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{{Neuropsychology}}
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'''Problem solving''' forms part of [[thought|thinking]]. Considered the most complex of all [[intelligence|intellectual]] functions, problem solving has been defined as higher-order [[cognitive]] process that requires the modulation and control of more routine or fundamental skills (McCarthy & Worthington, 1990). It occurs if an [[organism]] or an [[artificial intelligence]] [[system]] does not know how to proceed from a given state to a desired goal state. It is part of the larger [[problem]] process that includes [[problem finding]] and [[problem shaping]].
 
  +
'''Problem solving''' forms part of [[thought|thinking]]. Considered the most complex of all [[intelligence|intellectual]] functions, problem solving has been defined as higher-order [[cognitive]] process that requires the modulation and control of more routine or fundamental skills ([[#Reference-Goldstein |Goldstein & Levin, 1987]]). It occurs if an [[organism]] or an [[artificial intelligence]] [[system]] does not know how to proceed from a given state to a desired goal state. It is part of the larger [[problem]] process that includes [[problem finding]] and [[problem shaping]].
   
 
==Overview==
  
==Overview==
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The nature of human problem solving has been studied by [[psychologist]]s over the past hundred years. There are several methods of studying problem solving, including; [[introspection]], [[behaviorism]], [[simulation]] and [[computer modeling]], and [[experiment]].
 +
The nature of human problem solving methods has been studied by [[psychologist]]s over the past hundred years. There are several methods of studying problem solving, including; [[introspection]], [[behaviorism]], [[simulation]] and [[computer modeling]], and [[experiment]].
   
−
Beginning with the early experimental work of the [[Gestalt psychology|Gestaltist]]s in [[Germany]] (e.g. Duncker, 1935), and continuing through the 1960s and early 1970s, research on problem solving typically conducted relatively simple, laboratory tasks (e.g. Duncker's "X-ray" problem; Ewert & Lambert's 1932 "disk" problem, later known as [[Tower of Hanoi]]) that appeared novel to participants (e.g. Mayer, 1992). Various reasons account for the choice of simple novel tasks: they had clearly defined optimal solutions, they were solvable within a relatively short time frame, researchers could trace participants' problem-solving steps, and so on. The researchers made the underlying assumption, of course, that simple tasks such as the Tower of Hanoi captured the main properties of "real world" problems, and that the cognitive processes underlying participants' attempts to solve simple problems were representative of the processes engaged in when solving "real world" problems. Thus researchers used simple problems for reasons of convenience, and thought generalizations to more complex problems would become possible. Perhaps the best-known and most impressive example of this line of research remains the work by Newell and Simon (1972).
 +
Beginning with the early experimental work of the [[Gestalt psychology|Gestaltist]]s in [[Germany]] (e.g. [[#Reference-Duncker|Duncker, 1935]]), and continuing through the 1960s and early 1970s, research on problem solving typically conducted relatively simple, laboratory tasks (e.g. Duncker's "X-ray" problem; Ewert & Lambert's 1932 "disk" problem, later known as [[Tower of Hanoi]]) that appeared novel to participants (e.g. [[#Reference-Mayer|Mayer, 1992]]). Various reasons account for the choice of simple novel tasks: they had clearly defined optimal solutions, they were solvable within a relatively short time frame, researchers could trace participants' problem-solving steps, and so on. The researchers made the underlying assumption, of course, that simple tasks such as the Tower of Hanoi captured the main properties of "real world" problems, and that the cognitive processes underlying participants' attempts to solve simple problems were representative of the processes engaged in when solving "real world" problems. Thus researchers used simple problems for reasons of convenience, and thought generalizations to more complex problems would become possible. Perhaps the best-known and most impressive example of this line of research remains the work by [[#Reference-Newell|Newell and Simon]] (1972).
   
−
==History==
 +
==Europe==
  +
In Europe, two main approaches have surfaced, one initiated by [[Donald Broadbent]] (1977; see Berry & Broadbent, 1995) in the United Kingdom and the other one by [[Dietrich Dörner]] (1975, 1985; see Dörner & Wearing, 1995) in Germany. The two approaches have in common 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, however. 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 (e.g., Dörner, Kreuzig, Reither & Stäudel's 1983 LOHHAUSEN project; Ringelband, Misiak & Kluwe, 1990). Buchner (1995) describes the two traditions in detail.
−
However, beginning in the 1970s, researchers became increasingly convinced that [[empirical]] findings and theoretical concepts derived from simple laboratory tasks did not necessarily generalize to more complex, real-life problems. Even worse, it appeared that the processes underlying creative problem solving in different domains differed from each other (Sternberg, 1995). These realizations have led to rather different responses in North America and in Europe.
  
  +
  +
To sum up, researchers' realization that problem-solving processes differ across knowledge domains and across levels of expertise (e.g. Sternberg, 1995) and that, consequently, findings obtained in the laboratory cannot necessarily generalize to problem-solving situations outside the laboratory, has during the past two decades led to an emphasis on real-world problem solving. 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 (see Funke, 1991, for an overview).
   
 
==USA and Canada==
  
==USA and Canada==
−
In North America, initiated by the work of [[Herbert Simon]] on learning by doing in [[semantic]]ally rich domains (e.g. Anzai & Simon, 1979; Bhaskar & Simon, 1977), researchers began to investigate problem solving separately in different natural [[knowledge domain]]s - such as physics, writing, or chess playing - thus relinquishing their attempts to extract a global theory of problem solving (e.g. Sternberg & Frensch, 1991). Instead, these researchers have frequently focused on the development of problem solving within a certain domain, that is on the development of [[expertise]] (e.g. Anderson, Boyle & Reiser, 1985; Chase & Simon, 1973; Chi, Feltovich & Glaser, 1981).
+
In North America, initiated by the work of [[Herbert Simon]] on learning by doing in [[semantic]]ally rich domains (e.g. [[#Reference-Anzai|Anzai & Simon, 1979]]; [[#Reference-Bhaskar|Bhaskar & Simon, 1977]]), researchers began to investigate problem solving separately in different natural [[knowledge domain]]s - such as physics, writing, or [[chess]] playing - thus relinquishing their attempts to extract a global theory of problem solving (e.g. Sternberg & Frensch, 1991). Instead, these researchers have frequently focused on the development of problem solving within a certain domain, that is on the development of [[expertise]] (e.g. [[#Reference-Anderson|Anderson, Boyle & Reiser, 1985]]; [[#Reference-Chase|Chase & Simon, 1973]]; [[#Reference-Chi|Chi, Feltovich & Glaser, 1981]]).
   
