From regularities to concepts: The development of children's understanding of a mathematical relation

Cognitive Development

Volumn 20, Issue 1, 2005, Pages 65-86

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

^a UNIVERSITY OF CONNECTICUT   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Conceptual development; Mathematical concepts; Redescription; Theory revision

Indexed keywords

EID: 16844369502     PISSN: 08852014     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cogdev.2004.12.001     Document Type: Article

References (29)

1. T.M. Achenbach Research in developmental psychology 1978 Free Press New York
2. A. Bell B. Greer L. Grimison & C. Mangan Children's performance on multiplicative word problems: Elements of a descriptive theory Journal for Research in Mathematics Education 20 1989 434-449
3. M. Casasola L.B. Cohen & E. Chiarello Six-month-old infants' categorization of containment in spatial relations Child Development 74 2003 679-693
4. R. Case & Y. Okamoto The role of central conceptual structures in the development of children's thought. Monographs of the Society for Research in Child Development 61 1996 (1-2, Serial No. 246)
5. Z. Chen & D. Klahr All other things being equal: Acquisition and transfer of the control of variables strategy Child Development 70 1999 1098-1120
6. L.B. Cohen H.H. Chaput & C.H. Cashon A constructivist model of infant cognition Cognitive Development 17 2002 1323-1343
7. J.A. Dixon & A. Bangert The prehistory of discovery: Precursors of representational change in solving gear-system problems Developmental Psychology 38 2002 918-933
8. Dixon, J. A., & Bangert, A. (2004). The development of representations and mapping processes in mathematical problem solving. Manuscript submitted for publication
9. J.A. Dixon & M.C. Dohn Redescription disembeds relations: Evidence from relational transfer and use in problem solving Memory & Cognition 31 2003 1082-1093
10. J.A. Dixon & F. Tuccillo Generating initial models for reasoning Journal of Experimental Child Psychology 78 2001 178-212
11. J.A. Dixon J.K. Deets & A. Bangert The representations of the arithmetic operations include functional relationships Memory & Cognition 29 2001 462-477
12. K. Dunbar Concept discovery in a scientific domain Cognitive Science 17 1993 397-434
13. A. Gopnik D.M. Sobel L.E. Schulz & C. Glymour Causal learning mechanisms in very young children: Two-, three-, and four-year-olds infer causal relations from patterns of variation and covariation Developmental Psychology 37 2001 620-629
14. G.S. Halford C.A. Brown & R.M. Thompson Children's concepts of volume and flotation Developmental Psychology 22 1986 218-222
15. A. Karmiloff-Smith Beyond Modularity: A developmental perspective on cognitive science 1992 MIT Press Cambridge, MA
16. P.A. Klaczynski Analytic and heuristic processing influences on adolescent reasoning and decision-making Child Development 72 2001 844-861
17. D. Klahr A.L. Fay & K. Dunbar Heuristics for scientific experimentation: A developmental study Cognitive Psychology 25 1993 211-228
18. J. Klayman & Y. Ha Confirmation, disconfirmation, and information in hypothesis testing Psychological Review 94 1987 211-228
19. L. Kotovsky & D. Gentner Comparison and categorization in the development of relational similarity Child Development 67 1996 2797-2822
20. D. Kuhn A multi-component system that constructs knowledge: Insights from microgenetic study In N. Grannott J. Parziale (Eds.). Microdevelopment: Transition processes in development and learning 2002 Cambridge University Press Cambridge, UK 109-130
21. D. Kuhn What is scientific thinking, and how does it develop? In U. Goswami (Ed.). Blackwell handbook of childhood cognitive development 2002 Blackwell Publishers Malden, MA 371-393
22. D. Kuhn M. Garcia-Mila A. Zohar & C. Andersen Strategies of knowledge acquisition Monographs of the Society for Research in Child Development 60 1995 (4, Serial No. 245)
23. G.D. Logan An instance theory of attention and memory Psychological Review 109 2002 376-400
24. National Council of Teachers of Mathematics Principles and standards for school mathematics 2000 Author Reston, VA
25. S.E. Newstead V.A. Thompson & S.J. Handley Generating alternatives: A key component in human reasoning Memory & Cognition 30 2002 129-137
26. P.C. Quinn C.M. Norris R.N. Pasko Tm.M. Schmader & C. Mash Formation of a categorical representation for the spatial relation between by 6- to 7-month-old infants Visual Cognition 6 1999 569-585
27. B. Rittle-Johnson & M.W. Alibali Conceptual and procedural knowledge in mathematics: Does one lead to the other? Journal of Educational Psychology 91 1999 175-189
28. B. Rittle-Johnson R.S. Siegler & M.W. Alibali Developing conceptual understanding and procedural skill in mathematics: An iterative process Journal of Educational Psychology 93 2001 346-362
29. Schauble The development of scientific reasoning in knowledge-rich contexts Developmental Psychology 32 1996 102-119