View source for Problem solving

{{Short description|Approaches to problem solving}}
{{redirect|Problem|other uses|Problem (disambiguation)}}
{{more citations needed|date=September 2018}}
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'''Problem solving''' 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 simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles.<ref name="Complex Problem Solving">{{Cite book|date=2014-04-04|editor-last=Frensch|editor-first=Peter A.|editor2-last=Funke|editor2-first=Joachim|title=Complex Problem Solving|publisher=Psychology Press |doi=10.4324/9781315806723|isbn=978-1-315-80672-3}}</ref> 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.<ref name=":0" /> Similarly, one may distinguish formal or fact-based problems requiring [[G factor (psychometrics)|psychometric intelligence]], versus socio-emotional problems which depend on the changeable emotions of individuals or groups, such as [[Emotional intelligence|tactful]] behavior, fashion, or gift choices.<ref name="Blanchard-Fields">{{cite journal |author=[[Fredda Blanchard-Fields|Blanchard-Fields, F.]] |year=2007 |title=Everyday problem solving and emotion: An adult developmental perspective |journal=Current Directions in Psychological Science |volume=16 |issue=1 |pages=26–31 |doi=10.1111/j.1467-8721.2007.00469.x |ref=Reference-Blanchard |s2cid=145645352}}</ref>

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 [[Scalability|scalable]] solution.

There are many specialized problem-solving techniques and methods in fields such as [[science]], [[engineering]], [[business]], [[medicine]], [[mathematics]], [[computer science]], [[philosophy]], and [[societies|social organization]]. The mental techniques to identify, analyze, and solve problems are studied in [[psychology]] and [[cognitive science]]s. Also widely researched are the mental obstacles that prevent people from finding solutions; problem-solving impediments include [[confirmation bias]], [[mental set]], and [[functional fixedness]].

== Definition ==
The term ''problem solving'' has a slightly different meaning depending on the discipline. For instance, it is a mental process in [[psychology]] and a computerized process in [[computer science]]. 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.<ref name=":0">{{cite book|author-link1=Daniel Schacter|last1=Schacter|first1=D.L.|last2=Gilbert|first2= D.T.|last3=Wegner|first3=D.M.|title=Psychology|edition=2nd|location=New York|year=2011|publisher= Worth Publishers|page=376}}</ref> Solving problems sometimes involves dealing with [[pragmatics]] (the way that context contributes to meaning) and [[semantics]] (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 [[abstract thinking]] or coming up with a creative solution.

Problem solving has two major domains: [[Mathematical problem|mathematical problem solving]] and personal problem solving. Each concerns some difficulty or barrier that is encountered.<ref name="Zimmermann">{{cite conference |first=Bernd |last=Zimmermann |year=2004 |title=On mathematical problem-solving processes and history of mathematics |url=https://www.researchgate.net/publication/238733375 |conference=ICME 10|location=Copenhagen}}</ref>

=== Psychology ===
Problem solving in psychology refers to the process of finding solutions to problems encountered in life.<ref>{{cite book|first=Donald K.|last=Granvold|chapter=Cognitive-Behavioral Therapy with Adults|editor-first=Jerrold R.|editor-last=Brandell|title=Theory and Practice in Clinical Social Work|year=1997|publisher=Simon and Schuster|isbn=978-0-684-82765-0|pages=[https://books.google.com/books?id=K9Hm0UuFGJ0C&pg=PA189 189]}}</ref> Solutions to these problems are usually situation- or context-specific. The process starts with [[problem finding]] and [[problem shaping]], 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 ''end goal'' to be reached; how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis.<ref>{{cite book|chapter=Introduction to the study of problem solving|title=Problem Solving|first=S. Ian|last=Robertson|publisher=Psychology Press|year=2001|isbn=0-415-20300-7}}</ref>

Mental health professionals study the human problem-solving processes using methods such as [[introspection]], [[behaviorism]], [[simulation]], [[computer modeling]], and [[experiment]]. Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods.<ref>{{cite journal | last1 = Rubin | first1 = M. | last2 = Watt | first2 = S. E. | last3 = Ramelli | first3 = M. | year = 2012 | title = Immigrants' social integration as a function of approach-avoidance orientation and problem-solving style | journal = International Journal of Intercultural Relations | volume = 36 | issue = 4| pages = 498–505 | doi = 10.1016/j.ijintrel.2011.12.009 | hdl = 1959.13/931119 | hdl-access = free }}</ref> Problem solving has been defined as a higher-order [[cognitive]] process and [[intelligence|intellectual function]] that requires the modulation and control of more routine or fundamental skills.<ref name="G&L87">{{cite book | author1= Goldstein F. C. |author2=Levin H. S. |year=1987 |chapter=Disorders of reasoning and problem-solving ability |editor1=M. Meier |editor2=A. Benton |editor3=L. Diller |title=Neuropsychological rehabilitation |place=London |publisher=Taylor & Francis Group.}}</ref>

Empirical research shows many different strategies and factors influence everyday problem solving.<ref>{{multiref2
|1={{cite book |last1=Vallacher |first1=Robin |last2=M. Wegner |first2=Daniel |chapter=Action Identification Theory |title=Handbook of Theories of Social Psychology |pages=327–348 |doi=10.4135/9781446249215.n17|year=2012 |isbn=978-0-85702-960-7 }}
|2={{cite journal | doi = 10.1080/01650250143000319 | volume=26 | issue=1 | title=Gender differences in older adults' everyday cognitive collaboration | journal=International Journal of Behavioral Development | pages=45–59| pmc=2909137 |pmid=20657668| year=2002 | last1=Margrett | first1=J. A | last2=Marsiske | first2=M }}
|3={{cite journal | doi = 10.1093/geront/gnt118 | pmid=24142914 | volume=54 | issue=1 | title=The Convoy Model: Explaining Social Relations From a Multidisciplinary Perspective | journal=The Gerontologist | pages=82–92| pmc=3894851 | year=2013 | last1=Antonucci | first1=T. C | last2=Ajrouch | first2=K. J | last3=Birditt | first3=K. S }}
}}</ref> [[Rehabilitation psychology|Rehabilitation psychologists]] 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.<ref name="Rath2003">{{cite journal |last1=Rath |first1=Joseph F. |last2=Simon |first2=Dvorah |last3=Langenbahn |first3=Donna M. |last4=Sherr |first4=Rose Lynn |last5=Diller |first5=Leonard |title=Group treatment of problem-solving deficits in outpatients with traumatic brain injury: A randomised outcome study |journal=Neuropsychological Rehabilitation |year= 2003 |volume=13 |issue=4 |pages=461–488 |doi=10.1080/09602010343000039 |s2cid=143165070 |url=https://www.researchgate.net/publication/247514323}}</ref> Interpersonal everyday problem solving is dependent upon personal motivational and contextual components. One such component is the [[Valence (psychology)|emotional valence]] of "real-world" problems, which can either impede or aid problem-solving performance. Researchers have focused on the role of emotions in problem solving,<ref name=DZurilla>{{multiref2
|1={{cite journal | last1 = D'Zurilla | first1 = T. J. | last2 = Goldfried | first2 = M. R. | year=1971 | title = Problem solving and behavior modification | journal = Journal of Abnormal Psychology | volume = 78 | issue = 1| pages = 107–126 | doi=10.1037/h0031360 | pmid = 4938262 |ref=Reference-DZurilla1971}}
|2={{cite book |author1= D'Zurilla, T. J. |author2=Nezu, A. M. |year=1982 |chapter=Social problem solving in adults |editor=P. C. Kendall  |title=Advances in cognitive-behavioral research and therapy |volume=1 |pages=201–274 |place=New York |publisher=Academic Press}}
}}</ref> 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.<ref name="rath2004">{{cite journal |last1=Rath |first1=J. F. |last2=Langenbahn |first2=D. M. |last3=Simon |first3=D |last4=Sherr |first4=R. L. |last5=Fletcher |first5=J. |last6=Diller |first6=L. |year=2004 |title=The construct of problem solving in higher level neuropsychological assessment and rehabilitation*1 |journal=Archives of Clinical Neuropsychology |volume=19 |issue=5 |pages=613–635 |doi=10.1016/j.acn.2003.08.006 |pmid=15271407 |doi-access=free}}</ref> {{clarify|text=In conceptualization, |date=September 2023}}human problem solving consists of two related processes: problem orientation, and the motivational/attitudinal/affective approach to problematic situations and problem-solving skills.<ref>{{Cite journal|last1=Rath|first1=Joseph F.|last2=Hradil|first2=Amy L.|last3=Litke|first3=David R.|last4=Diller|first4=Leonard|date=2011|title=Clinical applications of problem-solving research in neuropsychological rehabilitation: Addressing the subjective experience of cognitive deficits in outpatients with acquired brain injury.|journal=Rehabilitation Psychology|language=en|volume=56|issue=4|pages=320–328|doi=10.1037/a0025817|pmid=22121939|pmc=9728040 |issn=1939-1544}}</ref> People's strategies cohere with their goals<ref>{{cite journal |last1=Hoppmann |first1=Christiane A. |last2=Blanchard-Fields |first2=Fredda |author-link2=Fredda Blanchard-Fields |title=Goals and everyday problem solving: Manipulating goal preferences in young and older adults |journal=Developmental Psychology |year= 2010 |volume=46 |issue=6 |pages=1433–1443 |doi=10.1037/a0020676|pmid=20873926 }}</ref> and stem from the process of comparing oneself with others.

