Implications of Cognitive Theory for Instruction in Problem Solving

Cognitive theories of problem solving and suggestions made by cognitive psychologists regarding how to teach problem solving are reviewed. Theories and suggestions from creativity research are also considered. The results are summarized in a description of how high levels of proficiency in problem solving are acquired and how problem solving skills might best be taught, keeping in mind a distinction between well-and ill-structured problems. The need for practice materials is discussed, and some desirable qualities of such materials are suggested. Finally, several unresolved issues regarding instructional methods are considered.

[1]  J. Frederiksen,et al.  Cognitive factors in the recognition of ambiguous auditory and visual stimuli. , 1967, Journal of personality and social psychology.

[2]  Ira Goldstein,et al.  Developing a Computational Representation for Problem Solving Skills , 1978 .

[3]  E. Tulving.  Subjective organization in free recall of "unrelated" words. , 1962, Psychological review.

[4]  R. Sternberg,et al.  Componential Approaches to the Training of Intelligent Performance. , 1980 .

[5]  R. Glaser.  Components of a Psychology of Instruction: Toward a Science of Design , 1976 .

[6]  P. Carpenter,et al.  Individual Differences in Integrating Information between and within Sentences. , 1983 .

[7]  J. Hadamard,et al.  The Psychology of Invention in the Mathematical Field. , 1945 .

[8]  Herbert A. Simon,et al.  Problem solving and education. , 1980 .

[9]  Charles N. Cofer,et al.  Reasoning as an Associative Process: II. “Direction” in Problem Solving as a Function of Prior Reinforcement of Relevant Responses , 1956 .

[10]  D. Moshman.  Development of formal hypothesis-testing ability. , 1979 .

[11]  John Seely Brown,et al.  Artificial Intelligence and Learning Strategies. , 1978 .

[12]  S. Parnes,et al.  Applied Creativity: The Creative Studies Project: Part II--Results of the Two-Year Program. , 1972 .

[13]  Lieven Verschaffel,et al.  Children's solution processes in elementary arithmetic problems: Analysis and improvement. , 1981 .

[14]  Walter Schneider,et al.  Controlled and Automatic Human Information Processing: 1. Detection, Search, and Attention. , 1977 .

[15]  G. Pólya,et al.  How to Solve It , 1945 .

[16]  F. Barron,et al.  Complexity-simplicity as a personality dimension. , 1953, Journal of abnormal psychology.

[17]  Paul J. Feltovich,et al.  Categorization and Representation of Physics Problems by Experts and Novices , 1981, Cogn. Sci..

[18]  P. Johnson,et al.  Psychological reality of physical concepts , 1970 .

[19]  Allen Newell,et al.  Human problem solving: The state of the theory in 1970. , 1971 .

[20]  H. M. Jenkins,et al.  JUDGMENT OF CONTINGENCY BETWEEN RESPONSES AND OUTCOMES. , 1965, Psychological monographs.

[21]  R. Feuerstein,et al.  Instrumental Enrichment: Theoretical Basis, Goals, and Instruments , 1980 .

[22]  H A Simon,et al.  How Big Is a Chunk? , 1974, Science.

[23]  H. F. Gollob,et al.  Social inference as a function of the number of instances and consistency of information presented. , 1973 .

[24]  Paul I. Jacobs,et al.  Evaluating the Teaching of Intelligence1 , 1972 .

[25]  J. Houston.  Information processing and memory , 1981 .

[26]  R. Shavelson.  Methods for examining representations of A subject-matter structure in a student's memory , 1974 .

[27]  William M. Smith,et al.  A Study of Thinking , 1956 .

[28]  P M Wortman,et al.  Medical diagnosis: an information-processing approach. , 1972, Computers and biomedical research, an international journal.

[29]  Charles A. Perfetti,et al.  Discourse Comprehension and Sources of Individual Differences. , 1977 .

[30]  N. Frederiksen,et al.  Effects of models of creative performance on ability to formulate hypotheses. , 1972, Journal of educational psychology.

[31]  D. W. Mackinnon.  PERSONALITY AND THE REALIZATION OF CREATIVE POTENTIAL. , 1965, The American psychologist.

[32]  John R. Frederiksen,et al.  A Componential Theory of Reading Skills and Their Interactions. , 1981 .

