ABSTRACT
Our work derives from a constructivist’s view of language and thought. On the one hand, the work is influenced by Piaget’s theory of equilibration, cognitive conflict, and the importance placed on peer interaction (Piaget, 1970a). And on the other, it is guided by Vygotsky’s view of the importance of learning within the context of social interaction and the crucial nature of human discourse (Vygotsky, 1962). Specifically, we have conducted a research and development project that investigated the mathematical learning of second-grade children as they used instructional materials designed to be compatible with models of early number learning (Steffe, von Glasersfeld, Richards, & Cobb, 1983; Steffe, Cobb, & von Glasersfeld, 1988). Small group problem solving and whole class discussions were the primary instructional strategies for all aspects of the mathematics, including arithmetical computation. These two strategies resulted in opportunities for learning that do not occur in traditional classrooms, including those that arise from collaborative dialogue (Barnes & Todd, 1977), as well as from the resolution of conflicting points of view (Perret-Clermont, 1980).
