• 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 Papyrology
  • Greek and Roman Epigraphy
  • Greek and Roman Law
  • 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 Evolution
  • Language Reference
  • Language Acquisition
  • 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 (Romanticism)
  • Literary Studies (American)
  • Literary Studies (Asian)
  • Literary Studies (European)
  • Literary Studies (Eco-criticism)
  • 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 Media
  • Music and Religion
  • 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 Language
  • Philosophy of Mind
  • Philosophy of Perception
  • Philosophy of Science
  • 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
  • Clinical Neuroscience
  • 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
  • Community Medical Services
  • Critical Care
  • Emergency Medicine
  • Forensic Medicine
  • Haematology
  • History of Medicine
  • Browse content in Medical Skills
  • Clinical Skills
  • Communication Skills
  • Nursing Skills
  • Surgical Skills
  • Browse content in Medical Dentistry
  • Oral and Maxillofacial Surgery
  • Paediatric Dentistry
  • Restorative Dentistry and Orthodontics
  • Surgical Dentistry
  • 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 Ethics
  • Business Strategy
  • Business History
  • Business and Technology
  • Business and Government
  • 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 History
  • Economic Systems
  • 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 Behaviour
  • Political Economy
  • Political Institutions
  • Political Methodology
  • Political Communication
  • Political Philosophy
  • Political Sociology
  • Political Theory
  • Politics and Law
  • Public Policy
  • Public Administration
  • 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

The Oxford Handbook of Cognitive Psychology

  • < Previous chapter
  • Next chapter >

48 Problem Solving

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

  • Published: 03 June 2013
  • Cite Icon Cite
  • Permissions Icon Permissions

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

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

Definition of Problem Solving

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

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

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

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

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

Definition of Problem

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

Types of Problems

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

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

Cognitive Processes in Problem Solving

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

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

Knowledge for Problem Solving

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

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

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

Historical Approaches to Problem Solving

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

Early Conceptions

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

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

Associationism

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

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

Gestalt Psychology

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

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

Information Processing

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

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

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

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

Classic Issues in Problem Solving

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

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

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

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

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

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

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

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

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

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

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

Current and Future Issues in Problem Solving

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

Decision Making

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

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

Intelligence and Creativity

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

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

Teaching of Thinking Skills

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

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

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

Expert Problem Solving

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

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

Analogical Reasoning

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

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

Mathematical and Scientific Problem Solving

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

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

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

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

Everyday Thinking

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

Cognitive Neuroscience of Problem Solving

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

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

Future Directions

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

Anderson L. W. , Krathwohl D. R. , Airasian P. W. , Cruikshank K. A. , Mayer R. E. , Pintrich P. R. , Raths, J., & Wittrock M. C. ( 2001 ). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. New York : Longman.

Baron J. ( 2000 ). Thinking and deciding (3rd ed.). New York : Cambridge University Press.

Google Scholar

Google Preview

Bloom B. S. , & Broder B. J. ( 1950 ). Problem-solving processes of college students: An exploratory investigation. Chicago : University of Chicago Press.

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

Chen Z. , & Klahr D. ( 1999 ). All other things being equal: Acquisition and transfer of the control of variable strategy . Child Development, 70, 1098–1120.

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.

Covington M. V. , Crutchfield R. S. , Davies L. B. , & Olton R. M. ( 1974 ). The productive thinking program. Columbus, OH : Merrill.

de Groot A. D. ( 1965 ). Thought and choice in chess. The Hague, The Netherlands : Mouton.

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

Ericsson K. A. , Feltovich P. J. , & Hoffman R. R. (Eds.). ( 2006 ). The Cambridge handbook of expertise and expert performance. New York : Cambridge University Press.

Fridja N. H. , & de Groot A. D. ( 1982 ). Otto Selz: His contribution to psychology. The Hague, The Netherlands : Mouton.

Gentner D. , & Stevens A. L. (Eds.). ( 1983 ). Mental models. Hillsdale, NJ : Erlbaum.

Gigerenzer G. , Todd P. M. , & ABC Research Group (Eds.). ( 1999 ). Simple heuristics that make us smart. Oxford, England : Oxford University Press.

Goel V. ( 2005 ). Cognitive neuroscience of deductive reasoning. In K. J. Holyoak & R. G. Morrison (Eds.), The Cambridge handbook of thinking and reasoning (pp. 475–492). New York : Cambridge University Press.

Guilford J. P. ( 1967 ). The nature of human intelligence. New York : McGraw-Hill.

Holyoak K. J. ( 2005 ). Analogy. In K. J. Holyoak & R. G. Morrison (Eds.), The Cambridge handbook of thinking and reasoning (pp. 117–142). New York : Cambridge University Press.

Humphrey G. ( 1963 ). Thinking: An introduction to experimental psychology. New York : Wiley.

Judd C. H. ( 1908 ). The relation of special training and general intelligence. Educational Review, 36, 28–42.

Kahneman D. , & Tversky A. ( 1984 ). Choices, values, and frames. American Psychologist, 39, 341–350.

Kahneman D. , & Tversky A. (Eds.). ( 2000 ). Choices, values, and frames. New York : Cambridge University Press.

Kohler W. ( 1925 ). The mentality of apes. New York : Liveright.

Larkin J. H. , McDermott J. , Simon D. P. , & Simon H. A. ( 1980 ). Expert and novice performance in solving physics problems. Science, 208, 1335–1342.

Luchins A. ( 1942 ). Mechanization in problem solving.   Psychological Monographs, 54 (6) (Whole No. 248).

Mandler J. M. , & Mandler G. ( 1964 ). Thinking from associationism to Gestalt. New York : Wiley.

Markman A. B. , & Medin D. L. ( 2002 ). Decision making. In D. Medin (Ed.), Stevens’ handbook of experimental psychology, Vol. 2. Memory and cognitive processes (2nd ed., pp. 413–466). New York : Wiley.

Mayer R. E. ( 1992 ). Thinking, problem solving, cognition (2nd ed). New York : Freeman.

Mayer R. E. ( 1995 ). The search for insight: Grappling with Gestalt psychology’s unanswered questions. In R. J. Sternberg & J. E. Davidson (Eds.), The nature of insight (pp. 3–32). Cambridge, MA : MIT Press.

Mayer R. E. ( 2008 ). Learning and instruction. Upper Saddle River, NJ : Merrill Prentice Hall.

Mayer R. E. ( 2009 ). Information processing. In T. L. Good (Ed.), 21st century education: A reference handbook (pp. 168–174). Thousand Oaks, CA : Sage.

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

McCloskey M. ( 1983 ). Intuitive physics.   Scientific American, 248 (4), 122–130.

Metcalfe J. , & Wiebe D. ( 1987 ). Intuition in insight and non-insight problem solving. Memory and Cognition, 15, 238–246.

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

Nickerson R. S. ( 1999 ). Enhancing creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 392–430). New York : Cambridge University Press.

Nunes T. , Schliemann A. D. , & Carraher D. W , ( 1993 ). Street mathematics and school mathematics. Cambridge, England : Cambridge University Press.