=== Cognitive sciences ===
Among the first experimental psychologists to study problem solving were the [[Gestalt psychology|Gestaltists]] in [[Germany]], such as [[Karl Duncker]] in ''The Psychology of Productive Thinking'' (1935).<ref name=Duncker>{{cite book | last= Duncker|first=Karl |year=1935 |title=Zur Psychologie des produktiven Denkens |trans-title=The psychology of productive thinking |location=Berlin |publisher=Julius Springer |language=de}}</ref> Perhaps best known is the work of [[Allen Newell]] and [[Herbert A. Simon]].<ref name="Newell">{{cite book |last1=Newell|first1= Allen |last2=Simon|first2= Herbert A. |year=1972 |title=Human problem solving |location=Englewood Cliffs, N.J. |publisher=Prentice-Hall}}</ref>

Experiments in the 1960s and early 1970s asked participants to solve relatively simple, well-defined, but not previously seen laboratory tasks.<ref>For example:
* X-ray problem, by {{cite book | last= Duncker|first= Karl |year=1935 |title=Zur Psychologie des produktiven Denkens |trans-title=The psychology of productive thinking |place=Berlin |publisher=Julius Springer |language=de}}
* Disk problem, later known as [[Tower of Hanoi]], by {{cite journal | last1=Ewert | first1=P. H. | last2=Lambert | first2=J. F. | title=Part II: The Effect of Verbal Instructions upon the Formation of a Concept | journal=The Journal of General Psychology | publisher=Informa UK Limited | volume=6 | issue=2 | year=1932 | issn=0022-1309 | doi=10.1080/00221309.1932.9711880 | pages=400–413 | url=https://www.tandfonline.com/doi/abs/10.1080/00221309.1932.9711880 | url-access=subscription | access-date=2019-06-09 | archive-date=2020-08-06 | archive-url=https://web.archive.org/web/20200806135752/https://www.tandfonline.com/doi/abs/10.1080/00221309.1932.9711880 | url-status=live }}</ref><ref>{{cite book | last= Mayer|first= R. E. |year=1992 |title=Thinking, problem solving, cognition |edition=Second |location=New York |publisher=W. H. Freeman and Company}}</ref> These simple problems, such as the [[Tower of Hanoi]], admitted [[optimal solution]]s that could be found quickly, allowing researchers to observe the full problem-solving process. Researchers assumed that these model problems would elicit the characteristic [[cognitive process]]es by which more complex "real world" problems are solved.

An outstanding problem-solving technique found by this research is the principle of [[Decomposition (computer science)|decomposition]].<ref>{{cite journal |first1=J. Scott|last1=Armstrong|first2=William B. Jr.|last2=Denniston|first3=Matt M.|last3=Gordon |year=1975|title=The Use of the Decomposition Principle in Making Judgments |url=http://marketing.wharton.upenn.edu/ideas/pdf/armstrong2/DecompositionPrinciple.pdf  |journal=Organizational Behavior and Human Performance |volume=14 |issue=2 |pages=257–263 |doi=10.1016/0030-5073(75)90028-8 |archive-url=https://web.archive.org/web/20100620221713/http://marketing.wharton.upenn.edu/ideas/pdf/armstrong2/DecompositionPrinciple.pdf |archive-date=2010-06-20 |s2cid=122659209}}</ref>

=== Computer science ===

{{Expand section|date=September 2018}}

Much of computer science and [[artificial intelligence]] involves designing automated systems to solve a specified type of problem: to accept input data and calculate a correct or adequate response, reasonably quickly. [[Algorithm]]s are recipes or instructions that direct such systems, written into [[computer program]]s.

Steps for designing such systems include problem determination, [[heuristic]]s, [[root cause analysis]], [[Data deduplication|de-duplication]], analysis, diagnosis, and repair. Analytic techniques include linear and nonlinear programming, [[queuing systems]], and simulation.<ref name="MalakootiMCDM">{{cite book |last1=Malakooti |first1=Behnam |title=Operations and Production Systems with Multiple Objectives |year=2013 |publisher=John Wiley & Sons |isbn=978-1-118-58537-5}}</ref> A large, perennial obstacle is to find and fix errors in computer programs: [[debugging]].

=== Logic ===
Formal [[logic]] 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.

The use of computers to prove mathematical theorems using formal logic emerged as the field of [[automated theorem proving]] in the 1950s. It included the use of [[heuristic]] methods designed to simulate human problem solving, as in the [[Logic Theory Machine]], developed by Allen Newell, Herbert A. Simon and J. C. Shaw, as well as algorithmic methods such as the [[Resolution (logic)|resolution]] principle developed by [[John Alan Robinson]].

In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for [[program verification]] in computer science. In 1958, [[John McCarthy (computer scientist)|John McCarthy]] proposed the [[advice taker]], 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 [[Cordell Green]] in 1969, who used a resolution theorem prover for question-answering and for such other applications in artificial intelligence as robot planning.

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, [[Robert Kowalski]] developed [[logic programming]] and [[SLD resolution]],<ref>{{cite journal|last=Kowalski|first=Robert|url=https://www.doc.ic.ac.uk/~rak/papers/IFIP%2074.pdf|title=Predicate Logic as a Programming Language|journal=Information Processing|volume=74|year=1974|access-date=2023-09-20|archive-date=2024-01-19|archive-url=https://web.archive.org/web/20240119025430/https://www.doc.ic.ac.uk/~rak/papers/IFIP%2074.pdf|url-status=live}}</ref> which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving<ref>{{cite book|last=Kowalski|first=Robert|url=https://www.doc.ic.ac.uk/~rak/papers/LogicForProblemSolving.pdf|title=Logic for Problem Solving|series=Artificial Intelligence Series|volume=7|publisher=Elsevier Science Publishing|year=1979|isbn=0-444-00368-1|access-date=2023-09-20|archive-date=2023-11-02|archive-url=https://web.archive.org/web/20231102032823/https://www.doc.ic.ac.uk/~rak/papers/LogicForProblemSolving.pdf|url-status=live}}</ref> and computational logic to improve human thinking.<ref>{{cite book|last=Kowalski|first=Robert|url=https://www.doc.ic.ac.uk/~rak/papers/newbook.pdf|title=Computational Logic and Human Thinking: How to be Artificially Intelligent|publisher=Cambridge University Press|year=2011|access-date=2023-09-20|archive-date=2024-06-01|archive-url=https://web.archive.org/web/20240601181910/https://www.doc.ic.ac.uk/~rak/papers/newbook.pdf|url-status=live}}</ref>

=== Engineering ===
When products or processes fail, problem solving techniques can be used to develop corrective actions that can be taken to prevent further [[failure]]s. 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 [[failure mode and effects analysis]] can proactively reduce the likelihood of problems.

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, [[Abductive reasoning|abduction]] generates new ideas or hypotheses (asking "how?"); [[Deductive reasoning|deduction]] evaluates and refines hypotheses based on other plausible premises (asking "why?"); and [[Inductive reasoning|induction]] justifies a hypothesis with empirical data (asking "how much?").<ref name="Staat">{{cite journal|last=Staat|first=Wim|title=On abduction, deduction, induction and the categories|journal=Transactions of the Charles S. Peirce Society|volume=29|number=2|year=1993|pages=225–237}}</ref> The objective of abduction is to determine which hypothesis or proposition to test, not which one to adopt or assert.<ref name="Sullivan">{{cite journal|last=Sullivan|first=Patrick F.|title=On Falsificationist Interpretations of Peirce|journal=Transactions of the Charles S. Peirce Society|volume=27|number=2|year=1991|pages=197–219}}</ref> In the [[Charles S. Peirce|Peircean]] 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.<ref name="Yu">{{cite conference|last=Ho|first=Yu Chong|title=Abduction? Deduction? Induction? Is There a Logic of Exploratory Data Analysis?|year=1994|conference=Annual Meeting of the American Educational Research Association|location=New Orleans, La.|url=https://files.eric.ed.gov/fulltext/ED376173.pdf|access-date=2023-09-20|archive-date=2023-11-02|archive-url=https://web.archive.org/web/20231102041717/https://files.eric.ed.gov/fulltext/ED376173.pdf|url-status=live}}</ref>

[[Forensic engineering]] is an important technique of [[failure analysis]] that involves tracing product defects and flaws. Corrective action can then be taken to prevent further failures.

