How mathematics propels the development of physical knowledge

Journal of Cognition and Development

Volumn 6, Issue 1, 2005, Pages 65-88

  Schwartz, Daniel L ^a   Martin, Taylor ^b   Pfaffman, Jay ^c  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c UNIVERSITY OF TENNESSEE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; COMPREHENSION; CONTROLLED STUDY; FEMALE; HUMAN; HUMAN EXPERIMENT; KNOWLEDGE; MALE; MATHEMATICAL PHENOMENA; MATHEMATICS; MENTAL DEVELOPMENT; NORMAL HUMAN; PROBLEM SOLVING; QUALITATIVE ANALYSIS; SCHOOL CHILD; TASK PERFORMANCE; TEACHING;

EID: 33645235444     PISSN: 15248372     EISSN: None     Source Type: Journal    
DOI: 10.1207/s15327647jcd0601_5     Document Type: Article

References (35)

1. Ahl, V. A., Moore, C. F., & Dixon, J. A. (1992). Development of intuitive and numerical proportional reasoning. Cognitive Development, 7, 81-108.
2. Baillargeon, R. (1994). How do infants learn about the physical world? Psychological Science, 3, 133-140.
3. Bransford, J. D., & Schwartz, D. L. (1999). Rethinking transfer: A simple proposal with multiple implications. Review of Research in Education, 24, 61-101.
4. Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University Press.
5. Case, R. (1985). Intellectual development: Birth to adulthood. New York: Academic.
6. Case, R., & Okamoto, Y. (1996). The role of central conceptual structures in the development of children's thought. Monographs of the Society for Research in Child Development, 61 (1-2, Serial No. 246).
7. Cole, M. (1996) Cultural psychology: A once and future discipline. Cambridge, MA: Harvard University Press.
8. Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284, 970-974.
9. diSessa, A. A. (1983). Phenomenology and the evolution of intuition. In D. Gentner & A. L. Gentner (Eds.), Mental models (pp. 15-33). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
10. Dixon, J. A., & Moore, C. F. (1996). The developmental role of intuitive principles in choosing mathematical strategies. Developmental Psychology, 32, 241-253.
11. Feynman, R. (1965). The character of physical law. Cambridge, MA: MIT Press.
12. Geary, K. C., Bow-Thomas, C. C., Liu, F., & Siegler, R. S. (1996). Development of arithmetical competencies in Chinese and American children: Influence of age, language and schooling. Child Development, 67, 2022-2044.
13. Gelman, R., & Gallistel, C. R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
14. Ginsburg, H. P. (1982). Children's arithmetic: How they learn it and how you teach it. Austin, TX: PRO-ED.
15. Halford, G. S. (1993). Children's understanding: The development of mental models. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
16. Huttenlocher, J., Jordan, N. C., & Levine, S. C. (1994). A mental model for early arithmetic. Journal of Experimental Psychology: General, 123, 284-296.
17. Kuhn, D. (1974). Inducing development experimentally: Comments on a research paradigm. Developmental Psychology 10, 590-600.
18. Metz, K. E. (1993). Preschooler's developing knowledge of the pan balance: From new representation to transformed problem solving. Cognition & Instruction, 11, 31-93.
19. Nasir, N. (2001). "Points ain't everything": Emergent goals and average and percent understanding in the play of basketball among African-American students. Anthropology and Education Quarterly, 31, 283-305.
20. Peng, K., & Nisbett, R. E. (1999). Culture, dialectics, and reasoning about contradiction. American Psychologist, 54, 741-754.
21. Piaget, J. (1954). The construction of reality in the child (M. Cook, Trans.). New York: Basic Books.
22. Reed, H. J., & Lave, J. (1979). Arithmetic as a tool for investigating the relations between culture and cognition. American Ethnologist, 6, 568-582.
23. Resnick, L. B. (1992). From protoquantities to operators: Building mathematical competence on a foundation of everyday knowledge. In G. Leinhardt, R. T. Putnam, & R. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 373-429). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
24. Saxe, G. B. (2001). Studying cognitive development in sociocultural context: The development of a practice-based approach. In A. Colby & D. Jessor (Eds.), Ethnographic approaches to the study of human development (pp. 275-303). Chicago: University of Chicago Press.
25. Schwartz, D. L., & Black, J. B. (1996). Analog imagery in mental model reasoning: Depictive models. Cognitive Psychology 30, 154-219.
26. Schwartz, D. L., & Moore, J. L. (1998). The role of mathematics in explaining the material world: Mental models for proportional reasoning. Cognitive Science, 22, 471-516.
27. Siegler, R. S. (1976). Three aspects of cognitive development. Cognitive Psychology 8, 481-520.
28. Siegler, R. S. (1981). Developmental sequences within and between concepts. Monographs of the Society for Research in Child Development, 46(2, Serial No. 189).
29. Spelke, E. S. (2000). Core knowledge. American Psychologist, 55, 1233-1243.
30. Spinillo, A. G., & Bryant, P. (1991). Children's proportional judgments: The importance of "half." Child Development, 62, 427-440.
31. Starkey, P. (1992). The early development of numerical reasoning. Cognition, 43, 93-126.
32. Stavy, R., & Tirosh, D. (2000). How students (mis-)understand science and mathematics. New York: Teachers College Press.
33. Surber, C. F., & Haines, B. A. (1987). The growth of proportional reasoning: Methodological issues. Annals of Child Development, 4, 35-87.
34. Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Harvard University Press.
35. White, B. (1993). ThinkerTools: Causal models, conceptual change and science education. Cognition and Instruction, 10, 1-100.