Editing Problem solving (section)

==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}}
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===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 }}
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