# How Middle Grade Teachers Think about Algebraic Reasoning

## Keywords:

algebraic reasoning, in-service teachers, functional thinking, generalizations## Abstract

Algebraic reasoning is an essential habit of mind for building conceptual knowledge in K-12 mathematics, yet little is known about how middle school mathematics teachers think about algebraic reasoning. In this article we describe a research project examining how algebraic reasoning was considered by grades 6, 7, or 8 mathematics teachers in a two-week professional development and over the following two months. We found these 21 teachers initially described algebraic reasoning in a way requiring only procedural knowledge to solve problems with a single solution, solution strategy, or representation. Teachers reported three activities influenced a shift in their thinking about algebraic reasoning, specifically by requiring conceptual knowledge to solve problems using multiple solutions, solution strategies, or representations. While some teachers also associated aspects of generalization and functional thinking as part of algebraic reasoning, two months after the professional development no teachers continued to associate these aspects as part of algebraic reasoning. These findings suggest the kinds of activities other teacher educators can use to develop teachers’ thinking about algebraic reasoning, and supports the need for additional research and interventions to support middle school teachers’ consideration of algebraic reasoning in more advanced ways.

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