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Counting and arithmetic principles first

Published online by Cambridge University Press:  11 December 2008

Rochel Gelman
Affiliation:
Rutgers Center for Cognitive Science and Department of Psychology, Rutgers University at New Brunswick, Piscataway, NJ [email protected]://ruccs.rutgers.edu/faculty/Gelman/

Abstract

The meaning and function of counting are subservient to the arithmetic principles of ordering, addition, and subtraction for positive cardinal values. Beginning language learners can take advantage of their nonverbal knowledge of counting and arithmetic principles to acquire sufficient knowledge of their initial verbal instantiations and move onto a relevant learning path to assimilate input for more advanced, abstract understandings.

Type
Open Peer Commentary
Copyright
Copyright © Cambridge University Press 2008

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References

Bloom, P. (2000) How children learn the meaning of words. MIT Press.CrossRefGoogle Scholar
Bloom, P. & Wynn, K. (1998) Linguistic cues in the acquisition of number words. Journal of Child Language 24:511–33.CrossRefGoogle Scholar
Bullock, M. & Gelman, R. (1977) Numerical reasoning in young children: The ordering principle. Child Development 48:427–34.CrossRefGoogle Scholar
Cordes, S. & Gelman, R. (2005) The young numerical mind: When does it count? In: Handbook of mathematical cognition, ed. Campbell, J. I. D., pp. 128–42. Psychology Press.Google Scholar
Gallistel, C. R. & Gelman, R. (2005) Mathematical cognition. In: Cambridge handbook of thinking and reasoning, ed. Holyoak, K. & Morrison, R.. Cambridge University Press.Google Scholar
Gelman, R. (1993) A rational-constructivist account of early learning about numbers and objects. In: Learning and motivation, vol. 30, ed. Medin, D., pp. 6196. Academic Press.Google Scholar
Gelman, R. (2006) The young child as natural-number arithmetician. Current Directions 15:193197.CrossRefGoogle Scholar
Gelman, R. & Gallistel, C. R. (1978) The child's understanding of number. Harvard University Press/MIT Press. (Second printing, 1985. Paperback issue with new preface, 1986).Google Scholar
Gelman, R. & Greeno, J. G. (1989) On the nature of competence: Principles for understanding in a domain. In: Knowing and learning: Issues for a cognitive science of instruction: Essays in honor of Robert Glaser, ed. Resnick, L. B., pp. 125–86. Erlbaum.Google Scholar
Hartnett, P. M. & Gelman, R. (1998) Early understandings of numbers: Paths or barriers to the construction of new understandings? Learning and Instruction: The Journal of the European Association for Research in Learning and Instruction 8(4):341–74.CrossRefGoogle Scholar
Leslie, A., Gelman, R. & Gallistel, C.R. (2008) The generative basis of natural number concepts. Trends in Cognitive Science 12:213–18.CrossRefGoogle ScholarPubMed
Wynn, K. (1992b) Children's acquisition of the number words and the counting system. Cognitive Psychology 24:220–51.CrossRefGoogle Scholar
Zur, O. (2004) “Young children's understanding of arithmetic: The commutativity principle.” Ph.D. dissertation, Department of Psychology, University of California, Los Angeles.Google Scholar
Zur, O. & Gelman, R. (2004) Doing arithmetic in preschool by predicting and checking. Early Childhood Quarterly Review 19:121–37.CrossRefGoogle Scholar