TEACHERS' APPROACHES TO STUDENT ERRORS IN MATHEMATICS TEACHING - AND NOTICING OF THEIR APPROACHES

Oct 15, 2026

Uploaded by Aditya

This study examines how middle school mathematics teachers approach student errors and how they notice and reflect on those approaches. Conducted as a qualitative case study during the pandemic with four teachers, it uses classroom video records segmented for analysis and online interviews for additional insight. Findings show teachers largely choose intervention approaches framed as questioning, accompanied by delineative and explanatory comments. Teachers also reach deductions through evaluating their own approaches, often proposing their error approaches as an educational recommendation.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages21

Reading Time53 min

AccessFree to download

Introduction

Background and rationale

Focus of the study

Research questions

TEACHERS' APPROACHES TO STUDENT ERRORS IN MATHEMATICS TEACHING AND NOTICING OF THEIR APPROACHES Gülşah ÖZDEMIR BAKI, Merve ÖZKAYA, Alper Cihan KONYALIOĞLU Abstract: The aim of this study is to examine the error approach of middle school teachers and their noticing of their approaches. The study was designed as a case study, which is a qualitative research method, and conducted through four middle school mathematics teachers during the pandemic. The data regarding the study were gathered via in class video records and online interviews with the teachers. The videos from the lectures of middle school mathematics teachers were segmented and analysed, hence, their approaches to student errors were identified. Moreover, noticing of the participant teachers on their and their peers' approach were investigated by means of online interviews. The findings of the research indicated the participant teachers mostly opt for the intervention approaches that fall into the category of questioning, and they make delineative and explanatory comments concerning their approaches. Furthermore, it has been observed that the teachers reached deductions through the evaluation of their own approaches, however, most of the time they recommended their own error approaches to the students as an educatory proposition. Key words: Error, Error approach, Intervention, Teacher noticing, Mathematics teacher, Video analysis 1. Introduction Due to the crucial role of teachers on the education quality, myriad of research material was produced in order to delineate the qualities of a good teacher and a plethora of views have been asserted regarding the issue. (Shulman, 1986; 1987, National Council of Teachers of Mathematics [NCTM], 2000, Charalambous & Hill, 2012; Ball, Thames & Phelps, 2008; Hill, Rowan & Ball, 2005; Ma, 2010) . Eventually, these qualities became more pronounced with more definitive components thanks to Shulman (1986;1987) and his fellows. Student knowledge became the center of interest among these subcomponents (Park & Oliver, 2008) . The term student knowledge encompasses teachers' noticing of errors that students might possess and being erudite on what knowledge student should have (NCTM, 1989; 1991; 2000) . It is important to analyse the student errors when this situation has been given thought (Graeber, 1999) . Apart from the analysis of student errors in the classroom, how teachers interested in and intervene the errors must be emphasized (Santagata, 2002) . Moreover, teachers must be encouraged to notice their approaches. Error approach, which is a fundamental pillar of mathematics education, is the most effective method (Pirie & Kieren, 1994) teachers employ to understand students and an invaluable part in improving the quality of education (NCTM, 1989; 1991) . Because teachers who adopt the correct approach to student errors can understand what errors students have and analyse the errors better (Shulman, 1986) . The ability to analyse student errors is directly pertinent to the conceptual knowledge level (Rach, Ufer & Heinze, 2013) . The importance of analysing the student errors is emphasized in the teachers'development of conceptual knowledge level as well (Borasi, 1986; Carpenter, Franke & Levi, 2003; Ma, 2010; Tsamir, 2007) . Most of the research that were conducted on error approach mostly focused on teachers' or teacher candidates' conceptual approaches to errors (Chick & Baker, 2005; Baker & Chick, 2006; Peng & Luo, 2009; Son & Crespo, 2009; Demirci, Ozkaya & Konyalioglu, 2017) . Nonetheless, there has been a scarcity on the research of error approaches in terms of interventions (Santagata, 2004; Son & Sinclair, 2010; Steuer, Rosentritt-Brunn & Dresel, 2013; Didis, Erbas & Cetinkaya, 2016) . Besides the studies on identification of errors and explaining the root causes, investigating the approaches including interventions is especially important when the teachers who will teach the posterity are considered. Hence,

FAQs

What is the purpose of the study on mathematics teaching errors?

The study aims to examine teachers' approaches to student errors and how teachers notice and reflect on those approaches.

How was the data collected for the case study?

Data were gathered through in-class video records and online interviews with four middle school mathematics teachers during the pandemic.

What intervention approach did teachers mostly choose?

Teachers mostly opted for intervention approaches categorized under questioning and provided delineative and explanatory comments.

Oct 15, 2026

Uploaded by Aditya