Evidence from cognitive neuropsychology suggests that our number processing and arithmetical capacities comprise a set of dissociable systems: verbal knowledge of number and stored precise number facts, procedural knowledge for numerical computations, visual knowledge of Arabic numerals, and a magnitude sense of numbers. Evidence from comparative and developmental psychology suggests that both human infants and nonhuman animals share one of these component systems: a magnitude sense of number that supports enumeration, numerical comparison, and numerical computation operations. Language and learning appear to play key roles in the formation of the other components; in particular, evidence suggests that we may store learned numerical facts in the specific natural human language in which they are learned. Much more remains to be learned about (a) how these systems interrelate, (b) precisely how we build onto the initial sense of numerical magnitude, and (c) how we obtain genuinely new mathematical knowledge.

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Suggested Reading

Ashcraft, M. H. (1995). Cognitive psychology and simple arithmetic: A review and summary of new directions. Mathemat. Cogn. 1, 3-34.

Boysen, S. T., and Capaldi, E. J. (Eds.). (1993). The Development of Numerical Competence: Animal and Human Models. LEA, Hillsdale, NJ.

Butterworth, B. (1999). The Mathematical Brain. Macmillan, London.

Campbell, J. D. (Ed.). (1992). The Nature and Origins of Mathematical Skills. Elsevier, Amsterdam.

Davis, H.,andPerusse, R. (1988). Numerical competence in animals: Definitional issues, current evidence and a new research agenda. Behav. Brain Sci. 11, 561-615.

Dehaene, S. (1997). The Number Sense: How the Mind Creates Mathematics. Oxford University Press, Oxford, UK.

Dehaene, S., and Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathemat. Cogn. 1, 83-120.

Donlan, C. (Ed.). (1998). The Development of Mathematical Skills. Psychology Press, East Sussex, UK.

Gallistel, C. R. (1990). Number. In The Organization of Learning, Chapter 10, pp. 317-350. MIT Press, Cambridge, MA.

Wynn, K. (1998). Psychological foundations of number: Numerical competence in human infants. Trends Cogn. Sci. 2, 296-303.

Wynn, K. (1998). An evolved capacity for number. In The Evolution of Mind (D. Cummins and C. Allen, Eds.). Oxford University Press, Oxford, UK.

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