SherbyNet - /page/wikibook/entry.mu

Micron Document

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<title>Problem solving</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Problem solving</span></span>

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</style><div role="note" class="hatnote navigation-not-searchable">"Problem" redirects here. For other uses, see <a href="Problem_(disambiguation)" class="mw-disambig" title="Problem (disambiguation)">Problem (disambiguation)</a>.</div>

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</style><table class="sidebar nomobile nowraplinks hlist"><tbody><tr><th class="sidebar-title"><a href="Cognitive_psychology" title="Cognitive psychology">Cognitive psychology</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File"></span></td></tr><tr><th class="sidebar-heading">

<a href="Perception" title="Perception">Perception</a></th></tr><tr><td class="sidebar-content">

<ul><li><a href="Visual_perception" title="Visual perception">Visual</a></li>

<li><a href="Visual_object_recognition" class="mw-redirect" title="Visual object recognition">Object recognition</a></li>

<li><a href="Face_perception" title="Face perception">Face recognition</a></li>

<li><a href="Pattern_recognition" title="Pattern recognition">Pattern recognition</a></li></ul></td>

</tr><tr><th class="sidebar-heading">

<a href="Attention" title="Attention">Attention</a></th></tr><tr><th class="sidebar-heading">

<a href="Memory" title="Memory">Memory</a></th></tr><tr><td class="sidebar-content">

<ul><li><a href="Memory_and_aging" title="Memory and aging">Aging</a></li>

<li><a href="Emotion_and_memory" title="Emotion and memory">Emotional</a></li>

<li><a href="Learning" title="Learning">Learning</a></li>

</tr><tr><th class="sidebar-heading">

<a href="Metacognition" title="Metacognition">Metacognition</a></th></tr><tr><th class="sidebar-heading">

<a href="Language" title="Language">Language</a></th></tr><tr><td class="sidebar-content">

<a href="Metalanguage" title="Metalanguage">Metalanguage</a></td>

</tr><tr><th class="sidebar-heading">

<a href="Thought" title="Thought">Thinking</a></th></tr><tr><td class="sidebar-content">

<ul><li><a href="Cognition" title="Cognition">Cognition</a></li>

<li><a href="Concept" title="Concept">Concept</a></li>

<li><a href="Reason" title="Reason">Reasoning</a></li>

<li><a href="Decision-making" title="Decision-making">Decision making</a></li>

</ul></td>

</tr><tr><th class="sidebar-heading">

<a href="Numerical_cognition" title="Numerical cognition">Numerical cognition</a></th></tr><tr><td class="sidebar-content">

<ul><li><a href="Number_sense" title="Number sense">Number sense</a>

<ul><li><a href="Number_sense_in_animals" title="Number sense in animals">in animals</a></li></ul></li>

<li><a href="Numerosity_adaptation_effect" title="Numerosity adaptation effect">Numerosity adaptation effect</a></li>

<li><a href="Approximate_number_system" title="Approximate number system">Approximate number system</a></li>

<li><a href="Parallel_individuation_system" title="Parallel individuation system">Parallel individuation system</a></li></ul></td>

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<table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><th class="sidebar-title" style="padding:0.2em"><a href="Neuropsychology" title="Neuropsychology">Neuropsychology</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File"></span></td></tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #ccc;text-align:center;;color: var(--color-base)"><span style="font-size:120%">Topics</span></div><div class="sidebar-list-content mw-collapsible-content hlist">

<ul><li><a href="List_of_regions_in_the_human_brain" title="List of regions in the human brain">Brain regions</a></li>

<li><a href="Clinical_neuropsychology" title="Clinical neuropsychology">Clinical neuropsychology</a></li>

<li><a href="Cognitive_neuropsychology" title="Cognitive neuropsychology">Cognitive neuropsychology</a></li>

<li><a href="Cognitive_neuroscience" title="Cognitive neuroscience">Cognitive neuroscience</a></li>

<li><a href="Dementia" title="Dementia">Dementia</a></li>

<li><a href="Human_brain" title="Human brain">Human brain</a></li>

<li><a href="Neuroanatomy" title="Neuroanatomy">Neuroanatomy</a></li>

<li><a href="Neurophysiology" title="Neurophysiology">Neurophysiology</a></li>

<li><a href="Neuropsychological_assessment" title="Neuropsychological assessment">Neuropsychological assessment</a></li>

<li><a href="Rehabilitation_(neuropsychology)" title="Rehabilitation (neuropsychology)">Neuropsychological rehabilitation</a></li>

<li><a href="Traumatic_brain_injury" title="Traumatic brain injury">Traumatic brain injury</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #ccc;text-align:center;;color: var(--color-base)"><span style="font-size:120%"><a href="Brain" title="Brain">Brain functions</a></span></div><div class="sidebar-list-content mw-collapsible-content hlist">

<ul><li><a href="Arousal" title="Arousal">Arousal</a></li>

<li><a href="Attention" title="Attention">Attention</a></li>

<li><a href="Consciousness" title="Consciousness">Consciousness</a></li>

<li><a href="Decision-making" title="Decision-making">Decision making</a></li>

<li><a href="Executive_functions" title="Executive functions">Executive functions</a></li>

<li><a href="Natural_language" title="Natural language">Natural language</a></li>

<li><a href="Learning" title="Learning">Learning</a></li>

<li><a href="Memory" title="Memory">Memory</a></li>

<li><a href="Motor_coordination" title="Motor coordination">Motor coordination</a></li>

<li><a href="Perception" title="Perception">Perception</a></li>

<li><a href="Planning" title="Planning">Planning</a></li>

<li><a href="Thought" title="Thought">Thought</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #ccc;text-align:center;;color: var(--color-base)"><span style="font-size:120%">People</span></div><div class="sidebar-list-content mw-collapsible-content hlist">

<ul><li><a href="Alan_Baddeley" title="Alan Baddeley">Alan Baddeley</a></li>

<li><a href="Arthur_Lester_Benton" title="Arthur Lester Benton">Arthur L. Benton</a></li>

<li><a href="David_Bohm" title="David Bohm">David Bohm</a></li>

<li><a href="Antonio_Damasio" title="Antonio Damasio">Antonio Damasio</a></li>

<li><a href="Phineas_Gage" title="Phineas Gage">Phineas Gage</a></li>

<li><a href="Norman_Geschwind" title="Norman Geschwind">Norman Geschwind</a></li>

<li><a href="Elkhonon_Goldberg" title="Elkhonon Goldberg">Elkhonon Goldberg</a></li>

<li><a href="Patricia_Goldman-Rakic" title="Patricia Goldman-Rakic">Patricia Goldman-Rakic</a></li>

<li><a href="Donald_O._Hebb" title="Donald O. Hebb">Donald O. Hebb</a></li>

<li><a href="Kenneth_Heilman" title="Kenneth Heilman">Kenneth Heilman</a></li>

<li><a href="Eric_Kandel" title="Eric Kandel">Eric Kandel</a></li>

<li><a href="Edith_Kaplan" title="Edith Kaplan">Edith Kaplan</a></li>

<li><a href="Muriel_Lezak" title="Muriel Lezak">Muriel Lezak</a></li>

<li><a href="Benjamin_Libet" title="Benjamin Libet">Benjamin Libet</a></li>

<li><a href="Rodolfo_Llin%C3%A1s" title="Rodolfo Llinás">Rodolfo Llinás</a></li>

<li><a href="Alexander_Luria" title="Alexander Luria">Alexander Luria</a></li>

<li><a href="Brenda_Milner" title="Brenda Milner">Brenda Milner</a></li>

<li><a href="Karl_H._Pribram" title="Karl H. Pribram">Karl H. Pribram</a></li>

<li><a href="Pasko_Rakic" title="Pasko Rakic">Pasko Rakic</a></li>

<li><a href="Oliver_Sacks" title="Oliver Sacks">Oliver Sacks</a></li>

<li><a href="Mark_Rosenzweig_(psychologist)" title="Mark Rosenzweig (psychologist)">Mark Rosenzweig</a></li>

<li><a href="Roger_Wolcott_Sperry" title="Roger Wolcott Sperry">Roger W. Sperry</a></li>

<li><a href="Hans-Lukas_Teuber" title="Hans-Lukas Teuber">Hans-Lukas Teuber</a></li>

<li><a href="Henry_Molaison" title="Henry Molaison">Henry Molaison <span style="font-size: 85%;">("H.M.", patient)</span></a></li>

<li><a href="Kent_Cochrane" title="Kent Cochrane">K.C. <span style="font-size: 85%;">(patient)</span></a></li></ul></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #ccc;text-align:center;;color: var(--color-base)"><span style="font-size:120%"><a href="Neuropsychological_test" title="Neuropsychological test">Tests</a></span></div><div class="sidebar-list-content mw-collapsible-content hlist">

<ul><li><a href="Benton_Visual_Retention_Test" title="Benton Visual Retention Test">Benton Visual Retention Test</a></li>

<li><a href="Continuous_performance_task" title="Continuous performance task">Continuous Performance Task</a></li>

<li><a href="Halstead%E2%80%93Reitan_Neuropsychological_Battery" title="Halstead–Reitan Neuropsychological Battery">Halstead–Reitan Neuropsychological Battery</a></li>

<li><a href="Hayling_and_Brixton_tests" title="Hayling and Brixton tests">Hayling and Brixton tests</a></li>

<li><a href="Lexical_decision_task" title="Lexical decision task">Lexical Decision Task</a></li>

<li><a href="Luria%E2%80%93Nebraska_Neuropsychological_Battery" title="Luria–Nebraska Neuropsychological Battery">Luria–Nebraska Neuropsychological Battery</a></li>

<li><a href="Mini%E2%80%93mental_state_examination" title="Mini–mental state examination">Mini–mental state examination</a></li>

<li><a href="Rey%E2%80%93Osterrieth_complex_figure" title="Rey–Osterrieth complex figure">Rey–Osterrieth complex figure</a></li>

<li><a href="Stroop_effect" title="Stroop effect">Stroop Test</a></li>

<li><a href="Wechsler_Adult_Intelligence_Scale" title="Wechsler Adult Intelligence Scale">Wechsler Adult Intelligence Scale</a></li>

<li><a href="Wechsler_Memory_Scale" title="Wechsler Memory Scale">Wechsler Memory Scale</a></li>

<li><a href="Wisconsin_Card_Sorting_Test" title="Wisconsin Card Sorting Test">Wisconsin Card Sorting Task</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-below" style="border-top:1px solid #aaa;padding:0.4em 0 0.5em;border-bottom:1px solid #aaa;">

<ul><li><span class="nowrap"><span class="skin-invert-image noviewer" typeof="mw:File"><span></span></span> </span><a href="Portal%3APsychology" title="Portal:Psychology">Psychology portal</a></li>

<li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span></span></span> </span><a href="Portal%3APhilosophy" title="Portal:Philosophy">Philosophy portal</a></li>

<li><span class="nowrap"><span class="skin-invert-image noviewer" typeof="mw:File"><span></span></span> </span><a href="Portal%3AMedicine" title="Portal:Medicine">Medicine portal</a></li></ul>

</div></td></tr><tr><td class="sidebar-navbar"></td></tr></tbody></table>

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</style><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="Puzzle" title="Puzzle">Puzzles</a></th></tr><tr><td class="sidebar-image" style="padding:0 0 1.0em;"><span class="noviewer" typeof="mw:File"></span></td></tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:lavender;text-align:center;;color: var(--color-base)"><span style="font-size:120%">Types</span></div><div class="sidebar-list-content mw-collapsible-content" style="padding-left:1.5em;padding-right:1.5em;"><table class="sidebar nomobile nowraplinks hlist" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="padding-bottom:0;">

<a href="Guessing_game" class="mw-redirect" title="Guessing game">Guessing</a></th></tr><tr><td class="sidebar-content" style="padding-top:0;padding-bottom:0.5em;">

<ul><li><a href="Riddle" title="Riddle">Riddle</a></li>

<li><a href="Situation_puzzle" title="Situation puzzle">Situation</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="padding-bottom:0;">

<a href="Logic_puzzle" title="Logic puzzle">Logic</a></th></tr><tr><td class="sidebar-content" style="padding-top:0;padding-bottom:0.5em;">

<ul><li><a href="Dissection_puzzle" title="Dissection puzzle">Dissection</a></li>

<li><a href="Induction_puzzles" title="Induction puzzles">Induction</a></li>

<li><a href="Logic_puzzle#Logic_grid_puzzles" title="Logic puzzle">Logic grid</a></li>

<li><a href="Self-reference_puzzle" title="Self-reference puzzle">Self-reference</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="padding-bottom:0;">

<a href="Mechanical_puzzle" title="Mechanical puzzle">Mechanical</a></th></tr><tr><td class="sidebar-content" style="padding-top:0;padding-bottom:0.5em;">

<ul><li><a href="Combination_puzzle" title="Combination puzzle">Combination</a></li>

<li><a href="Construction_puzzle" title="Construction puzzle">Construction</a></li>

<li><a href="Disentanglement_puzzle" title="Disentanglement puzzle">Disentanglement</a></li>

<li><a href="Tsumego" title="Tsumego"><i>Go</i> problems</a></li>

<li><a href="Mechanical_puzzle#Fold_puzzles" title="Mechanical puzzle">Folding</a></li>

<li><a href="Stick_puzzle" title="Stick puzzle">Stick</a></li>

<li><a href="Tiling_puzzle" title="Tiling puzzle">Tiling</a></li></ul></td>

</tr><tr><td class="sidebar-content" style="padding-top:0;padding-bottom:0.5em;">