Robbins P. , & Aydede M. (Eds.). ( 2009 ). The Cambridge handbook of situated cognition. New York : Cambridge University Press.

Rogers T. T. , & McClelland J. L. ( 2004 ). Semantic cognition: A parallel distributed processing approach. Cambridge, MA : MIT Press.

Singley M. K. , & Anderson J. R. ( 1989 ). The transfer of cognitive skill. Cambridge, MA : Harvard University Press.

Sternberg R. J. ( 1990 ). Metaphors of mind: Conceptions of the nature of intelligence. New York : Cambridge University Press.

Sternberg R. J. ( 1999 ). Handbook of creativity. New York : Cambridge University Press.

Sternberg R. J. , & Gregorenko E. L. (Eds.). ( 2003 ). The psychology of abilities, competencies, and expertise. New York : Cambridge University Press.

Tharp R. G. , & Gallimore R. ( 1988 ). Rousing minds to life: Teaching, learning, and schooling in social context. New York : Cambridge University Press.

Thorndike E. L. ( 1911 ). Animal intelligence. New York: Hafner.

Thorndike E. L. , & Woodworth R. S. ( 1901 ). The influence of improvement in one mental function upon the efficiency of other functions. Psychological Review, 8, 247–261.

Wertheimer M. ( 1959 ). Productive thinking. New York : Harper and Collins.

Wundt W. ( 1973 ). An introduction to experimental psychology. New York : Arno Press. (Original work published in 1911).

Further Reading

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

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

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

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

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

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

  • 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.

Book cover

Effective Multicultural Teams: Theory and Practice pp 239–274 Cite as

Problem Solving and Decision Making

  • Linda Drake Gobbo 3  

7271 Accesses

Part of the book series: Advances in Group Decision and Negotiation ((AGDN,volume 3))

Problem solving and decision making in multicultural work teams are the last of the skill areas to be covered in this book. This topic will be discussed from the cultural, individual, and organizational levels of multicultural team development, building on the frameworks that have been presented in previous chapters. Many theorists consider problem solving and decision making as synonymous-all decisions are made in response to a problem or opportunity. Simply stated, if problem solving is the process used to find a solution to the problem, challenge, or opportunity. However, how one solves problems can be quite varied. An individual can use analytical tools based on logic, deduction, or induction, or intuition based on an understanding of principles, or creative thinking. Problem-solving abilities and approaches may vary considerably, actually using different paradigms or frameworks. In this chapter one approach, with the steps and methods to do problem solving in work teams, will be presented.

There are six steps to the problem-solving model described and demonstrated in this chapter. Several of those steps within the model are used for decisionmaking, and are covered as well. How a team makes the decision, and who on the team makes it are important elements and will also be discussed. As prior chapters have noted, membership of multicultural teams varies greatly. The procedures each member follows, the different value orientations guiding their behavior (Smith et al. 2002), the nature of the tasks they must complete, and the communication tools they employ (face-to-face and/or technology-based) all impact how they approach problem solving and decision making. When done effectively, problem solving, which includes decision making, moves through all the steps described here equally, engaging the knowledge and skills of all team members.

This chapter will first present theoretical frameworks for problem solving, then define the steps that comprise problem solving and decision making within them. This will be followed by a discussion of the cultural variations, and impact of individual styles and societal assumptions on decision-making. Shared mental models and consensus are offered as methods to equalize participation in team decision making, and an overview of other methods provided. The last section will look at ways to coordinate the stages of team development with the variety of problemsolving and decision-making techniques in order to maximize a team’s effectiveness.

  • Team Member
  • Team Development
  • Power Distance
  • Virtual Team

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

Buying options

  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
  • Durable hardcover edition

Tax calculation will be finalised at checkout

Purchases are for personal use only

Unable to display preview.  Download preview PDF.

Adler, N.J. (2002). International Dimensions of Organizational Behavior (4th ed.). Cincinnati, OH: South-Western.

Google Scholar  

Cooperrider, D.L., Whitney, D. and Stavros, J.M. (2005). Appreciative Inquiry: The First in a Series of AI Workbooks for Leaders of Change. Brunswick, OH: Crown Custom Publishing.

Enayati, J. (2001). The research: Effective communication and decision-making in diverse groups. In Hemmati, M. (Ed.), Multi-Stakeholder Processes for Governance and Sustainability-Beyond Deadlock and Conflict. London, England: Earthscan.

Gardenswartz, L. and Rowe, A. (2003). In L. Gardenswartz and A. Rowe (Eds.), Diverse Teams at Work: Capitalizing on the Power of Diversity (1st ed.). Alexandria, VA: Society for Human Resource Management.

Halverson, C.B. (2004). Effective Multicultural Teams (5th ed.). Brattleboro, VT: School for International Training.

Harrington-Macklin, D. (1994). The Team Building Tool Kit: Tips, Tactics, and Rules for Effective Workplace Teams. New York: American Management Association.

Hofstede, G. (1980). Culture’s Consequences: International Differences in Work-related Values. Thousand Oaks, CA: Sage.

Janis, I. (1982). Groupthink: Psychological Studies of Policy Decisions and Fiascos (2nd ed.). Boston, MA: Houghton Mifflin.

Jeffery, A.B., Maes, J.D. and Bratton-Jeffery, M.F. (2005). Improving team decision-making performance with collaborative modeling. [Electronic version]. Team Performance Management, 11 (1/2), 40–50. Retrieved December 20, 2005, from the Emerald In sight database.

Article   Google Scholar  

Kayser, T.A. (1994). Building Team Power: How to Unleash the Collaborative Genius of Work Teams. New York: Irwin.

Kelly, K.P. (1994). Team Decision Making Techniques. Irvine, CA: Richard Chang Associates.

Kline, T. (1999). In M. Holt, D. Ullius and P. Berkman (Eds.), Remaking Teams: The Revolutionary Research-based Guide That Puts Theory into Practice. San Francisco, CA: Jossey-Bass/Pfeiffer.

Magruder Watkins, J. and Mohr, B.J. (2001). Appreciative Inquiry, Change at the Speed of Imagination. San Francisco, CA: Jossey-Bass/Pfieffer.

Mathieu, J., Heffner, T., Goodwin, G., Cannon-Bowers, J. and Salas, E. (2005). Scaling the quality of teammates’ mental models: equifinality and normative comparisons. Journal of Organizational Behavior, 26, 37–56.

McFadzean, E. (2002). Developing and supporting creative problem-solving teams: Part 1—a conceptual model. [Electronic version]. Management Decision, 40(5), 463–475. Retrieved December 20, 2005, from the Emerald Insight database.

McFadzean, E. (2002). Developing and supporting creative problem solving teams: Part 2-facili-tator competencies. [Electronic version]. Management Decision, 40(6), 537–551. Retrieved December 20, 2005, from the Emerald Insight database.

McKenna, R.J. and Martin-Smith, B. (2005). Decision making as a simplification process: New conceptual perspectives.[Electronic version]. Management Decision, 43(6), 821–836. Retrieved December 20, 2005, from the Emerald Insight database.

