Managing students’ non-canonical approaches to solving equations: Linguistic resources teachers use to respond to students’ mathematical work

Abstract

A historical review of mathematics curriculum suggests a long-standing canonical method to solving equations that teachers often see as “the” way to solve equations. In this paper, we examine data collected from a nationally-distributed sample of 524 secondary mathematics teachers who responded to a set of scenario-based survey items that represent the instructional situation of solving equations. The items featured scenarios in which students presented non- canonical solution methods and asked participants to share how they would respond to that situation. Using a framework that draws on systemic functional linguistics, we describe patterns in the various linguistic resources teachers use to manage the situation. While closed moves are frequently used to avoid discussion of non-canonical methods, our results suggest that teachers find ways to make regular use of: (1) closed moves when accommodating students' non- canonical solution methods and (2) open moves when steering the conversation back to the canonical solution method.