Evidence for use of mathematical inversion by three-year-old children

Journal of Cognition and Development

Volumn 8, Issue 3, 2007, Pages 333-344

  Sherman, Jody ^a   Bisanz, Jeffrey ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ARITHMETIC; ARTICLE; COGNITION; CONCEPT ANALYSIS; CONCEPT FORMATION; HUMAN; HUMAN EXPERIMENT; MENTAL PERFORMANCE; MOTOR PERFORMANCE; NORMAL HUMAN; PRESCHOOL CHILD; PROBLEM SOLVING; QUALITATIVE ANALYSIS; QUANTITATIVE ANALYSIS; SENSITIVITY AND SPECIFICITY; TASK PERFORMANCE; THINKING;

EID: 34848874734     PISSN: 15248372     EISSN: None     Source Type: Journal    
DOI: 10.1080/15248370701446798     Document Type: Article

References (24)

1. Bisanz, J., & LeFevre, J. (1990). Strategic and nonstrategic processing in the development of mathematical cognition. In D. F. Bjorkland (Ed.), Children's strategies: Contemporary views of cognitive development (pp. 213-244). Hillsdale, N J: Lawrence Erlbaum Associates.
2. Bisanz, J., Sherman, J., Rasmussen, C., & Ho, E. (2005). Development of arithmetic skills and knowledge in preschool children. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 143-162). New York: Psychology Press.
3. Bryant, P., Christie, C., & Rendu, A. (1999). Children's understanding of the relation between addition and subtraction: Inversion, identity, and decomposition. Journal of Experimental Child Psychology, 74, 194-212.
4. Canobi, K. H. (2005). Children's profiles of addition and subtraction understanding. Journal of Experimental Child Psychology, 92, 220-246.
5. Cordes, S., & Gelman, R. (2005). The young numerical mind: When does it count? In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 127-142). New York: Psychology Press.
6. Dehaene, S. (1991). Varieties of numerical abilities. In S. Dehaene (Ed.), Numerical cognition (pp. 1-42). Amsterdam, the Netherlands: Elsevier Science Publishers.
7. Fayol, M., & Seron, X. (2005). About numerical representations: Insights from neuropsychological, experimental, and developmental studies. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 3-22). New York: Psychology Press.
8. Feigenson, L., Carey, S., & Spelke, E. (2002). Infant's discrimination of number versus continuous extent. Cognitive Psychology, 44, 33-66.
9. Hughes, M. (1981). Can preschool children add and subtract? Educational Psychology, 1, 207-219.
10. Huttenlocher, J., Jordan, N. C., & Levine, S. C. (1994). A mental model for early arithmetic. Journal of Experimental Psychology: General, 123, 284-296.
11. Kahneman, D., Treisman, A., & Gibbs, B. J. (1992). The reviewing of object files: Object-specific integration of information. Cognitive Psychology, 24, 175-219.
12. Klahr, D. (1984). Transition processes in quantitative development. In R. J. Sternberg (Ed.), Mechanisms of cognitive development (pp. 101-139). New York: Freeman.
13. Klahr, D., & Wallace, J. G. (1976). Cognitive development: An information processing view. Hillsdale, NJ: Lawrence Erlbaum Associates.
14. Klein, J., & Bisanz, J. (2000). Preschoolers doing arithmetic: The concepts are willing but the working memory is weak. Canadian Journal of Experimental Psychology, 54, 105-115.
15. Mix, K. S., Huttenlocher, J., & Levine, S., C. (2002). Multiple cues for quantification in infancy: Is number one of them? Psychological Bulletin, 128, 278-294.
16. Piaget, J. (1952). The child's conception of number. London: Routledge & Keagan Paul.
17. Rasmussen, C., Ho, E., & Bisanz, J. (2003). Use of the mathematical principle of inversion in young children. Journal of Experimental Child Psychology, 85, 89-102.
18. Siegler, R. S., & Stern, E. (1998). Conscious and unconscious strategy discoveries: A microgenetic analysis. Journal of Experimental Psychology: General, 127, 377-397.
19. Simon, T. J. (1997). Reconceptualizing the origins of number knowledge: A "non-numericalaccount. Cognitive Development, 12, 349-372.
20. Simon, T. J.& Klahr, D.(1995) A computational theory of children's learning about number conservation. In T. J. Simon & G. S. Halford (Eds.), Developing cognitive competence: New approaches to process modeling (pp. 315-353). Hillsdale, NJ: Lawrence Erlbaum Associates.
21. Sophian, C., & Adams, N. (1987). Infants' understanding of numerical transformations. British Journal of Developmental Psychology, 5, 257-264.
22. Starkey, P. (1992). The early developmental of numerical reasoning. Cognition, 43, 93-126.
23. Starkey, P., & Gelman, R. (1982). The development of addition and subtraction abilities prior to formal schooling in arithmetic. In T.P. Carpenter, J.M. Moser, & T.A. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 99-116), Hillsdale, NJ: Lawrence Erlbaum Associates.
24. Vilette, B. (2002). Do young children grasp the inverse relationship between addition and subtraction? Evidence against early arithmetic. Cognitive Development, 17, 1365-1383.