Insights into the reversal error from a study with South African and Spanish prospective primary teachers

IF 0.3 Q4 EDUCATION, SCIENTIFIC DISCIPLINES
Calos Soneira, S. Bansilal, Reginald Gerald Govender
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Abstract

This study, using a quantitative approach, examined Spanish and South African pre-service teachers’ responses to translating word problems based on direct proportionality into equations. The participants were 79 South African and 211 Spanish prospective primary school teachers who were in their second year of a Bachelor of Education degree. The study’s general objective was to compare the students’ proficiency in expressing direct proportionality word problems as equations, with a particular focus on the extent of the reversal error among the students’ responses. Furthermore, the study sought to test the explanatory power of word order matching and the static comparison as causes of the reversal error in the two contexts. The study found that South African students had a higher proportion of correct responses across all the items. While nearly all the errors made by Spanish students were reversals, the South African group barely committed reversal errors. However, a subgroup of the South African students made errors consisting of equations that do not make sense in the situation, suggesting that they had poor foundational knowledge of the multiplicative comparison relation and did not understand the functioning of the algebraic language. The study also found that the word order matching strategy has some explanatory power for the reversal error in both contexts. However, the static comparison strategy offers explanatory power only in the Spanish context, suggesting that there may be a difference in curriculum and instructional approaches in the middle and secondary years of schooling, which is when equations are taught.
一项针对南非和西班牙未来小学教师的研究对逆转错误的见解
本研究采用定量方法,考察了西班牙和南非职前教师对将基于直接比例的单词问题翻译成等式的反应。参与者是79名南非和211名西班牙的准小学教师,他们正在攻读教育学士学位的第二年。这项研究的总体目标是比较学生将直接比例词问题表达为方程的熟练程度,特别关注学生回答中反向误差的程度。此外,本研究试图检验语序匹配和静态比较作为两种语境中反转错误原因的解释力。研究发现,南非学生在所有项目中的正确回答比例较高。虽然西班牙学生犯下的几乎所有错误都是逆转,但南非学生几乎没有犯下逆转错误。然而,一组南非学生犯了错误,这些错误由在这种情况下没有意义的方程组成,这表明他们对乘法比较关系的基础知识很差,也不理解代数语言的功能。研究还发现,语序匹配策略对两种语境中的反转错误都有一定的解释力。然而,静态比较策略仅在西班牙背景下提供解释力,这表明在中学和中学教育中,课程和教学方法可能存在差异,而中学和中学是教授方程式的时候。
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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