 
Areas that have attracted rather intensive attention in North America include such diverse fields as:
  
Areas that have attracted rather intensive attention in North America include such diverse fields as:
−
*Reading (Stanovich & Cunningham, 1991)
 +
*Reading ([[#Reference-Stanovich|Stanovich & Cunningham, 1991]])
−
*Writing (Bryson, Bereiter, Scardamalia & Joram, 1991)
 +
*Writing ([[#Reference-Bryson|Bryson, Bereiter, Scardamalia & Joram, 1991]])
−
*Calculation (Sokol & McCloskey, 1991)
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*Calculation ([[#Reference-Sokol|Sokol & McCloskey, 1991]])
−
*Political decision making (Voss, Wolfe, Lawrence & Engle, 1991)
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*Political decision making ([[#Reference-Voss|Voss, Wolfe, Lawrence & Engle, 1991]])
−
*Managerial problem solving (Wagner, 1991)
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*Managerial problem solving ([[#Reference-Wagner|Wagner, 1991]])
−
*Lawyers' reasoning (Amsel, Langer & Loutzenhiser, 1991)
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*Lawyers' reasoning ([[#Reference-Amsel|Amsel, Langer & Loutzenhiser, 1991]])
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*Mechanical problem solving (Hegarty, 1991)
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*Mechanical problem solving ([[#Reference-Hegarty|Hegarty, 1991]])
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*Problem solving in electronics (Lesgold & Lajoie, 1991)
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*Problem solving in electronics ([[#Reference-Lesgold|Lesgold & Lajoie, 1991]])
−
*Computer skills (Kay, 1991)
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*Computer skills ([[#Reference-Kay|Kay, 1991]])
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*Game playing (Frensch & Sternberg, 1991)
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*Game playing ([[#Reference-Frensch|Frensch & Sternberg, 1991]])
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*Personal problem solving (Heppner & Krauskopf, 1987)
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*Personal problem solving ([[#Reference-Heppner|Heppner & Krauskopf, 1987]])
−
*Mathematical problem solving (Polya, 1945; Schoenfeld, 1985)
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*Mathematical problem solving ([[Polya]], 1945; [[#Reference-Schoenfeld|Schoenfeld, 1985]])
 
*Social problem solving (D'Zurilla & Goldfreid, 1971; D'Zurilla & Nezu, 1982)
  
*Social problem solving (D'Zurilla & Goldfreid, 1971; D'Zurilla & Nezu, 1982)
  +
*Problem solving for innovations and inventions: TRIZ (Altshuller, 1973, 1984, 1994)
−  
−
==Europe==
  
−
In Europe, two main approaches have surfaced, one initiated by [[Donald Broadbent]] (1977; see Berry & Broadbent, 1995) in the United Kingdom and the other one by [[Dietrich Dörner]] (1975, 1985; see Dörner & Wearing, 1995) in Germany. The two approaches have in common 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, however. 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 (e.g., Dörner, Kreuzig, Reither & Stäudel's 1983 LOHHAUSEN project; Ringelband, Misiak & Kluwe, 1990). Buchner (1995) describes the two traditions in detail.
  
−  
−
To sum up, researchers' realization that problem-solving processes differ across knowledge domains and across levels of expertise (e.g. Sternberg, 1995) and that, consequently, findings obtained in the laboratory cannot necessarily generalize to problem-solving situations outside the laboratory, has during the past two decades led to an emphasis on real-world problem solving. 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 (see Funke, 1991, for an overview).
  
   
 
==Characteristics of difficult problems==
  
==Characteristics of difficult problems==
   
−
As elucidated by [[Dietrich Dorner]] and later expanded upon by [[Joachim Funke]], difficult problems have some typical characteristics. Recategorized and somewhat reformulated from these original works, these characteristics can be summarized as follows:
 +
As elucidated by [[Dietrich Dörner]] and later expanded upon by [[Joachim Funke]], difficult problems have some typical characteristics that can be summarized as follows:
   
 
*Intransparency (lack of clarity of the situation)
  
*Intransparency (lack of clarity of the situation)
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**[[connectivity]] (hierarchy relation, communication relation, allocation relation)
  
**[[connectivity]] (hierarchy relation, communication relation, allocation relation)
 
**[[heterogeneity]]
  
**[[heterogeneity]]
−
*[[Dynamism]] (time considerations)
 +
*[[Dynamics]] (time considerations)
 
**temporal constraints
  
**temporal constraints
 
**temporal sensitivity
  
**temporal sensitivity
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The resolution of difficult problems requires a direct attack on each of these characteristics that are encountered.
  
The resolution of difficult problems requires a direct attack on each of these characteristics that are encountered.
   
  +
In [[reform mathematics]], greater emphasis is placed on problem solving relative to basic skills, where basic operations can be done with calculators. However some "problems" may actually have standard solutions taught in higher grades. For example, kindergarteners could be asked how many fingers are there on all the gloves of 3 children, which can be solved with multiplication. <ref>2007 Draft, Washington State Revised Mathematics Standard</ref>
−
==Some problem-solving techniques==
  
  +
  +
==Problem-solving techniques==
  +
* [[Abstraction]]: solving the problem in a model of the system before applying it to the real system
  +
* [[Analogy]]: using a solution that solved an analogous problem
  +
* [[Brainstorming]]: (especially among groups of people) suggesting a large number of solutions or ideas and combining and developing them until an optimum is found
  +
* [[Divide and conquer]]: breaking down a large, complex problem into smaller, solvable problems
  +
* [[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
  +
* [[Method of focal objects]]: synthesizing seemingly non-matching characteristics of different objects into something new
  +
* [[Morphological analysis (problem-solving)|Morphological analysis]]: assessing the output and interactions of an entire system
  +
* [[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]]: eliminating the cause of the problem
  +
* [[Trial-and-error]]: testing possible solutions until the right one is found
  +
  +
# [[Working Backwards]] (Halpern,2002)
  +
# [[Forward-Looking Strategy]] (Halpern, 2002)
  +
# [[Simplification]] (Halpern, 2002)
  +
# [[Generalization]] (Halpern, 2002)
  +
# [[Specialization]] (Halpern, 2002)
  +
# [[Random Search]] (Halpern, 2002)
  +
# [[Split-Half Method]] (Halpern,2002)
  +
  +
==Problem-solving methodologies==
  +
* [[Eight Disciplines Problem Solving]]
  +
* [[GROW model]]
  +
* ''[[How to solve it]]''
  +
* [[Kepner-Tregoe]]
  +
* [[Southbeach Notation]]
  +
* [[PDCA]]
  +
* [[RPR Problem Diagnosis]]
  +
* [[TRIZ]] (Teoriya Resheniya Izobretatelskikh Zadatch, "theory of solving inventor's problems")
   
−
# [[Trial-and-error]]
  
−
# [[Brainstorming]]
  
−
# [[Morphological box]]
  
−
# [[Method of focal objects]]
  
−
# [[Lateral thinking]]
  
−
# [[George Pólya]]'s techniques in [[How to Solve It]]
  
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# Research: study what others have written about the problem (and related problems). Maybe there's already a solution?
  
