The construction of number concepts

Cognitive Development

Volumn 17, Issue 3-4, 2002, Pages 1345-1363

  Mix, Kelly S ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

Number concepts; One to one correspondence; Variability

Indexed keywords

EID: 0036748409     PISSN: 08852014     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0885-2014(02)00123-5     Document Type: Article

References (36)

1. Braine, M. D. S. (1959). The ontogeny of certain logical operations: Piaget's formulation examined by nonverbal methods. Psychological Monographs, 73 (5, Whole No. 475).
2. Bruner, J. S., Olver, R. R., Greenfield, P. M., et al. (1966). Studies in cognitive growth. New York: Wiley.
3. DeLoache, J. S. (1989). The development of representation in young children. In H. W. Reese (Ed.), Advances in child development and behavior (Vol. 22, pp. 1-39). New York: Academic Press.
4. Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43-74.
5. Gelman, R. (1969). Conservation acquisition: A problem of learning to attend to relevant attributes. Journal of Experimental Child Psychology, 7, 67-87.
6. Gelman, R. (1972). Logical capacity in very young children. Child Development, 43, 75-90.
7. Gelman, R. (1991). Epigenetic foundations of knowledge structures: Initial and transcendent constructions. In S. Carey & R. Gelman (Eds.), Epigenesis of mind: Essays on biology and cognition (pp. 293-322). Hillsdale, NJ: Lawrence Erlbaum.
8. Gelman, R. (1998). Domain specificity in cognitive development: Universals and nonuniversals. In M. Sabourin, F. Craik, & M. Robert (Eds.), Advances in psychological science: Biological and cognitive aspects (pp. 557-579). Hove, UK: Psychology Press.
9. Gelman, R., & Gallistel, C. R. (1978). The childs' understanding of number. Cambridge: Harvard University Press.
10. Gentner, D.,& Rattermann, M. J. (1991). Language and the career of similarity. In S. A. Gelman & J. P. Byrnes (Eds.), Perspectives on language and thought: Interrelations in development (pp. 225-277). London: Cambridge University Press.
11. Huttenlocher, J., Jordan, N., & Levine, S. C. (1994). A mental model for early arithmetic. Journal of Experimental Psychology: General, 123, 284-296.
12. Klibanoff, R. S., & Waxman, S. R. (1998). Preschoolers' acquisition of novel adjectives and the role of basic level kind. In A. Greenhill, M. Hughes, H. Littlefield, & H.Walsh (Eds.), Proceedings of the 22nd annual Boston University conference on language development (pp. 442-453). Somerville, MA: Cascadilla Press.
13. Kotovsky, L., & Gentner, D. (1996). Comparison and categorization in the development of relational similarity. Child Development, 67, 2797-2822.
14. Marzolf, D. P., & DeLoache, J. S. (1994). Transfer in young children's understanding of spatial representations. Child Development, 65, 1-15.
15. Mehler, J., & Bever, T. G. (1967). Cognitive capacity of very young children. Science, 158, 141-142.
16. Mix, K. S. (1999). Similarity and numerical equivalence: Appearances count. Cognitive Development, 14, 269-297.
17. Mix, K. S. (2001). Are number concepts special? Cross-mapping and complexity effects in children's numerical comparisons. Submitted for publication.
18. Mix, K. S. (2002). Evidence for a domain-general account of numerical development: Effects of surface similarity and label knowledge on early numerical comparisons. Submitted for publication.
19. Mix, K. S., Huttenlocher, J., & Levine, S. C. (1996). Do preschool children recognize auditory-visual numerical correspondences? Child Development, 67, 1592-1608.
20. Mix, K. S., Huttenlocher, J., & Levine, S. C. (2002a). Multiple cues for quantification in infancy: Is number one of them? Psychological Bulletin, 128(2), 278-294.
21. Mix, K. S., Huttenlocher, J., & Levine, S. C. (2002b). Quantitative development in infancy and early childhood. New York: Oxford University Press.
22. Nelson, K. (1999). Language in cognitive development: The emergence of the mediated mind. Cambridge: Cambridge University Press.
23. Piaget, J. (1941/1965). The child's conception of number. New York: Norton.
24. Rattermann, M. J., & Gentner, D. (1998). The effect of language on similarity: The use of relational labels improves young children's performance in a mapping task. In K. Holyoak, D. Gentner, & B. Kokinov (Eds.) Advances in analogy research: Integration of theory and data from cognitive computational and neural sciences (pp. 274-282). Sofia: New Bulgarian University.
25. Russac, R. J. (1978). The relation between two strategies of cardinal number: Correspondence and counting. Child Development, 49(3), 728-735.
26. Simon, T. J. (1997). Reconceptualizing the origins of number knowledge: A "non-numerical" account. Cognitive Development, 12, 349-372.
27. Smith, L. B. (1984). Young children's understanding of attributes and dimensions: A comparison of conceptual and linguistic measures. Child Development, 55, 363-380.
28. Smith, L. B. (1993). The concept of same. In R. W. Reese (Ed.), Advances in child development and behavior (Vol. 24, pp. 215-252). New York: Academic Press.
29. Sophian, C. (1997). Beyond competence: The significance of performance for conceptual development. Conitive Development, 12, 281-303.
30. Thelen, E., & Smith, L. B. (1994). A dynamic systems approach to the development of cognition and action. Cambridge: MIT Press.
31. Uller, C., Carey, S., Huntley-Fenner, F., & Klatt, L. (1999). What representations might underlie infant numerical knowledge? Cognitive Development, 14, 1-36.
32. Waxman, S. R., & Hall, D. G. (1993). The development of a linkage between count nouns and object categories: Evidence from 15-21-month-old infants. Child Development, 64, 1224-1241.
33. Wilcox, T. (1999). Object individuation: Infants' use of shape, size, pattern, and color. Cognition, 72, 125-166.
34. Wynn, K. (1990). Childrens understanding of counting. Cognition, 36, 155-193.
35. Wynn, K. (1995). Origins of numerical knowledge. Mathematical Cognition, 1(1), 35-60.
36. Xu, F., & Carey, S. (1996). Infants' metaphysics: The case of numerical identity. Cognitive Psychology, 30, 111-153.