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

IF 0.3 Q4 EDUCATION, SCIENTIFIC DISCIPLINES
T. Makgakga
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引用次数: 0

Abstract

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.
通过完成平方来解一元二次方程:应用纽曼错误分析模型分析 11 年级错误
错误分析是一种教学策略,可以帮助教师识别学生在数学方面的弱点,并指出这些错误的补救措施。本文探讨了学习器在使用纽曼误差分析模型完成平方求解二次方程时所表现出的误差。一项研究探讨了学习者通过完成平方来解二次方程时所表现出的错误。纽曼的误差分析模型为用于探索这些误差的定性方法提供了分析框架。对南非林波波省一所中学的35名学生进行了一项包含五个测试项目的诊断测试。随后,确定了12名学习者,他们的脚本中存在常见错误;这些学习者参加了一个半结构化的访谈来诊断错误。研究结果表明,学习者在理解、转换和处理方面存在错误。研究结果表明,如果学习者犯的错误被暴露和明确,错误可以被纠正,从而提高理解和学习。本研究的结果表明,教师要了解学习者在通过完成平方解二次方程时所犯的错误类型,解决这些错误是至关重要的。数学教师还应该考虑诊断学生犯这些错误的原因,因为他们会知道在教授这个主题和后续主题时应该采用的策略。贡献:这篇文章的发现增加了当前文献的价值,通过完成平方来解决二次方程时,提供了关于学习者挑战的经验知识。这项研究为数学教师提供了机会,让他们更多地关注帮助学习者理解这一主题的策略。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Pythagoras
Pythagoras EDUCATION, SCIENTIFIC DISCIPLINES-
CiteScore
1.50
自引率
16.70%
发文量
12
审稿时长
20 weeks
期刊介绍: Pythagoras is a scholarly research journal that provides a forum for the presentation and critical discussion of current research and developments in mathematics education at both national and international level. Pythagoras publishes articles that significantly contribute to our understanding of mathematics teaching, learning and curriculum studies, including reports of research (experiments, case studies, surveys, philosophical and historical studies, etc.), critical analyses of school mathematics curricular and teacher development initiatives, literature reviews, theoretical analyses, exposition of mathematical thinking (mathematical practices) and commentaries on issues relating to the teaching and learning of mathematics at all levels of education.
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