What Happens When a Child Learns to Count?

What happens when a child learns to count? Does he or she undergo a conceptual revolution? For centuries, philosophers have wondered whether the principles that define the formal system of the positive integers are the same as those that guide our cognitive intuitions about number and counting. In developmental psychology, it is generally accepted that learning to count involves the formation of an understanding of the ‘counting principles’ (e.g., 1 – 1 correspondence, stable order, cardinality; Gelman & Gallistel, 1978). However, vigorous debate remains as to whether children are born with these principles built into their cognitive systems, discover them out in the world, or construct them through experience and logical induction. We draw on recent findings from a large longitudinal study in which we examined the growth and change of different number skills, formal and informal, over two years of preschool. Our findings highlight the importance of two core capacities for the acquisition of children’s first symbolic mathematical knowledge: the counting routine. We discuss previous proposals in light of our findings, considering whether they support the notion of conceptual change, or whether the data are more consistent with conceptual elaboration.