Sociomathematical Norms, Argumentation, and Autonomy in Mathematics

TLDR

Sociomathematical norms build on prior work on classroom social norms that sustain inquiry‑based discussion and argumentation, and they clarify the teacher’s role as a representative of the mathematical community. The paper proposes an interpretive framework for mathematics classrooms that explains how students develop mathematical beliefs, values, and intellectual autonomy. The authors introduce sociomathematical norms—normative aspects of student discussions—and illustrate their interactive constitution and regulatory role in argumentation using episodes from a second‑grade inquiry‑based classroom. The study demonstrates that sociomathematical norms clarify students’ mathematical dispositions and foster increasing intellectual autonomy, while also shaping learning opportunities for students and teachers.

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.