Sagie, A. and Akcan, Z. (2003). A cross-cultural analysis of participative decision-making in organizations. Human Relations, 56(4), 453–473.

Selart, M. (2005). Understanding the role of locus of control in consultative decision-making: A case study. [Electronic version]. Management Decision, 43(3), 397–412. Retrieved December 20, 2005, from the Emerald Insight database.

Simon, T., Pelled, L.H. and Smith, K.A. (1999). Making use of difference: diversity, debate, and decision comprehensiveness in top management teams. Academy of Management Journal, 42 (6), 662–673.

Smith, P.B., Peterson, M.F. and Schwartz, S.H. (2002). Cultural values, sources of guidance, and their relevance to managerial behavior. [Electronic version]. Journal of Cross-Cultural Psychology, 33(2), 188–208.

Tomlinson, S. (1999). Comparison of consensus Japanese style and Quaker style. [Electronic version]. Retrieved July 1, 2006, from http://www.earlham.edu/~consense/scott2.shtml

Watkins, J.M. and Mohr, B.J. (2001). Appreciative Inquiry: Change at the Speed of Imagination. San Francisco, CA: Jossey-Bass/Pfeiffer.

Whitney, D. and Trosten-Bloom, A. (2003). The Power of Appreciative Inquiry: A Practical Guide to Positive Change. San Francisco, CA: Berrett-Koehler.

Download references

Author information

Authors and affiliations.

School for International Training, Brattleboro, VT, USA

Linda Drake Gobbo

You can also search for this author in PubMed   Google Scholar

Editor information

Editors and affiliations.

Claire B. Halverson  & S. Aqeel Tirmizi  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Science + Business Media B.V

About this chapter

Cite this chapter.

Gobbo, L.D. (2008). Problem Solving and Decision Making. In: Halverson, C.B., Tirmizi, S.A. (eds) Effective Multicultural Teams: Theory and Practice. Advances in Group Decision and Negotiation, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6957-4_9

Download citation

DOI : https://doi.org/10.1007/978-1-4020-6957-4_9

Publisher Name : Springer, Dordrecht

Print ISBN : 978-1-4020-6956-7

Online ISBN : 978-1-4020-6957-4

eBook Packages : Business and Economics Business and Management (R0)

Share this chapter

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • Publish with us

Policies and ethics

  • Find a journal
  • Track your research

For enquiries call:

+1-469-442-0620

banner-in1

What is Problem Solving? Process, Techniques, Examples

Home Blog others What is Problem Solving? Process, Techniques, Examples

Play icon

Whether tackling a technical issue at work or finding our way around a roadblock unnoticed by Google Maps, problem-solving is a daily occurrence for most people. But how prepared are you to overcome life's challenges? Do you rely on a structured process to ensure successful outcomes, or do you navigate through problems impulsively? 

Here's the crux: the strength of your problem-solving skills significantly impacts the ease and success of your life, both professionally and personally. Practical problem-solving is a valuable career and life skill. You're in the right place if you're eager to enhance your problem-solving abilities efficiently. 

In this blog post, I will delve into what is problem solving the steps, techniques, and exercises of the problem-solving process. Whether seeking to troubleshoot technical issues or navigate life's complexities, mastering organized problem-solving can elevate your capabilities and lead to more favorable outcomes. 

What is Problem Solving? And Its Importance

First, let me help you understand what is problem solving. Problem-solving is a comprehensive process involving identifying issues, prioritizing based on urgency and severity, analyzing root causes, gathering pertinent Information, devising and assessing solutions, making informed decisions, and planning and executing implementation strategies. 

This skill set also encompasses critical thinking, effective communication, active listening, creativity, research, data analysis, risk assessment, continuous learning, and decision-making abilities. Effective problem-solving strategies mitigate potential losses or damages and enhance self-confidence and reputation. Problem-solving is essential in personal and professional contexts as it allows individuals and teams to navigate obstacles, make informed decisions, and drive progress. 

Importance: 

  • Enhances Decision-Making: Effective problem solving leads to better decision-making by evaluating various options and selecting the most suitable solution. 
  • Promotes Innovation: Problem solving encourages innovation and creativity as individuals seek new approaches to tackle challenges. 
  • Improves Efficiency: By resolving issues efficiently, problem solving helps streamline processes and optimize resource allocation. 
  • Builds Resilience: Successfully overcoming obstacles builds confidence and resilience, enabling  
  • individuals and teams to tackle future challenges with greater confidence.  

Problem-solving Process 

Now that we have a clear understanding of the problem solving definition as to what is problem solving let us now navigate the problem solving process. Effective problem-solving is a valuable skill sought after by employers in various fields. Here's a breakdown of a common problem-solving process, presented in a pointwise manner: 

1. Identifying the Problem 

The first step in the problem-solving process is clearly defining the issue. This involves gathering relevant Information, observing patterns or trends, and understanding the impact of the problem on stakeholders. 

2. Analyzing the Situation 

Once the problem is identified, it's essential to analyze its root causes and contributing factors. This may involve conducting research, gathering data, and exploring different perspectives to comprehensively understand the situation. 

3. Generating Solutions 

With a clear understanding of the problem solving methods, brainstorming potential solutions is the next step. Encouraging creativity and considering various alternatives can lead to innovative ideas. Evaluating each solution based on feasibility, effectiveness, and alignment with goals and values is crucial. 

4. Evaluating Options 

After generating a list of potential solutions, it's essential to carefully evaluate each option. This involves weighing the pros and cons, considering potential risks and benefits, and assessing the likelihood of success. Consulting with relevant stakeholders or experts can provide valuable insights during this stage. 

5. Selecting the Best Solution 

Based on the evaluation, one or more solutions are the most viable options. It's essential to prioritize solutions that address the root cause of the problem and have the most significant potential for long-term success. Communicating the chosen solution effectively to stakeholders is crucial for garnering support and buy-in. 

6. Implementing the Solution 

Once a solution is selected, it's time to put it into action. This involves developing a detailed action plan, allocating resources, and assigning responsibilities. Effective communication, coordination, and monitoring are essential during the implementation phase to ensure smooth execution and timely resolution of the problem. 

7. Monitoring and Reviewing 

After implementing the solution, it's essential to monitor its progress and evaluate its effectiveness over time. This may involve collecting feedback, analyzing performance metrics, and making adjustments as needed. Continuous monitoring and review allow for ongoing improvement and refinement of the problem-solving process.  

How to Solve Problems in 5 Simple Steps? 

Here's a breakdown of the 5 problem-solving steps for your understanding: 

1. Define the Problem (Understand & Gather Information)  

  • Identify the Issue: Clearly understand what the problem is. What isn't working, or what needs improvement? 
  • Gather Information: Talk to people involved, collect data, and research relevant details to get a well-rounded picture of the situation. 
  • Ask Why? Don't just focus on symptoms. Ask "why" several times to identify the root cause of the problem. 

Example: Let's say customer complaints about slow website loading times have increased. 