[33]  R. Thouless.  Experimental Psychology , 1939, Nature.

[34]  Clifford R. Mynatt,et al.  Confirmation Bias in a Simulated Research Environment: An Experimental Study of Scientific Inference , 1977 .

[35]  James W. Pellegrino,et al.  Cognitive correlates and components in the analysis of individual differences , 1979 .

[36]  David L. Post,et al.  Medical Problem Solving: An Analysis of Clinical Reasoning , 1979 .

[37]  R. Sternberg,et al.  An Aptitude-Strategy Interaction in Linear Syllogistic Reasoning. , 1980 .

[38]  G. A. Miller.  THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[39]  G R Norman,et al.  Clinical experience and the structure of memory. , 1979, Annual Conference on Research in Medical Education. Conference on Research in Medical Education.

[40]  Earl Hunt,et al.  Individual Differences in the Verification of Sentence-Picture Relationships , 1978 .

[41]  G. Wallas.  The art of thought , 1926 .

[42]  R. Cattell.  Theory of fluid and crystallized intelligence: A critical experiment. , 1963 .

[43]  Ronald R. Schmeck,et al.  Individual differences in cognition , 1983 .

[44]  P. Carpenter,et al.  Individual differences in working memory and reading , 1980 .

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

[46]  Donald A. Norman,et al.  A process model for long-term memory. , 1972 .

[47]  Sybil B. Carlson,et al.  DEVELOPMENT OF METHODS FOR SELECTION AND EVALUATION IN UNDERGRADUATE MEDICAL EDUCATION , 1981 .

[48]  P. Preece,et al.  Mapping Cognitive Structure: A Comparison of Methods. , 1976 .

[49]  R. Glaser,et al.  Cognitive Dimensions of Numerical Rule Induction. , 1982 .

[50]  Allen Newell,et al.  Human Problem Solving. , 1973 .

[51]  Richard C. Atkinson,et al.  Human Memory: A Proposed System and its Control Processes , 1968, Psychology of Learning and Motivation.

[52]  Michelene T. H. Chi,et al.  Expertise in Problem Solving. , 1981 .

[53]  Morphological Astronomy , 1948, Nature.

[54]  Herbert A. Simon,et al.  Information-Processing Theory of Human Problem Solving , 1978 .

[55]  C. Adcock,et al.  Primary Mental Abilities. , 1971, The Journal of general psychology.

[56]  J. Guilford,et al.  The nature of human intelligence. , 1968 .

[57]  John R. Frederiksen,et al.  Understanding Anaphora: Rules Used by Readers in Assigning Pronominal Referents. Technical Report No. 3, December 1, 1976 through July 1, 1980. , 1981 .

[58]  Herbert A. Simon,et al.  The Structure of Ill Structured Problems , 1973, Artif. Intell..

[59]  J. Rossman,et al.  The psychology of the inventor : a study of the patentee , 1932 .

[60]  Donald A. Norman,et al.  Analogical Processes in Learning , 1980 .

[61]  M. Levine,et al.  Effects of Goal Specificity on Means-Ends Analysis and Learning. , 1982 .

[62]  Robert F. Stanners,et al.  The Assessment and Modification of Concept Interrelationships , 1983 .

[63]  E. Paul Torrance,et al.  Guiding creative talent , 1962 .

[64]  The future of IQ testing in education , 1979 .

[65]  E. Hunt,et al.  Individual Differences in Cognition: A New Approach to Intelligence , 1973 .

[66]  J. Feldhusen,et al.  Freedom and Play: Catalysts for Creativity , 1972, The Elementary School Journal.

[67]  E. Kris,et al.  Psychoanalytic Explorations in Art , 1952 .

[68]  K. Holyoak,et al.  Schema induction and analogical transfer , 1983, Cognitive Psychology.

[69]  D. Rumelhart,et al.  A system for perception and memory , 1970 .

[70]  Ruth B. Ekstrom,et al.  MANUAL FOR KIT OF REFERENCE TESTS FOR COGNITIVE FACTORS (REVISED 1963) , 1963 .

[71]  W. Montague,et al.  Cognitive process analyses of learning and problem solving , 1980 .

[72]  D. Bobrow,et al.  Representation and Understanding: Studies in Cognitive Science , 1975 .

[73]  Richard C. Anderson,et al.  Schooling and the Acquisition of Knowledge , 1978 .

