ABSTRACT
A landmark event in the study of children’s mathematical development was the publication of R. Gelman and Gallistel’s (1978) book, The Child’s Understanding of Number. In this book, R. Gelman and Gallistel undertook to remedy the perceived failure of Piaget’s (1952) account of logico-mathematical development, with its emphasis on the limitations of preoperational thought, to adequately characterize the knowledge that very young children do have about mathematics. To this end, they called attention to the richness of children’s counting knowledge. They made the ground-breaking observation that there is a high degree of systematicity in even very young children’s counting, which they argued belies the Piagetian idea that counting is initially merely a rote process without conceptual substance. R. Gelman and Gallistel maintained instead that the systematicities in children’s early counting reflect knowledge about the logical requirements of counting—characteristics a count must have if it is to provide valid information about numerosity. They claimed that, although young children cannot articulate the principles of counting explicitly, their adherence to them shows that they know principles in much the same way as speakers of a language give evidence of knowing its grammatical rules by adhering to them in their speech even though they seldom can state the grammatical rules explicitly.
