Developing early algebraic reasoning in a mathematical community of inquiry

Abstract

This study explores the development of early algebraic reasoning in mathematical communities of inquiry. Under consideration is the different pathways teachers take as they develop their own understanding of early algebra and then enact changes in their classroom to facilitate algebraic reasoning opportunities.

Teachers participated in a professional development intervention which focused on understanding of early algebraic concepts, task development, modification, and enactment, and classroom and mathematical practices.

Design research was employed to investigate both teaching and learning in the naturalistic setting of the schools and classrooms. The design approach supported the development of a model of professional development and the framework of teacher actions to facilitate algebraic reasoning. Data collection over the school year included participant observations, video recorded observations, documents, teacher interviews, and photo elicitation interviews with students. Retrospective data analysis drew the results together to be presented as cases of two teachers, their classrooms, and students.

The findings show that the integration of algebraic reasoning into classroom mathematical activity is a gradual process. It requires teachers to develop their own understanding of algebraic concepts which includes understanding of student reasoning, progression, and potential misconceptions. Task implementation and design, shifts in pedagogical actions, and the facilitation of new classroom and mathematical practices were also key elements of change. The important role which students have in the development of classrooms where algebraic reasoning is a focus was also highlighted.

These findings have significant implications for how teachers can be supported to develop their understanding of early algebra and use this understanding in their own classrooms to facilitate early algebraic reasoning.