A teacher’s engagement with learner errors in her Grade 9 mathematics classroom

Aarifah Gardee,Karin Brodie

doi:10.4102/pythagoras.v36i2.293

Abstract

How errors are dealt with in a mathematics classroom is important as it can either support or deny learner access to mathematical knowledge. This study examines how a teacher, who participated in a professional development programme that focused on learner errors, engaged with mathematical errors in her Grade 9 classroom. Data were collected over a twoyear period in the form of videotapes and were analysed qualitatively. Our findings illustrate that this teacher dealt with four types of mistakes: slips, errors derived from misconceptions, language-related errors and errors that occurred from the incorrect usage of the calculator. She dealt with these by correcting, probing or embracing them. We found that, over time, this teacher dealt with more errors and corrected and embraced errors in different ways. We recommend that teachers use their professional knowledge to decide when, why and how it is appropriate to correct, probe or embrace errors in light of their knowledge of the content and their learners.

Highlights

Errors play a central role in the mathematics classroom as they are a reflection of the manner in which learners reason and they illuminate the processes through which learners attempt to construct their own knowledge (Olivier, 1989)
While much research has been done on the nature of learners’ errors and their underlying misconceptions (Hansen, 2011; Nesher, 1987; Olivier, 1989) and how teachers might deal with errors (Borasi, 1994; Swan, 2001), very little work has illustrated how teachers deal with errors in their mathematics classrooms (Heinze & Reiss, 2007)
Data-Informed Practice Improvement Project (DIPIP) works with mathematics teachers in professional learning communities so that they may develop their understanding of the importance of mathematical errors in the classroom and the learners’ reasoning behind their errors and collectively strategise how to deal with them (Brodie, 2013)

Summary

Introduction

Errors play a central role in the mathematics classroom as they are a reflection of the manner in which learners reason and they illuminate the processes through which learners attempt to construct their own knowledge (Olivier, 1989). Errors can be used by teachers to provide learners with epistemological access to mathematics and contribute to developing learners’ conceptual understanding (Brodie, 2013). The manner in which a teacher deals with learner errors is crucial, as it can either enhance or limit learners’ understanding of mathematics. The purpose of this study is to investigate the type of errors a teacher chooses to deal with in her mathematics classroom and the manner in which she deals with the errors. DIPIP works with mathematics teachers in professional learning communities so that they may develop their understanding of the importance of mathematical errors in the classroom and the learners’ reasoning behind their errors and collectively strategise how to deal with them (Brodie, 2013)

Objectives

Findings

Discussion

Conclusion