<li><a href="Sliding_puzzle" title="Sliding puzzle">Sliding</a></li>

<li><a href="Chess_problem" title="Chess problem">Chess</a></li>

<li><br> <a href="Maze" title="Maze">Maze</a> (<a href="Logic_maze" title="Logic maze">Logic maze</a>)</li></ul></td>

</tr><tr><th class="sidebar-heading" style="padding-bottom:0;">

<a href="Word_game" title="Word game">Word</a> and <a href="Mathematical_puzzle" title="Mathematical puzzle">Number</a></th></tr><tr><td class="sidebar-content" style="padding-top:0;padding-bottom:0.5em;">

<ul><li><a href="Crossword" title="Crossword">Crossword</a></li>

<li><a href="Sudoku" title="Sudoku">Sudoku</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="padding-bottom:0;">

<a href="Puzzle_video_game" title="Puzzle video game">Puzzle video games</a></th></tr><tr><td class="sidebar-content" style="padding-top:0;padding-bottom:0.5em;">

<ul><li><a href="List_of_maze_video_games" title="List of maze video games">Mazes</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="padding-bottom:0;">

<a href="Metapuzzle" title="Metapuzzle">Metapuzzles</a></th></tr></tbody></table></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:lavender;text-align:center;;color: var(--color-base)"><span style="font-size:120%"><a href="List_of_puzzle_topics" title="List of puzzle topics">Topics</a></span></div><div class="sidebar-list-content mw-collapsible-content" style="padding-left:1.5em;padding-right:1.5em;"><div class="hlist">

<ul><li><a href="Brain_teaser" title="Brain teaser">Brain teaser</a></li>

<li><a href="Dilemma" title="Dilemma">Dilemma</a></li>

<li><a href="Optical_illusion" title="Optical illusion">Optical illusion</a></li>

<li><a href="Packing_problems" title="Packing problems">Packing problems</a></li>

<li><a href="Paradox" title="Paradox">Paradox</a></li>

<li><a href="Puzzlehunt" class="mw-redirect" title="Puzzlehunt">Puzzlehunt</a></li>

<li><a href="Syllogism" title="Syllogism">Syllogism</a></li>

</div></div></div></td>

</tr><tr><td class="sidebar-content">

<ul><li><a href="List_of_impossible_puzzles" title="List of impossible puzzles">Impossible puzzles</a></li>

<li><a href="List_of_maze_video_games" title="List of maze video games">Maze video games</a></li>

<li><a href="Nikoli_(publisher)" title="Nikoli (publisher)">Nikoli puzzle types</a></li>

<li><a href="List_of_puzzle_video_games" title="List of puzzle video games">Puzzle video games</a></li>

<li><a href="List_of_puzzle_topics" title="List of puzzle topics">Puzzle topics</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-navbar"></td></tr></tbody></table>

<p><b>Problem solving</b> is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of <b>simple problem solving</b> (<b>SPS</b>) addressing one issue, whereas the latter is <b>complex problem solving</b> (<b>CPS</b>) with multiple interrelated obstacles.<sup id="cite_ref-Complex_Problem_Solving_1-0" class="reference"><a href="#cite_note-Complex_Problem_Solving-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Another classification of problem-solving tasks is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is troublesome but it is not clear what kind of resolution to aim for.<sup id="cite_ref-:0_2-0" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Similarly, one may distinguish formal or fact-based problems requiring <a href="G_factor_(psychometrics)" title="G factor (psychometrics)">psychometric intelligence</a>, versus socio-emotional problems which depend on the changeable emotions of individuals or groups, such as <a href="Emotional_intelligence" title="Emotional intelligence">tactful</a> behavior, fashion, or gift choices.<sup id="cite_ref-Blanchard-Fields_3-0" class="reference"><a href="#cite_note-Blanchard-Fields-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>Solutions require sufficient resources and knowledge to attain the goal. Professionals such as lawyers, doctors, programmers, and consultants are largely problem solvers for issues that require technical skills and knowledge beyond general competence. Many businesses have found profitable markets by recognizing a problem and creating a solution: the more widespread and inconvenient the problem, the greater the opportunity to develop a <a href="Scalability" title="Scalability">scalable</a> solution.

</p><p>There are many specialized problem-solving techniques and methods in fields such as <a href="Science" title="Science">science</a>, <a href="Engineering" title="Engineering">engineering</a>, <a href="Business" title="Business">business</a>, <a href="Medicine" title="Medicine">medicine</a>, <a href="Mathematics" title="Mathematics">mathematics</a>, <a href="Computer_science" title="Computer science">computer science</a>, <a href="Philosophy" title="Philosophy">philosophy</a>, and <a href="Societies" class="mw-redirect" title="Societies">social organization</a>. The mental techniques to identify, analyze, and solve problems are studied in <a href="Psychology" title="Psychology">psychology</a> and <a href="Cognitive_science" title="Cognitive science">cognitive sciences</a>. Also widely researched are the mental obstacles that prevent people from finding solutions; problem-solving impediments include <a href="Confirmation_bias" title="Confirmation bias">confirmation bias</a>, <a href="Mental_set" class="mw-redirect" title="Mental set">mental set</a>, and <a href="Functional_fixedness" title="Functional fixedness">functional fixedness</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2></div>

<p>The term <i>problem solving</i> has a slightly different meaning depending on the discipline. For instance, it is a mental process in <a href="Psychology" title="Psychology">psychology</a> and a computerized process in <a href="Computer_science" title="Computer science">computer science</a>. There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Well-defined problems have specific end goals and clearly expected solutions, while ill-defined problems do not. Well-defined problems allow for more initial planning than ill-defined problems.<sup id="cite_ref-:0_2-1" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Solving problems sometimes involves dealing with <a href="Pragmatics" title="Pragmatics">pragmatics</a> (the way that context contributes to meaning) and <a href="Semantics" title="Semantics">semantics</a> (the interpretation of the problem). The ability to understand what the end goal of the problem is, and what rules could be applied, represents the key to solving the problem. Sometimes a problem requires <a href="Abstract_thinking" class="mw-redirect" title="Abstract thinking">abstract thinking</a> or coming up with a creative solution.

</p><p>Problem solving has two major domains: <a href="Mathematical_problem" title="Mathematical problem">mathematical problem solving</a> and personal problem solving. Each concerns some difficulty or barrier that is encountered.<sup id="cite_ref-Zimmermann_4-0" class="reference"><a href="#cite_note-Zimmermann-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Psychology">Psychology</h3></div>

<p>Problem solving in psychology refers to the process of finding solutions to problems encountered in life.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Solutions to these problems are usually situation- or context-specific. The process starts with <a href="Problem_finding" title="Problem finding">problem finding</a> and <a href="Problem_shaping" title="Problem shaping">problem shaping</a>, in which the problem is discovered and simplified. The next step is to generate possible solutions and evaluate them. Finally a solution is selected to be implemented and verified. Problems have an <i>end goal</i> to be reached; how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

</p><p>Mental health professionals study the human problem-solving processes using methods such as <a href="Introspection" title="Introspection">introspection</a>, <a href="Behaviorism" title="Behaviorism">behaviorism</a>, <a href="Simulation" title="Simulation">simulation</a>, <a href="Computer_modeling" class="mw-redirect" title="Computer modeling">computer modeling</a>, and <a href="Experiment" title="Experiment">experiment</a>. Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Problem solving has been defined as a higher-order <a href="Cognitive" class="mw-redirect" title="Cognitive">cognitive</a> process and <a href="Intelligence" title="Intelligence">intellectual function</a> that requires the modulation and control of more routine or fundamental skills.<sup id="cite_ref-G&L87_8-0" class="reference"><a href="#cite_note-G&L87-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>

</p><p>Empirical research shows many different strategies and factors influence everyday problem solving.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <a href="Rehabilitation_psychology" title="Rehabilitation psychology">Rehabilitation psychologists</a> studying people with frontal lobe injuries have found that deficits in emotional control and reasoning can be re-mediated with effective rehabilitation and could improve the capacity of injured persons to resolve everyday problems.<sup id="cite_ref-Rath2003_10-0" class="reference"><a href="#cite_note-Rath2003-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Interpersonal everyday problem solving is dependent upon personal motivational and contextual components. One such component is the <a href="Valence_(psychology)" title="Valence (psychology)">emotional valence</a> of "real-world" problems, which can either impede or aid problem-solving performance. Researchers have focused on the role of emotions in problem solving,<sup id="cite_ref-DZurilla_11-0" class="reference"><a href="#cite_note-DZurilla-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> demonstrating that poor emotional control can disrupt focus on the target task, impede problem resolution, and lead to negative outcomes such as fatigue, depression, and inertia.<sup id="cite_ref-rath2004_12-0" class="reference"><a href="#cite_note-rath2004-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> <span class="cleanup-needed-content" style="padding-left:0.1em; padding-right:0.1em; color:var(--color-subtle, #54595d); border:1px solid var(--border-color-subtle, #c8ccd1);">In conceptualization,</span>human problem solving consists of two related processes: problem orientation, and the motivational/attitudinal/affective approach to problematic situations and problem-solving skills.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> People's strategies cohere with their goals<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> and stem from the process of comparing oneself with others.

</p>

<div class="mw-heading mw-heading3"><h3 id="Cognitive_sciences">Cognitive sciences</h3></div>

<p>Among the first experimental psychologists to study problem solving were the <a href="Gestalt_psychology" title="Gestalt psychology">Gestaltists</a> in <a href="Germany" title="Germany">Germany</a>, such as <a href="Karl_Duncker" title="Karl Duncker">Karl Duncker</a> in <i>The Psychology of Productive Thinking</i> (1935).<sup id="cite_ref-Duncker_15-0" class="reference"><a href="#cite_note-Duncker-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Perhaps best known is the work of <a href="Allen_Newell" title="Allen Newell">Allen Newell</a> and <a href="Herbert_A._Simon" title="Herbert A. Simon">Herbert A. Simon</a>.<sup id="cite_ref-Newell_16-0" class="reference"><a href="#cite_note-Newell-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>

</p><p>Experiments in the 1960s and early 1970s asked participants to solve relatively simple, well-defined, but not previously seen laboratory tasks.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> These simple problems, such as the <a href="Tower_of_Hanoi" title="Tower of Hanoi">Tower of Hanoi</a>, admitted <a href="Optimal_solution" class="mw-redirect" title="Optimal solution">optimal solutions</a> that could be found quickly, allowing researchers to observe the full problem-solving process. Researchers assumed that these model problems would elicit the characteristic <a href="Cognitive_process" class="mw-redirect" title="Cognitive process">cognitive processes</a> by which more complex "real world" problems are solved.

</p><p>An outstanding problem-solving technique found by this research is the principle of <a href="Decomposition_(computer_science)" title="Decomposition (computer science)">decomposition</a>.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Computer_science">Computer science</h3></div>

<p>Much of computer science and <a href="Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a> involves designing automated systems to solve a specified type of problem: to accept input data and calculate a correct or adequate response, reasonably quickly. <a href="Algorithm" title="Algorithm">Algorithms</a> are recipes or instructions that direct such systems, written into <a href="Computer_program" title="Computer program">computer programs</a>.

</p><p>Steps for designing such systems include problem determination, <a href="Heuristic" title="Heuristic">heuristics</a>, <a href="Root_cause_analysis" title="Root cause analysis">root cause analysis</a>, <a href="Data_deduplication" title="Data deduplication">de-duplication</a>, analysis, diagnosis, and repair. Analytic techniques include linear and nonlinear programming, <a href="Queuing_systems" class="mw-redirect" title="Queuing systems">queuing systems</a>, and simulation.<sup id="cite_ref-MalakootiMCDM_20-0" class="reference"><a href="#cite_note-MalakootiMCDM-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> A large, perennial obstacle is to find and fix errors in computer programs: <a href="Debugging" title="Debugging">debugging</a>.

</p>

<div class="mw-heading mw-heading3"><h3 id="Logic">Logic</h3></div>

<p>Formal <a href="Logic" title="Logic">logic</a> concerns issues like validity, truth, inference, argumentation, and proof. In a problem-solving context, it can be used to formally represent a problem as a theorem to be proved, and to represent the knowledge needed to solve the problem as the premises to be used in a proof that the problem has a solution.

</p><p>The use of computers to prove mathematical theorems using formal logic emerged as the field of <a href="Automated_theorem_proving" title="Automated theorem proving">automated theorem proving</a> in the 1950s. It included the use of <a href="Heuristic" title="Heuristic">heuristic</a> methods designed to simulate human problem solving, as in the <a href="Logic_Theory_Machine" class="mw-redirect" title="Logic Theory Machine">Logic Theory Machine</a>, developed by Allen Newell, Herbert A. Simon and J. C. Shaw, as well as algorithmic methods such as the <a href="Resolution_(logic)" title="Resolution (logic)">resolution</a> principle developed by <a href="John_Alan_Robinson" title="John Alan Robinson">John Alan Robinson</a>.

</p><p>In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for <a href="Program_verification" class="mw-redirect" title="Program verification">program verification</a> in computer science. In 1958, <a href="John_McCarthy_(computer_scientist)" title="John McCarthy (computer scientist)">John McCarthy</a> proposed the <a href="Advice_taker" title="Advice taker">advice taker</a>, to represent information in formal logic and to derive answers to questions using automated theorem-proving. An important step in this direction was made by <a href="Cordell_Green" title="Cordell Green">Cordell Green</a> in 1969, who used a resolution theorem prover for question-answering and for such other applications in artificial intelligence as robot planning.

