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Factors influencing students’ understanding of mathematical equivalence

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posted on 2020-06-22, 08:44 authored by Emine Simsek

Most primary school students have difficulty understanding mathematical equivalence, and the literature has shown that the situation is worse in some countries than others. Differences between students’ understanding have significant and long-lasting effects, with understanding of equivalence predicting arithmetic and algebra achievement throughout school years. Currently, little is known about the factors influencing students’ understanding of mathematical equivalence. This thesis explores the individual and classroom-level factors that influence students’ understanding of mathematical equivalence and discusses the implications of the findings for future research, classroom practice, and policy.

The first study investigated the role of the substitution conception of the equals sign on algebra performance and found that endorsement of substitution predicts secondary school students’ algebra performance. In the second, the findings of the first were not replicated with undergraduate students. Next, the third study investigated whether problem features influence adults’ equation-solving performance, and found that use of shortcut and problem size related to adults’ performance. My final study was the first large-scale cross-cultural study in the field researching the individual and classroom level factors influencing primary students’ understanding of equivalence. Moreover, I used advanced statistical analysis methods, i.e. multilevel structural equation modelling. The findings of this study showed that (i) students’ knowledge of definitions of the equals sign, and (ii) teachers’ knowledge of students’ relational strategies related to students’ understanding of equivalence, but (iii) teachers’ knowledge of students’ operational strategies and (iv) textbooks did not. The findings also showed that these relationships were similar across the participating countries (namely, China, England, New Zealand, South Korea, Turkey and the US).

The results from the studies I conducted within the scope of this thesis make an original contribution to understanding factors influencing students’ understanding of mathematical equivalence, and have theoretical, methodological, and practical implications. Implications discussed in the thesis could inform practitioners and policy makers in particular about where to invest for improving students’ understanding of mathematical equivalence.

History

School

  • Science

Department

  • Mathematics Education Centre

Publisher

Loughborough University

Rights holder

© Emine Simsek

Publication date

2020

Notes

A doctoral thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.

Language

  • en

Supervisor(s)

Ian Jones ; Iro Xenidou-Dervou

Qualification name

  • PhD

Qualification level

  • Doctoral

This submission includes a signed certificate in addition to the thesis file(s)

  • I have submitted a signed certificate

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