23 Reasoning and Problem Solving

This chapter provides a revised review of the psychological literature on reasoning and problem solving. Four classes of deductive reasoning are presented, including rule (mental logic) theories, semantic (mental model) theories, evolutionary theories, and heuristic theories. Major developments in the study of reasoning are also presented such as unified theories of reasoning and neuroscientific evidence for reasoning performance. The section on reasoning concludes with factors that influence reasoning performance, for example, context, instructions, relevance, and emotions. The psychological literature on problem solving is presented by discussing knowledge representations and strategies, including production systems, parallel distributed processing systems, algorithms, and heuristics. Major theories of problem solving are reviewed such as Newell and Simon's theory of problem solving and Anderson's Adaptive Control of Thought—Rational (ACT-R). Next, situated or embodied problem solving, technology-based problem solving, and neuroscientific evidence for problem solving are discussed as new perspectives in the study of problem solving. Finally, the section on problem solving concludes by reviewing mental sets, strategy selection, the effects of experience level, and knowledge on successful problem solving. Keywords: reasoning; problem solving; deduction; cognitive processes; human rationality

[1]  Roisin Donnelly,et al.  Harmonizing technology with interaction in blended problem-based learning , 2010, Comput. Educ..

[2]  M. Braine,et al.  A Theory of If: A Lexical Entry, Reasoning Program, and Pragmatic Principles , 1991 .

[3]  Linden J. Ball,et al.  Belief–logic conflict resolution in syllogistic reasoning: Inspection-time evidence for a parallel-process model , 2008 .

[4]  Michael R. W. Dawson,et al.  A parallel distributed processing model of Wason’s selection task , 2001, Cognitive Systems Research.

[5]  J. Metcalfe,et al.  Intuition in insight and noninsight problem solving , 1987, Memory & cognition.

[6]  Kenneth D. Forbus,et al.  The Roles of Similarity in Transfer: Separating Retrievability From Inferential Soundness , 1993, Cognitive Psychology.

[7]  Allen Newell,et al.  Deduction as verbal reasoning. , 1995 .

[8]  Jonathan Evans,et al.  Suppositions, extensionality, and conditionals: a critique of the mental model theory of Johnson-Laird And Byrne (2002). , 2005, Psychological review.

[9]  S. Ohlsson,et al.  Constraint relaxation and chunk decomposition in insight problem solving , 1999 .

[10]  Alan D. Castel,et al.  Seeing is believing: The effect of brain images on judgments of scientific reasoning , 2008, Cognition.

[11]  R. Dolan,et al.  Dissociation of Mechanisms Underlying Syllogistic Reasoning , 2000, NeuroImage.

[12]  John R. Anderson,et al.  The roles of prefrontal and posterior parietal cortex in algebra problem solving: A case of using cognitive modeling to inform neuroimaging data , 2007, NeuroImage.

[13]  Sangeet Khemlani,et al.  Disjunctive illusory inferences and how to eliminate them , 2009, Memory & cognition.

[14]  Valerie A Thompson,et al.  Confidence and accuracy in deductive reasoning , 2006, Memory & cognition.

[15]  H. Simon,et al.  Studies of Scientific Discovery: Complementary Approaches and Convergent Findings , 1999 .

[16]  J. Sweller.  Instructional Implications of David C. Geary's Evolutionary Educational Psychology , 2008 .

[17]  Kathleen M. Galotti,et al.  Approaches to studying formal and everyday reasoning. , 1989 .

[18]  Michel Tuan Pham.  Emotion and Rationality: A Critical Review and Interpretation of Empirical Evidence , 2007 .

[19]  Jonathan Evans.  In two minds: dual-process accounts of reasoning , 2003, Trends in Cognitive Sciences.

[20]  Glenn Gunzelmann,et al.  Sleep Deprivation and Sustained Attention Performance: Integrating Mathematical and Cognitive Modeling , 2009, Cogn. Sci..

[21]  G. Weary,et al.  Causal uncertainty and metacognitive inferences about goal attainment , 2008 .

[22]  John R. Anderson,et al.  Cognitive Modeling and Intelligent Tutoring , 1990, Artif. Intell..

[23]  R. Sternberg.  The development of linear syllogistic reasoning , 1980 .

[24]  Günther Knoblich,et al.  Investigating the effect of mental set on insight problem solving. , 2008, Experimental psychology.