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.<ref>{{Cite web |url=https://litemind.com/problem-definition/|archive-url=https://web.archive.org/web/20170621145314/https://litemind.com/problem-definition/|archive-date=2017-06-21|title=Einstein's Secret to Amazing Problem Solving (and 10 Specific Ways You Can Use It)|website=Litemind|language=en-US|access-date=2017-06-11|date=2008-11-04 |last1=Passuello |first1=Luciano }}</ref>

=== Military science ===
In [[military Science|military science]], problem solving is linked to the concept of "end-states", the conditions or situations which are the aims of the strategy.<ref name="USJFCOM">{{cite web|date=27 October 2009|title=Commander's Handbook for Strategic Communication and Communication Strategy|url=http://www.au.af.mil/au/awc/awcgate/jfcom/cc_handbook_sc_27oct2009.pdf|archive-url=https://web.archive.org/web/20110429051434/http://www.au.af.mil/au/awc/awcgate/jfcom/cc_handbook_sc_27oct2009.pdf|archive-date=April 29, 2011|access-date=10 October 2016|publisher=[[United States Joint Forces Command]], Joint Warfighting Center, Suffolk, Va.}}</ref>{{rp|xiii, E-2}} Ability to solve problems is important at any [[military rank]], but is essential at the [[command and control]] level. It results from deep qualitative and quantitative understanding of possible scenarios. ''Effectiveness'' in this context is an evaluation of results: to what extent the end states were accomplished.<ref name="USJFCOM"/>{{rp|IV-24}} ''Planning'' is the process of determining how to effect those end states.<ref name="USJFCOM"/>{{rp|IV-1}}

== Processes ==
Some models of problem solving involve identifying a [[goal]] and then a sequence of subgoals towards achieving this goal. Andersson, who introduced the [[ACT-R]] model of cognition, modelled this collection of goals and subgoals as a [[Stack (abstract data type)|goal stack]] in which the mind contains a stack of goals and subgoals to be completed, and a single task being carried out at any time.<ref name=":1">{{Cite book |last=Robertson |first=S. Ian |title=Problem solving: perspectives from cognition and neuroscience |year=2017 |isbn=978-1-317-49601-4 |edition=2nd |location=London |publisher=Taylor & Francis |oclc=962750529}}</ref>{{rp|page=51}}

Knowledge of how to solve one problem can be applied to another problem, in a process known as [[Knowledge transfer|transfer]].{{r|:1|page=56}}

== Problem-solving strategies ==
{{See also|:Category:Problem solving skills}}
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".<ref name="Bransford1993">{{cite book | last1=Bransford|first1=J. D. |last2=Stein|first2=B. S | year = 1993 | title = The ideal problem solver: A guide for improving thinking, learning, and creativity |edition=2nd |location = New York | publisher = W.H. Freeman. |ref=Reference-Bransford}}</ref>

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.

Insight is the sudden [[Aha! moment|a''ha!'']] 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 ''move problem'', there is no consensus definition of an ''insight problem''.<ref>{{multiref2
|1={{Cite journal|last1=Ash|first1=Ivan K.|last2=Jee|first2=Benjamin D.|last3=Wiley|first3=Jennifer|year=2012|title=Investigating Insight as Sudden Learning|journal=The Journal of Problem Solving|volume=4|issue=2|doi=10.7771/1932-6246.1123|issn=1932-6246|doi-access=free}}
|2={{Cite journal|last1=Chronicle|first1=Edward P.|last2=MacGregor|first2=James N.|last3=Ormerod|first3=Thomas C.|year=2004|title=What Makes an Insight Problem? The Roles of Heuristics, Goal Conception, and Solution Recoding in Knowledge-Lean Problems.|journal=Journal of Experimental Psychology: Learning, Memory, and Cognition|volume=30|issue=1|pages=14–27|doi=10.1037/0278-7393.30.1.14|pmid=14736293|s2cid=15631498|issn=1939-1285|url=https://eprints.lancs.ac.uk/id/eprint/558/2/Chronicle_et_alJEP_LM%26C_03.pdf }}
|3={{Cite journal|last1=Chu|first1=Yun|last2=MacGregor|first2=James N.|year=2011|title=Human Performance on Insight Problem Solving: A Review|journal=The Journal of Problem Solving|volume=3|issue=2|doi=10.7771/1932-6246.1094|issn=1932-6246|doi-access=free}}
}}</ref>

Some problem-solving strategies include:<ref>{{cite journal | last1=Wang | first1=Y. | last2=Chiew | first2=V. | title=On the cognitive process of human problem solving | journal=Cognitive Systems Research | publisher=Elsevier BV | volume=11 | issue=1 | year=2010 | issn=1389-0417 | doi=10.1016/j.cogsys.2008.08.003 | pages=81–92 | s2cid=16238486 | url=https://www.researchgate.net/profile/Patricia_Ryser-Welch/post/Do_Machines_learn/attachment/59d6235b79197b8077981b28/AS:306908018216960@1450183981555/download/61-Elsevier-CogSys-ProblemSolving.pdf}}</ref>
; [[Abstraction]]: solving the problem in a tractable model system to gain insight into the real system
; [[Analogy]]: adapting the solution to a previous problem which has similar features or mechanisms
; [[Brainstorming]]: (especially among groups of people) suggesting a large number of solutions or ideas and combining and developing them until an optimum solution is found
; [[Wiktionary:bypass|Bypasses]]:  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.
; [[Critical thinking]]: analysis of available evidence and arguments to form a judgement via rational, skeptical, and unbiased evaluation
; [[Divide and conquer algorithm|Divide and conquer]]: breaking down a large, complex problem into smaller, solvable problems
; [[Help-seeking]]: obtaining external assistance to deal with obstacles
; [[Hypothesis testing]]: assuming a possible explanation to the problem and trying to prove (or, in some contexts, disprove) the assumption
; [[Lateral thinking]]: approaching solutions indirectly and creatively
; [[Means-ends analysis]]: choosing an action at each step to move closer to the goal
; [[Morphological analysis (problem-solving)|Morphological analysis]]: assessing the output and interactions of an entire system
; [[Observation]] / [[Question]]: in the [[natural sciences]] an observation is an act or instance of [[noticing]] or perceiving and the acquisition of [[information]] from a [[primary source]]. A question is an [[utterance]] which serves as a request for [[information]].{{citation needed|date=May 2024}}
; [[Proof (truth)|Proof of impossibility]]: try to prove that the problem cannot be solved. The point where the proof fails will be the starting point for solving it
; [[Reduction (complexity)|Reduction]]: transforming the problem into another problem for which solutions exist
; [[Research]]: employing existing ideas or adapting existing solutions to similar problems
; [[Root cause analysis]]: identifying the cause of a problem
; [[Trial-and-error]]: testing possible solutions until the right one is found

== Problem-solving methods ==
{{See also|:Category:Problem solving methods|:Category:Problem structuring methods}}
* {{annotated link|[[A3 problem solving]]}}
* {{annotated link|[[Design thinking]]}}
* {{annotated link|[[Eight Disciplines Problem Solving]]}}
* {{annotated link|[[GROW model]]}}
* {{annotated link|[[Help-seeking]]}}
* {{annotated link|[[How to Solve It]]}}
* {{annotated link|[[Lateral thinking]]}}
* {{annotated link|[[OODA loop]]}}
* {{annotated link|[[PDCA]]}}
* {{annotated link|[[Root cause analysis]]}}
* {{annotated link|[[RPR problem diagnosis]]}}
* {{annotated link|[[TRIZ]]}}
* [[Scientific method]] – is an [[Empirical evidence|empirical]] method for acquiring [[knowledge]] that has characterized the development of [[science]].
* {{annotated link|[[Swarm intelligence]]}}
* {{annotated link|[[System dynamics]]}}

==Common barriers{{anchor|Common_barriers_to_problem_solving}}==
Common barriers to problem solving include mental constructs that impede an efficient search for solutions. Five of the most common identified by researchers are: [[confirmation bias]], [[mental set]], [[functional fixedness]], unnecessary constraints, and irrelevant information.

===Confirmation bias===
{{Main|Confirmation bias}}
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.<ref name="Nickerson1998">{{cite journal |year=1998 |title=Confirmation bias: A ubiquitous phenomenon in many guises |journal=Review of General Psychology |volume=2 |issue=2 |page=176 |doi=10.1037/1089-2680.2.2.175 |last1=Nickerson |first1=Raymond S.|s2cid=8508954 }}</ref>

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.<ref>{{cite journal | last1=Hergovich | first1=Andreas | last2=Schott | first2=Reinhard | last3=Burger | first3=Christoph | title=Biased Evaluation of Abstracts Depending on Topic and Conclusion: Further Evidence of a Confirmation Bias Within Scientific Psychology | journal=Current Psychology | publisher=Springer Science and Business Media LLC | volume=29 | issue=3 | year= 2010 | issn=1046-1310 | doi=10.1007/s12144-010-9087-5 | pages=188–209| s2cid=145497196 }}</ref> 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 [[Witch-hunt|witchcraft]] demonstrated confirmation bias with motivation.{{cn|reason=|date=September 2023}} Researcher Michael Allen found evidence for confirmation bias with motivation in school children who worked to manipulate their science experiments to produce favorable results.<ref>{{cite journal | last=Allen | first=Michael | title=Theory-led confirmation bias and experimental persona | journal=Research in Science & Technological Education | publisher=Informa UK Limited | volume=29 | issue=1 | year=2011 | issn=0263-5143 | doi=10.1080/02635143.2010.539973|bibcode=2011RSTEd..29..107A | pages=107–127| s2cid=145706148 }}</ref>

However, confirmation bias does not necessarily require motivation. In 1960, [[Peter Cathcart Wason]] 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.<ref>{{cite journal|year=1960|title=On the failure to eliminate hypotheses in a conceptual task|journal=Quarterly Journal of Experimental Psychology|volume=12|issue=3|pages=129–140|doi=10.1080/17470216008416717|last1=Wason|first1=P. C.|s2cid=19237642}}
</ref>

===Mental set===
{{Main|Mental set}}
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.