</p><p>The resolution theorem-prover used by Cordell Green bore little resemblance to human problem solving methods. In response to criticism of that approach from researchers at MIT, <a href="Robert_Kowalski" title="Robert Kowalski">Robert Kowalski</a> developed <a href="Logic_programming" title="Logic programming">logic programming</a> and <a href="SLD_resolution" title="SLD resolution">SLD resolution</a>,<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> and computational logic to improve human thinking.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Engineering">Engineering</h3></div>

<p>When products or processes fail, problem solving techniques can be used to develop corrective actions that can be taken to prevent further <a href="Failure" title="Failure">failures</a>. Such techniques can also be applied to a product or process prior to an actual failure event—to predict, analyze, and mitigate a potential problem in advance. Techniques such as <a href="Failure_mode_and_effects_analysis" title="Failure mode and effects analysis">failure mode and effects analysis</a> can proactively reduce the likelihood of problems.

</p><p>In either the reactive or the proactive case, it is necessary to build a causal explanation through a process of diagnosis. In deriving an explanation of effects in terms of causes, <a href="Abductive_reasoning" title="Abductive reasoning">abduction</a> generates new ideas or hypotheses (asking "how?"); <a href="Deductive_reasoning" title="Deductive reasoning">deduction</a> evaluates and refines hypotheses based on other plausible premises (asking "why?"); and <a href="Inductive_reasoning" title="Inductive reasoning">induction</a> justifies a hypothesis with empirical data (asking "how much?").<sup id="cite_ref-Staat_24-0" class="reference"><a href="#cite_note-Staat-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> The objective of abduction is to determine which hypothesis or proposition to test, not which one to adopt or assert.<sup id="cite_ref-Sullivan_25-0" class="reference"><a href="#cite_note-Sullivan-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> In the <a href="Charles_S._Peirce" class="mw-redirect" title="Charles S. Peirce">Peircean</a> logical system, the logic of abduction and deduction contribute to our conceptual understanding of a phenomenon, while the logic of induction adds quantitative details (empirical substantiation) to our conceptual knowledge.<sup id="cite_ref-Yu_26-0" class="reference"><a href="#cite_note-Yu-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup>

</p><p><a href="Forensic_engineering" title="Forensic engineering">Forensic engineering</a> is an important technique of <a href="Failure_analysis" title="Failure analysis">failure analysis</a> that involves tracing product defects and flaws. Corrective action can then be taken to prevent further failures.

</p><p>Reverse engineering attempts to discover the original problem-solving logic used in developing a product by disassembling the product and developing a plausible pathway to creating and assembling its parts.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Military_science">Military science</h3></div>

<p>In <a href="Military_Science" class="mw-redirect" title="Military Science">military science</a>, problem solving is linked to the concept of "end-states", the conditions or situations which are the aims of the strategy.<sup id="cite_ref-USJFCOM_28-0" class="reference"><a href="#cite_note-USJFCOM-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: xiii, E-2">: xiii, E-2 </span></sup> Ability to solve problems is important at any <a href="Military_rank" title="Military rank">military rank</a>, but is essential at the <a href="Command_and_control" title="Command and control">command and control</a> level. It results from deep qualitative and quantitative understanding of possible scenarios. <i>Effectiveness</i> in this context is an evaluation of results: to what extent the end states were accomplished.<sup id="cite_ref-USJFCOM_28-1" class="reference"><a href="#cite_note-USJFCOM-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: IV-24">: IV-24 </span></sup> <i>Planning</i> is the process of determining how to effect those end states.<sup id="cite_ref-USJFCOM_28-2" class="reference"><a href="#cite_note-USJFCOM-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: IV-1">: IV-1 </span></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Processes">Processes</h2></div>

<p>Some models of problem solving involve identifying a <a href="Goal" title="Goal">goal</a> and then a sequence of subgoals towards achieving this goal. Andersson, who introduced the <a href="ACT-R" title="ACT-R">ACT-R</a> model of cognition, modelled this collection of goals and subgoals as a <a href="Stack_(abstract_data_type)" title="Stack (abstract data type)">goal stack</a> in which the mind contains a stack of goals and subgoals to be completed, and a single task being carried out at any time.<sup id="cite_ref-:1_29-0" class="reference"><a href="#cite_note-:1-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 51">: 51 </span></sup>

</p><p>Knowledge of how to solve one problem can be applied to another problem, in a process known as <a href="Knowledge_transfer" title="Knowledge transfer">transfer</a>.<sup id="cite_ref-:1_29-1" class="reference"><a href="#cite_note-:1-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 56">: 56 </span></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Problem-solving_strategies">Problem-solving strategies</h2></div>

<p>Problem-solving strategies are steps to overcoming the obstacles to achieving a goal. The iteration of such strategies over the course of solving a problem is the "problem-solving cycle".<sup id="cite_ref-Bransford1993_30-0" class="reference"><a href="#cite_note-Bransford1993-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup>

</p><p>Common steps in this cycle include recognizing the problem, defining it, developing a strategy to fix it, organizing knowledge and resources available, monitoring progress, and evaluating the effectiveness of the solution. Once a solution is achieved, another problem usually arises, and the cycle starts again.

</p><p>Insight is the sudden <a href="Aha!_moment" class="mw-redirect" title="Aha! moment">a<i>ha!</i></a> solution to a problem, the birth of a new idea to simplify a complex situation. Solutions found through insight are often more incisive than those from step-by-step analysis. A quick solution process requires insight to select productive moves at different stages of the problem-solving cycle. Unlike Newell and Simon's formal definition of a <i>move problem</i>, there is no consensus definition of an <i>insight problem</i>.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup>

</p><p>Some problem-solving strategies include:<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup>

</p>

<dl><dt><a href="Abstraction" title="Abstraction">Abstraction</a></dt>

<dd>solving the problem in a tractable model system to gain insight into the real system</dd>

<dt><a href="Analogy" title="Analogy">Analogy</a></dt>

<dd>adapting the solution to a previous problem which has similar features or mechanisms</dd>

<dt><a href="Brainstorming" title="Brainstorming">Brainstorming</a></dt>

<dd>(especially among groups of people) suggesting a large number of solutions or ideas and combining and developing them until an optimum solution is found</dd>

<dt><a href="https://en.wiktionary.org/wiki/bypass" class="extiw external" title="wiktionary:bypass">Bypasses</a></dt>

<dd>transform the problem into another problem that is easier to solve, bypassing the barrier, then transform that solution back to a solution to the original problem.</dd>

<dt><a href="Critical_thinking" title="Critical thinking">Critical thinking</a></dt>

<dd>analysis of available evidence and arguments to form a judgement via rational, skeptical, and unbiased evaluation</dd>

<dt><a href="Divide_and_conquer_algorithm" class="mw-redirect" title="Divide and conquer algorithm">Divide and conquer</a></dt>

<dd>breaking down a large, complex problem into smaller, solvable problems</dd>

<dt><a href="Help-seeking" title="Help-seeking">Help-seeking</a></dt>

<dd>obtaining external assistance to deal with obstacles</dd>

<dt><a href="Hypothesis_testing" class="mw-redirect" title="Hypothesis testing">Hypothesis testing</a></dt>

<dd>assuming a possible explanation to the problem and trying to prove (or, in some contexts, disprove) the assumption</dd>

<dt><a href="Lateral_thinking" title="Lateral thinking">Lateral thinking</a></dt>

<dd>approaching solutions indirectly and creatively</dd>

<dt><a href="Means-ends_analysis" class="mw-redirect" title="Means-ends analysis">Means-ends analysis</a></dt>

<dd>choosing an action at each step to move closer to the goal</dd>

<dt><a href="Morphological_analysis_(problem-solving)" title="Morphological analysis (problem-solving)">Morphological analysis</a></dt>

<dd>assessing the output and interactions of an entire system</dd>

<dt><a href="Observation" title="Observation">Observation</a> / <a href="Question" title="Question">Question</a></dt>

<dd>in the <a href="Natural_sciences" class="mw-redirect" title="Natural sciences">natural sciences</a> an observation is an act or instance of <a href="Noticing" class="mw-redirect" title="Noticing">noticing</a> or perceiving and the acquisition of <a href="Information" title="Information">information</a> from a <a href="Primary_source" title="Primary source">primary source</a>. A question is an <a href="Utterance" title="Utterance">utterance</a> which serves as a request for <a href="Information" title="Information">information</a>.</dd>

<dt><a href="Proof_(truth)" title="Proof (truth)">Proof of impossibility</a></dt>

<dd>try to prove that the problem cannot be solved. The point where the proof fails will be the starting point for solving it</dd>

<dt><a href="Reduction_(complexity)" title="Reduction (complexity)">Reduction</a></dt>

<dd>transforming the problem into another problem for which solutions exist</dd>

<dt><a href="Research" title="Research">Research</a></dt>

<dd>employing existing ideas or adapting existing solutions to similar problems</dd>

<dt><a href="Root_cause_analysis" title="Root cause analysis">Root cause analysis</a></dt>

<dd>identifying the cause of a problem</dd>

<dt><a href="Trial-and-error" class="mw-redirect" title="Trial-and-error">Trial-and-error</a></dt>

<dd>testing possible solutions until the right one is found</dd></dl>

<div class="mw-heading mw-heading2"><h2 id="Problem-solving_methods">Problem-solving methods</h2></div>

<ul><li><a href="A3_problem_solving" title="A3 problem solving">A3 problem solving</a> – Structured problem improvement approach</li>

<li><a href="Design_thinking" title="Design thinking">Design thinking</a> – Processes by which design concepts are developed</li>

<li><a href="Eight_Disciplines_Problem_Solving" class="mw-redirect" title="Eight Disciplines Problem Solving">Eight Disciplines Problem Solving</a> – Eight disciplines of team-oriented problem solving method<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li>

<li><a href="GROW_model" title="GROW model">GROW model</a> – Method for goal setting and problem solving</li>

<li><a href="Help-seeking" title="Help-seeking">Help-seeking</a> – Theory in psychology</li>

<li><a href="How_to_Solve_It" title="How to Solve It">How to Solve It</a> – Book by George Pólya</li>

<li><a href="Lateral_thinking" title="Lateral thinking">Lateral thinking</a> – Manner of solving problems</li>

<li><a href="OODA_loop" title="OODA loop">OODA loop</a> – Observe–orient–decide–act cycle</li>

<li><a href="PDCA" title="PDCA">PDCA</a> – Iterative design and management method</li>

<li><a href="Root_cause_analysis" title="Root cause analysis">Root cause analysis</a> – Method of identifying the fundamental causes of faults or problems</li>

<li><a href="RPR_problem_diagnosis" class="mw-redirect" title="RPR problem diagnosis">RPR problem diagnosis</a></li>

<li><a href="TRIZ" title="TRIZ">TRIZ</a> – Problem-solving tools</li>

<li><a href="Scientific_method" title="Scientific method">Scientific method</a> – is an <a href="Empirical_evidence" title="Empirical evidence">empirical</a> method for acquiring <a href="Knowledge" title="Knowledge">knowledge</a> that has characterized the development of <a href="Science" title="Science">science</a>.</li>

<li><a href="Swarm_intelligence" title="Swarm intelligence">Swarm intelligence</a> – Collective behavior of decentralized, self-organized systems</li>

<li><a href="System_dynamics" title="System dynamics">System dynamics</a> – Study of non-linear complex systems</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Common_barriers">Common barriers</h2></div>

<p>Common barriers to problem solving include mental constructs that impede an efficient search for solutions. Five of the most common identified by researchers are: <a href="Confirmation_bias" title="Confirmation bias">confirmation bias</a>, <a href="Mental_set" class="mw-redirect" title="Mental set">mental set</a>, <a href="Functional_fixedness" title="Functional fixedness">functional fixedness</a>, unnecessary constraints, and irrelevant information.

</p>

<div class="mw-heading mw-heading3"><h3 id="Confirmation_bias">Confirmation bias</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Confirmation_bias" title="Confirmation bias">Confirmation bias</a></div>

<p>Confirmation bias is an unintentional tendency to collect and use data which favors preconceived notions. Such notions may be incidental rather than motivated by important personal beliefs: the desire to be right may be sufficient motivation.<sup id="cite_ref-Nickerson1998_33-0" class="reference"><a href="#cite_note-Nickerson1998-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup>

</p><p>Scientific and technical professionals also experience confirmation bias. One online experiment, for example, suggested that professionals within the field of psychological research are likely to view scientific studies that agree with their preconceived notions more favorably than clashing studies.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> According to Raymond Nickerson, one can see the consequences of confirmation bias in real-life situations, which range in severity from inefficient government policies to genocide. Nickerson argued that those who killed people accused of <a href="Witch-hunt" class="mw-redirect" title="Witch-hunt">witchcraft</a> demonstrated confirmation bias with motivation. Researcher Michael Allen found evidence for confirmation bias with motivation in school children who worked to manipulate their science experiments to produce favorable results.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup>

</p><p>However, confirmation bias does not necessarily require motivation. In 1960, <a href="Peter_Cathcart_Wason" title="Peter Cathcart Wason">Peter Cathcart Wason</a> conducted an experiment in which participants first viewed three numbers and then created a hypothesis in the form of a rule that could have been used to create that triplet of numbers. When testing their hypotheses, participants tended to only create additional triplets of numbers that would confirm their hypotheses, and tended not to create triplets that would negate or disprove their hypotheses.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Mental_set">Mental set</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Mental_set" class="mw-redirect" title="Mental set">Mental set</a></div>

<p>Mental set is the inclination to re-use a previously successful solution, rather than search for new and better solutions. It is a reliance on habit.

