The Idea of an Exact Number: Children's Understanding of Cardinality and Equinumerosity

Cognitive Science

Volumn 37, Issue 8, 2013, Pages 1493-1506

  Sarnecka, Barbara W ^a   Wright, Charles E ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bootstrapping; Cardinality; Children; Concepts; Counting; Development; Early childhood; Equinumerosity; Exact equality; Kindergarten; Linear mixed models; Math; Number; Piaget; Preschool

Indexed keywords

ARTICLE; BOOTSTRAPPING; CARDINALITY; CHILD; CHILD DEVELOPMENT; CONCEPT FORMATION; CONCEPTS; COUNTING; DEVELOPMENT; EARLY CHILDHOOD; EQUINUMEROSITY; EXACT EQUALITY; FEMALE; HUMAN; KINDERGARTEN; KNOWLEDGE; LINEAR MIXED MODELS; MALE; MATH; MATHEMATICS; NUMBER; PHYSIOLOGY; PIAGET; PRESCHOOL; PRESCHOOL CHILD;

BOOTSTRAPPING; CARDINALITY; CHILDREN; CONCEPTS; COUNTING; DEVELOPMENT; EARLY CHILDHOOD; EQUINUMEROSITY; EXACT EQUALITY; KINDERGARTEN; LINEAR MIXED MODELS; MATH; NUMBER; PIAGET; PRESCHOOL;

CHILD DEVELOPMENT; CHILD, PRESCHOOL; CONCEPT FORMATION; FEMALE; HUMANS; KNOWLEDGE; MALE; MATHEMATICS;

EID: 84887614192     PISSN: 03640213     EISSN: None     Source Type: Journal    
DOI: 10.1111/cogs.12043     Document Type: Article

References (28)

1. Bates, D. M. (2005). Fitting linear mixed models in R. R News, 5, 27-30.
2. Block, N. J. (1986). Advertisement for a semantics for psychology. In P. A. French (Ed.), Midwest studies in philosophy (pp. 615-678). Minneapolis: University of Minnesota.
3. Carey, S. (2009). The origin of concepts. New York: Oxford University Press.
4. Condry, K. F., & Spelke, E. S. (2008). The development of language and abstract concepts: The case of natural number. Journal of Experimental Psychology: General, 137, 22-38.
5. Davidson, K., Eng, K., & Barner, D. (2012). Does learning to count involve a semantic induction? Cognition, 123, 162-173.
6. Dedekind, R. (1901). Essays in the theory of numbers, 1. Continuity of irrational numbers, 2. The nature and meaning of numbers (W. W. Beman, Trans.). Available at: Canadian Libraries Ebook and Texts Archive: http://www.archive.org/details/essaysintheoryof00dedeuoft (Originally published in 1872 and 1888, respectively).
7. Frege, G. (1980). The foundations of arithmetic: A logico-mathematical enquiry into the concept of number (J. L. Austin, Trans). Evanston, IL: Northwestern University Press (Originallly published 1884).
8. Frydman, O., & Bryant, P. (1988). Sharing and understanding of numerical equivalence by young children. Cognitive Development, 3, 323-339.
9. Gelman, R., & Gallistel, C. R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
10. Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the "number sense": The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44, 1457-1465.
11. Hurford, J. R. (1987). Language and number: The emergence of a cognitive system. Cambridge, MA: Blackwell.
12. Izard, V., Pica, P., Spelke, E. S., & Dehaene, S. (2008). Exact equality and successor function: Two key concepts on the path towards understanding exact numbers. Philosophical Psychology, 21, 491-505.
13. Klahr, D., & Wallace, J. G. (1976). Cognitive development: An information processing view. Hillsdale, NJ: Lawrence Erlbaum Associates.
14. Le Corre, M., & Carey, S. (2007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition, 105, 395-438.
15. Le Corre, M., Van de Walle, G., Brannon, E. M., & Carey, S. (2006). Re-visiting the competence/performance debate in the acquisition of counting as a representation of the positive integers. Cognitive Psychology, 52, 130-169.
16. Lee, M. D., & Sarnecka, B. W. (2010). A model of knower-level behavior in number-concept development. Cognitive Science, 34, 51-67. PMC2836733. doi:10.1111/j.1551-6709.2009.01063.x
17. McCulloch, C. E. (2003). Generalized linear mixed models. NSF-CBMS regional conference series in probability and statistics, v. 7. Beachwood, OH: Institute of Mathematical Statistics.
18. Muldoon, K., Lewis, C., & Freeman, N. (2009). Why set-comparison is vital in early number learning. Trends in Cognitive Sciences, 13, 203-208.
19. Piaget, J. (1952). The child's conception of number. London: Routledge & Kegan Paul Ltd.
20. Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., Dehaene, S., & Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116, 33-41.
21. Quine, W. V. O. (1960). Word and object. Cambridge, MA: MIT Press.
22. R Development Core Team (2006). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Available at: http://www.R-project.org.
23. Sarnecka, B. W., & Carey, S. (2008). How counting represents number: What children must learn and when they learn it. Cognition, 108, 662-674.
24. Sarnecka, B. W., & Gelman, S. (2004). Six does not just mean a lot: Preschoolers see number words as specific. Cognition, 92, 329-352.
25. Sarnecka, B. W., & Lee, M. D. (2009). Levels of number knowledge during early childhood. Journal of Experimental Child Psychology, 103, 325-337. PMC3127737. doi:10.1016/j.jecp.2009.02.007
26. Sophian, C. (1988). Early developments in children's understanding of number: Inferences about numerosity and one-to-one correspondence. Child Development, 59, 1397-1414.
27. Wynn, K. (1990). Children's understanding of counting. Cognition, 36, 155-193.
28. Wynn, K. (1992). Children's acquisition of number words and the counting system. Cognitive Psychology, 24, 220-251.