ABSTRACT
This chapter focuses on research on the numerical knowledge of preverbal infants; research on young children's counting and their understanding of what it means; and research on children's understanding of aspects of mathematics that do not fit well with the hypothesized principles, in particular, fractions. With the acquisition of language, children begin to learn the words for small numerosities, and over the preschool period their counting abilities grow rapidly. Alternative accounts of development in this period are generally in agreement about children's how-to-count knowledge but diverge in their views as to the relation between that procedural knowledge and developing conceptual knowledge. Specifically, the knowledge that counting provides information about the cardinal value of a set. The ideas about young children's counting that R. Gelman and Gallistel introduced more than 25 years ago have clearly been scientifically productive, in that they essentially gave birth to a field of inquiry that is still growing.