2. Brainstorm Solutions (Think Creatively & Be Open-Minded)  

  • Think Outside the Box: Don't settle for the first solution that comes to mind. Brainstorm a variety of options, even seemingly unconventional ones. 
  • Consider All Angles: Evaluate the problem from different perspectives. What are potential solutions from a technical standpoint? From a user experience point of view? 
  • Build on Ideas: Don't shut down ideas prematurely. Encourage others to build upon and refine suggestions collaboratively. 

Example: Potential solutions for slow website loading times could include optimizing images, upgrading server capacity, or implementing a content delivery network (CDN). 

3. Evaluate & Choose a Solution (Consider Feasibility & Impact)  

  • Weigh the Pros & Cons: Analyze the feasibility, resource requirements, and potential risks and benefits of each solution. 
  • Align with Goals: Ensure the chosen solution directly addresses the root cause of the problem and aligns with your overall objectives. 
  • Prioritize Impact: Choose the solution with the most significant potential to achieve a positive outcome and lasting improvement. 

Example: Upgrading server capacity might be a very effective solution, but it could be expensive. Optimizing images is a more feasible solution that could yield significant improvement. 

4. Implement the Solution (Take Action & Communicate Clearly)  

  • Develop a Plan: Create a clear action plan outlining the steps involved in implementing the chosen solution. Assign tasks and set deadlines. 
  • Communication is Key: Clearly communicate the plan to everyone involved, including stakeholders and team members. 
  • Monitor Progress: Track the implementation process and make adjustments as needed based on the results. 

Example: The website optimization plan might involve tasks like image resizing, code minification, and implementing caching mechanisms. 

5. Evaluate the Outcome (Learn & Adapt)  

  • Measure Success: Assess whether the implemented solution effectively resolved the problem. Did it meet your goals? 
  • Lessons Learned: Reflect on what worked well and what could be improved during the problem-solving process. 
  • Continuous Improvement: Use this experience to refine your problem-solving approach and enhance your skills for future challenges. Enroll in free online certification courses for professional development and skill enhancement. 

Example: After website optimization, monitor website loading times and customer feedback to see if the issue has been resolved. If not, repeat the process, considering new solutions based on the learnings from this attempt. 

Remember, problem-solving is an iterative process. Be prepared to adapt your approach as you gather more Information and evaluate the effectiveness of your solutions.  

Essential Things to Consider in Each of the Problem-solving Steps

Creative problem solving requires careful consideration at each stage. Here are vital things to focus on: 

1. Identifying & Defining the Problem 

  • Gather Information: Consult stakeholders, review data, and gain insights from various perspectives. 
  • Identify Root Cause: Address the underlying reason, not just symptoms. 
  • Define Scope: Clearly outline the problem's boundaries to maintain focus. 

2. Analyzing the Problem 

  • Consider Multiple Perspectives: Explore diverse angles to uncover potential factors. 
  • Brainstorm Freely: Foster creativity without judgment to generate innovative ideas. 
  • Analyze Impact: Evaluate the severity and consequences of the problem if left unresolved. 
  • Think Creatively: Explore unconventional solutions beyond initial ideas. 
  • Consider Feasibility: Assess the practicality and resource requirements of each option. 
  • Identify Potential Risks & Benefits: Weigh the pros and cons to select the most balanced approach. 

4. Evaluating and Selecting a Solution 

  • Align with Goals: Ensure the chosen solution addresses the core issue and aligns with objectives. 
  • Consider Long-Term Impact: Choose solutions with lasting benefits beyond immediate results. 
  • Team Input: Involve team members to gain diverse perspectives during evaluation. 

5. Implementing the Solution  

  • Develop a Clear Plan: Outline implementation steps with clear timelines and responsibilities. 
  • Communication is Key: Ensure all stakeholders understand the plan to facilitate smooth execution. 
  • Monitor Progress: Track implementation and adjust as needed based on results. 

6. Evaluating the Outcome  

  • Measure Effectiveness: Assess if the solution effectively resolves the problem or needs refinement. 
  • Lessons Learned: Identify successes and areas for improvement to enhance future problem-solving efforts. 

Problem Solving Examples

Let us look at problem solving example scenarios in a typical workplace: , example 1: project deadline challenge .

  • Situation: You're a project manager leading a team that is developing a new marketing campaign website. The launch date is approaching, but a critical developer is unexpectedly out sick for a week. 
  • Action: You immediately assess the workload and delegate tasks among the remaining team members. You identify an opportunity to streamline a design element, reducing development time. You also reach out to a freelancer with a proven track record to fill in for the missing developer on specific tasks. 
  • Result: The team successfully launches the website on time and within budget. The streamlined design element is praised by stakeholders for its user-friendliness. 
  • Highlight: This example showcases your problem-solving skills, leadership, adaptability, and ability to manage resources effectively under pressure. 

Example 2: Client Communication Breakdown 

  • Situation: You're a Customer Service Representative for an e-commerce company. A regular customer expresses extreme dissatisfaction with a recent purchase due to a malfunctioning product and a negative experience with a previous representative. 
  • Action: You actively listen to the customer's concerns, apologizing for the inconvenience. You then troubleshoot the product issue and offer a solution (replacement or refund). Additionally, you acknowledge the previous negative experience and offer to ensure better communication going forward. 
  • Result: The customer is satisfied with the resolution and expresses appreciation for your attentiveness and problem-solving approach. They remain a loyal customer of the company. 
  • Highlight: This example demonstrates your active listening skills, empathy, ability to de-escalate situations, and commitment to customer satisfaction. 

By following these examples of problem-solving skills, you can effectively tackle challenges and achieve successful outcomes. Also, explore KnowledgeHut’ s best online courses for further skill enhancement. 

Problem Solving Techniques

Effective problem-solving techniques are essential for tackling challenges and achieving desired outcomes. Here are some problem solving tools and techniques commonly used in problem-solving: 

  • Brainstorming : Encourages the generation of a wide range of ideas and solutions in a non-judgmental environment. This technique promotes creativity and can uncover innovative approaches to problems. 
  • Root Cause Analysis : Focuses on identifying the underlying causes of a problem rather than just addressing its symptoms. By pinpointing root causes, solutions can be targeted more effectively to prevent recurrence. 
  • Fishbone Diagram (Ishikawa Diagram): Provides a visual representation of the various factors contributing to a problem, categorized into branches such as people, process, equipment, environment, and management. This technique helps analyze complex issues and identify potential causes. 
  • SWOT Analysis : Evaluates the strengths, weaknesses, opportunities, and threats associated with a problem or situation. This technique helps assess the internal and external factors influencing the problem and guides decision-making. 
  • Pareto Analysis: Focuses on identifying and prioritizing the most significant causes contributing to a problem. By allocating resources to address the vital few rather than the trivial many, this technique maximizes impact and efficiency. 
  • 5 Whys : Involves asking "why" repeatedly to trace the root cause of a problem. This iterative questioning technique helps uncover more profound layers of causation beyond surface-level symptoms. 
  • Decision Matrix Analysis: Helps evaluate multiple options by systematically comparing their pros and cons against predetermined criteria. This technique facilitates objective decision-making by considering various factors and their relative importance. 

By incorporating these problem-solving techniques in the workplace, you can approach problems systematically, generate creative solutions, and develop a well-rounded plan for achieving success.  

