Sophian, C. (1997). Young children's numerical cognition: What develops? In R. Vasta (Ed.), Annals of Child Development, vol. 12 (pp. 49-86). London: Jessica Kingsley Publishers.

The focus of the present chapter is on developmental changes in two major aspects of children's numerical cognition: their counting, and their reasoning about fractional quantities. These two aspects of numerical development are chosen in part because of the apparent contrast between them. While counting appears to be a universal ability, acquired without schooling and with little difficulty, fractions pose considerable difficulty even when they are explicitly taught. Clearly, one's conclusions about what develops depend in part on one's conclusions about how much and what kind of knowledge children have to start with, in infancy. Therefore, the treatment of both counting knowledge and knowledge about ratios in this chapter begins with a careful look at the available evidence concerning potentially relevant infant abilities--infants' sensitivity to numerical properties of sets and to ratio relations among quantities, respectively. Developmental changes beyond infancy are then reviewed. A concluding section reflects on relations between the research on children's knowledge about counting and on their knowledge about ratio, and draws implications for theories of numerical development.

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