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# Assumption reversal (write down your assumptions about the problem, and then reverse them all)
  
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# [[Analogy]]: has a similar problem (possibly in a different field) been solved before?
  
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# Hypothesise a world in which the current problem wouldn't exist
  
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# Constraint examination: are you assuming a constraint which doesn't really exist?
  
−
# Take more time: time pressure can cause one to think in circles (the brain, unhelpfully, tends to be "pulled" towards a particular solution, or aspect of the problem)
  
−
# Incubation: input the details of a problem into your mind, then stop focusing on it. The subconscious mind will continue to work on the problem, and the solution might just "pop up" while you are doing something else
  
−
# Build (or write) one or more abstract models of the problem
  
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# Try to prove that the problem cannot be solved. Where the proof breaks down can be your starting point for resolving it
  
−
# Get help from friends or online problem solving community (e.g. [[Human-based genetic algorithm|3form]])
  
−
# [[Root Cause Analysis]]
  
   
−
These are also known as [[creativity techniques]]. Also, please see the [[thinking]] article.
  
   
 
==See also==
  
==See also==
  +
<div style="-moz-column-count:3; column-count:3;">
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{{col-begin}}
  
−
{{col-break}}
  
−
* [[Automated Problem Solving]]
  
 
* [[Abductive reasoning]]
  
* [[Abductive reasoning]]
  +
* [[Anagram problem solving]]
 
* [[Analogy]]
  
* [[Analogy]]
 
* [[Artificial intelligence]]
  
* [[Artificial intelligence]]
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* [[Common sense]]
  
* [[Common sense]]
 
* [[Common sense reasoning]]
  
* [[Common sense reasoning]]
  +
* [[Cognitive hypothesis testing]]
  +
* [[Cognitive processes]]
 
* [[Creative problem solving]]
  
* [[Creative problem solving]]
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* [[Cyc]]
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* [[Decision making]]
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* [[Declarative knowledge]]
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{{col-break}}
  
 
* [[Deductive reasoning]]
  
* [[Deductive reasoning]]
  +
* [[Divergent thinking]]
 
* [[Educational psychology]]
  
* [[Educational psychology]]
 
* [[Executive function]]
  
* [[Executive function]]
  +
* [[Expert systems]]
  +
* [[Facilitation]]
  +
* [[Gagné's hierarchy of learning]]
 
* [[General Problem Solver|General problem solver]]
  
* [[General Problem Solver|General problem solver]]
  +
* [[Group problem solving]]
 
* [[Inductive reasoning]]
  
* [[Inductive reasoning]]
 
* [[Innovation]]
  
* [[Innovation]]
 
* [[Intelligence amplification]]
  
* [[Intelligence amplification]]
−
{{col-break}}
  
 
* [[Inquiry]]
  
* [[Inquiry]]
  +
* [[Kepner-Tregoe]]
−
* [[Alan Lesgold|Lesgold, Alan]]
  
  +
* [[Morphological Analysis]]
 
* [[Allen Newell|Newell, Allen]]
  
* [[Allen Newell|Newell, Allen]]
  +
* [[PDCA]]
  +
* [[Problem-solving in psychotherapy]]
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* [[Problem Solving Therapy]]
  +
* [[Problem Statement]]
  +
* [[Reasoning]]
  +
* [[RPR Problem Diagnosis]]
 
* [[Herbert Simon|Simon, Herbert]]
  
* [[Herbert Simon|Simon, Herbert]]
 
* [[Soar (cognitive architecture)]]
  
* [[Soar (cognitive architecture)]]
  +
* [[Thought]]
  +
* [[Transdisciplinary Studies]]
 
* [[TRIZ]]
  
* [[TRIZ]]
 
* [[Troubleshooting]]
  
* [[Troubleshooting]]
 
* [[Wicked problem]]
  