[25]  A. Damasio,et al.  Insensitivity to future consequences following damage to human prefrontal cortex , 1994, Cognition.

[26]  Jonathan Evans,et al.  Thinking about conditionals: A study of individual differences , 2007, Memory & cognition.

[27]  Richard L. Lewis,et al.  Dual-route processing of complex words: New fMRI evidence from derivational suffixation , 2005, Cognitive, affective & behavioral neuroscience.

[28]  Jennifer L. Ferris,et al.  Lateral inferior prefrontal cortex and anterior cingulate cortex are engaged at different stages in the solution of insight problems , 2009, Proceedings of the National Academy of Sciences.

[29]  Stephen E. Newstead,et al.  Mental models as an explanation of belief bias effects in syllogistic reasoning , 1993, Cognition.

[30]  N. Charness,et al.  Expert Performance Its Structure and Acquisition , 2002 .

[31]  R. Sternberg,et al.  Unities in inductive reasoning , 1983 .

[32]  Vinod Goel,et al.  Explaining modulation of reasoning by belief , 2003, Cognition.

[33]  G. Gigerenzer,et al.  Domain-specific reasoning: Social contracts, cheating, and perspective change , 1992, Cognition.

[34]  Janet E. Davidson,et al.  The Role of Insight in Intellectual Giftedness , 1984 .

[35]  A. Damasio,et al.  Deciding Advantageously Before Knowing the Advantageous Strategy , 1997, Science.

[36]  Nira Liberman,et al.  Hypothesis testing in Wason's selection task: social exchange cheating detection or task understanding , 1996, Cognition.

[37]  R. Sternberg.  Reasoning with determinate and indeterminate linear syllogisms , 1981 .

[38]  R. Sternberg.  Representation and Process in Linear Syllogistic Reasoning. , 1980 .

[39]  M. Braine.  On the Relation Between the Natural Logic of Reasoning and Standard Logic. , 1978 .

[40]  J. Wiley.  Expertise as mental set: The effects of domain knowledge in creative problem solving , 1998, Memory & cognition.

[41]  Vinod Goel,et al.  Anatomy of deductive reasoning , 2007, Trends in Cognitive Sciences.

[42]  R. Sousa.  Reasoning: Logic and Biology: Emotional Inference and Emotions in Reasoning , 2008 .

[43]  William Revelle,et al.  Caffeine, impulsivity, and memory scanning: A comparison of two explanations for the Yerkes-Dodson Effect , 1989 .

[44]  Jeff Shrager,et al.  SCADS: A Model of Children's Strategy Choices and Strategy Discoveries , 1998 .

[45]  P. D. de Jong,et al.  Deductive Reasoning and Social Anxiety: Evidence for a Fear-confirming Belief Bias , 2008, Cognitive Therapy and Research.

[46]  Joshua W. Brown,et al.  Learned Predictions of Error Likelihood in the Anterior Cingulate Cortex , 2005, Science.

[47]  H. Simon,et al.  Perception in chess , 1973 .

[48]  Elena G. Patsenko,et al.  How planful is routine behavior? A selective-attention model of performance in the Tower of Hanoi. , 2010, Journal of experimental psychology. General.

[49]  Michael R. W. Dawson,et al.  PDP networks can provide models that are not mere implementations of classical theories , 1997 .

[50]  Karl Christoph Klauer,et al.  Conditional reasoning in context: a dual-source model of probabilistic inference. , 2010, Journal of experimental psychology. Learning, memory, and cognition.

[51]  John R. Anderson,et al.  Using Brain Imaging to Extract the Structure of Complex Events at the Rational Time Band , 2008, Journal of Cognitive Neuroscience.

[52]  Cameron S. Carter,et al.  Separating semantic conflict and response conflict in the Stroop task: A functional MRI study , 2005, NeuroImage.

[53]  P. Johnson-Laird,et al.  Understanding cumulative risk , 2009 .

[54]  David A. Krauss,et al.  The development of abstract letter representations for reading: Evidence for the role of context , 2009, Cognitive neuropsychology.

[55]  T. Polk,et al.  Lifespan Development and the Brain: Reading, Writing, and Arithmetic in the Brain: Neural Specialization for Acquired Functions , 2006 .

[56]  David P. O'Brien.  Human reasoning includes a mental logic , 2009 .

[57]  Keith J Holyoak,et al.  Pragmatic reasoning schemas , 1985, Cognitive Psychology.

