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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>
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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.
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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" />
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=== 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.{{example needed|date=September 2023}} 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>
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=== Europe ===
In Europe, two main approaches have surfaced, one initiated by [[Donald Broadbent]]<ref>{{multiref2
|1={{cite journal
|2={{cite book
}}</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}}
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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
* 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>
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