* [[Wicked problem]]
  +
</div>
−
{{col-end}}
  
  +
  +
== Notes ==
  +
  +
<references/>
  +
  +
== References ==
  +
<div class="references-small">
  +
*{{wikicite | id= Amsel| reference= Amsel, E., Langer, R., & Loutzenhiser, L. (1991). Do lawyers reason differently from psychologists? A comparative design for studying expertise. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 223-250). Hillsdale, NJ: Lawrence Erlbaum Associates. ISBN 978-0-8058-1783-6}}
  +
*{{wikicite | id= Anderson| reference= {{cite journal
  +
| author = Anderson, J. R., Boyle, C. B., & Reiser, B. J.
  +
| title = Intelligent tutoring systems
  +
| journal = Science
  +
| date = 1985
  +
| volume = 228
  +
| pages = 456–462
  +
| doi = 10.1126/science.228.4698.456
  +
| pmid = 17746875
  +
}}
  +
}}
  +
*{{wikicite | id= Anzai| reference= {{cite journal
  +
|author=Anzai, K., & Simon, H. A. (1979)
  +
|title=The theory of learning by doing
  +
|journal=Psychological Review
  +
|volume=86
  +
|pages=124–140
  +
|url=http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=493441&dopt=Abstract
  +
|doi=10.1037/0033-295X.86.2.124
  +
|year=1979}}
  +
}}
  +
*{{wikicite | id= Beckmann| reference= Beckmann, J. F., & Guthke, J. (1995). Complex problem solving, intelligence, and learning ability. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 177-200). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Berry| reference= Berry, D. C., & Broadbent, D. E. (1995). Implicit learning in the control of complex systems: A reconsideration of some of the earlier claims. In P.A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 131-150). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Bhaskar| reference= Bhaskar, R., & Simon, H. A. (1977). Problem solving in semantically rich domains: An example from engineering thermodynamics. ''Cognitive Science'', 1, 193-215.}}
  +
*{{wikicite | id= Brehmer1995| reference= Brehmer, B. (1995). Feedback delays in dynamic decision making. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 103-130). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Brehmer1993| reference= Brehmer, B., & Dörner, D. (1993). Experiments with computer-simulated microworlds: Escaping both the narrow straits of the laboratory and the deep blue sea of the field study. ''Computers in Human Behavior'', 9, 171-184.}}
  +
*{{wikicite | id= Broadbent| reference= Broadbent, D. E. (1977). Levels, hierarchies, and the locus of control. ''Quarterly Journal of Experimental Psychology'', 29, 181-201.}}
  +
*{{wikicite | id= Bryson| reference= Bryson, M., Bereiter, C., Scardamalia, M., & Joram, E. (1991). Going beyond the problem as given: Problem solving in expert and novice writers. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 61-84). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Buchner1995a| reference= Buchner, A. (1995). Theories of complex problem solving. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 27-63). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Buchner1995b| reference= Buchner, A., Funke, J., & Berry, D. C. (1995). Negative correlations between control performance and verbalizable knowledge: Indicators for implicit learning in process control tasks? ''Quarterly Journal of Experimental Psychology'', 48A, 166-187.}}
  +
*{{wikicite | id= Chase| reference= Chase, W. G., & Simon, H. A. (1973). Perception in chess. ''Cognitive Psychology'', 4, 55-81.}}
  +
*{{wikicite | id= Chi| reference= {{cite journal
  +
|author=Chi, M. T. H., Feltovich, P. J., & Glaser, R.
  +
|year=1981
  +
|title=Categorization and representation of physics problems by experts and novices
  +
|journal=Cognitive Science
  +
|volume=5
  +
|pages=121–152
  +
|url=http://www.usabilityviews.com/uv007206.html}}
  +
}}
  +
*{{wikicite | id= Dörner1975| reference= Dörner, D. (1975). Wie Menschen eine Welt verbessern wollten [How people wanted to improve the world]. ''Bild der Wissenschaft'', 12, 48-53.}}
  +
*{{wikicite | id= Dörner1985| reference= Dörner, D. (1985). Verhalten, Denken und Emotionen [Behavior, thinking, and emotions]. In L. H. Eckensberger & E. D. Lantermann (Eds.), ''Emotion und Reflexivität'' (pp. 157-181). München, Germany: Urban & Schwarzenberg.}}
  +
*{{wikicite | id= Dörner1992| reference= Dörner, D. (1992). Über die Philosophie der Verwendung von Mikrowelten oder "Computerszenarios" in der psychologischen Forschung [On the proper use of microworlds or "computer scenarios" in psychological research]. In H. Gundlach (Ed.), ''Psychologische Forschung und Methode: Das Versprechen des Experiments. [[Festschrift]] für Werner Traxel'' (pp. 53-87). Passau, Germany: Passavia-Universitäts-Verlag.}}
  +
*{{wikicite | id= Dörner1983| reference= Dörner, D., Kreuzig, H. W., Reither, F., & Stäudel, T. (Eds.). (1983). ''Lohhausen. Vom Umgang mit Unbestimmtheit und Komplexität'' [Lohhausen. On dealing with uncertainty and complexity]. Bern, Switzerland: Hans Huber.}}
  +
*{{wikicite | id= Dörner1995| reference= Dörner, D., & Wearing, A. (1995). Complex problem solving: Toward a (computer-simulated) theory. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 65-99). Hillsdale, NJ: Lawrence Erlbaum Associates. }}
  +
*{{wikicite | id= Duncker| reference= Duncker, K. (1935). ''Zur Psychologie des produktiven Denkens'' [The psychology of productive thinking]. Berlin: Julius Springer.}}
  +
*{{wikicite | id= Ewert| reference= Ewert, P. H., & Lambert, J. F. (1932). Part II: The effect of verbal instructions upon the formation of a concept. ''Journal of General Psychology'', 6, 400-411.}}
  +
*{{wikicite | id= Eyferth| reference= Eyferth, K., Schömann, M., & Widowski, D. (1986). Der Umgang von Psychologen mit Komplexität [On how psychologists deal with complexity]. ''Sprache & Kognition'', 5, 11-26.}}
  +
*{{wikicite | id= Frensch1995| reference= Frensch, P. A., & Funke, J. (Eds.). (1995). ''Complex problem solving: The European Perspective''. Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Frensch1991| reference= Frensch, P. A., & Sternberg, R. J. (1991). Skill-related differences in game playing. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 343-381). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Funke1991| reference= Funke, J. (1991). Solving complex problems: Human identification and control of complex systems. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 185-222). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Funke1993| reference= Funke, J. (1993). Microworlds based on linear equation systems: A new approach to complex problem solving and experimental results. In G. Strube & K.-F. Wender (Eds.), ''The cognitive psychology of knowledge'' (pp. 313-330). Amsterdam: Elsevier Science Publishers.}}
  +
*{{wikicite | id= Funke1995a| reference= Funke, J. (1995). Experimental research on complex problem solving. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 243-268). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Funke1995b| reference= Funke, U. (1995). Complex problem solving in personnel selection and training. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 219-240). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
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*{{wikicite | id= Goldstein | reference= Goldstein F. C., & Levin H. S. (1987). Disorders of reasoning and problem-solving ability. In M. Meier, A. Benton, & L. Diller (Eds.), ''Neuropsychological rehabilitation''. London: Taylor & Francis Group.}}
  +
  +
*{{wikicite | id= Groner| reference= Groner, M., Groner, R., & Bischof, W. F. (1983). Approaches to heuristics: A historical review. In R. Groner, M. Groner, & W. F. Bischof (Eds.), ''Methods of heuristics'' (pp. 1-18). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id=Halpern| reference= Halpern, Diane F. (2002).Thought & Knowledge. Lawrence Erlbaum Associates.}} [http://worldcat.org/oclc/50065032&tab=holdings Worldcat Library Catalog]
  +