[74]  E. Bono.  Lateral thinking: Creativity Step by Step , 1970 .

[75]  Donald A. Norman,et al.  Comments on learning: Schemata and memory representation , 1976 .

[76]  T. Shuell.  The effect of instructions to organize for good and poor learners , 1983 .

[77]  Norman Frederiksen,et al.  Construct Validity of Free-Response and Machine-Scorable Forms of a Test. , 1980 .

[78]  Roger L. Dominowski,et al.  Learning to solve insight problems , 1981 .

[79]  Walter Schneider,et al.  Controlled and automatic human information processing: II. Perceptual learning, automatic attending and a general theory. , 1977 .

[80]  J. Greeno,et al.  Natures of problem-solving abilities. , 1978 .

[81]  James G Greeno,et al.  Some Examples of Cognitive Task Analysis with Instructional Implications , 1979, Aptitude, Learning, and Instruction.

[82]  S. Parnes.  Creative behavior guidebook , 1967 .

[83]  Allen and Rosenbloom Paul S. Newell,et al.  Mechanisms of Skill Acquisition and the Law of Practice , 1993 .

[84]  M. Scheerer,et al.  Problem Solving , 1967, Nature.

[85]  W. C. Ward,et al.  MEASURES FOR THE STUDY OF CREATIVITY IN SCIENTIFIC PROBLEM‐SOLVING , 1975 .

[86]  Experimental studies in the training of originality. , 1960 .

[87]  J. P. Guilford,et al.  Creativity: Retrospect and Prospect* , 1970 .

[88]  D E Egan,et al.  Chunking in recall of symbolic drawings , 1979, Memory & cognition.

[89]  E. Feigenbaum.  13 – Information Processing and Memory , 1970 .

[90]  F. Barron.  Creative person and creative process , 1969 .

[91]  J. Guilford.  Cognitive Psychology's Ambiguities: Some Suggested Remedies. , 1982 .

[92]  C. Richard Puff,et al.  Memory Organization and Structure , 1979 .

[93]  Joan I. Heller,et al.  Knowledge structure and problem solving in physics , 1982 .

[94]  D. W. Mackinnon,et al.  The nature and nurture of creative talent. , 1962 .

[95]  Daryl E. Chubin,et al.  Scientists in Organizations: Productive Climates for Research and Development , 1967 .

[96]  Earl David Sacerdoti,et al.  A Structure for Plans and Behavior , 1977 .

[97]  THE LEARNING AND TRANSFER OF DOUBLE-CLASSIFICATION SKILLS: A REPLICATION AND EXTENSION , 1969 .

[98]  R. Rosenfeld.  Anxiety and Learning. , 1978 .

[99]  Robert Glaser,et al.  Trends and Research Questions in Psychological Research on Learning and Schooling , 1979 .

[100]  W. Doyle.  Academic Work , 1983 .

[101]  John Seely Brown,et al.  Diagnostic Models for Procedural Bugs in Basic Mathematical Skills , 1978, Cogn. Sci..

[102]  L. Cronbach,et al.  Aptitudes and instructional methods: A handbook for research on interactions , 1977 .

[103]  R. Cattell,et al.  Abilities : Their Structure , Growth , and Action , 2015 .

[104]  S. Klein,et al.  Anxiety and learning to formulate hypotheses. , 1969, Journal of educational psychology.

[105]  S. P. Marshall.  Procedural networks and production systems in adaptive diagnosis , 1980 .

[106]  Raymond B. Cattell,et al.  A CHECK ON THE THEORY OF FLUID AND CRYSTALLIZED INTELLIGENCE WITH DESCRIPTION OF NEW SUBTEST DESIGNS , 1978 .

[107]  J. Chall.  Literacy: Trends and Explanations , 1983 .

[108]  N. Frederiksen.  The real test bias: Influences of testing on teaching and learning. , 1984 .

[109]  G. Diekhoff.  Testing Through Relationship Judgments. , 1983 .

[110]  F. Reif,et al.  Problem solving and education: Issues in teaching and research , 1980 .

[111]  M. F. Rubinstein.  Patterns of Problem Solving , 1975 .

[112]  John R. Anderson,et al.  Knowledge Compilation: Mechanisms for the Automatization of Cognitive Skills. , 1980 .

