Original Research

Solving quadratic equations by completing the square: Applying Newman’s Error Analysis Model to analyse Grade 11 errors

Tšhegofatšo P. Makgakga
Pythagoras | Vol 44, No 1 | a742 | DOI: https://doi.org/10.4102/pythagoras.v44i1.742 | © 2023 Tšhegofatšo P. Makgakga | This work is licensed under CC Attribution 4.0
Submitted: 14 February 2023 | Published: 07 December 2023

About the author(s)

Tšhegofatšo P. Makgakga, Department of Mathematics Education, College of Education, University of South Africa, Pretoria, South Africa


Error analysis is an instructional strategy that can assist teachers to identify learners’ areas of weakness in mathematics and that can point to remediation of those errors. This article explores the errors learners exhibit when solving quadratic equations by completing the square using Newman’s Error Analysis Model. A research study explored the errors learners exhibit when solving quadratic equations by completing the square. Newman’s Error Analysis Model provided the analytic framework for the qualitative approach that was used to explore those errors. A diagnostic test with five test items was administered to 35 learners in one secondary school in Limpopo province of South Africa. Subsequently, 12 learners whose scripts featured common mistakes were identified; these learners participated in a semi-structured interview to diagnose the errors. The findings revealed that learners commit comprehension, transformation and process errors. The findings suggest that if the errors that learners make are exposed and made explicit, the errors can be remediated and thereby enhance understanding and learning. The findings of this study indicate that for teachers to understand the types of errors learners commit when solving quadratic equations by completing the square it is vital for them (errors) to be addressed. Mathematics teachers should also consider diagnosing why learners commit those errors, as they would know the strategies to be employed to teach this topic and subsequent topics.

Contribution: The findings of this article add value to the current literature by providing empirical knowledge on learner challenges when solving quadratic equations by completing the square. This study provides opportunities for mathematics teachers to focus more on the strategies that would assist learners to understand this topic.


error analysis; quadratic equations; comprehension errors; transformation errors; process errors

Sustainable Development Goal

Goal 4: Quality education


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