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Original Research

Engaging with learners’ errors when teaching mathematics

Ingrid Sapire, Yael Shalem, Bronwen Wilson-Thompson, Ronél Paulsen

Pythagoras; Vol 37, No 1 (2016), 11 pages. doi: 10.4102/pythagoras.v37i1.331

Submitted: 08 February 2016
Published:  31 October 2016

Abstract

Teachers come across errors not only in tests but also in their mathematics classrooms virtually every day. When they respond to learners’ errors in their classrooms, during or after teaching, teachers are actively carrying out formative assessment. In South Africa the Annual National Assessment, a written test under the auspices of the Department of Basic Education, requires that teachers use learner data diagnostically. This places a new and complex cognitive demand on teachers’ pedagogical content knowledge. We argue that teachers’ involvement in, and application of, error analysis is an integral aspect of teacher knowledge. The Data Informed Practice Improvement Project was one of the first attempts in South Africa to include teachers in a systematic process of interpretation of learners’ performance data. In this article we analyse video data of teachers’ engagement with errors during interactions with learners in their classrooms and in one-on-one interviews with learners (17 lessons and 13 interviews). The schema of teachers’ knowledge of error analysis and the complexity of its application are discussed in relation to Ball’s domains of knowledge and Hugo’s explanation of the relation between cognitive and pedagogical loads. The analysis suggests that diagnostic assessment requires teachers to focus their attention on the germane load of the task and this in turn requires awareness of error and the use of specific probing questions in relation to learners’ diagnostic reasoning. Quantitative and qualitative data findings show the difficulty of this activity. For the 62 teachers who took part in this project, the demands made by diagnostic assessment exceeded their capacity, resulting in many instances (mainly in the classroom) where teachers ignored learners’ errors or dealt with them partially.

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Author affiliations

Ingrid Sapire, School of Education, University of the Witwatersrand, South Africa
Yael Shalem, School of Education, University of the Witwatersrand, South Africa
Bronwen Wilson-Thompson, School of Education, University of the Witwatersrand, South Africa
Ronél Paulsen, Department of Mathematics Education, University of South Africa, South Africa

Keywords

error analysis; mathematics teaching; cognitive and pedagogic load; formative assessment

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ISSN: 1012-2346 (print) | ISSN: 2223-7895 (online)

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