Sociomathematical Norms, Argumentation, and Autonomy in Mathematics

Abstract

This paper sets forth a way of interpreting mathematics classrooms that aims to account for how students develop mathematical beliefs and values and, consequently, how they become intellectually autonomous in mathematics. To do so, we advance the notion of sociomathematical norms, that is, normative aspects of mathematical discussions that are specific to students' mathematical activity. The explication of sociomathematical norms extends our previous work on general classroom social norms that sustain inquiry-based discussion and argumentation. Episodes from a second-grade classroom where mathematics instruction generally followed an inquiry tradition are used to clarify the processes by which sociomathematical norms are interactively constituted and to illustrate how these norms regulate mathematical argumentation and influence learning opportunities for both the students and the teacher. In doing so, we both clarify how students develop a mathematical disposition and account for students' development of increasing intellectual autonomy in mathematics. In the process, the teacher's role as a representative of the mathematical community is elaborated. For the past several years, we have been engaged in a research and development project at the elementary school level that has both pragmatic and theoretical goals. On one hand, we wish to support teachers as they establish classroom environments that facilitate students' mathematical conceptual development. On the other hand, we wish to investigate children's mathematical learning in the classroom. The latter involves developing perspectives that are useful for interpreting and attempting to make sense of the complexity of classroom life. The purpose of this paper is to set forth a way of interpreting classroom life that aims to account for how students develop specific mathematical beliefs and values and, consequently, how they become intellectually autonomous in mathematics, that is, how they come to develop a mathematical disposition (National Council of Teachers of Mathematics, 1991). To that end, we focus on classroom norms that we call sociomathematical norms. These norms are distinct from general classroom social norms in that they are specific to the mathematical aspects of students' activity. As a means of introducing and elaborating the theoretical discussion in this paper, we present episodes from a classroom that we have studied extensively. The episodes have been