Original Research - Special Collection: Supporting Excellence in Early Childhood Mathematics Education

Young students’ understanding of mathematical equivalence across different schools in South Africa

Sharon McAuliffe, Cosmas Tambara, Emine Simsek
South African Journal of Childhood Education | Vol 10, No 1 | a807 | DOI: https://doi.org/10.4102/sajce.v10i1.807 | © 2020 Sharon McAuliffe, Cosmas Tambara, Emine Simsek | This work is licensed under CC Attribution 4.0
Submitted: 31 August 2019 | Published: 26 November 2020

About the author(s)

Sharon McAuliffe, Faculty of Education, Cape Peninsula University of Technology, Cape Town, South Africa
Cosmas Tambara, Faculty of Education, Cape Peninsula University of Technology, Cape Town, South Africa
Emine Simsek, Centre for Mathematical Cognition, Loughborough University, Loughborough, United Kingdom

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Background: Mathematical equivalence is a critical element of arithmetic understanding and a key component of algebraic thinking which is necessary for success in all levels of mathematics. Research studies continue to highlight misconceptions related to equivalence and reveal that many primary school students have a narrow and limiting view of the equals sign as an operation.

Aim: This study aims to investigate young students’ understanding of mathematical equivalence in South Africa with a particular focus on their interpretations of the equals sign.

Setting: Research data was obtained from students across six schools from different contexts within the Western Cape.

Methods: We gave students an adapted standardised assessment containing 15 items related to equivalence.

Results: Our analyses indicated that students focus more on the equals sign as an operation which involves calculating an answer. While some referred to equivalence as meaning the same as, most of them were inclined to accept the operational definition of the equals sign (i.e. the answer to the problem) as a better and preferred definition. In addition, student performance was poor on equation-solving problems and they rarely used comparative relational strategies in their solutions.

Conclusion: The findings of this research confirmed that difficulties with equivalence reported by earlier research is widespread across this group of grade 4 students. This has implications for both curriculum, textbook and materials design and teacher professional development.


Mathematical equivalence; The equals sign; Early algebra; Operational view; Relational view


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