On the spontaneous discovery of a mathematical relation during problem solving

Cognitive Science

Volumn 28, Issue 3, 2004, Pages 433-449

  Dixon, James A ^a   Bangert, Ashley S ^b  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Comparison; Discovery; Mathematical relations; Problem solving; Schema abstraction; Structure mapping

Indexed keywords

EID: 2442695430     PISSN: 03640213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cogsci.2003.12.004     Document Type: Article

References (42)

1. Allison, P. D. (1984). Event history analysis: Regression for longitudinal event data. Beverly Hills, CA: Sage.
2. Bernardo A.B.I. Principle explanation and strategic schema abstraction Memory & Cognition 29 2001 627-633
3. Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Belknap Press.
4. Chen Z. Schema induction in children's analogical problem solving Journal of Educational Psychology 91 1999 703-715
5. Dixon J.A. Bangert A. The prehistory of discovery: Precursors of representational change in solving gear-system problems Developmental Psychology 38 2002 918-933
6. Dixon J.A. Dohn M.C. Redescription disembeds relations: Evidence from relational transfer and use in problem solving Memory & Cognition 31 2003 1082-1093
7. Foard C.F. Kemler-Nelson D.G. Holistic and analytic modes of processing: The multiple determinants of perceptual analysis Journal of Experimental Psychology: General 113 1984 94-111
8. Gentner D. Structure-mapping: A theoretical framework for analogy Cognitive Science 7 1983 155-170
9. Gentner D. Markman A.B. Structure mapping in analogy and similarity American Psychologist 52 1997 45-56
10. Gentner D. Medina J. Similarity and the development of rules Cognition 65 1998 263-287
11. Gentner D. Namy L.L. Comparison in the development of categories Cognitive Development 14 1999 487-513
12. Gick M.L. Holyoak K.J. Schema induction and analogical transfer Cognitive Psychology 15 1983 1-39
13. Goldinger S.D. Echoes of echoes? An episodic theory of lexical access Psychological Review 105 1998 251-279
14. Goldstone R.L. Sakamoto Y. The transfer of abstract principles governing complex adaptive systems Cognitive Psychology 46 2003 414-466
15. Gomez R.L. Variability and detection of invariant structure Psychological Science 13 2002 431-436
16. Hintzman D.L. "Schema abstraction" in a multiple-trace memory model Psychological Review 93 1986 411-428
17. Holyoak K.J. Thagard P. Analogical mapping by constraint satisfaction Cognitive Science 13 1989 295-355
18. Hummel J.E. Holyoak K.J. Distributed representations of structure: A theory of analogical access and mapping Psychological Review 104 1997 427-466
19. Kaplan C.A. Simon H.A. In search of insight Cognitive Psychology 22 1990 374-419
20. Keane M.T. What makes an analogy difficult? The effects of order and causal structure on analogical mapping Journal of Experimental Psychology: Learning, Memory, and Cognition 23 1997 946-967
21. Kemler-Nelson D.G. Processing integral dimensions: The whole view Journal of Experimental Psychology: Human Perception and Performance 19 1993 1105-1113
22. Kotovsky L. Gentner D. Comparison and categorization in the development of relational similarity Child Development 67 1996 2797-2822
23. Loewenstein J. Gentner D. Spatial mapping in preschoolers: Close comparisons facilitate far mappings Journal of Cognition and Development 2 2001 189-219
24. Markman A.B. Gentner D. Structural alignment during similarity comparisons Cognitive Psychology 25 1993 431-467
25. Markman A.B. Gentner D. Structure mapping in the comparison process American Journal of Psychology 113 2000 501-538
26. Medin, D. L., & Ross, B. H. (1989). The specific character of abstract thought: Categorization, problem solving, and induction. In R. J. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 5, pp. 189-223). Hillsdale, NJ: Lawrence Erlbaum Associates.
27. Menard, S. (1995). Applied logistic regression analysis. Thousand Oaks, CA: Sage.
28. Mosteller, F., & Tukey, J. W. (1977). Data analysis and regression: A second course in statistics. Reading, MA: Addision-Wesley.
29. Namy L.L. Gentner D. Making a silk purse out of two sow's ears: Young children's use of comparison in category learning Journal of Experimental Psychology: General 131 2002 5-15
30. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
31. Reeves L.M. Weisberg R.W. The role of content and abstract information in analogical transfer Psychological Bulletin 115 1994 381-400
32. Reyna V.F. Brainerd C.J. Fuzzy-trace theory: An interim synthesis Learning and Individual Differences 7 1995 1-75
33. Ross B.H. Remindings and their effects in learning a cognitive skill Cognitive Psychology 16 1984 371-416
34. Ross, B. H. (1989). Remindings in learning and instruction. In S. Vosniadou & A. Ortony (Eds.), Similarity and analogical reasoning (pp. 438-469). Cambridge: Cambridge University Press.
35. Ross B.H. Kennedy P.T. Generalizing from the use of earlier examples in problem solving Journal of Experimental Psychology: Learning, Memory, and Cognition 16 1990 42-55
36. Ross B.H. Warren J.L. Learning abstract relations from using categories Memory & Cognition 5 2002 657-665
37. Ross G. Nelson K. Wetstone H. Tanouye E. Acquisition and generalization of novel object concepts by young language learners Journal of Child Language 13 1986 67-83
38. Schwartz D.L. Black J.B. Shuttling between depictive models and abstract rules: Induction and fallback Cognitive Science 20 1996 457-497
39. Shrager J. Siegler R.S. A model of children's strategy choices and strategy discoveries Psychological Science 9 1998 405-410
40. Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis. New York: Oxford University Press.
41. Ward T.B. Response tempo and separable-integral responding: Evidence for an integral-to-separable processing sequence in visual perception Journal of Experimental Psychology: Human Perception and Performance 9 1983 103-112
42. Wickens, T. D. (1989). Multiway contingency tables for the social sciences. Hillsdale, NJ: Lawrence Erlbaum Associates.