It was first articulated by [[Abraham S. Luchins]] in the 1940s with his well-known water jug experiments.<ref>{{cite journal|last=Luchins|first=Abraham S.|year=1942|title=Mechanization in problem solving: The effect of Einstellung|journal=Psychological Monographs|volume=54|number=248|pages=i-95 |doi=10.1037/h0093502 }}</ref> 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.<ref>{{cite journal | last1=Öllinger | first1=Michael | last2=Jones | first2=Gary | last3=Knoblich | first3=Günther | title=Investigating the Effect of Mental Set on Insight Problem Solving | journal=Experimental Psychology | publisher=Hogrefe Publishing Group | volume=55 | issue=4 | year=2008 | issn=1618-3169 | doi=10.1027/1618-3169.55.4.269 | pages=269–282 | pmid=18683624 | url=http://irep.ntu.ac.uk/id/eprint/23048/1/193183_1563%20Jones%20Postprint.pdf | access-date=2023-01-31 | archive-date=2023-03-16 | archive-url=https://web.archive.org/web/20230316064717/http://irep.ntu.ac.uk/id/eprint/23048/1/193183_1563%20Jones%20Postprint.pdf | url-status=live }}</ref> This was again demonstrated in [[Norman Maier]]'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).

Rigidly clinging to a mental set is called ''fixation'', which can deepen to an obsession or preoccupation with attempted strategies that are repeatedly unsuccessful.<ref name="Wiley1998">{{cite journal|year=1998|title=Expertise as mental set: The effects of domain knowledge in creative problem solving|journal=Memory & Cognition|volume=24|issue=4|pages=716–730|doi=10.3758/bf03211392|pmid=9701964|last1=Wiley|first1=Jennifer|doi-access=free}}</ref> In the late 1990s, researcher Jennifer Wiley found that professional expertise in a field can create a mental set, perhaps leading to fixation.<ref name="Wiley1998" />

[[Groupthink]], in which each individual takes on the mindset of the rest of the group, can produce and exacerbate mental set.<ref>{{cite book|last1=Cottam|first1=Martha L.|last2=Dietz-Uhler|first2=Beth|last3=Mastors|first3=Elena|last4=Preston|first4=Thomas|year=2010|title=Introduction to Political Psychology|edition=2nd|location=New York|publisher=Psychology Press}}</ref> Social pressure leads to everybody thinking the same thing and reaching the same conclusions.

===Functional fixedness===
{{Main|Functional fixedness}}

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.

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.

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."<ref>{{cite journal | last1=German | first1=Tim P. | last2=Barrett | first2=H. Clark | title=Functional Fixedness in a Technologically Sparse Culture | journal=Psychological Science | publisher=SAGE Publications | volume=16 | issue=1 | year=2005 | issn=0956-7976 | doi=10.1111/j.0956-7976.2005.00771.x | pages=1–5| pmid=15660843 | s2cid=1833823 }}</ref> Their research found that young children's limited knowledge of an object's intended function reduces this barrier<ref>{{cite journal | last1 = German | first1 = Tim P. | last2 = Defeyter | first2 = Margaret A. | year = 2000| title = Immunity to functional fixedness in young children | journal = Psychonomic Bulletin and Review | volume = 7 | issue = 4| pages = 707–712| doi = 10.3758/BF03213010 | pmid = 11206213 | doi-access = free }}</ref> 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."<ref>{{cite journal |last1=Furio |first1=C. |last2=Calatayud |first2=M. L. |last3=Baracenas |first3=S. |last4=Padilla |first4=O. |year=2000 |title=Functional fixedness and functional reduction as common sense reasonings in chemical equilibrium and in geometry and polarity of molecules|journal=Science Education |volume=84 |issue=5 |pages=545–565 |doi=10.1002/1098-237X(200009)84:5<545::AID-SCE1>3.0.CO;2-1|bibcode=2000SciEd..84..545F }}</ref>

There are several hypotheses in regards to how functional fixedness relates to problem solving.<ref>{{cite journal |last1=Adamson |first1=Robert E |year=1952 |title=Functional fixedness as related to problem solving: A repetition of three experiments |journal=Journal of Experimental Psychology |volume=44 |issue=4 |pages=288–291 |doi=10.1037/h0062487|pmid=13000071 }}</ref> It may waste time, delaying or entirely preventing the correct use of a tool.

===Unnecessary constraints===
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.<ref name="Kellogg, R. T. 2003">{{cite book|last=Kellogg|first=R. T.|year=2003|title=Cognitive psychology|edition=2nd|location=California|publisher=Sage Publications, Inc.}}</ref>{{page needed|date=September 2023}}

Visual problems can also produce mentally invented constraints.<ref>{{cite book|last=Meloy|first=J. R.|year=1998|title=The Psychology of Stalking, Clinical and Forensic Perspectives|edition=2nd|location=London, England|publisher=Academic Press}}</ref>{{page needed|date=September 2023}} 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.<ref>{{cite journal|last2=Ormerod|first2=T.C.|last3=Chronicle|first3=E.P.|year=2001|title=Information-processing and insight: A process model of performance on the nine-dot and related problems|journal=Journal of Experimental Psychology: Learning, Memory, and Cognition|volume=27|issue=1|pages=176–201|doi=10.1037/0278-7393.27.1.176|last1=MacGregor|first1=J.N.|pmid=11204097}}</ref>

This problem has produced the expression "[[think outside the box]]".<ref name="Weiten, Wayne 2011">{{cite book|last=Weiten|first=Wayne|year=2011|title=Psychology: themes and variations|edition=8th|location=California|publisher=Wadsworth}}</ref>{{page needed|date=September 2023}} Such problems are typically solved via a sudden insight which leaps over the mental barriers, often after long toil against them.<ref>{{cite book|last1=Novick|first1=L. R.|last2=Bassok|first2=M.|year=2005|chapter=Problem solving|editor-first1=K. J.|editor-last1=Holyoak|editor-first2=R. G.|editor-last2=Morrison|title=Cambridge handbook of thinking and reasoning|pages=321–349|location=New York, N.Y.|publisher=Cambridge University Press}}</ref> 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.<ref name="Weiten, Wayne 2011" />

===Irrelevant information===
{{See also|Information overload|Mass media}}
Irrelevant information is a specification or data presented in a problem that is unrelated to the solution.<ref name="Kellogg, R. T. 2003" /> 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.<ref>{{cite journal|year=2010|title=From walls to windows: Using barriers as pathways to insightful solutions|journal=The Journal of Creative Behavior|volume=44|issue=3|pages=143–167|doi=10.1002/j.2162-6057.2010.tb01331.x|last1=Walinga|first1=Jennifer}}</ref>

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?"{{r|Weiten, Wayne 2011}}{{page needed|date=September 2023}} The "obvious" answer is 15%, but in fact none of the unlisted people would be listed among the 200. This kind of "[[trick question]]" is often used in aptitude tests or cognitive evaluations.<ref name="Walinga, Jennifer 2011">{{cite journal|last1=Walinga|first1=Jennifer|last2=Cunningham|first2=J. Barton|last3=MacGregor|first3=James N.|year=2011|title=Training insight problem solving through focus on barriers and assumptions|journal=The Journal of Creative Behavior|volume=45 |pages=47–58 |doi=10.1002/j.2162-6057.2011.tb01084.x }}</ref> Though not inherently difficult, they require independent thinking that is not necessarily common. Mathematical [[Word problem (mathematics education)|word problem]]s often include irrelevant qualitative or numerical information as an extra challenge.

=== Avoiding barriers by changing problem representation ===
The disruption caused by the above cognitive biases can depend on how the information is represented:<ref name="Walinga, Jennifer 2011" /> visually, verbally, or mathematically. A classic example is the Buddhist monk problem:

{{quote|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.}}

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 [[Graph of a function|graph]] 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.

