Teacher Interventions for Advancing Students’ Mathematical Understanding

Xiangquan Yao,Azita Manouchehri

doi:10.3390/educsci10060164

Xiangquan Yao, Azita Manouchehri

Open Access

https://doi.org/10.3390/educsci10060164

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Abstract

The relationship between teacher interventions and students’ mathematical thinking has been the subject of inquiry for quite some time. Using the Pirie–Kieren theory for dynamic growth in mathematical understanding, this study documents teacher interventions that support students’ growth toward developing a general understanding of a mathematical idea in a designed learning environment. By studying the interactions of seven middle school students and the teacher-researcher working on a two-week unit on geometric transformations within a dynamic geometry environment, this study identified nine major categories of teacher interventions that support and extend students’ investigations of mathematical ideas around geometric transformations. The typology of teacher interventions reported in this study provides a cognition-based framework for teacher moves that extend and advance students’ mathematical understanding.

Highlights

The relationship between teacher interventions and students’ mathematical thinking has been the subject of inquiry for quite some time [1]
We examined the types of teacher interventions that seemingly assisted a cohort of middle school students in discovering and generalizing the properties of geometric transformations in a dynamic geometry environment
Each category describes a type of intervention that appeared to foster the construction, refinement, or justification of a mathematical idea by the students

Summary

Introduction

The relationship between teacher interventions and students’ mathematical thinking has been the subject of inquiry for quite some time [1]. There is a consensus that the teacher plays a crucial role in guiding students towards developing a deeper understanding of mathematical ideas [2], relying on approaches and tools that support mathematical reasoning [3,4]. Common to all these various characterizations are three specific teaching actions that are assumed to optimize both student autonomy and their mathematical advancement. These include eliciting, supporting, and extending [5,6,7]. Extending actions are considered to be interventions that extend mathematical reasoning, in terms of generalizing their strategies or ideas and developing mathematically appropriate justifications [6,7]

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