From the Field to the Classroom: Studies in Mathematical Understanding
Geoffrey B. Saxe University of California at Los Angeles
Children's social and cultural lives are interwoven with their developing mathematical understandings in fundamental ways. In their efforts to document children's understandings, researchers have often sidestepped analyses of sociocultural processes in children's mathematics. In this chapter, I sketch a research framework in which dimensions of daily life are elevated to a central target of analysis. I show that research guided by the framework is useful for informing the creation of classroom practices for children's mathematics learning, and that the research framework, in turn, is useful for understanding children's learning in such practices.
The guiding assumption of the framework is one consistent with constructivist treatments of various theorists including Piaget ( 1963b, 1977) and Vygotsky ( 1978, 1986): Individuals construct novel understandings as they attempt to accomplish goals rooted in both their prior understandings and socially organized activities. To date, however, these treatments have not been adequately extended into systematic frameworks for the analysis of the interplay between culture and cognitive development. For Piaget, sociocultural processes were largely unanalyzed. For Vygotsky, such processes, although of central importance, were not incorporated into a systematic research approach (for a more extensive critique, see Saxe, 1991).