Similar strategies can often improve problem solving on tests.<ref name="Kellogg, R. T. 2003" /><ref>{{cite journal |last1=Vlamings |first1=Petra H. J. M. |last2=Hare |first2=Brian |last3=Call |first3=Joseph |year=2009 |title=Reaching around barriers: The performance of great apes and 3–5-year-old children |journal=Animal Cognition |volume=13 |issue=2 |pages=273–285 |doi=10.1007/s10071-009-0265-5 |pmc=2822225 |pmid=19653018}}</ref>

=== Other barriers for individuals ===
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 [[cognitive load]]s such as [[information overload]].<ref>{{multiref2
|1={{cite news |first=Sujata |last=Gupta |title=People add by default even when subtraction makes more sense |url=https://www.sciencenews.org/article/psychology-numbers-people-add-default-subtract-better |access-date=10 May 2021 |work=Science News |date=7 April 2021 |archive-date=21 May 2021 |archive-url=https://web.archive.org/web/20210521134851/https://www.sciencenews.org/article/psychology-numbers-people-add-default-subtract-better |url-status=live }}
|2={{cite journal |last1=Adams |first1=Gabrielle S. |last2=Converse |first2=Benjamin A. |last3=Hales |first3=Andrew H. |last4=Klotz |first4=Leidy E. |title=People systematically overlook subtractive changes |journal=Nature |date=April 2021 |volume=592 |issue=7853 |pages=258–261 |doi=10.1038/s41586-021-03380-y |pmid=33828317 |bibcode=2021Natur.592..258A |s2cid=233185662 |url=https://www.nature.com/articles/s41586-021-03380-y |url-access=subscription |access-date=10 May 2021 |language=en |issn=1476-4687 |archive-date=10 May 2021 |archive-url=https://web.archive.org/web/20210510130853/https://www.nature.com/articles/s41586-021-03380-y |url-status=live }}
}}</ref>

== Dreaming: problem solving without waking consciousness ==
People can also solve problems while they are asleep. There are many reports of scientists and engineers who solved problems in their [[dream]]s. For example, [[Elias Howe]], inventor of the sewing machine, figured out the structure of the bobbin from a dream.<ref>{{cite book|last=Kaempffert|first=Waldemar B.|year=1924|title=A Popular History of American Invention|volume=2|location=New York|publisher=Charles Scribner's Sons|page=[https://archive.org/details/popularhistoryof02kaem/page/385/mode/1up 385]}}</ref>

The chemist [[August Kekulé]] 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,

{{blockquote|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.<ref>{{multiref2|1={{cite journal | last1 = Kekulé | first1 = August | year = 1890 | title = Benzolfest-Rede. | journal=Berichte der Deutschen Chemischen Gesellschaft|volume=23|pages= 1302–1311 }} 
|2={{cite journal | last1 = Benfey | first1 =  O. | year = 1958 | title = Kekulé and the birth of the structural theory of organic chemistry in 1858 | doi = 10.1021/ed035p21 | journal = Journal of Chemical Education | volume = 35 | issue = 1 | pages = 21–23 | bibcode = 1958JChEd..35...21B}} }}</ref>}}

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 [[William C. Dement]] 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.<ref name="Dement 1972">{{cite book|last=Dement|first=W.C.|year=1972|title=Some Must Watch While Some Just Sleep|location=New York|publisher=Freeman}}</ref>{{page needed|date=September 2023}} 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.

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:<ref name="Dement 1972"/>{{page needed|date=September 2023}}

{{blockquote|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!}}

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.

[[Albert Einstein]] believed that much problem solving goes on unconsciously, and the person must then figure out and formulate consciously what the mindbrain{{jargon inline|date=September 2023}} has already solved. He believed this was his process in formulating the theory of relativity: "The creator of the problem possesses the solution."<ref>{{cite journal | last1 = Fromm | first1 = Erika O. | year = 1998 | title = Lost and found half a century later: Letters by Freud and Einstein | journal = American Psychologist | volume = 53 | issue = 11| pages = 1195–1198 | doi = 10.1037/0003-066x.53.11.1195 }}</ref> 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."<ref>{{cite book|last=Einstein|first=Albert|year=1954|chapter=A Mathematician's Mind|title=Ideas and Opinions|location=New York|publisher=Bonanza Books|page=25}}</ref>

== Cognitive sciences: two schools ==
{{anchor|acrossDomainsExpertise}}
Problem-solving processes differ across knowledge domains and across levels of expertise.<ref>{{cite book|last=Sternberg|first=R. J.|year=1995|chapter=Conceptions of expertise in complex problem solving: A comparison of alternative conceptions|editor-first1=P. A.|editor-last1=Frensch|editor-first2=J.|editor-last2=Funke|title=Complex problem solving: The European Perspective|pages=295–321|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates}}</ref> For this reason, [[cognitive sciences]] 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.<ref>{{cite book |last1=Funke |first1=J. |year=1991 |chapter=Solving complex problems: Human identification and control of complex systems |pages=185–222 |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, N.J. |publisher=Lawrence Erlbaum Associates |isbn=0-8058-0650-4 |oclc=23254443}}</ref>

=== Europe ===
In Europe, two main approaches have surfaced, one initiated by [[Donald Broadbent]]<ref>{{multiref2
|1={{cite journal|last=Broadbent|first=Donald E.|year=1977|url=https://journals.sagepub.com/doi/abs/10.1080/14640747708400596|url-access=subscription|title=Levels, hierarchies, and the locus of control|journal=Quarterly Journal of Experimental Psychology|volume=29|issue=2|pages=181–201|doi=10.1080/14640747708400596|s2cid=144328372|access-date=2019-06-09|archive-date=2020-08-06|archive-url=https://web.archive.org/web/20200806214714/https://journals.sagepub.com/doi/abs/10.1080/14640747708400596|url-status=live}}
|2={{cite book|last1=Berry|first1=Dianne C.|last2=Broadbent|first2=Donald E.|year=1995|chapter-url=https://www.researchgate.net/publication/200134353|chapter=Implicit learning in the control of complex systems: A reconsideration of some of the earlier claims|editor-first1=P.A.|editor-last1=Frensch|editor-first2=J.|editor-last2=Funke|title=Complex problem solving: The European Perspective|pages=131–150|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates}}
}}</ref> in the United Kingdom and the other one by [[Dietrich Dörner]]<ref>{{multiref2
|1={{cite journal | last= Dörner|first= Dietrich|year=1975|title=Wie Menschen eine Welt verbessern wollten|trans-title=How people wanted to improve the world|journal=Bild der Wissenschaft|volume=12|pages=48–53|lang=de}}
|2={{cite book | last= Dörner|first= Dietrich|year=1985|chapter= Verhalten, Denken und Emotionen|trans-chapter=Behavior, thinking, and emotions|editor-first1=L. H.|editor-last1= Eckensberger |editor-first2= E. D.|editor-last2= Lantermann |title=Emotion und Reflexivität|pages=157–181|location=München, Germany|publisher=Urban & Schwarzenberg|lang=de}}
|3={{cite book | last1= Dörner|first1= Dietrich|last2= Wearing|first2= Alex J. |year=1995|chapter-url=https://www.researchgate.net/publication/200134353 |chapter=Complex problem solving: Toward a (computer-simulated) theory|editor-first1=P.A.|editor-last1=Frensch|editor-first2=J.|editor-last2=Funke|title=Complex problem solving: The European Perspective|pages=65–99|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates}}
}}</ref> 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.<ref>{{multiref2
|1={{cite book | last= Buchner|first= A. |year=1995|chapter=Theories of complex problem solving|editor-first1=P.A.|editor-last1=Frensch|editor-first2=J.|editor-last2=Funke|title=Complex problem solving: The European Perspective|pages=27–63|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates}}
|2={{cite book | editor-last1= Dörner|editor-first1=D.|editor-last2= Kreuzig|editor-first2= H. W.|editor-last3= Reither|editor-first3= F.|editor-last4= Stäudel|editor-first4=T.|year=1983|title=Lohhausen. Vom Umgang mit Unbestimmtheit und Komplexität|trans-title=Lohhausen. On dealing with uncertainty and complexity|location=Bern, Switzerland|publisher=Hans Huber|lang=de}}
|3={{cite book | last1= Ringelband|first1= O. J.|last2= Misiak|first2= C.|last3= Kluwe|first3= R. H.|year=1990|chapter=Mental models and strategies in the control of a complex system|editor-first1=D.|editor-last1=Ackermann|editor-first2=M. J.|editor-last2=Tauber|title=Mental models and human-computer interaction|volume=1|pages=151–164|location=Amsterdam|publisher=Elsevier Science Publishers}}
}}</ref>

=== North America ===
In North America, initiated by the work of Herbert A. Simon on "learning by doing" in [[semantic]]ally rich domains,<ref>{{multiref2
|1={{cite journal |last1=Anzai|first1=K. |last2=Simon|first2= H. A. |title=The theory of learning by doing |journal=Psychological Review |volume=86 |pages=124–140 |doi=10.1037/0033-295X.86.2.124 |year=1979 |pmid=493441 |issue=2 |ref=Reference-Anzai}}
|2={{cite journal | last1=Bhaskar | first1=R. | last2=Simon | first2=Herbert A. | title=Problem Solving in Semantically Rich Domains: An Example from Engineering Thermodynamics | journal=Cognitive Science | publisher=Wiley | volume=1 | issue=2 | year=1977 | issn=0364-0213 | doi=10.1207/s15516709cog0102_3 |doi-access=free | pages=193–215}}
}}</ref> researchers began to investigate problem solving separately in different natural [[knowledge domain]]s—such as physics, writing, or [[chess]] playing—rather than attempt to extract a global theory of problem solving.<ref>e.g., {{cite book |year=1991 |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, N.J. |publisher=Lawrence Erlbaum Associates |isbn=0-8058-0650-4 |oclc=23254443}}</ref> These researchers have focused on the development of problem solving within certain domains, that is on the development of [[expertise]].<ref>{{multiref2
|1={{cite journal | last1= Chase|first1=W. G.|last2=Simon|first2=H. A.|year=1973|title=Perception in chess|journal=Cognitive Psychology|volume=4|pages=55–81|doi=10.1016/0010-0285(73)90004-2 }}
|2={{cite journal |last1=Chi|first1= M. T. H. |last2=Feltovich|first2= P. J. |last3=Glaser|first3= R. |year=1981 |title=Categorization and representation of physics problems by experts and novices |journal=Cognitive Science |volume=5 |issue=2 |pages=121–152 |ref=Reference-Chi |doi=10.1207/s15516709cog0502_2|doi-access=free }}
|3={{cite journal |last1=Anderson|first1=J. R. |last2=Boyle|first2= C. B. |last3=Reiser|first3= B. J. | title = Intelligent tutoring systems | journal = Science | year = 1985 | volume = 228 | pages = 456–462 | doi = 10.1126/science.228.4698.456 | pmid = 17746875 | issue = 4698 |ref=Reference-Anderson|bibcode=1985Sci...228..456A |s2cid=62403455}}
}}</ref>