*{{wikicite | id= Hayes| reference= Hayes, J. (1980). ''The complete problem solver''. Philadelphia: The Franklin Institute Press.}}
  +
*{{wikicite | id= Hegarty| reference= Hegarty, M. (1991). Knowledge and processes in mechanical problem solving. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 253-285). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Heppner| reference= Heppner, P. P., & Krauskopf, C. J. (1987). An information-processing approach to personal problem solving. ''The Counseling Psychologist'', 15, 371-447.}}
  +
*{{wikicite | id= Huber| reference= Huber, O. (1995). Complex problem solving as multi stage decision making. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 151-173). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Hübner| reference= Hübner, R. (1989). Methoden zur Analyse und Konstruktion von Aufgaben zur kognitiven Steuerung dynamischer Systeme [Methods for the analysis and construction of dynamic system control tasks]. ''Zeitschrift für Experimentelle und Angewandte Psychologie'', 36, 221-238.}}
  +
*{{wikicite | id= Hunt| reference= Hunt, E. (1991). Some comments on the study of complexity. In R. J. Sternberg, & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 383-395). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Hussy| reference= Hussy, W. (1985). Komplexes Problemlösen - Eine Sackgasse? [Complex problem solving - a dead end?]. ''Zeitschrift für Experimentelle und Angewandte Psychologie'', 32, 55-77.}}
  +
*{{wikicite | id= Kay| reference= Kay, D. S. (1991). Computer interaction: Debugging the problems. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 317-340). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Kluwe1993| reference= Kluwe, R. H. (1993). Knowledge and performance in complex problem solving. In G. Strube & K.-F. Wender (Eds.), ''The cognitive psychology of knowledge'' (pp. 401-423). Amsterdam: Elsevier Science Publishers.}}
  +
*{{wikicite | id= Kluwe1995| reference= Kluwe, R. H. (1995). Single case studies and models of complex problem solving. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 269-291). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Kolb| reference= Kolb, S., Petzing, F., & Stumpf, S. (1992). Komplexes Problemlösen: Bestimmung der Problemlösegüte von Probanden mittels Verfahren des Operations Research ? ein interdisziplinärer Ansatz [Complex problem solving: determining the quality of human problem solving by operations research tools - an interdisciplinary approach]. ''Sprache & Kognition'', 11, 115-128.}}
  +
*{{wikicite | id= Krems| reference= Krems, J. F. (1995). Cognitive flexibility and complex problem solving. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 201-218). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Lesgold| reference= Lesgold, A., & Lajoie, S. (1991). Complex problem solving in electronics. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 287-316). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Mayer| reference= Mayer, R. E. (1992). ''Thinking, problem solving, cognition''. Second edition. New York: W. H. Freeman and Company.}}
  +
*{{wikicite | id= Müller| reference= Müller, H. (1993). ''Komplexes Problemlösen: Reliabilität und Wissen'' [Complex problem solving: Reliability and knowledge]. Bonn, Germany: Holos.}}
  +
*{{wikicite | id= Newell| reference= Newell, A., & Simon, H. A. (1972). ''Human problem solving''. Englewood Cliffs, NJ: Prentice-Hall.}}
  +
*{{wikicite | id= Paradies| reference= Paradies, M.W., & Unger, L. W. (2000). ''TapRooT - The System for Root Cause Analysis, Problem Investigation, and Proactive Improvement''. Knoxville, TN: System Improvements.}}
  +
*{{wikicite | id= Putz| reference= Putz-Osterloh, W. (1993). Strategies for knowledge acquisition and transfer of knowledge in dynamic tasks. In G. Strube & K.-F. Wender (Eds.), ''The cognitive psychology of knowledge'' (pp. 331-350). Amsterdam: Elsevier Science Publishers.}}
  +
*{{wikicite | id= Riefer| reference= Riefer, D.M., & Batchelder, W.H. (1988). Multinomial modeling and the measurement of cognitive processes. ''Psychological Review'', 95, 318-339.}}
  +
*{{wikicite | id= Ringelband| reference= Ringelband, O. J., Misiak, C., & Kluwe, R. H. (1990). Mental models and strategies in the control of a complex system. In D. Ackermann, & M. J. Tauber (Eds.), ''Mental models and human-computer interaction'' (Vol. 1, pp. 151-164). Amsterdam: Elsevier Science Publishers.}}
  +
*{{wikicite | id= Schaub| reference= Schaub, H. (1993). ''Modellierung der Handlungsorganisation''. Bern, Switzerland: Hans Huber.}}
  +
*{{wikicite | id= Sokol| reference= Sokol, S. M., & McCloskey, M. (1991). Cognitive mechanisms in calculation. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 85-116). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Stanovich| reference= Stanovich, K. E., & Cunningham, A. E. (1991). Reading as constrained reasoning. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 3-60). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Sternberg1995| reference= Sternberg, R. J. (1995). Conceptions of expertise in complex problem solving: A comparison of alternative conceptions. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 295-321). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Sternberg1991| reference= Sternberg, R. J., & Frensch, P. A. (Eds.). (1991). ''Complex problem solving: Principles and mechanisms''. Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Strauß| reference= Strauß, B. (1993). ''Konfundierungen beim Komplexen Problemlösen. Zum Einfluß des Anteils der richtigen Lösungen (ArL) auf das Problemlöseverhalten in komplexen Situationen'' [Confoundations in complex problem solving. On the influence of the degree of correct solutions on problem solving in complex situations]. Bonn, Germany: Holos.}}
  +
*{{wikicite | id= Strohschneider| reference= Strohschneider, S. (1991). Kein System von Systemen! Kommentar zu dem Aufsatz "Systemmerkmale als Determinanten des Umgangs mit dynamischen Systemen" von Joachim Funke [No system of systems! Reply to the paper "System features as determinants of behavior in dynamic task environments" by Joachim Funke]. ''Sprache & Kognition'', 10, 109-113.}}
  +
*{{wikicite | id= Van | reference= Van Lehn, K. (1989). Problem solving and cognitive skill acquisition. In M. I. Posner (Ed.), ''Foundations of cognitive science'' (pp. 527-579). Cambridge, MA: MIT Press.}}
  +
*{{wikicite | id= Voss| reference= Voss, J. F., Wolfe, C. R., Lawrence, J. A., & Engle, R. A. (1991). From representation to decision: An analysis of problem solving in international relations. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 119-158). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Wagner| reference= Wagner, R. K. (1991). Managerial problem solving. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 159-183). Hillsdale, NJ: Lawrence Erlbaum Associates.}}
  +
*{{wikicite | id= Wisconsin | reference= Wisconsin Educational Media Association. (1993). "Information literacy: A position paper on information problem-solving." Madison, WI: WEMA Publications. (ED 376 817). (Portions adapted from Michigan State Board of Education's Position Paper on Information Processing Skills, 1992).}}
  +
* {{cite book
  +
| last = Altshuller
  +
| first = Genrich
  +
| year = 1973
  +
| title = Innovation Algorithm
  +
| location = Worcester, MA
  +
| publisher = Technical Innovation Center
  +
| isbn = 0-9640740-2-8
  +
}}
  +
* {{cite book
  +
| last = Altshuller
  +
| first = Genrich
  +
| year = 1984
  +
| title = Creativity as an Exact Science
  +
| location = New York, NY
  +
| publisher = Gordon & Breach
  +
| isbn = 0-677-21230-5
  +
}}
  +
* {{cite book
  +
| last = Altshuller
  +
| first = Genrich
  +
| year = 1994
  +
| title = And Suddenly the Inventor Appeared
  +
| others = translated by Lev Shulyak
  +
| location = Worcester, MA
  +
| publisher = Technical Innovation Center
  +
| isbn = 0-9640740-1-X
  +
}}
  +
  +
</div>
   
