ABSTRACT
In this chapter, our intention is to illustrate a view of learning and teaching elementary school mathematics that is influenced both by constructivist perspectives on conceptual development (e.g., Piaget, 1970a, 1980; von Glasersfeld, 1984, 1987a) and symbolic interactionist theory as advanced by Schutz (1962), Mead (1934), and Blumer (1969). In taking this stance, we implicitly question claims that either cognitive or social process should be relegated to a secondary role as we attempt to understand mathematics learning and teaching in public school classrooms. On the one hand, we question that mathematics is essentially cognitive although influenced by social processes. On the other hand, we question that mathematics is essentially social or cultural in nature, and that accounts of cognitive activity can be derived from analyses of these processes. Both these views make claims about the essence of mathematics—about the way mathematics really is, always has been, and always will be independent of the theorist's interpretive activity. These claims about the ahistorical, mind-independent essence of mathematics are incompatible with the epistemology that underpins both constructivism and symbolic interactionism. Constructivism is a view that attempts to apply this epistemology to the theorist's own interpretive activity. The divisive issue of whether mathematics is essentially cognitive or whether it is essentially social is then seen to be ill-founded. The issue of central interest is not that of making a choice between the two interpretations of mathematics, but instead concerns the potential relevance and value of the two interpretations for us as mathematics educators when we formulate our goals and attempt to resolve what we find problematic. Constructivism finds value in both perspectives and considers that they are complementary rather than in opposition. From this point of view, it is useful to see mathematics as both cognitive activity constrained by social and cultural processes and a sociocultural phenomenon that is constituted by a community of actively cognizing individuals. Cognitive and social processes are then seen as complementary: Each serves as the background against which the other comes to the fore. We present analyses of specific classroom events conducted from this point of view once we briefly consider the nature and consequences of the practices that one typically observes in elementary school classrooms during mathematics lessons.
