ABSTRACT
The initial motivation for conducting the four case studies of small-group activity presented in this chapter was primarily theoretical. In concert with the general theme of this book, the neo-Piagetian and Vygotskian perspectives were deemed to be inappropriate given the purposes of the investigation. From the neo-Piagetian perspective, social interaction is treated as a catalyst for autonomous cognitive development. Thus, although social interaction is considered to stimulate individual cognitive development, it is not viewed as integral to either this constructive process or to its products, increasingly sophisticated mathematical conceptions. Vygotskian perspectives, on the other hand, tend to subordinate individual cognition to interpersonal or social relations. In the case of adult-child interactions, for example, it is argued that the child learns by internalizing mental functions that are initially social and exist between people. In recent years, several attempts have been made to extend these arguments to small-group interactions between peers (Forman & Cazden, 1985; Forman & McPhail, 1993). It was against the background of these two competing perspectives that an approach was developed that acknowledges the importance of both cognitive and social processes without subordinating one to the other.