 
==External links==
  
==External links==
−
* [http://www.lifeskills.endlex.com/article/solving_problems.html How to Solve Problems: Constructive Approaches to Improving Problem-Solving Skills]
  
−
* [http://www.nextd.org/02/01/01/index.html Innovation Teaching HOW Now! from NextD Journal]
  
 
* [http://www.ericdigests.org/1996-4/skills.htm Computer Skills for Information Problem-Solving: Learning and Teaching Technology in Context]
  
* [http://www.ericdigests.org/1996-4/skills.htm Computer Skills for Information Problem-Solving: Learning and Teaching Technology in Context]
−
* [http://www.ericdigests.org/1993/early.htm Problem Solving in Early Childhood Classrooms]
  
−
* [http://www.ericdigests.org/pre-9212/problem.htm Teaching Problem Solving--Secondary School Science]
  
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* [http://www.ericdigests.org/pre-9213/cooperative.htm Cooperative Problem-Solving in the Classroom]
  
 
* [http://moodle.ed.uiuc.edu/wiked/index.php/Problem_solving-Elementary_level Problem solving-Elementary level]
  
* [http://moodle.ed.uiuc.edu/wiked/index.php/Problem_solving-Elementary_level Problem solving-Elementary level]
 
* [http://ceap.wcu.edu/houghton/Learner/basicidea.html CROP (Communities Resolving Our Problems)]
  
* [http://ceap.wcu.edu/houghton/Learner/basicidea.html CROP (Communities Resolving Our Problems)]
 
* [http://www.teach-kids-math-by-model-method.com Teach Kids Math With Model Method]
  
* [http://www.teach-kids-math-by-model-method.com Teach Kids Math With Model Method]
  +
* [http://www.aitriz.org The Altshuller Institute for TRIZ Studies, Worcester, MA]
−
* [http://sfhelp.org/02/prblmslv.htm Nine steps to effective verbal problem solving (article)]
  
−
* [http://www.giacomo.lorenzoni.name/solprobcombengl/ The solution of a combinatorial problem]
  
−
* [http://www.problemistics.org/courseware/front.page.html Problemistics. A courseware on problem finding & problem solving]
  
−
* [http://3form.com Online problem-solving community]
  
   
−
== References ==
  
−
<div class="references-small">
  
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*Amsel, E., Langer, R., & Loutzenhiser, L. (1991). Do lawyers reason differently from psychologists? A comparative design for studying expertise. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 223-250). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
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*Anderson, J. R., Boyle, C. B., & Reiser, B. J. (1985). Intelligent tutoring systems. ''Science'', 228, 456-462.
  
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*Anzai, K., & Simon, H. A. (1979). The theory of learning by doing. ''Psychological Review'', 86, 124-140.
  
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*Beckmann, J. F., & Guthke, J. (1995). Complex problem solving, intelligence, and learning ability. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 177-200). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
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*Berry, D. C., & Broadbent, D. E. (1995). Implicit learning in the control of complex systems: A reconsideration of some of the earlier claims. In P.A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 131-150). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
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*Bhaskar, R., & Simon, H. A. (1977). Problem solving in semantically rich domains: An example from engineering thermodynamics. ''Cognitive Science'', 1, 193-215.
  
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*Brehmer, B. (1995). Feedback delays in dynamic decision making. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 103-130). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
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*Brehmer, B., & Dörner, D. (1993). Experiments with computer-simulated microworlds: Escaping both the narrow straits of the laboratory and the deep blue sea of the field study. ''Computers in Human Behavior'', 9, 171-184.
  
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*Broadbent, D. E. (1977). Levels, hierarchies, and the locus of control. ''Quarterly Journal of Experimental Psychology'', 29, 181-201.
  
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*Bryson, M., Bereiter, C., Scardamalia, M., & Joram, E. (1991). Going beyond the problem as given: Problem solving in expert and novice writers. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 61-84). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
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*Buchner, A. (1995). Theories of complex problem solving. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 27-63). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
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*Buchner, A., Funke, J., & Berry, D. C. (1995). Negative correlations between control performance and verbalizable knowledge: Indicators for implicit learning in process control tasks? ''Quarterly Journal of Experimental Psychology'', 48A, 166-187.
  
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*Chase, W. G., & Simon, H. A. (1973). Perception in chess. ''Cognitive Psychology'', 4, 55-81.
  
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*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science'', 5, 121-152.
  
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*Dörner, D. (1975). Wie Menschen eine Welt verbessern wollten [How people wanted to improve the world]. ''Bild der Wissenschaft'', 12, 48-53.
  
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*Dörner, D. (1985). Verhalten, Denken und Emotionen [Behavior, thinking, and emotions]. In L. H. Eckensberger & E. D. Lantermann (Eds.), ''Emotion und Reflexivität'' (pp. 157-181). München, Germany: Urban & Schwarzenberg.
  
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*Dörner, D. (1992). Über die Philosophie der Verwendung von Mikrowelten oder "Computerszenarios" in der psychologischen Forschung [On the proper use of microworlds or "computer scenarios" in psychological research]. In H. Gundlach (Ed.), ''Psychologische Forschung und Methode: Das Versprechen des Experiments. [[Festschrift]] für Werner Traxel'' (pp. 53-87). Passau, Germany: Passavia-Universitäts-Verlag.
  
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*Dörner, D., Kreuzig, H. W., Reither, F., & Stäudel, T. (Eds.). (1983). ''Lohhausen. Vom Umgang mit Unbestimmtheit und Komplexität'' [Lohhausen. On dealing with uncertainty and complexity]. Bern, Switzerland: Hans Huber.
  
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*Dörner, D., & Wearing, A. (1995). Complex problem solving: Toward a (computer-simulated) theory. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 65-99). Hillsdale, NJ: Lawrence Erlbaum Associates.
 
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*Duncker, K. (1935). ''Zur Psychologie des produktiven Denkens'' [The psychology of productive thinking]. Berlin: Julius Springer.
  
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*Ernst, G.W. and Newell, A. (1969) GPS: a Case Study in Generality and Problem Solving, London: Academic Press
  
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*Ewert, P. H., & Lambert, J. F. (1932). Part II: The effect of verbal instructions upon the formation of a concept. ''Journal of General Psychology'', 6, 400-411.
  
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*Eyferth, K., Schömann, M., & Widowski, D. (1986). Der Umgang von Psychologen mit Komplexität [On how psychologists deal with complexity]. ''Sprache & Kognition'', 5, 11-26.
  
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*Frensch, P. A., & Funke, J. (Eds.). (1995). ''Complex problem solving: The European Perspective''. Hillsdale, NJ: Lawrence Erlbaum Associates.
  
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*Frensch, P. A., & Sternberg, R. J. (1991). Skill-related differences in game playing. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 343-381). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
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*Funke, J. (1991). Solving complex problems: Human identification and control of complex systems. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 185-222). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
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*Funke, J. (1993). Microworlds based on linear equation systems: A new approach to complex problem solving and experimental results. In G. Strube & K.-F. Wender (Eds.), ''The cognitive psychology of knowledge'' (pp. 313-330). Amsterdam: Elsevier Science Publishers.
  
