until the time we reach each and every stage in life. I have spent time with my grandchildren who are from age 19 months, through 15 years old , and spend time with children who are 35, 34, and 32, and my parents who are 88 and 84. I appreciate your article and your time in writing it. Sincerely,

Cognitive Psychology creates & build human capacity to push physical and mental limits. My concept of cognition in human behavior was judged by the most time I met my lawyer or the doctor. Most of the time while listening a pause, oh I see and it is perpetual transition to see. Cognition emergence is very vital support as we see & perceive. My practices in engineering solution are base on my cognitive sensibilities.You article provokes the same perceptions. Thank you

Let us know your thoughts Cancel reply

Your email address will not be published.

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

Related articles

Hierarchy of Needs: A 2024 Take on Maslow’s Findings

One of the most influential theories in human psychology that addresses our quest for wellbeing is Abraham Maslow’s Hierarchy of Needs. While Maslow’s theory of [...]

Emotional Development in Childhood: 3 Theories Explained

We have all witnessed a sweet smile from a baby. That cute little gummy grin that makes us smile in return. Are babies born with [...]

Using Classical Conditioning for Treating Phobias & Disorders

Does the name Pavlov ring a bell? Classical conditioning, a psychological phenomenon first discovered by Ivan Pavlov in the late 19th century, has proven to [...]

Read other articles by their category

• Body & Brain (49)
• Coaching & Application (58)
• Compassion (25)
• Counseling (51)
• Emotional Intelligence (23)
• Gratitude (18)
• Grief & Bereavement (21)
• Happiness & SWB (40)
• Meaning & Values (26)
• Meditation (20)
• Mindfulness (44)
• Motivation & Goals (45)
• Optimism & Mindset (34)
• Positive CBT (29)
• Positive Communication (20)
• Positive Education (47)
• Positive Emotions (32)
• Positive Leadership (18)
• Positive Parenting (15)
• Positive Psychology (33)
• Positive Workplace (37)
• Productivity (17)
• Relationships (43)
• Resilience & Coping (37)
• Self Awareness (21)
• Self Esteem (38)
• Strengths & Virtues (32)
• Stress & Burnout Prevention (34)
• Theory & Books (46)
• Therapy Exercises (37)
• Types of Therapy (63)

3 Positive Psychology Tools (PDF)

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 a therapist 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
• United States
• Brooklyn, NY
• Chicago, IL
• Houston, TX
• Los Angeles, CA
• New York, NY
• Portland, OR
• San Diego, CA
• San Francisco, CA
• Seattle, WA
• Washington, DC
• Asperger's
• Bipolar Disorder
• Chronic Pain
• Eating Disorders
• Passive Aggression
• Personality
• Goal Setting
• Positive Psychology
• Stopping Smoking
• Low Sexual Desire
• Relationships
• Child Development
• Therapy Center NEW
• 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