</p><p>It was first articulated by <a href="Abraham_S._Luchins" title="Abraham S. Luchins">Abraham S. Luchins</a> in the 1940s with his well-known water jug experiments.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> Participants were asked to fill one jug with a specific amount of water by using other jugs with different maximum capacities. After Luchins gave a set of jug problems that could all be solved by a single technique, he then introduced a problem that could be solved by the same technique, but also by a novel and simpler method. His participants tended to use the accustomed technique, oblivious of the simpler alternative.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> This was again demonstrated in <a href="Norman_Maier" title="Norman Maier">Norman Maier</a>'s 1931 experiment, which challenged participants to solve a problem by using a familiar tool (pliers) in an unconventional manner. Participants were often unable to view the object in a way that strayed from its typical use, a type of mental set known as functional fixedness (see the following section).

</p><p>Rigidly clinging to a mental set is called <i>fixation</i>, which can deepen to an obsession or preoccupation with attempted strategies that are repeatedly unsuccessful.<sup id="cite_ref-Wiley1998_39-0" class="reference"><a href="#cite_note-Wiley1998-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> In the late 1990s, researcher Jennifer Wiley found that professional expertise in a field can create a mental set, perhaps leading to fixation.<sup id="cite_ref-Wiley1998_39-1" class="reference"><a href="#cite_note-Wiley1998-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup>

</p><p><a href="Groupthink" title="Groupthink">Groupthink</a>, in which each individual takes on the mindset of the rest of the group, can produce and exacerbate mental set.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> Social pressure leads to everybody thinking the same thing and reaching the same conclusions.

</p>

<div class="mw-heading mw-heading3"><h3 id="Functional_fixedness">Functional fixedness</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Functional_fixedness" title="Functional fixedness">Functional fixedness</a></div>

<p>Functional fixedness is the tendency to view an object as having only one function, and to be unable to conceive of any novel use, as in the Maier pliers experiment described above. Functional fixedness is a specific form of mental set, and is one of the most common forms of cognitive bias in daily life.

</p><p>As an example, imagine a man wants to kill a bug in his house, but the only thing at hand is a can of air freshener. He may start searching for something to kill the bug instead of squashing it with the can, thinking only of its main function of deodorizing.

</p><p>Tim German and Clark Barrett describe this barrier: "subjects become 'fixed' on the design function of the objects, and problem solving suffers relative to control conditions in which the object's function is not demonstrated."<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> Their research found that young children's limited knowledge of an object's intended function reduces this barrier<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> Research has also discovered functional fixedness in educational contexts, as an obstacle to understanding: "functional fixedness may be found in learning concepts as well as in solving chemistry problems."<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup>

</p><p>There are several hypotheses in regards to how functional fixedness relates to problem solving.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> It may waste time, delaying or entirely preventing the correct use of a tool.

</p>

<div class="mw-heading mw-heading3"><h3 id="Unnecessary_constraints">Unnecessary constraints</h3></div>

<p>Unnecessary constraints are arbitrary boundaries imposed unconsciously on the task at hand, which foreclose a productive avenue of solution. The solver may become fixated on only one type of solution, as if it were an inevitable requirement of the problem. Typically, this combines with mental set—clinging to a previously successful method.<sup id="cite_ref-Kellogg,_R._T._2003_45-0" class="reference"><a href="#cite_note-Kellogg,_R._T._2003-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup>

</p><p>Visual problems can also produce mentally invented constraints.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> A famous example is the dot problem: nine dots arranged in a three-by-three grid pattern must be connected by drawing four straight line segments, without lifting pen from paper or backtracking along a line. The subject typically assumes the pen must stay within the outer square of dots, but the solution requires lines continuing beyond this frame, and researchers have found a 0% solution rate within a brief allotted time.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup>

</p><p>This problem has produced the expression "<a href="Think_outside_the_box" class="mw-redirect" title="Think outside the box">think outside the box</a>".<sup id="cite_ref-Weiten,_Wayne_2011_48-0" class="reference"><a href="#cite_note-Weiten,_Wayne_2011-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> Such problems are typically solved via a sudden insight which leaps over the mental barriers, often after long toil against them.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> This can be difficult depending on how the subject has structured the problem in their mind, how they draw on past experiences, and how well they juggle this information in their working memory. In the example, envisioning the dots connected outside the framing square requires visualizing an unconventional arrangement, which is a strain on working memory.<sup id="cite_ref-Weiten,_Wayne_2011_48-1" class="reference"><a href="#cite_note-Weiten,_Wayne_2011-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Irrelevant_information">Irrelevant information</h3></div>

<div role="note" class="hatnote navigation-not-searchable">See also: <a href="Information_overload" title="Information overload">Information overload</a> and <a href="Mass_media" title="Mass media">Mass media</a></div>

<p>Irrelevant information is a specification or data presented in a problem that is unrelated to the solution.<sup id="cite_ref-Kellogg,_R._T._2003_45-1" class="reference"><a href="#cite_note-Kellogg,_R._T._2003-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> If the solver assumes that all information presented needs to be used, this often derails the problem solving process, making relatively simple problems much harder.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup>

</p><p>For example: "Fifteen percent of the people in Topeka have unlisted telephone numbers. You select 200 names at random from the Topeka phone book. How many of these people have unlisted phone numbers?"<sup id="cite_ref-Weiten,_Wayne_2011_48-2" class="reference"><a href="#cite_note-Weiten,_Wayne_2011-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> The "obvious" answer is 15%, but in fact none of the unlisted people would be listed among the 200. This kind of "<a href="Trick_question" title="Trick question">trick question</a>" is often used in aptitude tests or cognitive evaluations.<sup id="cite_ref-Walinga,_Jennifer_2011_51-0" class="reference"><a href="#cite_note-Walinga,_Jennifer_2011-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> Though not inherently difficult, they require independent thinking that is not necessarily common. Mathematical <a href="Word_problem_(mathematics_education)" title="Word problem (mathematics education)">word problems</a> often include irrelevant qualitative or numerical information as an extra challenge.

</p>

<div class="mw-heading mw-heading3"><h3 id="Avoiding_barriers_by_changing_problem_representation">Avoiding barriers by changing problem representation</h3></div>

<p>The disruption caused by the above cognitive biases can depend on how the information is represented:<sup id="cite_ref-Walinga,_Jennifer_2011_51-1" class="reference"><a href="#cite_note-Walinga,_Jennifer_2011-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> visually, verbally, or mathematically. A classic example is the Buddhist monk problem:

</p>

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</style><blockquote class="templatequote"><p>A Buddhist monk begins at dawn one day walking up a mountain, reaches the top at sunset, meditates at the top for several days until one dawn when he begins to walk back to the foot of the mountain, which he reaches at sunset. Making no assumptions about his starting or stopping or about his pace during the trips, prove that there is a place on the path which he occupies at the same hour of the day on the two separate journeys.</p></blockquote>

<p>The problem cannot be addressed in a verbal context, trying to describe the monk's progress on each day. It becomes much easier when the paragraph is represented mathematically by a function: one visualizes a <a href="Graph_of_a_function" title="Graph of a function">graph</a> whose horizontal axis is time of day, and whose vertical axis shows the monk's position (or altitude) on the path at each time. Superimposing the two journey curves, which traverse opposite diagonals of a rectangle, one sees they must cross each other somewhere. The visual representation by graphing has resolved the difficulty.

</p><p>Similar strategies can often improve problem solving on tests.<sup id="cite_ref-Kellogg,_R._T._2003_45-2" class="reference"><a href="#cite_note-Kellogg,_R._T._2003-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Other_barriers_for_individuals">Other barriers for individuals</h3></div>

<p>People who are engaged in problem solving tend to overlook subtractive changes, even those that are critical elements of efficient solutions. For example, a city planner may decide that the solution to decrease traffic congestion would be to add another lane to a highway, rather than finding ways to reduce the need for the highway in the first place. This tendency to solve by first, only, or mostly creating or adding elements, rather than by subtracting elements or processes is shown to intensify with higher <a href="Cognitive_load" title="Cognitive load">cognitive loads</a> such as <a href="Information_overload" title="Information overload">information overload</a>.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Dreaming:_problem_solving_without_waking_consciousness">Dreaming: problem solving without waking consciousness</h2></div>

<p>People can also solve problems while they are asleep. There are many reports of scientists and engineers who solved problems in their <a href="Dream" title="Dream">dreams</a>. For example, <a href="Elias_Howe" title="Elias Howe">Elias Howe</a>, inventor of the sewing machine, figured out the structure of the bobbin from a dream.<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup>

</p><p>The chemist <a href="August_Kekul%C3%A9" title="August Kekulé">August Kekulé</a> was considering how benzene arranged its six carbon and hydrogen atoms. Thinking about the problem, he dozed off, and dreamt of dancing atoms that fell into a snakelike pattern, which led him to discover the benzene ring. As Kekulé wrote in his diary,

</p>

<blockquote class="templatequote"><p>One of the snakes seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke; and this time also I spent the rest of the night in working out the consequences of the hypothesis.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup></p></blockquote>

<p>There also are empirical studies of how people can think consciously about a problem before going to sleep, and then solve the problem with a dream image. Dream researcher <a href="William_C._Dement" title="William C. Dement">William C. Dement</a> told his undergraduate class of 500 students that he wanted them to think about an infinite series, whose first elements were OTTFF, to see if they could deduce the principle behind it and to say what the next elements of the series would be.<sup id="cite_ref-Dement_1972_56-0" class="reference"><a href="#cite_note-Dement_1972-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> He asked them to think about this problem every night for 15 minutes before going to sleep and to write down any dreams that they then had. They were instructed to think about the problem again for 15 minutes when they awakened in the morning.

</p><p>The sequence OTTFF is the first letters of the numbers: one, two, three, four, five. The next five elements of the series are SSENT (six, seven, eight, nine, ten). Some of the students solved the puzzle by reflecting on their dreams. One example was a student who reported the following dream:<sup id="cite_ref-Dement_1972_56-1" class="reference"><a href="#cite_note-Dement_1972-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup>

</p>

<blockquote class="templatequote"><p>I was standing in an art gallery, looking at the paintings on the wall. As I walked down the hall, I began to count the paintings: one, two, three, four, five. As I came to the sixth and seventh, the paintings had been ripped from their frames. I stared at the empty frames with a peculiar feeling that some mystery was about to be solved. Suddenly I realized that the sixth and seventh spaces were the solution to the problem!</p></blockquote>

<p>With more than 500 undergraduate students, 87 dreams were judged to be related to the problems students were assigned (53 directly related and 34 indirectly related). Yet of the people who had dreams that apparently solved the problem, only seven were actually able to consciously know the solution. The rest (46 out of 53) thought they did not know the solution.

</p><p><a href="Albert_Einstein" title="Albert Einstein">Albert Einstein</a> believed that much problem solving goes on unconsciously, and the person must then figure out and formulate consciously what the mindbrain has already solved. He believed this was his process in formulating the theory of relativity: "The creator of the problem possesses the solution."<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> Einstein said that he did his problem solving without words, mostly in images. "The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined."<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Cognitive_sciences:_two_schools">Cognitive sciences: two schools</h2></div>

<p>

Problem-solving processes differ across knowledge domains and across levels of expertise.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> For this reason, <a href="Cognitive_sciences" class="mw-redirect" title="Cognitive sciences">cognitive sciences</a> findings obtained in the laboratory cannot necessarily generalize to problem-solving situations outside the laboratory. This has led to a research emphasis on real-world problem solving, since the 1990s. This emphasis has been expressed quite differently in North America and Europe, however. Whereas North American research has typically concentrated on studying problem solving in separate, natural knowledge domains, much of the European research has focused on novel, complex problems, and has been performed with computerized scenarios.<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Europe">Europe</h3></div>

<p>In Europe, two main approaches have surfaced, one initiated by <a href="Donald_Broadbent" title="Donald Broadbent">Donald Broadbent</a><sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> in the United Kingdom and the other one by <a href="Dietrich_D%C3%B6rner" title="Dietrich Dörner">Dietrich Dörner</a><sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> in Germany. The two approaches share an emphasis on relatively complex, semantically rich, computerized laboratory tasks, constructed to resemble real-life problems. The approaches differ somewhat in their theoretical goals and methodology. The tradition initiated by Broadbent emphasizes the distinction between cognitive problem-solving processes that operate under awareness versus outside of awareness, and typically employs mathematically well-defined computerized systems. The tradition initiated by Dörner, on the other hand, has an interest in the interplay of the cognitive, motivational, and social components of problem solving, and utilizes very complex computerized scenarios that contain up to 2,000 highly interconnected variables.<sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="North_America">North America</h3></div>

<p>In North America, initiated by the work of Herbert A. Simon on "learning by doing" in <a href="Semantic" class="mw-redirect" title="Semantic">semantically</a> rich domains,<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> researchers began to investigate problem solving separately in different natural <a href="Knowledge_domain" class="mw-redirect" title="Knowledge domain">knowledge domains</a>—such as physics, writing, or <a href="Chess" title="Chess">chess</a> playing—rather than attempt to extract a global theory of problem solving.<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> These researchers have focused on the development of problem solving within certain domains, that is on the development of <a href="Expertise" class="mw-redirect" title="Expertise">expertise</a>.<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup>