Areas that have attracted rather intensive attention in North America include:
* calculation<ref>{{cite book |last1=Sokol |first1=S. M. |last2=McCloskey |first2=M. |year=1991 |chapter-url=https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA85 |chapter-url-access=limited|chapter=Cognitive mechanisms in calculation |pages=85–116 |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, N.J. |publisher=Lawrence Erlbaum Associates |isbn=0-8058-0650-4 |oclc=23254443}}</ref>
* computer skills<ref>{{cite book |last1=Kay |first1=D. S. |year=1991 |chapter-url=https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA317 |chapter-url-access=limited |chapter=Computer interaction: Debugging the problems |pages=317–340 |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, N.J. |publisher=Lawrence Erlbaum Associates |isbn=0-8058-0650-4 |oclc=23254443 |access-date=2022-12-04 |archive-date=2022-12-04 |archive-url=https://web.archive.org/web/20221204055601/https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA317 |url-status=live }}</ref>
* game playing<ref>{{cite book |last1=Frensch |first1=P. A. |last2=Sternberg |first2=R. J. |year=1991 |chapter-url=https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA343 |chapter-url-access=limited|chapter=Skill-related differences in game playing |pages=343–381 |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, N.J .|publisher=Lawrence Erlbaum Associates |isbn=0-8058-0650-4 |oclc=23254443}}</ref>
* lawyers' reasoning<ref name="Amsel1991">{{cite book |last1=Amsel |first1=E. |last2=Langer |first2=R. |last3=Loutzenhiser |first3=L. |year=1991 |chapter=Do lawyers reason differently from psychologists? A comparative design for studying expertise |pages=223–250 |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, N.J. |publisher=Lawrence Erlbaum Associates |isbn=0-8058-0650-4 |oclc=23254443}}</ref>
* managerial problem solving<ref name="Wagner">{{cite book |last1=Wagner |first1=R. K. |year=1991 |chapter=Managerial problem solving |pages=159–183 |id=[[PsycNET]]: [https://psycnet.apa.org/record/1991-98396-005 1991-98396-005] |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, N.J. |publisher=Lawrence Erlbaum Associates}}</ref>
* mathematical problem solving<ref>{{multiref2|1={{cite book|author-link=George Pólya|last=Pólya|first=George|year=1945|title=How to Solve It|publisher=Princeton University Press}}|2={{cite book|last=Schoenfeld|first=A. H.|year=1985|url=https://books.google.com/books?id=0cbSBQAAQBAJ|url-access=limited|title=Mathematical Problem Solving|location=Orlando, Fla.|publisher=Academic Press|isbn=978-1-4832-9548-0|access-date=2019-06-09|archive-date=2023-10-23|archive-url=https://web.archive.org/web/20231023053840/https://books.google.com/books?id=0cbSBQAAQBAJ|url-status=live}} }}</ref>
* mechanical problem solving<ref>{{cite book |last=Hegarty |first=M. |year=1991 |chapter-url=https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA253 |chapter-url-access=limited |chapter=Knowledge and processes in mechanical problem solving |pages=253–285 |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, N.J. |publisher=Lawrence Erlbaum Associates |isbn=0-8058-0650-4 |oclc=23254443 |access-date=2022-12-04 |archive-date=2022-12-04 |archive-url=https://web.archive.org/web/20221204055603/https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA253 |url-status=live }}</ref>
* personal problem solving<ref>{{cite journal | last1= Heppner|first1= P. P.|last2= Krauskopf|first2= C. J. |year=1987|title= An information-processing approach to personal problem solving|journal=The Counseling Psychologist|volume=15|issue= 3|pages=371–447|doi= 10.1177/0011000087153001|s2cid= 146180007}}</ref>
* political decision making<ref>{{cite book |last1=Voss |first1=J. F. |last2=Wolfe |first2=C. R. |last3=Lawrence |first3=J. A. |last4=Engle |first4=R. A. |year=1991 |chapter=From representation to decision: An analysis of problem solving in international relations |pages=119–158 |id=[[PsycNET]]: [https://psycnet.apa.org/record/1991-98396-004 1991-98396-004] |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, N.J. |publisher=Lawrence Erlbaum Associates |isbn=0-8058-0650-4 |oclc=23254443}}</ref>
* problem solving in electronics<ref>{{cite book |last1=Lesgold |first1=A. |last2=Lajoie |first2=S. |year=1991 |chapter-url=https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA287 |chapter-url-access=limited |chapter=Complex problem solving in electronics |pages=287–316 |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, N.J. |publisher=Lawrence Erlbaum Associates |isbn=0-8058-0650-4 |oclc=23254443 |access-date=2022-12-04 |archive-date=2022-12-04 |archive-url=https://web.archive.org/web/20221204055601/https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA287 |url-status=live }}</ref>
* problem solving for innovations and inventions: [[TRIZ]]<ref name="Altshuller1994">{{cite book | last = Altshuller | first = Genrich | year = 1994 | title = And Suddenly the Inventor Appeared | translator = Lev Shulyak | location = Worcester, Mass. | publisher = Technical Innovation Center | isbn = 978-0-9640740-1-9 |ref=Reference-Altshuller1994}}</ref>
* reading<ref>{{cite book |last1=Stanovich |first1=K. E. |last2=Cunningham |first2=A. E. |year=1991 |chapter-url=https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA3 |chapter-url-access=limited |chapter=Reading as constrained reasoning |pages=3–60 |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, N.J. |publisher=Lawrence Erlbaum Associates |isbn=0-8058-0650-4 |oclc=23254443 |access-date=2022-12-04 |archive-date=2023-09-03 |archive-url=https://web.archive.org/web/20230903202339/https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA3 |url-status=live }}</ref>
* social problem solving<ref name=DZurilla />
* writing<ref>{{cite book |last1=Bryson |first1=M. |last2=Bereiter |first2=C. |last3=Scardamalia |first3=M. |last4=Joram |first4=E. |year=1991 |chapter=Going beyond the problem as given: Problem solving in expert and novice writers |pages=61–84 |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, N.J. |publisher=Lawrence Erlbaum Associates |isbn=0-8058-0650-4 |oclc=23254443}}</ref>

== Characteristics of complex problems ==

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:<ref name="Complex Problem Solving"/>

* [[complexity]] (large numbers of items, interrelations, and decisions)
* [[enumerability]]{{clarify|reason=what is enumerable? does this mean enumerable in the formal mathematical sense? what would it mean for a complex problem to be unenumerable?|date=September 2023}}
* [[Homogeneity and heterogeneity|heterogeneity]]{{Specify|reason=of what?|date=September 2023}}
* [[:wikt:connectivity|connectivity]] (hierarchy relation, communication relation, allocation relation){{clarify|reason=it's unclear what this refers to or what that parenthetical list means|date=September 2023}}
* [[Dynamics (physics)|dynamics]] (time considerations){{clarify|reason=what do either "dynamics" or "time considerations" mean in this context?|date=September 2023}}
** temporal constraints
** temporal sensitivity{{clarify|reason=how does this differ from "temporal constraints"?|date=September 2023}}
** phase effects{{Definition needed|date=September 2023}}
** dynamic [[Predictability|unpredictability]]{{Specify|reason=of what?|date=September 2023}}
* intransparency (lack of clarity of the situation)
** commencement opacity{{Definition needed|date=September 2023}}
** continuation opacity{{Definition needed|date=September 2023}}
* [[polytely]] (multiple goals)<ref>{{cite book |year=1991 |editor-first1=R. J. |editor-last1=Sternberg |editor-first2=P. A. |editor-last2=Frensch |title=Complex problem solving: Principles and mechanisms |place=Hillsdale, NJ |publisher=Lawrence Erlbaum Associates |isbn=0-8058-0650-4 |oclc=23254443}}</ref>
** inexpressivenes{{Specify|reason=of what to what?|date=September 2023}}
** opposition{{Specify|reason=to what by what?|date=September 2023}}
** transience{{Specify|reason=of what|date=September 2023}}

==Collective problem solving==
{{See also|Crowdsolving|Collective action|Collaborative intelligence|Mass collaboration|Collective wisdom|The Wisdom of Crowds|Distributed knowledge|Online participation|Group decision-making}}
People solve problems on many different levels—from the individual to the civilizational. Collective problem solving refers to problem solving performed collectively. [[Social issue]]s and global issues can typically only be solved collectively.