Conquering challenges is a key to professional success, and practical problem-solving equips you to do just that. By following a structured approach, you can transform from a bystander to a solution-oriented individual. This involves gathering Information to clearly define the problem and identify its root cause. Analyzing the situation from various angles and brainstorming freely unlock creative solutions. Evaluating potential solutions ensures you choose the one that aligns with your goals and is feasible to implement. Clear communication and a well-defined plan are crucial for successful execution. Finally, reflecting on the outcome allows you to learn and continuously improve your problem-solving skills, making you an invaluable asset in any environment. 

Frequently Asked Questions (FAQs)

The best method involves identifying the problem, brainstorming solutions, evaluating options, implementing the chosen solution, and assessing outcomes for improvement.

The principles include defining the problem, generating alternatives, evaluating options, implementing solutions, and reviewing outcomes for continuous improvement.

Different types include analytical problem-solving, creative problem-solving, critical thinking, decision-making, and systematic problem-solving.

The significant elements include understanding the problem, devising a plan, executing the plan, and evaluating the results.

The skills encompass critical thinking, decision-making, and analytical reasoning. These abilities aid in identifying, analyzing, and resolving problems effectively. 

Profile

KnowledgeHut .

KnowledgeHut is an outcome-focused global ed-tech company. We help organizations and professionals unlock excellence through skills development. We offer training solutions under the people and process, data science, full-stack development, cybersecurity, future technologies and digital transformation verticals.

Avail your free 1:1 mentorship session.

Something went wrong

Course advisor icon

New method for solving the Collatz Conjecture (Summary video) high-prize problem

omoideCS

  • #mathematics
  • #conjecture
  • #oscillation
  • #dimentional

この記事が気に入ったらサポートをしてみませんか?

Help | Advanced Search

Physics > General Physics

Title: solving maxwell's equations.

Abstract: This paper discusses the use of the Riemann-Silberstein vector to solve the source-free Maxwell's equations and obtains novel analytical solutions. The solving process naturally leads to the spinor form of the source-free Maxwell's equations. Several powerful theorems are established to solve this spinor form equation. The Waveguide Solution Theorem provides an elegant way to solve waveguide problems, while The Schrodinger Solution Theorem connects the Maxwell's equations with the two-dimensional Schrodinger equation. By utilizing The Schrodinger Solution Theorem, a precise formula for spatiotemporal diffraction of the Maxwell's equations is derived, which allows for the reconstruction of electromagnetic waves throughout space and time based on the field distribution on the diffraction screen.

Submission history

Access paper:.

  • Download PDF
  • HTML (experimental)
  • Other Formats

license icon

References & Citations

  • Google Scholar
  • Semantic Scholar

BibTeX formatted citation

BibSonomy logo

Bibliographic and Citation Tools

Code, data and media associated with this article, recommenders and search tools.

  • Institution

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

The Philippines economy in 2024: Stronger for longer?

The Philippines ended 2023 on a high note, being the fastest growing economy across Southeast Asia with a growth rate of 5.6 percent—just shy of the government's target of 6.0 to 7.0 percent. 1 “National accounts,” Philippine Statistics Authority, January 31, 2024; "Philippine economic updates,” Bangko Sentral ng Pilipinas, November 16, 2023. Should projections hold, the Philippines is expected to, once again, show significant growth in 2024, demonstrating its resilience despite various global economic pressures (Exhibit 1). 2 “Economic forecast 2024,” International Monetary Fund, November 1, 2023; McKinsey analysis.

The growth in the Philippine economy in 2023 was driven by a resumption in commercial activities, public infrastructure spending, and growth in digital financial services. Most sectors grew, with transportation and storage (13 percent), construction (9 percent), and financial services (9 percent), performing the best (Exhibit 2). 3 “National accounts,” Philippine Statistics Authority, January 31, 2024. While the country's trade deficit narrowed in 2023, it remains elevated at $52 billion due to slowing global demand and geopolitical uncertainties. 4 “Highlights of the Philippine export and import statistics,” Philippine Statistics Authority, January 28, 2024. Looking ahead to 2024, the current economic forecast for the Philippines projects a GDP growth of between 5 and 6 percent.

Inflation rates are expected to temper between 3.2 and 3.6 percent in 2024 after ending 2023 at 6.0 percent, above the 2.0 to 4.0 percent target range set by the government. 5 “Nomura downgrades Philippine 2024 growth forecast,” Nomura, September 11, 2023; “IMF raises Philippine growth rate forecast,” International Monetary Fund, July 16, 2023.

For the purposes of this article, most of the statistics used for our analysis have come from a common thread of sources. These include the Central Bank of the Philippines (Bangko Sentral ng Pilipinas); the Department of Energy Philippines; the IT and Business Process Association of the Philippines (IBPAP); and the Philippines Statistics Authority.

The state of the Philippine economy across seven major sectors and themes

In the article, we explore the 2024 outlook for seven key sectors and themes, what may affect each of them in the coming year, and what could potentially unlock continued growth.

Financial services

The recovery of the financial services sector appears on track as year-on-year growth rates stabilize. 6 Philippines Statistics Authority, November 2023; McKinsey in partnership with Oxford Economics, November 2023. In 2024, this sector will likely continue to grow, though at a slower pace of about 5 percent.

Financial inclusion and digitalization are contributing to growth in this sector in 2024, even if new challenges emerge. Various factors are expected to impact this sector:

  • Inclusive finance: Bangko Sentral ng Pilipinas continues to invest in financial inclusion initiatives. For example, basic deposit accounts (BDAs) reached $22 million in 2023 and banking penetration improved, with the proportion of adults with formal bank accounts increasing from 29 percent in 2019 to 56 percent in 2021. 7 “Financial inclusion dashboard: First quarter 2023,” Bangko Sentral ng Pilipinas, February 6, 2024.
  • Digital adoption: Digital channels are expected to continue to grow, with data showing that 60 percent of adults who have a mobile phone and internet access have done a digital financial transaction. 8 “Financial inclusion dashboard: First quarter 2023,” Bangko Sentral ng Pilipinas, February 6, 2024. Businesses in this sector, however, will need to remain vigilant in navigating cybersecurity and fraud risks.
  • Unsecured lending growth: Growth in unsecured lending is expected to continue, but at a slower pace than the past two to three years. For example, unsecured retail lending for the banking system alone grew by 27 percent annually from 2020 to 2022. 9 “Loan accounts: As of first quarter 2023,” Bangko Sentral ng Pilipinas, February 6, 2024; "Global banking pools,” McKinsey, November 2023. Businesses in this field are, however, expected to recalibrate their risk profiling models as segments with high nonperforming loans emerge.
  • High interest rates: Key interest rates are expected to decline in the second half of 2024, creating more accommodating borrowing conditions that could boost wholesale and corporate loans.