</p><p>Areas that have attracted rather intensive attention in North America include:

</p>

<ul><li>calculation<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup></li>

<li>computer skills<sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup></li>

<li>game playing<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup></li>

<li>lawyers' reasoning<sup id="cite_ref-Amsel1991_70-0" class="reference"><a href="#cite_note-Amsel1991-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup></li>

<li>managerial problem solving<sup id="cite_ref-Wagner_71-0" class="reference"><a href="#cite_note-Wagner-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup></li>

<li>mathematical problem solving<sup id="cite_ref-72" class="reference"><a href="#cite_note-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup></li>

<li>mechanical problem solving<sup id="cite_ref-73" class="reference"><a href="#cite_note-73"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup></li>

<li>personal problem solving<sup id="cite_ref-74" class="reference"><a href="#cite_note-74"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup></li>

<li>political decision making<sup id="cite_ref-75" class="reference"><a href="#cite_note-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup></li>

<li>problem solving in electronics<sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup></li>

<li>problem solving for innovations and inventions: <a href="TRIZ" title="TRIZ">TRIZ</a><sup id="cite_ref-Altshuller1994_77-0" class="reference"><a href="#cite_note-Altshuller1994-77"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup></li>

<li>reading<sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup></li>

<li>social problem solving<sup id="cite_ref-DZurilla_11-1" class="reference"><a href="#cite_note-DZurilla-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></li>

<li>writing<sup id="cite_ref-79" class="reference"><a href="#cite_note-79"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Characteristics_of_complex_problems">Characteristics of complex problems</h2></div>

<p>Complex problem solving (CPS) is distinguishable from simple problem solving (SPS). In SPS there is a singular and simple obstacle. In CPS there may be multiple simultaneous obstacles. For example, a surgeon at work has far more complex problems than an individual deciding what shoes to wear. As elucidated by Dietrich Dörner, and later expanded upon by Joachim Funke, complex problems have some typical characteristics, which include:<sup id="cite_ref-Complex_Problem_Solving_1-1" class="reference"><a href="#cite_note-Complex_Problem_Solving-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p>

<ul><li><a href="Complexity" title="Complexity">complexity</a> (large numbers of items, interrelations, and decisions)</li>

<li><a href="Enumerability" class="mw-redirect" title="Enumerability">enumerability</a></li>

<li><a href="Homogeneity_and_heterogeneity" title="Homogeneity and heterogeneity">heterogeneity</a></li>

<li><a href="https://en.wiktionary.org/wiki/connectivity" class="extiw external" title="wikt:connectivity">connectivity</a> (hierarchy relation, communication relation, allocation relation)</li>

<li><a href="Dynamics_(physics)" class="mw-redirect" title="Dynamics (physics)">dynamics</a> (time considerations)

<ul><li>temporal constraints</li>

<li>temporal sensitivity</li>

<li>phase effects</li>

<li>dynamic <a href="Predictability" title="Predictability">unpredictability</a></li></ul></li>

<li>intransparency (lack of clarity of the situation)

<ul><li>commencement opacity</li>

<li>continuation opacity</li></ul></li>

<li><a href="Polytely" title="Polytely">polytely</a> (multiple goals)<sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup>

<ul><li>inexpressivenes</li>

<li>opposition</li>

<li>transience</li></ul></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Collective_problem_solving">Collective problem solving</h2></div>

<div role="note" class="hatnote navigation-not-searchable">See also: <a href="Crowdsolving" class="mw-redirect" title="Crowdsolving">Crowdsolving</a>, <a href="Collective_action" title="Collective action">Collective action</a>, <a href="Collaborative_intelligence" title="Collaborative intelligence">Collaborative intelligence</a>, <a href="Mass_collaboration" title="Mass collaboration">Mass collaboration</a>, <a href="Collective_wisdom" title="Collective wisdom">Collective wisdom</a>, <a href="The_Wisdom_of_Crowds" title="The Wisdom of Crowds">The Wisdom of Crowds</a>, <a href="Distributed_knowledge" title="Distributed knowledge">Distributed knowledge</a>, <a href="Online_participation" title="Online participation">Online participation</a>, and <a href="Group_decision-making" title="Group decision-making">Group decision-making</a></div>

<p>People solve problems on many different levels—from the individual to the civilizational. Collective problem solving refers to problem solving performed collectively. <a href="Social_issue" title="Social issue">Social issues</a> and global issues can typically only be solved collectively.

</p><p>The complexity of contemporary problems exceeds the cognitive capacity of any individual and requires different but complementary varieties of expertise and collective problem solving ability.<sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup>

</p><p><a href="Collective_intelligence" title="Collective intelligence">Collective intelligence</a> is shared or group intelligence that emerges from the <a href="Collaboration" title="Collaboration">collaboration</a>, collective efforts, and competition of many individuals.

</p><p>In collaborative problem solving people <a href="Teamwork" title="Teamwork">work together</a> to solve real-world problems. Members of problem-solving groups share a common concern, a similar passion, and/or a commitment to their work. Members can ask questions, wonder, and try to understand common issues. They share expertise, experiences, tools, and methods.<sup id="cite_ref-82" class="reference"><a href="#cite_note-82"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup> Groups may be fluid based on need, may only occur temporarily to finish an assigned task, or may be more permanent depending on the nature of the problems.

</p><p>For example, in the educational context, members of a group may all have input into the decision-making process and a role in the learning process. Members may be responsible for the thinking, teaching, and monitoring of all members in the group. Group work may be coordinated among members so that each member makes an equal contribution to the whole work. Members can identify and build on their individual strengths so that everyone can make a significant contribution to the task.<sup id="cite_ref-83" class="reference"><a href="#cite_note-83"><span class="cite-bracket">[</span>83<span class="cite-bracket">]</span></a></sup> Collaborative group work has the ability to promote critical thinking skills, problem solving skills, <a href="Social_skills" title="Social skills">social skills</a>, and <a href="Self-esteem" title="Self-esteem">self-esteem</a>. By using collaboration and communication, members often learn from one another and construct meaningful knowledge that often leads to better learning outcomes than individual work.<sup id="cite_ref-84" class="reference"><a href="#cite_note-84"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup>

</p><p>Collaborative groups require joint intellectual efforts between the members and involve <a href="Social_interaction" class="mw-redirect" title="Social interaction">social interactions</a> to solve problems together. The <a href="Knowledge_sharing" title="Knowledge sharing">knowledge shared</a> during these interactions is acquired during communication, negotiation, and production of materials.<sup id="cite_ref-85" class="reference"><a href="#cite_note-85"><span class="cite-bracket">[</span>85<span class="cite-bracket">]</span></a></sup> Members actively seek information from others by asking questions. The capacity to use questions to acquire new information increases understanding and the ability to solve problems.<sup id="cite_ref-86" class="reference"><a href="#cite_note-86"><span class="cite-bracket">[</span>86<span class="cite-bracket">]</span></a></sup>

</p><p>In a 1962 research report, <a href="Douglas_Engelbart" title="Douglas Engelbart">Douglas Engelbart</a> linked collective intelligence to organizational effectiveness, and predicted that proactively "augmenting human intellect" would yield a multiplier effect in group problem solving: "Three people working together in this augmented mode [would] seem to be more than three times as effective in solving a complex problem as is one augmented person working alone".<sup id="cite_ref-87" class="reference"><a href="#cite_note-87"><span class="cite-bracket">[</span>87<span class="cite-bracket">]</span></a></sup>

</p><p><a href="Henry_Jenkins" title="Henry Jenkins">Henry Jenkins</a>, a theorist of new media and media convergence, draws on the theory that collective intelligence can be attributed to media convergence and <a href="Participatory_culture" title="Participatory culture">participatory culture</a>.<sup id="cite_ref-88" class="reference"><a href="#cite_note-88"><span class="cite-bracket">[</span>88<span class="cite-bracket">]</span></a></sup> He criticizes contemporary education for failing to incorporate online trends of collective problem solving into the classroom, stating "whereas a collective intelligence community encourages ownership of work as a group, schools grade individuals". Jenkins argues that interaction within a knowledge community builds vital skills for young people, and teamwork through collective intelligence communities contributes to the development of such skills.<sup id="cite_ref-:25_89-0" class="reference"><a href="#cite_note-:25-89"><span class="cite-bracket">[</span>89<span class="cite-bracket">]</span></a></sup>

</p><p><a href="Collective_impact" title="Collective impact">Collective impact</a> is the commitment of a group of actors from different sectors to a common agenda for solving a specific social problem, using a structured form of collaboration.

</p><p>After <a href="World_War_II" title="World War II">World War II</a> the <a href="UN" class="mw-redirect" title="UN">UN</a>, the <a href="Bretton_Woods_system" title="Bretton Woods system">Bretton Woods organization</a>, and the <a href="WTO" class="mw-redirect" title="WTO">WTO</a> were created. Collective problem solving on the international level crystallized around these three types of organization from the 1980s onward. As these global institutions remain state-like or state-centric it is unsurprising that they perpetuate state-like or state-centric approaches to collective problem solving rather than alternative ones.<sup id="cite_ref-90" class="reference"><a href="#cite_note-90"><span class="cite-bracket">[</span>90<span class="cite-bracket">]</span></a></sup>

</p><p><a href="Crowdsourcing" title="Crowdsourcing">Crowdsourcing</a> is a process of accumulating ideas, thoughts, or information from many independent participants, with aim of finding the best solution for a given challenge. Modern <a href="Information_technologies" class="mw-redirect" title="Information technologies">information technologies</a> allow for many people to be involved and facilitate managing their suggestions in ways that provide good results.<sup id="cite_ref-91" class="reference"><a href="#cite_note-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup> The <a href="Internet" title="Internet">Internet</a> allows for a new capacity of collective (including planetary-scale) problem solving.<sup id="cite_ref-92" class="reference"><a href="#cite_note-92"><span class="cite-bracket">[</span>92<span class="cite-bracket">]</span></a></sup>

</p>

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<div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Problem_solving" class="extiw external" title="q:Special:Search/Problem solving">Problem solving</a></b></i>.</div></div>

</div>

<ul><li><a href="Actuarial_science" title="Actuarial science">Actuarial science</a> – Statistics applied to risk in insurance and other financial products</li>

<li><a href="Analytical_skill" title="Analytical skill">Analytical skill</a> – Crucial skill in all different fields of work and life</li>

<li><a href="Creative_problem-solving" title="Creative problem-solving">Creative problem-solving</a> – Mental process of problem solving</li>

<li><a href="Collective_intelligence" title="Collective intelligence">Collective intelligence</a> – Group intelligence that emerges from collective efforts</li>

<li><a href="Community_of_practice" title="Community of practice">Community of practice</a></li>

<li><a href="Coworking" title="Coworking">Coworking</a> – Practice of independent contractors or scientists sharing office space without supervision</li>

<li><a href="Crowdsolving" class="mw-redirect" title="Crowdsolving">Crowdsolving</a> – Sourcing services or funds from a group<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li>

<li><a href="Divergent_thinking" title="Divergent thinking">Divergent thinking</a> – A process of generating creative ideas</li>

<li><a href="Grey_problem" title="Grey problem">Grey problem</a></li>

<li><a href="Innovation" title="Innovation">Innovation</a> – Practical implementation of improvements</li>

<li><a href="Instrumentalism" title="Instrumentalism">Instrumentalism</a> – Position in the philosophy of science</li>

<li><a href="Problem-posing_education" title="Problem-posing education">Problem-posing education</a> – Method of teaching coined by Paulo Freire</li>

<li><a href="Problem_statement" title="Problem statement">Problem statement</a> – Description of an issue</li>

<li><a href="Problem_structuring_methods" title="Problem structuring methods">Problem structuring methods</a></li>

<li><a href="Shared_intentionality" title="Shared intentionality">Shared intentionality</a> – Ability to engage with others' psychological states</li>

<li><a href="Structural_fix" title="Structural fix">Structural fix</a></li>

<li><a href="Subgoal_labeling" title="Subgoal labeling">Subgoal labeling</a> – Cognitive process</li>

<li><a href="Troubleshooting" title="Troubleshooting">Troubleshooting</a> – Form of problem solving, often applied to repair failed products or processes</li>

<li><a href="Wicked_problem" title="Wicked problem">Wicked problem</a> – Problem that is difficult or impossible to solve</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2></div>

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<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite id="CITEREFGranvold1997" class="citation book cs1">Granvold, Donald K. (1997). "Cognitive-Behavioral Therapy with Adults". In Brandell, Jerrold R. (ed.). <i>Theory and Practice in Clinical Social Work</i>. Simon and Schuster. pp. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=K9Hm0UuFGJ0C&pg=PA189">189</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-684-82765-0</bdi>.</cite></span>

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<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFRobertson2001" class="citation book cs1">Robertson, S. Ian (2001). "Introduction to the study of problem solving". <i>Problem Solving</i>. Psychology Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-415-20300-7</bdi>.</cite></span>

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<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite id="CITEREFRubinWattRamelli2012" class="citation journal cs1">Rubin, M.; Watt, S. E.; Ramelli, M. (2012). "Immigrants' social integration as a function of approach-avoidance orientation and problem-solving style". <i>International Journal of Intercultural Relations</i>. <b>36</b> (4): <span class="nowrap">498–</span>505. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.ijintrel.2011.12.009">10.1016/j.ijintrel.2011.12.009</a>. <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/1959.13%2F931119">1959.13/931119</a></span>.</cite></span>

