ABSTRACT
This chapter describes the contrasting ideas and observations into a coherent picture of how children think about numbers and how that thinking changes with age. It deals with the question of what children start with—what the innate foundations for numerical knowledge might be—and then turns to the question of developmental change. The notion that children begin the process of number development with a domain-specific mechanism as powerful as the accumulator has been hotly debated. Like the accumulator model, the notion of a “discrete physical object” bias predicts that working with fractions should be less natural than working with the counting numbers. Considering the difficulties of determining what is going on in a preverbal infant’s mind, it is not surprising that diverging views about the scope of infants’ early numerical knowledge persist. Once children can use numbers to quantify sets, it can be difficult to be sure whether they are using protoquantitative or quantitative reasoning to solve some classes of problems.