Supportive frameworks have a pivotal role to play in unlocking growth in this sector to meet the ever-increasing demand from the financially underserved. For example, financial literacy programs and easier-to-access accounts—such as BDAs—are some measures that can help widen market access to financial services. Continued efforts are being made to build an open finance framework that could serve the needs of the unbanked population, as well as a unified credit scoring mechanism to increase the ability of historically under-financed segments, such as small and medium-sized enterprises (SMEs), to access formal credit. 10 “BSP launches credit scoring model,” Bangko Sentral ng Pilipinas, April 26, 2023.

Energy and Power

The outlook for the energy sector seems positive, with the potential to grow by 7 percent in 2024 as the country focuses on renewable energy generation. 11 McKinsey analysis based on input from industry experts. Currently, stakeholders are focused on increasing energy security, particularly on importing liquefied natural gas (LNG) to meet power plants’ requirements as production in one of the country’s main sources of natural gas, the Malampaya gas field, declines. 12 Myrna M. Velasco, “Malampaya gas field prod’n declines steeply in 2021,” Manila Bulletin , July 9, 2022. High global inflation and the fact that the Philippines is a net fuel importer are impacting electricity prices and the build-out of planned renewable energy projects. Recent regulatory moves to remove foreign ownership limits on exploration, development, and utilization of renewable energy resources could possibly accelerate growth in the country’s energy and power sector. 13 “RA 11659,” Department of Energy Philippines, June 8, 2023.

Gas, renewables, and transmission are potential growth drivers for the sector. Upgrading power grids so that they become more flexible and better able to cope with the intermittent electricity supply that comes with renewables will be critical as the sector pivots toward renewable energy. A recent coal moratorium may position natural gas as a transition fuel—this could stimulate exploration and production investments for new, indigenous natural gas fields, gas pipeline infrastructure, and LNG import terminal projects. 14 Philippine energy plan 2020–2040, Department of Energy Philippines, June 10, 2022; Power development plan 2020–2040 , Department of Energy Philippines, 2021. The increasing momentum of green energy auctions could facilitate the development of renewables at scale, as the country targets 35 percent share of renewables by 2030. 15 Power development plan 2020–2040 , 2022.

Growth in the healthcare industry may slow to 2.8 percent in 2024, while pharmaceuticals manufacturing is expected to rebound with 5.2 percent growth in 2024. 16 McKinsey analysis in partnership with Oxford Economics.

Healthcare demand could grow, although the quality of care may be strained as the health worker shortage is projected to increase over the next five years. 17 McKinsey analysis. The supply-and-demand gap in nursing alone is forecast to reach a shortage of approximately 90,000 nurses by 2028. 18 McKinsey analysis. Another compounding factor straining healthcare is the higher than anticipated benefit utilization and rising healthcare costs, which, while helping to meet people's healthcare budgets, may continue to drive down profitability for health insurers.

Meanwhile, pharmaceutical companies are feeling varying effects of people becoming increasingly health conscious. Consumers are using more over the counter (OTC) medication and placing more beneficial value on organic health products, such as vitamins and supplements made from natural ingredients, which could impact demand for prescription drugs. 19 “Consumer health in the Philippines 2023,” Euromonitor, October 2023.

Businesses operating in this field may end up benefiting from universal healthcare policies. If initiatives are implemented that integrate healthcare systems, rationalize copayments, attract and retain talent, and incentivize investments, they could potentially help to strengthen healthcare provision and quality.

Businesses may also need to navigate an increasingly complex landscape of diverse health needs, digitization, and price controls. Digital and data transformations are being seen to facilitate improvements in healthcare delivery and access, with leading digital health apps getting more than one million downloads. 20 Google Play Store, September 27, 2023. Digitization may create an opportunity to develop healthcare ecosystems that unify touchpoints along the patient journey and provide offline-to-online care, as well as potentially realizing cost efficiencies.

Consumer and retail

Growth in the retail and wholesale trade and consumer goods sectors is projected to remain stable in 2024, at 4 percent and 5 percent, respectively.

Inflation, however, continues to put consumers under pressure. While inflation rates may fall—predicted to reach 4 percent in 2024—commodity prices may still remain elevated in the near term, a top concern for Filipinos. 21 “IMF raises Philippine growth forecast,” July 26, 2023; “Nomura downgrades Philippines 2024 growth forecast,” September 11, 2023. In response to challenging economic conditions, 92 percent of consumers have changed their shopping behaviors, and approximately 50 percent indicate that they are switching brands or retail providers in seek of promotions and better prices. 22 “Philippines consumer pulse survey, 2023,” McKinsey, November 2023.

Online shopping has become entrenched in Filipino consumers, as they find that they get access to a wider range of products, can compare prices more easily, and can shop with more convenience. For example, a McKinsey Philippines consumer sentiment survey in 2023 found that 80 percent of respondents, on average, use online and omnichannel to purchase footwear, toys, baby supplies, apparel, and accessories. To capture the opportunity that this shift in Filipino consumer preferences brings and to unlock growth in this sector, retail organizations could turn to omnichannel strategies to seamlessly integrate online and offline channels. Businesses may need to explore investments that increase resilience across the supply chain, alongside researching and developing new products that serve emerging consumer preferences, such as that for natural ingredients and sustainable sources.

Manufacturing

Manufacturing is a key contributor to the Philippine economy, contributing approximately 19 percent of GDP in 2022, employing about 7 percent of the country’s labor force, and growing in line with GDP at approximately 6 percent between 2023 and 2024. 23 McKinsey analysis based on input from industry experts.

Some changes could be seen in 2024 that might affect the sector moving forward. The focus toward building resilient supply chains and increasing self-sufficiency is growing. The Philippines also is likely to benefit from increasing regional trade, as well as the emerging trend of nearshoring or onshoring as countries seek to make their supply chains more resilient. With semiconductors driving approximately 45 percent of Philippine exports, the transfer of knowledge and technology, as well as the development of STEM capabilities, could help attract investments into the sector and increase the relevance of the country as a manufacturing hub. 24 McKinsey analysis based on input from industry experts.

To secure growth, public and private sector support could bolster investments in R&D and upskill the labor force. In addition, strategies to attract investment may be integral to the further development of supply chain infrastructure and manufacturing bases. Government programs to enable digital transformation and R&D, along with a strategic approach to upskilling the labor force, could help boost industry innovation in line with Industry 4.0 demand. 25 Industry 4.0 is also referred to as the Fourth Industrial Revolution. Priority products to which manufacturing industries could pivot include more complex, higher value chain electronic components in the semiconductor segment; generic OTC drugs and nature-based pharmaceuticals in the pharmaceutical sector; and, for green industries, products such as EVs, batteries, solar panels, and biomass production.

Information technology business process outsourcing

The information technology business process outsourcing (IT-BPO) sector is on track to reach its long-term targets, with $38 billion in forecast revenues in 2024. 26 Khriscielle Yalao, “WHF flexibility key to achieving growth targets—IBPAP,” Manila Bulletin , January 23, 2024. Emerging innovations in service delivery and work models are being observed, which could drive further growth in the sector.