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*Funke, J. (1995). Experimental research on complex problem solving. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 243-268). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Funke, U. (1995). Complex problem solving in personnel selection and training. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 219-240). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Gick, M.L. and Holyoak, K.J. (1980) Analogical problem solving, Cognitive Psychology 12: 306-55.
  
−
*Groner, M., Groner, R., & Bischof, W. F. (1983). Approaches to heuristics: A historical review. In R. Groner, M. Groner, & W. F. Bischof (Eds.), ''Methods of heuristics'' (pp. 1-18). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Hayes, J. (1980). ''The complete problem solver''. Philadelphia: The Franklin Institute Press.
  
−
*Hegarty, M. (1991). Knowledge and processes in mechanical problem solving. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 253-285). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Heppner, P. P., & Krauskopf, C. J. (1987). An information-processing approach to personal problem solving. ''The Counseling Psychologist'', 15, 371-447.
  
−
*Huber, O. (1995). Complex problem solving as multi stage decision making. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 151-173). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Hübner, R. (1989). Methoden zur Analyse und Konstruktion von Aufgaben zur kognitiven Steuerung dynamischer Systeme [Methods for the analysis and construction of dynamic system control tasks]. ''Zeitschrift für Experimentelle und Angewandte Psychologie'', 36, 221-238.
  
−
*Hunt, E. (1991). Some comments on the study of complexity. In R. J. Sternberg, & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 383-395). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Hussy, W. (1985). Komplexes Problemlösen - Eine Sackgasse? [Complex problem solving - a dead end?]. ''Zeitschrift für Experimentelle und Angewandte Psychologie'', 32, 55-77.
  
−
*Kay, D. S. (1991). Computer interaction: Debugging the problems. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 317-340). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Kluwe, R. H. (1993). Knowledge and performance in complex problem solving. In G. Strube & K.-F. Wender (Eds.), ''The cognitive psychology of knowledge'' (pp. 401-423). Amsterdam: Elsevier Science Publishers.
  
−
*Kluwe, R. H. (1995). Single case studies and models of complex problem solving. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 269-291). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Kolb, S., Petzing, F., & Stumpf, S. (1992). Komplexes Problemlösen: Bestimmung der Problemlösegüte von Probanden mittels Verfahren des Operations Research ? ein interdisziplinärer Ansatz [Complex problem solving: determining the quality of human problem solving by operations research tools - an interdisciplinary approach]. ''Sprache & Kognition'', 11, 115-128.
  
−
*Krems, J. F. (1995). Cognitive flexibility and complex problem solving. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 201-218). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Lesgold, A., & Lajoie, S. (1991). Complex problem solving in electronics. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 287-316). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Luchins, A.S. (1942) Mechanisation in problem-solving:the effects of Einstellung, Psychological Monographs 54: no- 248.
  
−
*Mayer, R. E. (1992). ''Thinking, problem solving, cognition''. Second edition. New York: W. H. Freeman and Company.
  
−
*Müller, H. (1993). ''Komplexes Problemlösen: Reliabilität und Wissen'' [Complex problem solving: Reliability and knowledge]. Bonn, Germany: Holos.
  
−
*Newell, A., & Simon, H. A. (1972). ''Human problem solving''. Englewood Cliffs, NJ: Prentice-Hall.
  
−
*Paradies, M.W., & Unger, L. W. (2000). ''TapRooT - The System for Root Cause Analysis, Problem Investigation, and Proactive Improvement''. Knoxville, TN: System Improvements.
  
−
*Putz-Osterloh, W. (1993). Strategies for knowledge acquisition and transfer of knowledge in dynamic tasks. In G. Strube & K.-F. Wender (Eds.), ''The cognitive psychology of knowledge'' (pp. 331-350). Amsterdam: Elsevier Science Publishers.
  
−
*Riefer, D.M., & Batchelder, W.H. (1988). Multinomial modeling and the measurement of cognitive processes. ''Psychological Review'', 95, 318-339.
  
−
*Ringelband, O. J., Misiak, C., & Kluwe, R. H. (1990). Mental models and strategies in the control of a complex system. In D. Ackermann, & M. J. Tauber (Eds.), ''Mental models and human-computer interaction'' (Vol. 1, pp. 151-164). Amsterdam: Elsevier Science Publishers.
  
−
*Schaub, H. (1993). ''Modellierung der Handlungsorganisation''. Bern, Switzerland: Hans Huber.
  
−
*Sokol, S. M., & McCloskey, M. (1991). Cognitive mechanisms in calculation. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 85-116). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Stanovich, K. E., & Cunningham, A. E. (1991). Reading as constrained reasoning. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 3-60). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Sternberg, R. J. (1995). Conceptions of expertise in complex problem solving: A comparison of alternative conceptions. In P. A. Frensch & J. Funke (Eds.), ''Complex problem solving: The European Perspective'' (pp. 295-321). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Sternberg, R. J., & Frensch, P. A. (Eds.). (1991). ''Complex problem solving: Principles and mechanisms''. Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Strauß, B. (1993). ''Konfundierungen beim Komplexen Problemlösen. Zum Einfluß des Anteils der richtigen Lösungen (ArL) auf das Problemlöseverhalten in komplexen Situationen'' [Confoundations in complex problem solving. On the influence of the degree of correct solutions on problem solving in complex situations]. Bonn, Germany: Holos.
  
−
*Strohschneider, S. (1991). Kein System von Systemen! Kommentar zu dem Aufsatz "Systemmerkmale als Determinanten des Umgangs mit dynamischen Systemen" von Joachim Funke [No system of systems! Reply to the paper "System features as determinants of behavior in dynamic task environments" by Joachim Funke]. ''Sprache & Kognition'', 10, 109-113.
  
−
*Van Lehn, K. (1989). Problem solving and cognitive skill acquisition. In M. I. Posner (Ed.), ''Foundations of cognitive science'' (pp. 527-579). Cambridge, MA: MIT Press.
  
−
*Voss, J. F., Wolfe, C. R., Lawrence, J. A., & Engle, R. A. (1991). From representation to decision: An analysis of problem solving in international relations. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 119-158). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Wagner, R. K. (1991). Managerial problem solving. In R. J. Sternberg & P. A. Frensch (Eds.), ''Complex problem solving: Principles and mechanisms'' (pp. 159-183). Hillsdale, NJ: Lawrence Erlbaum Associates.
  
−
*Wisconsin Educational Media Association. (1993). "Information literacy: A position paper on information problem-solving." Madison, WI: WEMA Publications. (ED 376 817). (Portions adapted from Michigan State Board of Education's Position Paper on Information Processing Skills, 1992).
  
