The evolution of mathematical practices: A case study

In this article, we describe an approach for documenting students' mathemat ical development in the social context of a classroom over a prolonged peri od of time. Our theoretical perspective is based on the view that the ways in which children participate in classroom discussions are influenced by th eir views of themselves as members of the classroom community and their ind ividual ways of knowing. Thus, our analysis aims to document both the evolu tion of the communal mathematical practices in which students participate a nd the development of their individual understandings as they participate i n those evolving practices. In this article, we frame our discussion of the se mathematical practices by presenting a case study from a 3rd-grade teach ing experiment. The goal of this teaching experiment was to support 3rd-gra de 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 proc ess terms by describing the evolution of mathematical practices that emerge d 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.