The industry continues to outperform headcount and revenue targets, shaping its position as a country leader for employment and services. 27 McKinsey analysis based in input from industry experts. Demand from global companies for offshoring is expected to increase, due to cost containment strategies and preference for Philippine IT-BPO providers. New work setups continue to emerge, ranging from remote-first to office-first, which could translate to potential net benefits. These include a 10 to 30 percent increase in employee retention; a three- to four-hour reduction in commute times; an increase in enabled talent of 350,000; and a potential reduction in greenhouse gas emissions of 1.4 to 1.5 million tons of CO 2 per year. 28 McKinsey analysis based in input from industry experts. It is becoming increasingly more important that the IT-BPO sector adapts to new technologies as businesses begin to harness automation and generative AI (gen AI) to unlock productivity.

Talent and technology are clear areas where growth in this sector can be unlocked. The growing complexity of offshoring requirements necessitates building a proper talent hub to help bridge employee gaps and better match local talent to employers’ needs. Businesses in the industry could explore developing facilities and digital infrastructure to enable industry expansion outside the metros, especially in future “digital cities” nationwide. Introducing new service areas could capture latent demand from existing clients with evolving needs as well as unserved clients. BPO centers could explore the potential of offering higher-value services by cultivating technology-focused capabilities, such as using gen AI to unlock revenue, deliver sales excellence, and reduce general administrative costs.

Sustainability

The Philippines is considered to be the fourth most vulnerable country to climate change in the world as, due to its geographic location, the country has a higher risk of exposure to natural disasters, such as rising sea levels. 29 “The Philippines has been ranked the fourth most vulnerable country to climate change,” Global Climate Risk Index, January 2021. Approximately $3.2 billion, on average, in economic loss could occur annually because of natural disasters over the next five decades, translating to up to 7 to 8 percent of the country’s nominal GDP. 30 “The Philippines has been ranked the fourth most vulnerable country to climate change,” Global Climate Risk Index, January 2021.

The Philippines could capitalize on five green growth opportunities to operate in global value chains and catalyze growth for the nation:

  • Renewable energy: The country could aim to generate 50 percent of its energy from renewables by 2040, building on its high renewable energy potential and the declining cost of producing renewable energy.
  • Solar photovoltaic (PV) manufacturing: More than a twofold increase in annual output from 2023 to 2030 could be achieved, enabled by lower production costs.
  • Battery production: The Philippines could aim for a $1.5 billion domestic market by 2030, capitalizing on its vast nickel reserves (the second largest globally). 31 “MineSpans,” McKinsey, November 2023.
  • Electric mobility: Electric vehicles could account for 15 percent of the country’s vehicle sales by 2030 (from less than 1 percent currently), driven by incentives, local distribution, and charging infrastructure. 32 McKinsey analysis based on input from industry experts.
  • Nature-based solutions: The country’s largely untapped total abatement potential could reach up to 200 to 300 metric tons of CO 2 , enabled by its biodiversity and strong demand.

The Philippine economy: Three scenarios for growth

Having grown faster than other economies in Southeast Asia in 2023 to end the year with 5.6 percent growth, the Philippines can expect a similarly healthy growth outlook for 2024. Based on our analysis, there are three potential scenarios for the country’s growth. 33 McKinsey analysis in partnership with Oxford Economics.

Slower growth: The first scenario projects GDP growth of 4.8 percent if there are challenging conditions—such as declining trade and accelerated inflation—which could keep key policy rates high at about 6.5 percent and dampen private consumption, leading to slower long-term growth.

Soft landing: The second scenario projects GDP growth of 5.2 percent if inflation moderates and global conditions turn out to be largely favorable due to a stable investment environment and regional trade demand.

Accelerated growth: In the third scenario, GDP growth is projected to reach 6.1 percent if inflation slows and public policies accommodate aspects such as loosening key policy rates and offering incentive programs to boost productivity.

Focusing on factors that could unlock growth in its seven critical sectors and themes, while adapting to the macro-economic scenario that plays out, would allow the Philippines to materialize its growth potential in 2024 and take steps towards achieving longer-term, sustainable economic growth.

Jon Canto is a partner in McKinsey’s Manila office, where Frauke Renz is an associate partner, and Vicah Villanueva is a consultant.

The authors wish to thank Charlene Chua, Charlie del Rosario, Ryan delos Reyes, Debadrita Dhara, Evelyn C. Fong, Krzysztof Kwiatkowski, Frances Lee, Aaron Ong, and Liane Tan for their contributions to this article.

Explore a career with us

Related articles.

Philippines Growth Dialogues

The Philippines Growth Dialogues

plane flying over Philippines - line drawing

What does 2023 hold for the Philippines’ economy?

Close-up of woman's hand typing on a smartphone in the city in front of cars at beautiful sunset

On the verge of a digital banking revolution in the Philippines

IMAGES

  1. What Is Problem-Solving? Steps, Processes, Exercises to do it Right

    what is problem solving method pdf

  2. problem solving guide step

    what is problem solving method pdf

  3. What are the problem solving steps?

    what is problem solving method pdf

  4. Problem Solving Method

    what is problem solving method pdf

  5. problem solving processes or models

    what is problem solving method pdf

  6. 3 Tips for Effective Problem Solving

    what is problem solving method pdf

VIDEO

  1. problem solving

  2. 5 Powerful Problem Solving Techniques

  3. Teaching Methods

  4. Criminal case gameplay in DR Gaming

  5. LINEAR DIFFERENTIAL EQUATION

  6. problem solving method

COMMENTS

  1. PDF THIRTEEN PROBLEM-SOLVING MODELS

    The Six-Step method provides a focused procedure for the problem solving (PS) group. It ensures consistency, as everyone understands the approach to be used. By using data, it helps eliminate bias and preconceptions, leading to greater objectivity. It helps to remove divisions and encourages collaborative working.

  2. PDF A Problem Solving Approach to Designing and Implementing a Strategy to

    Problem-Solving Approach to Strategy Design and Implementation. The problem-solving approach to designing and implementing a strategy includes eight steps (see. Figure A): 1. Identify the Problem. 2. Analyze the Problem and Diagnose Its Causes. 3. Develop a Theory of Action.

  3. PDF Creative Problem Solving

    Creative Problem Solving is a proven method for approaching a problem or a challenge in an imaginative and innovative way. It's a process that helps people re-define the problems they think they face, come up with breakthrough ideas and then take action on these new ideas all with the same innovative spirit. ...

  4. PDF Step Problem Solving Process

    The Six Step Problem Solving Model Problem solving models are used to address the many challenges that arise in the workplace. While many people regularly solve problems, there are a range of different approaches that can be used to find a solution. Complex challenges for teams, working groups and boards etc., are usually solved more quickly by ...

  5. PDF Introduction to Problem-Solving Strategies

    can use problem solving to teach the skills of mathematics, and how prob-lem solving should be presented to their students. They must understand that problem solving can be thought of in three different ways: 1. Problem solving is a subject for study in and of itself. 2. Problem solving is an approach to a particular problem. 3.

  6. PDF 7-step approach to problem solving

    Problem statements should commence with a question or a firm hypothesis. Be specific, actionable and focus on what the decision maker needs to move forward. Break a problem into component parts so that problems can be divided and allocated. The parts should be MECE. Do it as a team, share with Experts and client to get input and alignment.