−
</div>
  
   
 
[[Category:Problem solving| ]]
  
[[Category:Problem solving| ]]
 
[[Category:Cognition]]
  
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[[category:Cognitive processes]]
 
[[Category:Educational psychology]]
  
[[Category:Educational psychology]]
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[[Category:Neuropsychological assessment]]
   
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{{enWP|Problem solving}}
  
{{enWP|Problem solving}}

Revision as of 11:33, 4 January 2011

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Cognitive Psychology: Attention · Decision making · Learning · Judgement · Memory · Motivation · Perception · Reasoning · Thinking  - Cognitive processes Cognition - Outline Index

Neuropsychology
Brain animated color nevit

Topics
Brain functions

Arousal • Attention
Concentration • Consciousness
Decision-making • Executive functions
Language • Learning • Memory
Motor coordination • Perception
Planning • Problem solving
Thinking

People

Arthur L. Benton • Antonio Damasio
Phineas Gage • Norman Geschwind
Donald Hebb • Alexander Luria •
Muriel D. Lezak • Brenda Milner
Karl Pribram • Oliver Sacks
Roger Sperry

Tests

Bender-Gestalt Test
Benton Visual Retention Test
Clinical Dementia Rating
Continuous Performance Task
Hayling and Brixton tests
Lexical decision task
Mini mental state examination
Stroop task
Wechsler Adult Intelligence Scale
Wisconsin card sorting task

Problem solving forms part of thinking. Considered the most complex of all intellectual functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of more routine or fundamental skills (Goldstein & Levin, 1987). It occurs if an organism or an artificial intelligence system does not know how to proceed from a given state to a desired goal state. It is part of the larger problem process that includes problem finding and problem shaping.

Overview

The nature of human problem solving methods has been studied by psychologists over the past hundred years. There are several methods of studying problem solving, including; introspection, behaviorism, simulation and computer modeling, and experiment.

Beginning with the early experimental work of the Gestaltists in Germany (e.g. Duncker, 1935), and continuing through the 1960s and early 1970s, research on problem solving typically conducted relatively simple, laboratory tasks (e.g. Duncker's "X-ray" problem; Ewert & Lambert's 1932 "disk" problem, later known as Tower of Hanoi) that appeared novel to participants (e.g. Mayer, 1992). Various reasons account for the choice of simple novel tasks: they had clearly defined optimal solutions, they were solvable within a relatively short time frame, researchers could trace participants' problem-solving steps, and so on. The researchers made the underlying assumption, of course, that simple tasks such as the Tower of Hanoi captured the main properties of "real world" problems, and that the cognitive processes underlying participants' attempts to solve simple problems were representative of the processes engaged in when solving "real world" problems. Thus researchers used simple problems for reasons of convenience, and thought generalizations to more complex problems would become possible. Perhaps the best-known and most impressive example of this line of research remains the work by Newell and Simon (1972).

Europe

In Europe, two main approaches have surfaced, one initiated by Donald Broadbent (1977; see Berry & Broadbent, 1995) in the United Kingdom and the other one by Dietrich Dörner (1975, 1985; see Dörner & Wearing, 1995) in Germany. The two approaches have in common 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, however. 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 (e.g., Dörner, Kreuzig, Reither & Stäudel's 1983 LOHHAUSEN project; Ringelband, Misiak & Kluwe, 1990). Buchner (1995) describes the two traditions in detail.

To sum up, researchers' realization that problem-solving processes differ across knowledge domains and across levels of expertise (e.g. Sternberg, 1995) and that, consequently, findings obtained in the laboratory cannot necessarily generalize to problem-solving situations outside the laboratory, has during the past two decades led to an emphasis on real-world problem solving. 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 (see Funke, 1991, for an overview).

USA and Canada

In North America, initiated by the work of Herbert Simon on learning by doing in semantically rich domains (e.g. Anzai & Simon, 1979; Bhaskar & Simon, 1977), researchers began to investigate problem solving separately in different natural knowledge domains - such as physics, writing, or chess playing - thus relinquishing their attempts to extract a global theory of problem solving (e.g. Sternberg & Frensch, 1991). Instead, these researchers have frequently focused on the development of problem solving within a certain domain, that is on the development of expertise (e.g. Anderson, Boyle & Reiser, 1985; Chase & Simon, 1973; Chi, Feltovich & Glaser, 1981).

Areas that have attracted rather intensive attention in North America include such diverse fields as:

Characteristics of difficult problems

As elucidated by Dietrich Dörner and later expanded upon by Joachim Funke, difficult problems have some typical characteristics that can be summarized as follows:

  • Intransparency (lack of clarity of the situation)
    • commencement opacity
    • continuation opacity
  • Polytely (multiple goals)
    • inexpressiveness
    • opposition
    • transience
  • Complexity (large numbers of items, interrelations, and decisions)
    • enumerability
    • connectivity (hierarchy relation, communication relation, allocation relation)
    • heterogeneity
  • Dynamics (time considerations)
    • temporal constraints
    • temporal sensitivity
    • phase effects
    • dynamic unpredictability

The resolution of difficult problems requires a direct attack on each of these characteristics that are encountered.

In reform mathematics, greater emphasis is placed on problem solving relative to basic skills, where basic operations can be done with calculators. However some "problems" may actually have standard solutions taught in higher grades. For example, kindergarteners could be asked how many fingers are there on all the gloves of 3 children, which can be solved with multiplication. [1]

Problem-solving techniques

  • Abstraction: solving the problem in a model of the system before applying it to the real system
  • Analogy: using a solution that solved an analogous problem
  • Brainstorming: (especially among groups of people) suggesting a large number of solutions or ideas and combining and developing them until an optimum is found
  • Divide and conquer: breaking down a large, complex problem into smaller, solvable problems
  • 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
  • Method of focal objects: synthesizing seemingly non-matching characteristics of different objects into something new
  • Morphological analysis: assessing the output and interactions of an entire system
  • 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: eliminating the cause of the problem
  • Trial-and-error: testing possible solutions until the right one is found
  1. Working Backwards (Halpern,2002)
  2. Forward-Looking Strategy (Halpern, 2002)
  3. Simplification (Halpern, 2002)
  4. Generalization (Halpern, 2002)
  5. Specialization (Halpern, 2002)
  6. Random Search (Halpern, 2002)
  7. Split-Half Method (Halpern,2002)

Problem-solving methodologies

  • Eight Disciplines Problem Solving
  • GROW model
  • How to solve it
  • Kepner-Tregoe
  • Southbeach Notation
  • PDCA
  • RPR Problem Diagnosis
  • TRIZ (Teoriya Resheniya Izobretatelskikh Zadatch, "theory of solving inventor's problems")


See also

Notes

  1. ↑ 2007 Draft, Washington State Revised Mathematics Standard

References

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