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<li id="cite_note-G&L87-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-G&L87_8-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFGoldstein_F._C.Levin_H._S.1987" class="citation book cs1">Goldstein F. C.; Levin H. S. (1987). "Disorders of reasoning and problem-solving ability". In M. Meier; A. Benton; L. Diller (eds.). <i>Neuropsychological rehabilitation</i>. London: Taylor & Francis Group.</cite></span>

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<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><div class="plainlist" style="display:inline;"><ul style="display:inline;"><li style="margin-bottom:.5em; display:block;;display:inline; margin:0;"><cite id="CITEREFVallacherM._Wegner2012" class="citation book cs1">Vallacher, Robin; M. Wegner, Daniel (2012). "Action Identification Theory". <i>Handbook of Theories of Social Psychology</i>. pp. <span class="nowrap">327–</span>348. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4135%2F9781446249215.n17">10.4135/9781446249215.n17</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-85702-960-7</bdi>.</cite></li><li style="margin-bottom:.5em; display:block;;margin-top:.5em;"><cite id="CITEREFMargrettMarsiske2002" class="citation journal cs1">Margrett, J. A; Marsiske, M (2002). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2909137">"Gender differences in older adults' everyday cognitive collaboration"</a>. <i>International Journal of Behavioral Development</i>. <b>26</b> (1): <span class="nowrap">45–</span>59. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F01650250143000319">10.1080/01650250143000319</a>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2909137">2909137</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/20657668">20657668</a>.</cite></li><li style="margin-bottom:.5em; display:block;"><cite id="CITEREFAntonucciAjrouchBirditt2013" class="citation journal cs1">Antonucci, T. C; Ajrouch, K. J; Birditt, K. S (2013). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3894851">"The Convoy Model: Explaining Social Relations From a Multidisciplinary Perspective"</a>. <i>The Gerontologist</i>. <b>54</b> (1): <span class="nowrap">82–</span>92. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fgeront%2Fgnt118">10.1093/geront/gnt118</a>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3894851">3894851</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/24142914">24142914</a>.</cite></li></ul></div></span>

</li>

<li id="cite_note-Rath2003-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Rath2003_10-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFRathSimonLangenbahnSherr2003" class="citation journal cs1">Rath, Joseph F.; Simon, Dvorah; Langenbahn, Donna M.; Sherr, Rose Lynn; Diller, Leonard (2003). <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/247514323">"Group treatment of problem-solving deficits in outpatients with traumatic brain injury: A randomised outcome study"</a>. <i>Neuropsychological Rehabilitation</i>. <b>13</b> (4): <span class="nowrap">461–</span>488. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F09602010343000039">10.1080/09602010343000039</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:143165070">143165070</a>.</cite></span>

</li>

<li id="cite_note-DZurilla-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-DZurilla_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-DZurilla_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><div class="plainlist" style="display:inline;"><ul style="display:inline;"><li style="margin-bottom:.5em; display:block;;display:inline; margin:0;"><cite id="Reference-DZurilla1971" class="citation journal cs1">D'Zurilla, T. J.; Goldfried, M. R. (1971). "Problem solving and behavior modification". <i>Journal of Abnormal Psychology</i>. <b>78</b> (1): <span class="nowrap">107–</span>126. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1037%2Fh0031360">10.1037/h0031360</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/4938262">4938262</a>.</cite></li><li style="margin-bottom:.5em; display:block;;margin-top:.5em;"><cite id="CITEREFD'Zurilla,_T._J.Nezu,_A._M.1982" class="citation book cs1">D'Zurilla, T. J.; Nezu, A. M. (1982). "Social problem solving in adults". In P. C. Kendall (ed.). <i>Advances in cognitive-behavioral research and therapy</i>. Vol. 1. New York: Academic Press. pp. <span class="nowrap">201–</span>274.</cite></li></ul></div></span>

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<li id="cite_note-rath2004-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-rath2004_12-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFRathLangenbahnSimonSherr2004" class="citation journal cs1">Rath, J. F.; Langenbahn, D. M.; Simon, D; Sherr, R. L.; Fletcher, J.; Diller, L. (2004). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.acn.2003.08.006">"The construct of problem solving in higher level neuropsychological assessment and rehabilitation*1"</a>. <i>Archives of Clinical Neuropsychology</i>. <b>19</b> (5): <span class="nowrap">613–</span>635. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.acn.2003.08.006">10.1016/j.acn.2003.08.006</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15271407">15271407</a>.</cite></span>

</li>

<li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><cite id="CITEREFRathHradilLitkeDiller2011" class="citation journal cs1">Rath, Joseph F.; Hradil, Amy L.; Litke, David R.; Diller, Leonard (2011). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9728040">"Clinical applications of problem-solving research in neuropsychological rehabilitation: Addressing the subjective experience of cognitive deficits in outpatients with acquired brain injury"</a>. <i>Rehabilitation Psychology</i>. <b>56</b> (4): <span class="nowrap">320–</span>328. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1037%2Fa0025817">10.1037/a0025817</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1939-1544">1939-1544</a>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9728040">9728040</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/22121939">22121939</a>.</cite></span>

</li>

<li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><cite id="CITEREFHoppmannBlanchard-Fields2010" class="citation journal cs1">Hoppmann, Christiane A.; <a href="Fredda_Blanchard-Fields" title="Fredda Blanchard-Fields">Blanchard-Fields, Fredda</a> (2010). "Goals and everyday problem solving: Manipulating goal preferences in young and older adults". <i>Developmental Psychology</i>. <b>46</b> (6): <span class="nowrap">1433–</span>1443. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1037%2Fa0020676">10.1037/a0020676</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/20873926">20873926</a>.</cite></span>

</li>

<li id="cite_note-Duncker-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Duncker_15-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFDuncker1935" class="citation book cs1 cs1-prop-foreign-lang-source">Duncker, Karl (1935). <i>Zur Psychologie des produktiven Denkens</i> [<i>The psychology of productive thinking</i>] (in German). Berlin: Julius Springer.</cite></span>

</li>

<li id="cite_note-Newell-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-Newell_16-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFNewellSimon1972" class="citation book cs1">Newell, Allen; Simon, Herbert A. (1972). <i>Human problem solving</i>. Englewood Cliffs, N.J.: Prentice-Hall.</cite></span>

</li>

<li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">For example:

<ul><li>X-ray problem, by <cite id="CITEREFDuncker1935" class="citation book cs1 cs1-prop-foreign-lang-source">Duncker, Karl (1935). <i>Zur Psychologie des produktiven Denkens</i> [<i>The psychology of productive thinking</i>] (in German). Berlin: Julius Springer.</cite></li>

<li>Disk problem, later known as <a href="Tower_of_Hanoi" title="Tower of Hanoi">Tower of Hanoi</a>, by <cite id="CITEREFEwertLambert1932" class="citation journal cs1">Ewert, P. H.; Lambert, J. F. (1932). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.tandfonline.com/doi/abs/10.1080/00221309.1932.9711880">"Part II: The Effect of Verbal Instructions upon the Formation of a Concept"</a></span>. <i>The Journal of General Psychology</i>. <b>6</b> (2). Informa UK Limited: <span class="nowrap">400–</span>413. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F00221309.1932.9711880">10.1080/00221309.1932.9711880</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0022-1309">0022-1309</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200806135752/https://www.tandfonline.com/doi/abs/10.1080/00221309.1932.9711880">Archived</a> from the original on 2020-08-06<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-06-09</span></span>.</cite></li></ul>

</span></li>

<li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><cite id="CITEREFMayer1992" class="citation book cs1">Mayer, R. E. (1992). <i>Thinking, problem solving, cognition</i> (Second ed.). New York: W. H. Freeman and Company.</cite></span>

</li>

<li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><cite id="CITEREFArmstrongDennistonGordon1975" class="citation journal cs1">Armstrong, J. Scott; Denniston, William B. Jr.; Gordon, Matt M. (1975). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100620221713/http://marketing.wharton.upenn.edu/ideas/pdf/armstrong2/DecompositionPrinciple.pdf">"The Use of the Decomposition Principle in Making Judgments"</a> <span class="cs1-format">(PDF)</span>. <i>Organizational Behavior and Human Performance</i>. <b>14</b> (2): <span class="nowrap">257–</span>263. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0030-5073%2875%2990028-8">10.1016/0030-5073(75)90028-8</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:122659209">122659209</a>. Archived from <a rel="nofollow" class="external text" href="http://marketing.wharton.upenn.edu/ideas/pdf/armstrong2/DecompositionPrinciple.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2010-06-20.</cite></span>

</li>

<li id="cite_note-MalakootiMCDM-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-MalakootiMCDM_20-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFMalakooti2013" class="citation book cs1">Malakooti, Behnam (2013). <i>Operations and Production Systems with Multiple Objectives</i>. John Wiley & Sons. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-118-58537-5</bdi>.</cite></span>

</li>

<li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><cite id="CITEREFKowalski1974" class="citation journal cs1">Kowalski, Robert (1974). <a rel="nofollow" class="external text" href="https://www.doc.ic.ac.uk/~rak/papers/IFIP%2074.pdf">"Predicate Logic as a Programming Language"</a> <span class="cs1-format">(PDF)</span>. <i>Information Processing</i>. <b>74</b>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240119025430/https://www.doc.ic.ac.uk/~rak/papers/IFIP%2074.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2024-01-19<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-09-20</span></span>.</cite></span>

</li>

<li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><cite id="CITEREFKowalski1979" class="citation book cs1">Kowalski, Robert (1979). <a rel="nofollow" class="external text" href="https://www.doc.ic.ac.uk/~rak/papers/LogicForProblemSolving.pdf"><i>Logic for Problem Solving</i></a> <span class="cs1-format">(PDF)</span>. Artificial Intelligence Series. Vol. 7. Elsevier Science Publishing. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-444-00368-1</bdi>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20231102032823/https://www.doc.ic.ac.uk/~rak/papers/LogicForProblemSolving.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2023-11-02<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-09-20</span></span>.</cite></span>

</li>

<li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><cite id="CITEREFKowalski2011" class="citation book cs1">Kowalski, Robert (2011). <a rel="nofollow" class="external text" href="https://www.doc.ic.ac.uk/~rak/papers/newbook.pdf"><i>Computational Logic and Human Thinking: How to be Artificially Intelligent</i></a> <span class="cs1-format">(PDF)</span>. Cambridge University Press. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240601181910/https://www.doc.ic.ac.uk/~rak/papers/newbook.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2024-06-01<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-09-20</span></span>.</cite></span>

</li>

<li id="cite_note-Staat-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-Staat_24-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFStaat1993" class="citation journal cs1">Staat, Wim (1993). "On abduction, deduction, induction and the categories". <i>Transactions of the Charles S. Peirce Society</i>. <b>29</b> (2): <span class="nowrap">225–</span>237.</cite></span>

</li>

<li id="cite_note-Sullivan-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-Sullivan_25-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFSullivan1991" class="citation journal cs1">Sullivan, Patrick F. (1991). "On Falsificationist Interpretations of Peirce". <i>Transactions of the Charles S. Peirce Society</i>. <b>27</b> (2): <span class="nowrap">197–</span>219.</cite></span>

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<li id="cite_note-Yu-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-Yu_26-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFHo1994" class="citation conference cs1">Ho, Yu Chong (1994). <a rel="nofollow" class="external text" href="https://files.eric.ed.gov/fulltext/ED376173.pdf"><i>Abduction? Deduction? Induction? Is There a Logic of Exploratory Data Analysis?</i></a> <span class="cs1-format">(PDF)</span>. Annual Meeting of the American Educational Research Association. New Orleans, La. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20231102041717/https://files.eric.ed.gov/fulltext/ED376173.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2023-11-02<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-09-20</span></span>.</cite></span>

</li>

<li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><cite id="CITEREFPassuello2008" class="citation web cs1">Passuello, Luciano (2008-11-04). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170621145314/https://litemind.com/problem-definition/">"Einstein's Secret to Amazing Problem Solving (and 10 Specific Ways You Can Use It)"</a>. <i>Litemind</i>. Archived from <a rel="nofollow" class="external text" href="https://litemind.com/problem-definition/">the original</a> on 2017-06-21<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-06-11</span></span>.</cite></span>

</li>

<li id="cite_note-USJFCOM-28"><span class="mw-cite-backlink">^ <a href="#cite_ref-USJFCOM_28-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-USJFCOM_28-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-USJFCOM_28-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110429051434/http://www.au.af.mil/au/awc/awcgate/jfcom/cc_handbook_sc_27oct2009.pdf">"Commander's Handbook for Strategic Communication and Communication Strategy"</a> <span class="cs1-format">(PDF)</span>. <a href="United_States_Joint_Forces_Command" title="United States Joint Forces Command">United States Joint Forces Command</a>, Joint Warfighting Center, Suffolk, Va. 27 October 2009. Archived from <a rel="nofollow" class="external text" href="http://www.au.af.mil/au/awc/awcgate/jfcom/cc_handbook_sc_27oct2009.pdf">the original</a> <span class="cs1-format">(PDF)</span> on April 29, 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">10 October</span> 2016</span>.</cite></span>