  7. PDF Polya's Problem Solving Techniques

    Polya's Problem Solving Techniques In 1945 George Polya published the book How To Solve It which quickly became his most prized publication. It sold over one million copies and has been translated into 17 languages. In this book he identi es four basic principles of problem solving. Polya's First Principle: Understand the problem

  8. PDF 1. Understand Polya's problem-solving method. 2. State and apply

    Step 1: Understand the problem. It would seem unnecessary to state this obvious advice, but yet in my years of teaching, I have seen many students try to solve a problem before they completely understand it. The techniques that we will explain shortly will help you to avoid this critical mistake. Step 2: Devise a plan.

  9. What is Problem Solving? Steps, Process & Techniques

    Finding a suitable solution for issues can be accomplished by following the basic four-step problem-solving process and methodology outlined below. Step. Characteristics. 1. Define the problem. Differentiate fact from opinion. Specify underlying causes. Consult each faction involved for information. State the problem specifically.

  10. PDF The Psychology of Problem Solving

    personal resourcefulness influence problem-solving performance in both formal and informal contexts. In addition, these authors present a cycli-cal model of problem solving that identifies self-regulatory processes and sources of motivation that are central to successful problem solving in a wide range of situations.

  11. Problem Solving

    Cognitive—Problem solving occurs within the problem solver's cognitive system and can only be inferred indirectly from the problem solver's behavior (including biological changes, introspections, and actions during problem solving).. Process—Problem solving involves mental computations in which some operation is applied to a mental representation, sometimes resulting in the creation of ...

  12. (PDF) Problem Solving Approach

    Problem solving is defined as the area of. cognitive psychology which deals with the processe s. involved in solving problems. Fig. 1: Deviation is Problem. Problem solving depends on individual ...

  13. PDF Problem solving in mathematics

    Therefore, high-quality assessment of problem solving in public tests and assessments1 is essential in order to ensure the effective learning and teaching of problem solving throughout primary and secondary education. Although the focus here is on the assessment of problem solving in mathematics, many of the ideas will be directly transferable ...

  14. PDF Chapter 12

    Aspects of Problem Solving • Problem space: the domain of the problem and the choices the solver evaluates during solution • Plan: a hierarchical process that controls the order in which a sequence of operations is to be performed Representation • The price of a notebook is four times that of a pencil. The pencil costs 30 cents less than

  15. PDF A Problem With Problem Solving: Teaching Thinking Without Teaching ...

    Three examples of a problem solving heuristic are presented in Table 1. The first belongs to John Dewey, who explicated a method of problem solving in How We Think (1933). The second is George Polya's, whose method is mostly associated with problem solving in mathematics. The last is a more contemporary version

  16. Problem Solving

    Problem solving is the process of articulating solutions to problems. Problems have two critical attributes. First, a problem is an unknown in some context. That is, there is a situation in which there is something that is unknown (the difference between a goal state and a current state). Those situations vary from algorithmic math problems to ...

  17. PDF The 4-Step Problem-Solving Process

    The 4-Step Problem-Solving Process. This document is the third in a series intended to help school and district leaders maximize the effectiveness and fluidity of their multi-tiered system of supports (MTSS) across different learning environments. Specifically, the document is designed to support the use of problem solving to improve outcomes ...

  18. PDF Chapter 9 Problem Solving and Decision Making

    The actual decision is only a part of the whole process. Problem solving has a broader scope than decision making, and strategic decision making uses many of the same steps used in problem solving. For example, the same team above may find the workload among team members is uneven and the timeline

  19. PDF Six-step Problem Solving Model

    problem solving: To ensure consistency Everyone needs to know what method everyone else is using to solve a problem. It keeps the process more scientific and less susceptible to individual biases and perceptions. To help manage the group process The six steps in the problem solving model provide a focus for the group and help set the

  20. PDF COGNITION Chapter 9: Problem Solving Fundamentals of Cognitive Psychology

    Fixation occurs when solver is fixated on wrong approach to problem. It often is result of past experience. Fixation refers to the blocking of solution paths to a problem that is caused by past experiences related to the problem. NEGATIVE SET (set effects) - bias or tendency to solve a problem a particular way.

  21. (Pdf) Learning and Problem Solving: the Use of Problem Solving Method

    Abstract. Problem-based learning is a recognized teaching method in which complex real-world problems are used as the vehicle to promote student learning of concepts and principles as opposed to ...

  22. PDF Polya's four-step approach to problem solving

    Remember, problem solving is as much an art as it is a science!! Remember Some of the Possible Strategies Given Earlier. 1. Draw pictures. 2. Use a variable and choose helpful names for variables or unknowns. 3. Be systematic.

  23. PDF Teaching Problem Solving and Decision Making

    Solving a problem, therefore, is the process of identifying a solution that resolves the initial perplexity or diffi-culty. Most of the research in teaching problem solving has derived from the work of D'Zurilla (D'Zurilla, 1986; D'Zurilla & Goldfried, 1971) and Spivack, Shure, and

  24. What is Problem Solving? Process, Techniques, Examples

    Now that we have a clear understanding of the problem solving definition as to what is problem solving let us now navigate the problem solving process. Effective problem-solving is a valuable skill sought after by employers in various fields. Here's a breakdown of a common problem-solving process, presented in a pointwise manner: 1. Identifying ...

  25. PDF Looking Ahead to Avoid Being Late: Solving Hard-Constrained Traveling

    methods train an end-to-end solver in the RL paradigm and relax the time windows as soft constraints [Tang et al., 2022] or solve a soft-constrained variant of TSPTW, e.g., Trav-eling Salesman Problem with Time Windows and Rejec-tions [Zhang et al., 2020]. In contrast to RL methods re-quiring elaborate reward designs and millions of environment

  26. Series for even powers of Pi by generalization Euler's method for

    Download PDF HTML (experimental) Abstract: The purpose of this paper is to present series expansions for even powers of the number $\pi$. This is accomplished by generalizing Euler's method for solving the Basel Problem, which was published in 1735.

  27. New method for solving the Collatz Conjecture (Summary video) high

    I was able to replace the Collatz problem with a one-dimensional linear mapping problem of Chaos Theory. All that's left is whether it can be solved using the Chaos Theory. ... (No is a positive odd number.) ログイン. 会員登録. New method for solving the Collatz Conjecture (Summary video) high-prize problem omoideCS 2024年3月17日 21:02.

  28. [2403.11181] Solving Maxwell's Equations

    Download PDF HTML (experimental) Abstract: This paper discusses the use of the Riemann-Silberstein vector to solve the source-free Maxwell's equations and obtains novel analytical solutions. The solving process naturally leads to the spinor form of the source-free Maxwell's equations. Several powerful theorems are established to solve this spinor form equation.

  29. The Philippines economy in 2024

    The Philippines ended 2023 on a high note, being the fastest growing economy across Southeast Asia with a growth rate of 5.6 percent—just shy of the government's target of 6.0 to 7.0 percent. 1 "National accounts," Philippine Statistics Authority, January 31, 2024; "Philippine economic updates," Bangko Sentral ng Pilipinas, November 16, 2023. ...