Sophian, C. (1998). A developmental perspective on children's counting. In C. Donlan (Ed.), The development of mathematical thinking, pp. 27-46. University College London Press.

Any satisfactory theory of development must tell us not only how children's knowledge originates but also how it grows. This chapter begins with a careful analysis of the available evidence concerning infant numerical abilities. A central question in this analysis will be whether the evidence supports the conclusion that infants count, albeit in a nonverbal way, or whether number-related aspects of infant behavior might be based on a more limited mechanism called subitizing. Next I consider the evidence of developmental changes in children's counting over the preschool years and even beyond, considering first developments related to the principles of counting identified in Gelman and Gallistel's (1978) seminal work, and then developments related to children's understanding of the functions of counting or the purposes it can serve. These findings underscore the developmental side of children's counting, and the need for a theory of numerical development that can account not only for what children know at an early age but also for how their knowledge changes with age.  The concluding section of the chapter, therefore, takes up the question of what kind of developmental theory can account for both the richness of children's early numerical knowledge and the continuing development of their knowledge over the preschool years and beyond. I hypothesize that socially mediated goals may function as a source of changing constraints on children's numerical development; and I outline some ways in which an analysis of changing goals can help to elucidate early numerical development.

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