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<li id="cite_note-:1-29"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_29-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_29-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFRobertson2017" class="citation book cs1">Robertson, S. Ian (2017). <i>Problem solving: perspectives from cognition and neuroscience</i> (2nd ed.). London: Taylor & Francis. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-317-49601-4</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/962750529">962750529</a>.</cite></span>

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<li id="cite_note-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-65">^</a></b></span> <span class="reference-text">e.g., <cite id="CITEREFSternbergFrensch1991" class="citation book cs1">Sternberg, R. J.; Frensch, P. A., eds. (1991). <i>Complex problem solving: Principles and mechanisms</i>. Hillsdale, N.J.: Lawrence Erlbaum Associates. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-8058-0650-4</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/23254443">23254443</a>.</cite></span>

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<li id="cite_note-72"><span class="mw-cite-backlink"><b><a href="#cite_ref-72">^</a></b></span> <span class="reference-text"><div class="plainlist" style="display:inline;"><ul style="display:inline;"><li style="margin-bottom:.5em; display:block;;display:inline; margin:0;"><cite id="CITEREFPólya1945" class="citation book cs1"><a href="George_P%C3%B3lya" title="George Pólya">Pólya, George</a> (1945). <i>How to Solve It</i>. Princeton University Press.</cite></li><li style="margin-bottom:.5em; display:block;;margin-top:.5em;"><cite id="CITEREFSchoenfeld1985" class="citation book cs1">Schoenfeld, A. H. (1985). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=0cbSBQAAQBAJ"><i>Mathematical Problem Solving</i></a></span>. Orlando, Fla.: Academic Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-4832-9548-0</bdi>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20231023053840/https://books.google.com/books?id=0cbSBQAAQBAJ">Archived</a> from the original on 2023-10-23<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-06-09</span></span>.</cite></li></ul></div></span>

</li>

<li id="cite_note-73"><span class="mw-cite-backlink"><b><a href="#cite_ref-73">^</a></b></span> <span class="reference-text"><cite id="CITEREFHegarty1991" class="citation book cs1">Hegarty, M. (1991). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA253">"Knowledge and processes in mechanical problem solving"</a></span>. In Sternberg, R. J.; Frensch, P. A. (eds.). <i>Complex problem solving: Principles and mechanisms</i>. Hillsdale, N.J.: Lawrence Erlbaum Associates. pp. <span class="nowrap">253–</span>285. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-8058-0650-4</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/23254443">23254443</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20221204055603/https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA253">Archived</a> from the original on 2022-12-04<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-12-04</span></span>.</cite></span>

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<li id="cite_note-74"><span class="mw-cite-backlink"><b><a href="#cite_ref-74">^</a></b></span> <span class="reference-text"><cite id="CITEREFHeppnerKrauskopf1987" class="citation journal cs1">Heppner, P. P.; Krauskopf, C. J. (1987). "An information-processing approach to personal problem solving". <i>The Counseling Psychologist</i>. <b>15</b> (3): <span class="nowrap">371–</span>447. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F0011000087153001">10.1177/0011000087153001</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:146180007">146180007</a>.</cite></span>

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<li id="cite_note-90"><span class="mw-cite-backlink"><b><a href="#cite_ref-90">^</a></b></span> <span class="reference-text"><cite id="CITEREFFinger2008" class="citation book cs1">Finger, Matthias (2008-03-27). "Which governance for sustainable development? An organizational and institutional perspective". In Park, Jacob; Conca, Ken; Finger, Matthias (eds.). <i>The Crisis of Global Environmental Governance: Towards a New Political Economy of Sustainability</i>. Routledge. p. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=lrr3K50r144C&pg=PA48">48</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-134-05982-9</bdi>.</cite></span>

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<li id="cite_note-91"><span class="mw-cite-backlink"><b><a href="#cite_ref-91">^</a></b></span> <span class="reference-text"><div class="plainlist" style="display:inline;"><ul style="display:inline;"><li style="margin-bottom:.5em; display:block;;display:inline; margin:0;"><cite id="CITEREFGuazziniViloneDonatiNardi2015" class="citation journal cs1">Guazzini, Andrea; Vilone, Daniele; Donati, Camillo; Nardi, Annalisa; Levnajić, Zoran (10 November 2015). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4639727">"Modeling crowdsourcing as collective problem solving"</a>. <i>Scientific Reports</i>. <b>5</b> 16557. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1506.09155">1506.09155</a></span>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2015NatSR...516557G">2015NatSR...516557G</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fsrep16557">10.1038/srep16557</a>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4639727">4639727</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26552943">26552943</a>.</cite></li><li style="margin-bottom:.5em; display:block;;margin-top:.5em;"><cite id="CITEREFBoroomandSmaldino2021" class="citation journal cs1">Boroomand, A.; Smaldino, P.E. (2021). <a rel="nofollow" class="external text" href="https://doi.org/10.18564%2Fjasss.4704">"Hard Work, Risk-Taking, and Diversity in a Model of Collective Problem Solving"</a>. <i>Journal of Artificial Societies and Social Simulation</i>. <b>24</b> (4) 10. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.18564%2Fjasss.4704">10.18564/jasss.4704</a></span>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:240483312">240483312</a>.</cite></li></ul></div></span>

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<li id="cite_note-92"><span class="mw-cite-backlink"><b><a href="#cite_ref-92">^</a></b></span> <span class="reference-text"><cite id="CITEREFStefanovitchAlshamsiCebrianRahwan2014" class="citation journal cs1">Stefanovitch, Nicolas; Alshamsi, Aamena; Cebrian, Manuel; Rahwan, Iyad (30 September 2014). <a rel="nofollow" class="external text" href="https://doi.org/10.1140%2Fepjds%2Fs13688-014-0013-1">"Error and attack tolerance of collective problem solving: The DARPA Shredder Challenge"</a>. <i>EPJ Data Science</i>. <b>3</b> (1) 13. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1140%2Fepjds%2Fs13688-014-0013-1">10.1140/epjds/s13688-014-0013-1</a></span>. <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/21.11116%2F0000-0002-D39F-D">21.11116/0000-0002-D39F-D</a></span>.</cite></span>

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</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><cite id="CITEREFBeckmannGuthke1995" class="citation book cs1">Beckmann, Jens F.; Guthke, Jürgen (1995). <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/200134353">"Complex problem solving, intelligence, and learning ability"</a>. In Frensch, P. A.; Funke, J. (eds.). <i>Complex problem solving: The European Perspective</i>. Hillsdale, N.J.: Lawrence Erlbaum Associates. pp. <span class="nowrap">177–</span>200.</cite></li>

<li><cite id="CITEREFBrehmer1995" class="citation book cs1">Brehmer, Berndt (1995). "Feedback delays in dynamic decision making". In Frensch, P. A.; Funke, J. (eds.). <i>Complex problem solving: The European Perspective</i>. Hillsdale, N.J.: Lawrence Erlbaum Associates. pp. <span class="nowrap">103–</span>130.</cite></li>

<li><cite id="CITEREFBrehmerDörner1993" class="citation journal cs1">Brehmer, Berndt; Dörner, D. (1993). "Experiments with computer-simulated microworlds: Escaping both the narrow straits of the laboratory and the deep blue sea of the field study". <i>Computers in Human Behavior</i>. <b>9</b> (<span class="nowrap">2–</span>3): <span class="nowrap">171–</span>184. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0747-5632%2893%2990005-D">10.1016/0747-5632(93)90005-D</a>.</cite></li>

<li><cite id="CITEREFDörner1992" class="citation book cs1 cs1-prop-foreign-lang-source">Dörner, D. (1992). "Über die Philosophie der Verwendung von Mikrowelten oder 'Computerszenarios' in der psychologischen Forschung" [On the proper use of microworlds or "computer scenarios" in psychological research]. In Gundlach, H. (ed.). <i>Psychologische Forschung und Methode: Das Versprechen des Experiments. Festschrift für Werner Traxel</i> (in German). Passau, Germany: Passavia-Universitäts-Verlag. pp. <span class="nowrap">53–</span>87.</cite></li>

<li><cite id="CITEREFEyferthSchömannWidowski1986" class="citation journal cs1 cs1-prop-foreign-lang-source">Eyferth, K.; Schömann, M.; Widowski, D. (1986). "Der Umgang von Psychologen mit Komplexität" [On how psychologists deal with complexity]. <i>Sprache & Kognition</i> (in German). <b>5</b>: <span class="nowrap">11–</span>26.</cite></li>

<li><cite id="CITEREFFunke1993" class="citation book cs1">Funke, Joachim (1993). <a rel="nofollow" class="external text" href="https://web-archive.southampton.ac.uk/cogprints.org/1679/2/Funke_1993_micro.pdf">"Microworlds based on linear equation systems: A new approach to complex problem solving and experimental results"</a> <span class="cs1-format">(PDF)</span>. In Strube, G.; Wender, K.-F. (eds.). <i>The cognitive psychology of knowledge</i>. Amsterdam: Elsevier Science Publishers. pp. <span class="nowrap">313–</span>330.</cite></li>

<li><cite id="CITEREFFunke1995" class="citation book cs1">Funke, Joachim (1995). <a rel="nofollow" class="external text" href="https://web-archive.southampton.ac.uk/cogprints.org/3003/1/Funke_1995_CPS.pdf">"Experimental research on complex problem solving"</a> <span class="cs1-format">(PDF)</span>. In Frensch, P. A.; Funke, J. (eds.). <i>Complex problem solving: The European Perspective</i>. Hillsdale, N.J.: Lawrence Erlbaum Associates. pp. <span class="nowrap">243–</span>268.</cite></li>

<li><cite id="CITEREFFunke1995" class="citation book cs1">Funke, U. (1995). "Complex problem solving in personnel selection and training". In Frensch, P. A.; Funke, J. (eds.). <i>Complex problem solving: The European Perspective</i>. Hillsdale, N.J.: Lawrence Erlbaum Associates. pp. <span class="nowrap">219–</span>240.</cite></li>

<li><cite id="CITEREFGronerGronerBischof1983" class="citation book cs1">Groner, M.; Groner, R.; Bischof, W. F. (1983). "Approaches to heuristics: A historical review". In Groner, R.; Groner, M.; Bischof, W. F. (eds.). <i>Methods of heuristics</i>. Hillsdale, N.J.: Lawrence Erlbaum Associates. pp. <span class="nowrap">1–</span>18.</cite></li>

<li><cite id="CITEREFHayes1980" class="citation book cs1">Hayes, J. (1980). <i>The complete problem solver</i>. Philadelphia: The Franklin Institute Press.</cite></li>

<li><cite id="CITEREFHuber1995" class="citation book cs1">Huber, O. (1995). "Complex problem solving as multistage decision making". In Frensch, P. A.; Funke, J. (eds.). <i>Complex problem solving: The European Perspective</i>. Hillsdale, N.J.: Lawrence Erlbaum Associates. pp. <span class="nowrap">151–</span>173.</cite></li>

<li><cite id="CITEREFHübner1989" class="citation journal cs1 cs1-prop-foreign-lang-source">Hübner, Ronald (1989). <a rel="nofollow" class="external text" href="https://www.cogpsych.uni-konstanz.de/pdf/Hubner_1989_Methoden.pdf">"Methoden zur Analyse und Konstruktion von Aufgaben zur kognitiven Steuerung dynamischer Systeme"</a> [Methods for the analysis and construction of dynamic system control tasks] <span class="cs1-format">(PDF)</span>. <i>Zeitschrift für Experimentelle und Angewandte Psychologie</i> (in German). <b>36</b>: <span class="nowrap">221–</span>238.</cite></li>

<li><cite id="CITEREFHunt1991" class="citation book cs1">Hunt, Earl (1991). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA383">"Some comments on the study of complexity"</a></span>. In Sternberg, R. J.; Frensch, P. A. (eds.). <i>Complex problem solving: Principles and mechanisms</i>. Hillsdale, N.J.: Lawrence Erlbaum Associates. pp. <span class="nowrap">383–</span>395. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-317-78386-2</bdi>.</cite></li>

<li><cite id="CITEREFHussy1985" class="citation journal cs1 cs1-prop-foreign-lang-source">Hussy, W. (1985). "Komplexes Problemlösen—Eine Sackgasse?" [Complex problem solving—a dead end?]. <i>Zeitschrift für Experimentelle und Angewandte Psychologie</i> (in German). <b>32</b>: <span class="nowrap">55–</span>77.</cite></li>

<li><cite id="CITEREFKluwe1993" class="citation book cs1">Kluwe, R. H. (1993). "Chapter 19 Knowledge and Performance in Complex Problem Solving". <i>The Cognitive Psychology of Knowledge</i>. Advances in Psychology. Vol. 101. pp. <span class="nowrap">401–</span>423. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0166-4115%2808%2962668-0">10.1016/S0166-4115(08)62668-0</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-444-89942-2</bdi>.</cite></li>

<li><cite id="CITEREFKluwe1995" class="citation book cs1">Kluwe, R. H. (1995). "Single case studies and models of complex problem solving". In Frensch, P. A.; Funke, J. (eds.). <i>Complex problem solving: The European Perspective</i>. Hillsdale, N.J.: Lawrence Erlbaum Associates. pp. <span class="nowrap">269–</span>291.</cite></li>

<li><cite id="CITEREFKolbPetzingStumpf1992" class="citation journal cs1 cs1-prop-foreign-lang-source">Kolb, S.; Petzing, F.; Stumpf, S. (1992). "Komplexes Problemlösen: Bestimmung der Problemlösegüte von Probanden mittels Verfahren des Operations Research—ein interdisziplinärer Ansatz" [Complex problem solving: determining the quality of human problem solving by operations research tools—an interdisciplinary approach]. <i>Sprache & Kognition</i> (in German). <b>11</b>: <span class="nowrap">115–</span>128.</cite></li>

