ABSTRACT
In this chapter I address the topic of communication in early childhood mathematics by describing parts of a research project I have recently completed. A theory of children’s counting types (Steffe, von Glasersfeld, Richards, & Cobb, 1983) was used as a framework in conducting a teaching experiment (Cobb & Steffe, 1983) which focused on the numerical development of four children during their kindergarten year of school (Wright, 1988, 1989). The purpose of this chapter is to illustrate how the counting types theory was used in the teaching experiment and how certain constructs of that theory were manifest in the children’s problem solutions. There are three features of my work that are complementary to the earlier work (cf. Cobb, 1983; Steffe, 1983; Steffe, 1984a; Steffe et al., 1983; Steffe, Cobb & von Glasersfeld, 1988). First, the children in this teaching experiment were in the kindergarten year of school, whereas in the earlier study the children were in the first and second years of school. Second, the children in this study were Australian, whereas the earlier study focused on children from the United States. Finally, this study focused on aspects of children’s mathematics that were not studied in detail in the earlier study. These included activities such as counting temporal sequences of sounds and movements, and children’s number word sequence development.
