Sociomathematical Norms, Argumenta- Tion, and Autonomy in Mathematics

  • Yackel E
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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 intel-lectually 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' math-ematical activity. The explication of sociomathematical norms extends our previous work on gen-eral 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 influ-ence 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 increas-ing 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 envi-ronments 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 attempt-ing 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 stu-dents 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 intro-ducing and elaborating the theoretical discussion in this paper, we present episodes from a classroom that we have studied extensively. The episodes have been A previous version of this paper was presented at the 1993 annual meeting of the American Educational Research Association, Atlanta, GA. Several notions central to this paper were elaborated in the course of discussions with Heinrich Bauersfeld,

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Authors

  • Erna Yackel

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