[58]  Myeong-Ho Sohn,et al.  An information-processing model of three cortical regions: evidence in episodic memory retrieval , 2005, NeuroImage.

[59]  Evan Heit,et al.  Modeling the effects of argument length and validity on inductive and deductive reasoning. , 2009, Journal of experimental psychology. Learning, memory, and cognition.

[60]  R. Weisberg,et al.  Following the wrong footsteps: fixation effects of pictorial examples in a design problem-solving task. , 2005, Journal of experimental psychology. Learning, memory, and cognition.

[61]  Donna Torrens.  Individual Differences and the Belief Bias Effect: Mental Models, Logical Necessity, and Abstract Reasoning , 1999 .

[62]  Jonathan A. Fugelsang,et al.  Automatic activation of categorical and abstract analogical relations in analogical reasoning , 2006, Memory & cognition.

[63]  Jonathan Evans,et al.  Reasoning about necessity and possibility : a test of the mental model theory of deduction , 1999 .

[64]  M. Mather.  Emotional Arousal and Memory Binding: An Object-Based Framework , 2007, Perspectives on psychological science : a journal of the Association for Psychological Science.

[65]  G. Gigerenzer,et al.  One-reason decision-making: Modeling violations of expected utility theory , 2008 .

[66]  Maxwell J. Roberts,et al.  Human Reasoning: Deduction Rules or Mental Models, or Both? , 1993 .

[67]  Jean-François Rouet,et al.  Information problem solving instruction: Some cognitive and metacognitive issues , 2008, Comput. Hum. Behav..

[68]  Marsha C. Lovett,et al.  Neural correlates of arithmetic calculation strategies , 2009, Cognitive, affective & behavioral neuroscience.

[69]  Albert T. Corbett,et al.  Cognitive Tutor: Applied research in mathematics education , 2007, Psychonomic bulletin & review.

[70]  K. A. Ericsson,et al.  Long-term working memory. , 1995, Psychological review.

[71]  L. Cosmides.  The logic of social exchange: Has natural selection shaped how humans reason? Studies with the Wason selection task , 1989, Cognition.

[72]  E. Brunswik.  Organismic achievement and environmental probability. , 1943 .

[73]  M. D’Esposito,et al.  The neural basis of the central executive system of working memory , 1995, Nature.

[74]  S. Quartz,et al.  Reason, emotion and decision-making: risk and reward computation with feeling , 2009, Trends in Cognitive Sciences.

[75]  M. Henle.  On the relation between logic and thinking. , 1962, Psychological review.

[76]  Nick Chater,et al.  A rational analysis of the selection task as optimal data selection. , 1994 .

[77]  P. Klaczynski,et al.  Individual differences in conditional reasoning: A dual-process account , 2005 .

[78]  John R. Anderson,et al.  Using fMRI to Test Models of Complex Cognition , 2008, Cogn. Sci..

[79]  Florin Dolcos,et al.  Similarities and Differences in the Neural Correlates of Episodic Memory Retrieval and Working Memory , 2002, NeuroImage.

[80]  M. Osman.  An evaluation of dual-process theories of reasoning , 2004, Psychonomic bulletin & review.

[81]  Lance J. Rips,et al.  Reasoning: Logical Approaches to Human Deductive Reasoning , 2008 .

[82]  Tingyong Feng,et al.  Neural correlates of the “Aha” experiences: Evidence from an fMRI study of insight problem solving , 2010, Cortex.

[83]  K. Stenning,et al.  Image and Language in Human Reasoning: A Syllogistic Illustration , 1997, Cognitive Psychology.

[84]  Using dual-process theory and analogical transfer to explain facilitation on a hypothetico-deductive reasoning task , 2007, Psychological research.

[85]  E. Heit,et al.  Assessing the belief bias effect with ROCs: it's a response bias effect. , 2010, Psychological review.

[86]  Fernand Gobet,et al.  A pattern-recognition theory of search in expert problem solving , 1997 .

[87]  L. Cosmides,et al.  Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty , 1996, Cognition.

[88]  Gerd Gigerenzer,et al.  We favor formal models of heuristics rather than lists of loose dichotomies: a reply to Evans and Over , 2009, Cognitive Processing.

[89]  A. G. Priest,et al.  New light on novice—expert differences in physics problem solving , 1992 .