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.<ref>{{cite journal|last1=Hung|first1=Woei|title=Team-based complex problem solving: a collective cognition perspective|journal=Educational Technology Research and Development|year=2013|volume=61|issue=3|pages=365–384 |doi=10.1007/s11423-013-9296-3 |s2cid=62663840}}</ref>

[[Collective intelligence]] is shared or group intelligence that emerges from the [[collaboration]], collective efforts, and competition of many individuals.

In collaborative problem solving people [[teamwork|work together]] 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.<ref>{{cite journal|last1=Jewett|first1=Pamela|first2=Deborah|last2= MacPhee|title=Adding Collaborative Peer Coaching to Our Teaching Identities|journal=The Reading Teacher|year=2012|volume=66|issue=2|pages=105–110|doi=10.1002/TRTR.01089}}</ref> 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.

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.<ref>{{cite journal|last=Wang|first=Qiyun|title=Design and Evaluation of a Collaborative Learning Environment|journal=Computers and Education|year=2009|volume=53|issue=4|pages=1138–1146|doi=10.1016/j.compedu.2009.05.023}}</ref> Collaborative group work has the ability to promote critical thinking skills, problem solving skills, [[social skills]], and [[self-esteem]]. 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.<ref>{{cite journal|last=Wang|first=Qiyan|title=Using online shared workspaces to support group collaborative learning|journal=Computers and Education|year=2010|volume=55|issue=3|pages=1270–1276|doi= 10.1016/j.compedu.2010.05.023}}</ref>

Collaborative groups require joint intellectual efforts between the members and involve [[social interaction]]s to solve problems together. The [[knowledge sharing|knowledge shared]] during these interactions is acquired during communication, negotiation, and production of materials.<ref>{{cite journal|last1=Kai-Wai Chu|first1=Samuel|first2=David M.|last2=Kennedy|title=Using Online Collaborative tools for groups to Co-Construct Knowledge|journal=Online Information Review|year=2011|volume=35|issue=4|pages=581–597|doi=10.1108/14684521111161945 |s2cid=206388086|issn=1468-4527 }}</ref> 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.<ref>{{cite journal|last1=Legare|first1=Cristine|first2=Candice |last2=Mills |first3=Andre|last3= Souza |first4=Leigh |last4=Plummer |first5=Rebecca|last5= Yasskin |title=The use of questions as problem-solving strategies during early childhood|journal=Journal of Experimental Child Psychology|year=2013|volume=114|issue=1|pages=63–7 |doi=10.1016/j.jecp.2012.07.002 |pmid=23044374}}</ref>

In a 1962 research report, [[Douglas Engelbart]] 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".<ref>{{cite book|last=Engelbart|first=Douglas|year=1962|chapter-url=https://www.dougengelbart.org/pubs/augment-3906.html#3b9|chapter=Team Cooperation|title=Augmenting Human Intellect: A Conceptual Framework|publisher=Stanford Research Institute|volume=AFOSR-3223}}</ref>

[[Henry Jenkins]], a theorist of new media and media convergence, draws on the theory that collective intelligence can be attributed to media convergence and [[participatory culture]].<ref>{{cite book | last=Flew | first=Terry | year= 2008 | title=New Media: an introduction | publisher=Oxford University Press | location=Melbourne}}</ref> 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.<ref name=":25">{{Cite web|url=http://labweb.education.wisc.edu/curric606/readings/Jenkins2002.pdf|title=Interactive audiences? The 'collective intelligence' of media fans |last=Henry|first=Jenkins|access-date=December 11, 2016|archive-url=https://web.archive.org/web/20180426232104/https://labweb.education.wisc.edu/curric606/readings/Jenkins2002.pdf|archive-date=April 26, 2018}}</ref>

[[Collective impact]] 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.

After [[World War II]] the [[UN]], the [[Bretton Woods system|Bretton Woods organization]], and the [[WTO]] 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.<ref>{{cite book|last=Finger|first=Matthias|chapter=Which governance for sustainable development? An organizational and institutional perspective|editor-last1=Park|editor-first1=Jacob|editor-last2=Conca|editor-first2=Ken|editor-last3=Finger |editor-first3=Matthias |title=The Crisis of Global Environmental Governance: Towards a New Political Economy of Sustainability |publisher=Routledge |isbn=978-1-134-05982-9 |language=en|date=2008-03-27|page=[https://books.google.com/books?id=lrr3K50r144C&pg=PA48 48]}}</ref><!--https://books.google.com/books?id=CtXvBwAAQBAJ&pg=PA189-->

[[Crowdsourcing]] 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 [[information technologies]] allow for many people to be involved and facilitate managing their suggestions in ways that provide good results.<ref>{{multiref2
|1={{cite journal|last1=Guazzini|first1=Andrea|last2=Vilone|first2=Daniele|last3=Donati|first3=Camillo|last4=Nardi|first4=Annalisa|last5=Levnajić|first5=Zoran|title=Modeling crowdsourcing as collective problem solving|journal=Scientific Reports|date=10 November 2015|volume=5|page=16557|doi=10.1038/srep16557 |pmid=26552943 |pmc=4639727 |bibcode=2015NatSR...516557G|arxiv=1506.09155}}
|2={{cite journal|last1=Boroomand|first1=A.|last2=Smaldino|first2=P.E.|year=2021|title=Hard Work, Risk-Taking, and Diversity in a Model of Collective Problem Solving|journal=Journal of Artificial Societies and Social Simulation|volume=24|number=4|doi=10.18564/jasss.4704 |s2cid=240483312 |doi-access=free}}
}}</ref> The [[Internet]] allows for a new capacity of collective (including planetary-scale) problem solving.<ref>{{cite journal|last1=Stefanovitch|first1=Nicolas|last2=Alshamsi |first2=Aamena |last3=Cebrian |first3=Manuel |last4=Rahwan|first4=Iyad|title=Error and attack tolerance of collective problem solving: The DARPA Shredder Challenge|journal=EPJ Data Science |date=30 September 2014|volume=3|issue=1|doi=10.1140/epjds/s13688-014-0013-1|doi-access=free|hdl=21.11116/0000-0002-D39F-D|hdl-access=free}}</ref>

==See also==
{{Portal|Philosophy|Psychology}}
{{Wikiquote}}
* {{annotated link|[[Actuarial science]]}}
* {{annotated link|[[Analytical skill]]}}
* {{annotated link|[[Creative problem-solving]]}}
* {{annotated link|[[Collective intelligence]]}}
* {{annotated link|[[Community of practice]]}}
* {{annotated link|[[Coworking]]}}
* {{annotated link|[[Crowdsolving]]}}
* {{annotated link|[[Divergent thinking]]}}
* {{annotated link|[[Grey problem]]}}
* {{annotated link|[[Innovation]]}}
* {{annotated link|[[Instrumentalism]]}}
*{{Annotated link|[[Problem-posing education]]}}
* {{annotated link|[[Problem statement]]}}
* {{annotated link|[[Problem structuring methods]]}}
* {{annotated link|[[Shared intentionality]]}}
* {{annotated link|[[Structural fix]]}}
* {{annotated link|[[Subgoal labeling]]}}
* {{annotated link|[[Troubleshooting]]}}
* {{annotated link|[[Wicked problem]]}}

