The evolution of mathematical practices: A case study

In this article, we describe an approach for documenting students' mathematical development in the social context of a classroom over a prolonged period of time. Our theoretical perspective is based on the view that the ways in which children participate in classroom discussions are influenced by their views of themselves as members of the classroom community and their individual ways of knowing. Thus, our analysis aims to document both the evolution of the communal mathematical practices in which students participate and the development of their individual understandings as they participate in those evolving practices. In this article, we frame our discussion of these mathematical practices by presenting a case study from a 3rd-grade teaching experiment. The goal of this teaching experiment was to support 3rd-grade students' development of place value conceptions. We begin by describing the changes in individual students' mathematical conceptions that occurred over the 9-week teaching experiment as indicated from analyses of pre- and postinterviews. Next, we attempt to account for these developments in process terms by describing the evolution of mathematical practices that emerged over the course of 9 weeks of instruction. In the discussion section, we situate this analysis within the larger frame of developmental research by describing the ways in which the findings feed back to inform instructional design and further classroom-based research.