[90]  Evan Heit,et al.  Relations between inductive reasoning and deductive reasoning. , 2010, Journal of experimental psychology. Learning, memory, and cognition.

[91]  J. Gregory Trafton,et al.  “Like-Me” Simulation as an Effective and Cognitively Plausible Basis for Social Robotics , 2009, Int. J. Soc. Robotics.

[92]  Dennis H. Holding,et al.  Theories of chess skill , 1992 .

[93]  Roger L. Dominowski,et al.  Effects of hints and interpolated activity on solution of an insight problem , 1972 .

[94]  Lael J. Schooler,et al.  From recognition to decisions: Extending and testing recognition-based models for multialternative inference , 2010, Psychonomic bulletin & review.

[95]  Robert J. Sternberg,et al.  A transitive-chain theory of syllogistic reasoning , 1981, Cognitive Psychology.

[96]  K. Dunbar,et al.  How analogies are generated: The roles of structural and superficial similarity , 2000, Memory & cognition.

[97]  Stephen E. Newstead,et al.  Predicting the difficulty of complex logical reasoning problems , 2006 .

[98]  Mitchell J. Nathan,et al.  The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning , 2004 .

[99]  Robert J. Sternberg,et al.  Component Processes in Analogical Reasoning. , 1977 .

[100]  Valerie A. Thompson,et al.  The role of training, alternative models, and logical necessity in determining confidence in syllogistic reasoning , 2009 .

[101]  Jonathan Evans.  On the resolution of conflict in dual process theories of reasoning , 2007 .

[102]  S. Sloman.  The empirical case for two systems of reasoning. , 1996 .

[103]  Jacqueline P. Leighton.  Teaching and Assessing Deductive Reasoning Skills , 2006 .

[104]  T. Gilovich,et al.  Motivated Reasoning and Performance on the was on Selection Task , 2002 .

[105]  Ravit Golan Duncan,et al.  The Role of Domain-Specific Knowledge in Generative Reasoning About Complicated Multileveled Phenomena , 2007 .

[106]  Slava Kalyuga,et al.  Facilitating Flexible Problem Solving: A Cognitive Load Perspective , 2010 .

[107]  Ruth M. J. Byrne,et al.  ‘If’ and the problems of conditional reasoning , 2009, Trends in Cognitive Sciences.

[108]  Jonathan D. Cohen,et al.  Distinct neural substrates for deductive and mathematical processing , 2008, Brain Research.

[109]  Ron Sun,et al.  Incubation, insight, and creative problem solving: a unified theory and a connectionist model. , 2010, Psychological review.

[110]  Jonathan A. Fugelsang,et al.  Connecting long distance: semantic distance in analogical reasoning modulates frontopolar cortex activity. , 2010, Cerebral cortex.

[111]  John R Anderson,et al.  An integrated theory of the mind. , 2004, Psychological review.

[112]  Jennifer Wiley,et al.  Effects of working memory capacity on mental set due to domain knowledge , 2007, Memory & cognition.

[113]  F. Giusberti,et al.  Trait anxiety and reasoning under uncertainty , 2007 .

[114]  J. Donoghue,et al.  Frontal and parietal lobe activation during transitive inference in humans. , 2002, Cerebral cortex.

[115]  Patricia M. Greenfield,et al.  Technology and Informal Education: What Is Taught, What Is Learned , 2009, Science.

[116]  K. Dunbar.  How scientists think: On-line creativity and conceptual change in science. , 1997 .

[117]  Marilyn Ford,et al.  Two modes of mental representation and problem solution in syllogistic reasoning , 1995, Cognition.

[118]  Robert J. Sternberg,et al.  Components of human intelligence , 1983, Cognition.

[119]  R. Sternberg.  Toward a Unified Theory of Human Reasoning. , 1986 .

[120]  D. Sperber,et al.  Relevance theory explains the selection task , 1995, Cognition.

[121]  Jérôme Prado,et al.  Overcoming Perceptual Features in Logical Reasoning: A Parametric Functional Magnetic Resonance Imaging Study , 2007, Journal of Cognitive Neuroscience.

[122]  Herbert A. Simon,et al.  Templates in Chess Memory: A Mechanism for Recalling Several Boards , 1996, Cognitive Psychology.

[123]  N. Chater,et al.  The Probability Heuristics Model of Syllogistic Reasoning , 1999, Cognitive Psychology.