[113]  H. Krebs.  The Making of a Scientist , 1967, Nature.

[114]  R. Crutchfield,et al.  Programed instruction and creativity , 1966 .

[115]  J. Smedslund.  THE CONCEPT OF CORRELATION IN ADULTS , 1963 .

[116]  R. Glaser.  Advances in Instructional Psychology , 1978 .

[117]  I. Maltzman,et al.  On the training of originality. , 1960, Psychological review.

[118]  N. Maier.  Reasoning in humans. I. On direction. , 1930 .

[119]  A. D. D. Groot.  Thought and Choice in Chess , 1978 .

[120]  J. Read,et al.  Longitudinal tracking of difficult memory retrievals , 1982, Cognitive Psychology.

[121]  Jay J.J. Christensen-Szalanski,et al.  Physicians' use of probabilistic information in a real clinical setting. , 1981 .

[122]  C. Patrick,et al.  Creative thought in poets , 1935 .

[123]  K. Duncker,et al.  On problem-solving , 1945 .

[124]  S. Parnes,et al.  Guiding Creative Action , 1977 .

[125]  James G. Greeno,et al.  Indefinite Goals in Well-Structured Problems. , 1976 .

[126]  A. D. Fisk,et al.  Concurrent Automatic and Controlled Visual Search: Can Processing Occur Without Resource Cost? , 1982 .

[127]  Jill H. Larkin,et al.  Analysis and Teaching of a General Skill For Studying Scientific Text. , 1976 .

[128]  James G. Greeno,et al.  Acquiring Cognitive Structure by Discovery and Rule Learning. , 1973 .

[129]  Anne Roe,et al.  A psychological study of eminent psychologists and anthropologists, and a comparison with biological and physical scientists. , 1953 .

[130]  K. A. Ericsson,et al.  Verbal reports as data. , 1980 .

[131]  Albert E. Beaton,et al.  Prediction of organizational behavior , 1972 .

[132]  Joe L. Lewis,et al.  What does it mean to be high verbal? , 1975, Cognitive Psychology.

[133]  W. Chase,et al.  Cognitive Skill: Implications for Spatial Skill in Large-Scale Environments. , 1979 .

[134]  Roger C. Schank,et al.  Scripts, plans, goals and understanding: an inquiry into human knowledge structures , 1978 .

[135]  W. Michael.  Cognitive and Affective Components of Creativity in Mathematics and the Physical Sciences , 1976 .

[136]  John R. Anderson,et al.  Concepts, propositions, and schemata: what are the cognitive units? , 1980, Nebraska Symposium on Motivation. Nebraska Symposium on Motivation.

[137]  Richard E. Snow,et al.  Theory and method for research on aptitude processes , 1976 .

[138]  Herbert A. Simon,et al.  Problem Solving in Semantically Rich Domains: An Example from Engineering Thermodynamics , 1977, Cogn. Sci..

[139]  John R. Anderson.  Acquisition of cognitive skill. , 1982 .

[140]  Michael A. Wallach,et al.  Modes of thinking in young children: A study of the creativity-intelligence distinction. , 1965 .

[141]  A. Roe,et al.  Artists and their work. , 1946, Journal of personality.

[142]  Effect of the Number of Pre-Utilization Functions on Functional Fixedness in Problem Solving , 1958 .

[143]  S. Parnes,et al.  Applied Creativity: The Creative Studies Project: Part I -- The Development. , 1972 .

[144]  Judith S Reitman,et al.  Skilled perception in Go: Deducing memory structures from inter-response times , 1976, Cognitive Psychology.

[145]  John Seely Brown,et al.  An Investigation of Computer Coaching for Informal Learning Activities. , 1978 .

[146]  E. Torrance.  Ten Ways of Helping Young Children Gifted in Creative Writing and Speech , 1962 .

[147]  L. O. Brooks,et al.  The facilitation of problem solving by prior exposure to uncommon responses. , 1958, Journal of experimental psychology.

[148]  C. Lunneborg.  Some Information-Processing Correlates Of Measures Of Intelligence. , 1978, Multivariate behavioral research.

[149]  G. A. Ferguson,et al.  Further factorial studies of tests of rigidity. , 1952, Canadian journal of psychology.

[150]  A. R. Hall,et al.  Scientific Thought , 1972, Nature.