A basic challenge in understanding human cognitive development is to understand how children acquire number concepts. Since the time of Piaget (1952), the concept of number has been one of the most active areas of research in the field. This chapter focuses on one prominent current theory about the origin of integer concepts, called the “knower-level” theory (Carey, 2001; Carey & Sarnecka, 2006; Wynn, 1990, 1992).

The knower-level theory asserts that children learn the exact cardinal meanings of the first three or four number words one-by-one and in order. That is, children begin by learning the meaning of “one” first, then “two,” then “three,” and then (for some children) “four,” at which point they make an inductive leap, and infer the meanings of the rest of the words in their counting list. In the terminology of the theory, children start as PN-knowers (for “Pre-Number”), progress to one-knowers once they understand “one,” through the two-knower, three-knower, and (for some children) four-knower levels, until they eventually become CP-knowers (for “Cardinal Principle”).

There are at least two common behavioral tasks that are used to assess children's number knowledge. In the “Give-N” task, children are asked to give some number of objects, such as small toys, to the experimenter, or an experimenter substitute, such as a puppet (e.g., Frye, Braisby, Lowe, Maroudas, & Nicholls, 1989; Fuson, 1988; Schaeffer, Eggleston, & Scott, 1974; Wynn, 1990, 1992).