<li><cite id="CITEREFKrems1995" class="citation book cs1">Krems, Josef F. (1995). <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/200134353">"Cognitive flexibility and complex problem solving"</a>. In Frensch, P. A.; Funke, J. (eds.). <i>Complex problem solving: The European Perspective</i>. Hillsdale, N.J.: Lawrence Erlbaum Associates. pp. <span class="nowrap">201–</span>218.</cite></li>

<li><cite id="CITEREFMelzak1983" class="citation book cs1">Melzak, Z. (1983). <i>Bypasses: A Simple Approach to Complexity</i>. London, UK: Wiley.</cite></li>

<li><cite id="CITEREFMüller1993" class="citation book cs1 cs1-prop-foreign-lang-source">Müller, H. (1993). <i>Komplexes Problemlösen: Reliabilität und Wissen</i> [<i>Complex problem solving: Reliability and knowledge</i>] (in German). Bonn, Germany: Holos.</cite></li>

<li><cite id="CITEREFParadiesUnger2000" class="citation book cs1">Paradies, M.W.; Unger, L. W. (2000). <i>TapRooT—The System for Root Cause Analysis, Problem Investigation, and Proactive Improvement</i>. Knoxville, Tenn.: System Improvements.</cite></li>

<li><cite id="CITEREFPutz-Osterloh1993" class="citation book cs1">Putz-Osterloh, Wiebke (1993). "Chapter 15 Strategies for Knowledge Acquisition and Transfer of Knowledge in Dynamic Tasks". <i>The Cognitive Psychology of Knowledge</i>. Advances in Psychology. Vol. 101. pp. <span class="nowrap">331–</span>350. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0166-4115%2808%2962664-3">10.1016/S0166-4115(08)62664-3</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-444-89942-2</bdi>.</cite></li>

<li><cite id="CITEREFRieferBatchelder1988" class="citation journal cs1">Riefer, David M.; Batchelder, William H. (1988). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20181125115507/https://pdfs.semanticscholar.org/9bf7/c2bb2a621983c0e590ea1f019bd1eb8029d4.pdf">"Multinomial modeling and the measurement of cognitive processes"</a> <span class="cs1-format">(PDF)</span>. <i>Psychological Review</i>. <b>95</b> (3): <span class="nowrap">318–</span>339. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1037%2F0033-295x.95.3.318">10.1037/0033-295x.95.3.318</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:14994393">14994393</a>. Archived from <a rel="nofollow" class="external text" href="https://pdfs.semanticscholar.org/9bf7/c2bb2a621983c0e590ea1f019bd1eb8029d4.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2018-11-25.</cite></li>

<li><cite id="CITEREFSchaub1993" class="citation book cs1 cs1-prop-foreign-lang-source">Schaub, H. (1993). <i>Modellierung der Handlungsorganisation</i> (in German). Bern, Switzerland: Hans Huber.</cite></li>

<li><cite id="CITEREFStrauß1993" class="citation book cs1 cs1-prop-foreign-lang-source">Strauß, B. (1993). <i>Konfundierungen beim Komplexen Problemlösen. Zum Einfluß des Anteils der richtigen Lösungen (ArL) auf das Problemlöseverhalten in komplexen Situationen</i> [<i>Confoundations in complex problem solving. On the influence of the degree of correct solutions on problem solving in complex situations</i>] (in German). Bonn, Germany: Holos.</cite></li>

<li><cite id="CITEREFStrohschneider1991" class="citation journal cs1 cs1-prop-foreign-lang-source">Strohschneider, S. (1991). "Kein System von Systemen! Kommentar zu dem Aufsatz 'Systemmerkmale als Determinanten des Umgangs mit dynamischen Systemen' von Joachim Funke" [No system of systems! Reply to the paper 'System features as determinants of behavior in dynamic task environments' by Joachim Funke]. <i>Sprache & Kognition</i> (in German). <b>10</b>: <span class="nowrap">109–</span>113.</cite></li>

<li><cite id="CITEREFTonelli2011" class="citation book cs1">Tonelli, Marcello (2011). <i>Unstructured Processes of Strategic Decision-Making</i>. Saarbrücken, Germany: Lambert Academic Publishing. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-8465-5598-9</bdi>.</cite></li>

<li><cite id="CITEREFVan_Lehn1989" class="citation book cs1">Van Lehn, Kurt (1989). "Problem solving and cognitive skill acquisition". In Posner, M. I. (ed.). <a rel="nofollow" class="external text" href="https://apps.dtic.mil/dtic/tr/fulltext/u2/a218905.pdf"><i>Foundations of cognitive science</i></a> <span class="cs1-format">(PDF)</span>. Cambridge, Mass.: MIT Press. pp. <span class="nowrap">527–</span>579.</cite></li>

<li><cite id="CITEREFWisconsin_Educational_Media_Association1993" class="citation cs2 cs1-prop-long-vol">Wisconsin Educational Media Association (1993), <a rel="nofollow" class="external text" href="https://eric.ed.gov/?id=ED376817"><i>Information literacy: A position paper on information problem-solving</i></a>, WEMA Publications, vol. ED 376 817, Madison, Wis.</cite><span class="cs1-maint citation-comment"><code class="cs1-code">{{citation}}</code>: CS1 maint: location missing publisher (link)</span> (Portions adapted from <a href="Michigan_State_Board_of_Education" class="mw-redirect" title="Michigan State Board of Education">Michigan State Board of Education</a>'s Position Paper on Information Processing Skills, 1992.)</li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><span class="noviewer" typeof="mw:File"></span> Learning materials related to <a href="https://en.wikiversity.org/wiki/Solving_Problems" class="extiw external" title="v:Solving Problems">Solving Problems</a> at Wikiversity</li></ul>

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</style></div><div role="navigation" class="navbox" aria-labelledby="Human_intelligence_topics324" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Human_intelligence_topics324" style="font-size:114%;margin:0 4em"><a href="Human_intelligence" title="Human intelligence">Human</a> <a href="Intelligence" title="Intelligence">intelligence</a> <a href="Outline_of_human_intelligence" title="Outline of human intelligence">topics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Collective_intelligence" title="Collective intelligence">Collective</a></li>

<li><a href="Emotional_intelligence" title="Emotional intelligence">Emotional</a></li>

<li><a href="Intellectual_giftedness" title="Intellectual giftedness">Intellectual</a></li>

<li><a href="Linguistic_intelligence" class="mw-redirect" title="Linguistic intelligence">Linguistic</a></li>

<li><a href="Theory_of_multiple_intelligences" title="Theory of multiple intelligences">Multiple</a></li>

<li><a href="Social_intelligence" title="Social intelligence">Social</a></li>

<li><a href="Spatial_intelligence_(psychology)" title="Spatial intelligence (psychology)">Spatial</a> (<a href="Spatial_visualization_ability" title="Spatial visualization ability">visuospatial</a>)</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Ability" title="Ability">Abilities</a>, traits,<br>and constructs</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cognition" title="Cognition">Cognition</a></li>

<li><a href="Cognitive_liberty" title="Cognitive liberty">Cognitive liberty</a></li>

<li><a href="Communication" title="Communication">Communication</a></li>

<li><a href="Creativity" title="Creativity">Creativity</a></li>

<li><a href="Fluid_and_crystallized_intelligence" title="Fluid and crystallized intelligence">Fluid and crystallized intelligence</a></li>

<li><a href="G_factor_(psychometrics)" title="G factor (psychometrics)"><i>g</i> factor</a></li>

<li><a href="Intellect" title="Intellect">Intellect</a></li>

<li><a href="Intelligence_quotient" title="Intelligence quotient">Intelligence quotient</a></li>

<li><a href="Knowledge" title="Knowledge">Knowledge</a></li>

<li><a href="Learning" title="Learning">Learning</a></li>

<li><a href="Memory" title="Memory">Memory</a></li>

<li><a href="Reason" title="Reason">Reasoning</a></li>

<li><a href="Skill" title="Skill">Skill</a></li>

<li><a href="Thought" title="Thought">Thought</a> (<a href="Abstraction" title="Abstraction">abstraction</a>)</li>

<li><a href="Understanding" title="Understanding">Understanding</a></li>

<li><a href="Visual_system" title="Visual system">Visual processing</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Models and theories</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cattell%E2%80%93Horn%E2%80%93Carroll_theory" title="Cattell–Horn–Carroll theory">Cattell–Horn–Carroll theory</a></li>

<li><a href="Fluid_and_crystallized_intelligence" title="Fluid and crystallized intelligence">Fluid and crystallized intelligence</a></li>

<li><a href="Theory_of_multiple_intelligences" title="Theory of multiple intelligences">Multiple-intelligences theory</a></li>

<li><a href="PASS_theory_of_intelligence" title="PASS theory of intelligence">PASS theory</a></li>

<li><a href="Three-stratum_theory" title="Three-stratum theory">Three-stratum theory</a></li>

<li><a href="Triarchic_theory_of_intelligence" title="Triarchic theory of intelligence">Triarchic theory</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Areas of research</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Evolution_of_human_intelligence" title="Evolution of human intelligence">Evolution of human intelligence</a></li>

<li><a href="Heritability_of_IQ" title="Heritability of IQ">Heritability of IQ</a></li>

<li><a href="Psychometrics" title="Psychometrics">Psychometrics</a></li>

<li><a href="Environment_and_intelligence" title="Environment and intelligence">Intelligence and environment</a> / <a href="Fertility_and_intelligence" title="Fertility and intelligence">fertility</a> / <a href="Height_and_intelligence" title="Height and intelligence">height</a> / <a href="Impact_of_health_on_intelligence" class="mw-redirect" title="Impact of health on intelligence">health</a> / <a href="Cognitive_epidemiology" title="Cognitive epidemiology">longevity</a> / <a href="Neuroscience_and_intelligence" title="Neuroscience and intelligence">neuroscience</a> / <a href="Intelligence_and_personality" title="Intelligence and personality">personality</a> / <a href="Race_and_intelligence" title="Race and intelligence">race</a> / <a href="Sex_differences_in_intelligence" title="Sex differences in intelligence">sex</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow plainlist" colspan="2"><div>

<ul><li><span class="noviewer" typeof="mw:File"><span title="Outline"></span></span> <a href="Outline_of_human_intelligence" title="Outline of human intelligence">Outline of human intelligence</a> / <a href="Outline_of_thought" title="Outline of thought">thought</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Neuropsychology687" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Neuropsychology687" style="font-size:114%;margin:0 4em"><a href="Neuropsychology" title="Neuropsychology">Neuropsychology</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Topics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Brain%E2%80%93computer_interface" title="Brain–computer interface">Brain–computer interface</a></li>

<li><a href="List_of_regions_in_the_human_brain" title="List of regions in the human brain">Brain regions</a></li>

<li><a href="Clinical_neuropsychology" title="Clinical neuropsychology">Clinical neuropsychology</a></li>

<li><a href="Cognitive_neuroscience" title="Cognitive neuroscience">Cognitive neuroscience</a></li>

<li><a href="Human_brain" title="Human brain">Human brain</a></li>

<li><a href="List_of_misconceptions_about_the_brain" class="mw-redirect" title="List of misconceptions about the brain">Misconceptions</a></li>

<li><a href="Neuroanatomy" title="Neuroanatomy">Neuroanatomy</a></li>

<li><a href="Neurophysiology" title="Neurophysiology">Neurophysiology</a></li>

<li><a href="Phrenology" title="Phrenology">Phrenology</a></li>

<li><a href="Traumatic_brain_injury" title="Traumatic brain injury">Traumatic brain injury</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Brain_function" class="mw-redirect" title="Brain function">Brain functions</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Arousal" title="Arousal">Arousal</a></li>

<li><a href="Attention" title="Attention">Attention</a></li>

<li><a href="Consciousness" title="Consciousness">Consciousness</a></li>

<li><a href="Decision_making" class="mw-redirect" title="Decision making">Decision making</a></li>

<li><a href="Executive_functions" title="Executive functions">Executive functions</a></li>

<li><a href="Learning" title="Learning">Learning</a></li>

<li><a href="Memory" title="Memory">Memory</a></li>

<li><a href="Motor_coordination" title="Motor coordination">Motor coordination</a></li>

<li><a href="Natural_language" title="Natural language">Natural language</a></li>

<li><a href="Perception" title="Perception">Perception</a></li>

<li><a href="Planning" title="Planning">Planning</a></li>

<li><a href="Thought" title="Thought">Thought</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Arthur_Lester_Benton" title="Arthur Lester Benton">Arthur Lester Benton</a></li>

<li><a href="David_Bohm" title="David Bohm">David Bohm</a></li>

<li><a href="Ant%C3%B3nio_Dam%C3%A1sio" class="mw-redirect" title="António Damásio">António Damásio</a></li>

<li><a href="Phineas_Gage" title="Phineas Gage">Phineas Gage</a></li>

<li><a href="Norman_Geschwind" title="Norman Geschwind">Norman Geschwind</a></li>

<li><a href="Elkhonon_Goldberg" title="Elkhonon Goldberg">Elkhonon Goldberg</a></li>

<li><a href="Kurt_Goldstein" title="Kurt Goldstein">Kurt Goldstein</a></li>