==Notes==
{{reflist}}

==Further reading==
* {{cite book|last1=Beckmann|first1=Jens F.|last2=Guthke|first2=Jürgen|year=1995|chapter-url=https://www.researchgate.net/publication/200134353|chapter=Complex problem solving, intelligence, and learning ability|editor-first1=P. A.|editor-last1=Frensch|editor-first2=J.|editor-last2=Funke|title=Complex problem solving: The European Perspective|pages=177–200|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates}}
* {{cite book | last= Brehmer|first= Berndt |year=1995|chapter= Feedback delays in dynamic decision making|editor-first1=P. A.|editor-last1=Frensch|editor-first2=J.|editor-last2=Funke|title=Complex problem solving: The European Perspective|pages=103–130|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates}}
* {{cite journal | last1= Brehmer|first1= Berndt|last2= Dörner|first2= D. |year=1993|title=Experiments with computer-simulated microworlds: Escaping both the narrow straits of the laboratory and the deep blue sea of the field study|journal=Computers in Human Behavior|volume=9|issue= 2–3|pages=171–184|doi= 10.1016/0747-5632(93)90005-D}}
* {{cite book | last= Dörner|first= D. |year=1992|chapter= Über die Philosophie der Verwendung von Mikrowelten oder 'Computerszenarios' in der psychologischen Forschung|trans-chapter=On the proper use of microworlds or "computer scenarios" in psychological research|editor-first=H.|editor-last=Gundlach|title=Psychologische Forschung und Methode: Das Versprechen des Experiments. Festschrift für Werner Traxel|pages=53–87|location=Passau, Germany|publisher=Passavia-Universitäts-Verlag|lang=de}}
* {{cite journal |last1=Eyferth |first1=K. |last2=Schömann |first2=M. |last3=Widowski |first3=D. |year=1986 |title=Der Umgang von Psychologen mit Komplexität |trans-title=On how psychologists deal with complexity |journal=Sprache & Kognition |volume=5 |pages=11–26 |language=de}}
* {{cite book|last=Funke|first=Joachim|year=1993|chapter-url=https://web-archive.southampton.ac.uk/cogprints.org/1679/2/Funke_1993_micro.pdf|chapter=Microworlds based on linear equation systems: A new approach to complex problem solving and experimental results|editor-first1=G.|editor-last1=Strube|editor-first2=K.-F.|editor-last2=Wender|title=The cognitive psychology of knowledge|pages=313–330|location=Amsterdam|publisher=Elsevier Science Publishers}}
* {{cite book |last=Funke|first=Joachim|year=1995|chapter-url=https://web-archive.southampton.ac.uk/cogprints.org/3003/1/Funke_1995_CPS.pdf|chapter=Experimental research on complex problem solving|editor-first1=P. A.|editor-last1=Frensch|editor-first2=J.|editor-last2=Funke|title=Complex problem solving: The European Perspective|pages=243–268|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates}}
* {{cite book |last=Funke|first=U.|year=1995|chapter=Complex problem solving in personnel selection and training|editor-first1=P. A.|editor-last1=Frensch|editor-first2=J.|editor-last2=Funke|title=Complex problem solving: The European Perspective|pages=219–240|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates}}
* {{cite book | last1= Groner|first1= M.|last2= Groner|first2= R.|last3= Bischof|first3= W. F. |year=1983|chapter= Approaches to heuristics: A historical review|editor-first1= R.|editor-last1= Groner|editor-first2= M.|editor-last2= Groner|editor-first3= W. F.|editor-last3= Bischof|title=Methods of heuristics|pages=1–18|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates}}
* {{cite book | last= Hayes|first=J.|year=1980|title=The complete problem solver|location=Philadelphia|publisher=The Franklin Institute Press}}
* {{cite book | last= Huber|first= O. |year=1995|chapter= Complex problem solving as multistage decision making|editor-first1=P. A.|editor-last1=Frensch|editor-first2=J.|editor-last2=Funke|title=Complex problem solving: The European Perspective|pages=151–173|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates}}
* {{cite journal | last= Hübner|first= Ronald |year=1989|url=https://www.cogpsych.uni-konstanz.de/pdf/Hubner_1989_Methoden.pdf|title=Methoden zur Analyse und Konstruktion von Aufgaben zur kognitiven Steuerung dynamischer Systeme|trans-title=Methods for the analysis and construction of dynamic system control tasks|journal=Zeitschrift für Experimentelle und Angewandte Psychologie|volume=36|pages=221–238|lang=de}}
* {{cite book | last= Hunt|first= Earl|year=1991|chapter-url=https://books.google.com/books?id=ZECYAgAAQBAJ&pg=PA383|chapter-url-access=limited|chapter=Some comments on the study of complexity|editor-first1=R. J.|editor-last1=Sternberg|editor-first2=P. A.|editor-last2=Frensch|title=Complex problem solving: Principles and mechanisms|pages=383–395|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates|isbn= 978-1-317-78386-2}}
* {{cite journal |last= Hussy|first= W.|year=1985|title=Komplexes Problemlösen—Eine Sackgasse?|trans-title=Complex problem solving—a dead end?|journal=Zeitschrift für Experimentelle und Angewandte Psychologie|volume=32|pages=55–77|lang=de}}
* {{cite book |last1=Kluwe|first1=R. H. |year=1993 |doi=10.1016/S0166-4115(08)62668-0|chapter=Chapter 19 Knowledge and Performance in Complex Problem Solving|title=The Cognitive Psychology of Knowledge|volume=101|pages=401–423|series=Advances in Psychology |isbn=978-0-444-89942-2}}
* {{cite book | last= Kluwe|first= R. H. |year=1995|chapter=Single case studies and models of complex problem solving|editor-first1=P. A.|editor-last1=Frensch|editor-first2=J.|editor-last2=Funke|title=Complex problem solving: The European Perspective|pages=269–291|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates}}
* {{cite journal| last1= Kolb|first1=S.|last2= Petzing|first2= F.|last3=Stumpf|first3=S.|year=1992|title=Komplexes Problemlösen: Bestimmung der Problemlösegüte von Probanden mittels Verfahren des Operations Research—ein interdisziplinärer Ansatz|trans-title=Complex problem solving: determining the quality of human problem solving by operations research tools—an interdisciplinary approach|journal=Sprache & Kognition|volume=11|pages=115–128|lang=de}}
* {{cite book|last= Krems|first=Josef F. |year=1995 |chapter-url=https://www.researchgate.net/publication/200134353|chapter=Cognitive flexibility and complex problem solving|editor-first1=P. A.|editor-last1=Frensch|editor-first2=J.|editor-last2=Funke|title=Complex problem solving: The European Perspective|pages=201–218|location=Hillsdale, N.J.|publisher=Lawrence Erlbaum Associates}}
* {{cite book | last= Melzak| first= Z. |year=1983|title=Bypasses: A Simple Approach to Complexity|location=London, UK|publisher=Wiley|lang=en}}
* {{cite book | last= Müller| first= H. |year=1993|title=Komplexes Problemlösen: Reliabilität und Wissen|trans-title=Complex problem solving: Reliability and knowledge|location=Bonn, Germany|publisher=Holos|lang=de}}
* {{cite book | last1= Paradies| first1= M.W.|last2= Unger|first2=L. W. |year=2000|title=TapRooT—The System for Root Cause Analysis, Problem Investigation, and Proactive Improvement|location=Knoxville, Tenn.|publisher= System Improvements}}
* {{cite book |last1=Putz-Osterloh |first1=Wiebke |doi=10.1016/S0166-4115(08)62664-3 |chapter=Chapter 15 Strategies for Knowledge Acquisition and Transfer of Knowledge in Dynamic Tasks |title=The Cognitive Psychology of Knowledge |volume=101 |pages=331–350 |series=Advances in Psychology |year=1993 |isbn=978-0-444-89942-2 }}
* {{cite journal | last1= Riefer| first1= David M.|last2=Batchelder|first2= William H. |year=1988|url=https://pdfs.semanticscholar.org/9bf7/c2bb2a621983c0e590ea1f019bd1eb8029d4.pdf|archive-url=https://web.archive.org/web/20181125115507/https://pdfs.semanticscholar.org/9bf7/c2bb2a621983c0e590ea1f019bd1eb8029d4.pdf|archive-date=2018-11-25|title=Multinomial modeling and the measurement of cognitive processes|journal=Psychological Review|volume=95| issue= 3|pages=318–339| doi= 10.1037/0033-295x.95.3.318| s2cid= 14994393}}
* {{cite book | last= Schaub|first= H.|year=1993|title=Modellierung der Handlungsorganisation|location=Bern, Switzerland|publisher= Hans Huber|lang=de}}
* {{cite book | last= Strauß|first= B. |year=1993|title=Konfundierungen beim Komplexen Problemlösen. Zum Einfluß des Anteils der richtigen Lösungen (ArL) auf das Problemlöseverhalten in komplexen Situationen|trans-title=Confoundations in complex problem solving. On the influence of the degree of correct solutions on problem solving in complex situations|location=Bonn, Germany|publisher=Holos|lang=de}}
* {{cite journal | last= Strohschneider|first=S.|year=1991|title=Kein System von Systemen! Kommentar zu dem Aufsatz 'Systemmerkmale als Determinanten des Umgangs mit dynamischen Systemen' von Joachim Funke|trans-title=No system of systems! Reply to the paper 'System features as determinants of behavior in dynamic task environments' by Joachim Funke|journal=Sprache & Kognition|volume=10|pages=109–113|lang=de}}
* {{cite book | last=Tonelli | first=Marcello | title=Unstructured Processes of Strategic Decision-Making | year=2011 |location=Saarbrücken, Germany|publisher= Lambert Academic Publishing| isbn=978-3-8465-5598-9}}
* {{cite book | last= Van Lehn|first=Kurt |year=1989|url=https://apps.dtic.mil/dtic/tr/fulltext/u2/a218905.pdf|chapter= Problem solving and cognitive skill acquisition|editor-first=M. I.|editor-last=Posner|title=Foundations of cognitive science|pages=527–579|location=Cambridge, Mass.|publisher=MIT Press}}
* {{citation|author= Wisconsin Educational Media Association|year=1993|url=https://eric.ed.gov/?id=ED376817|title=Information literacy: A position paper on information problem-solving|location=Madison, Wis.|series=WEMA Publications|volume=ED 376 817}} (Portions adapted from [[Michigan State Board of Education]]'s Position Paper on Information Processing Skills, 1992.)

==External links==
*{{Wikiversity inline|Solving Problems}}

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[[Category:Problem solving| ]]
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[[Category:Artificial intelligence]]
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