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

Abstract

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.

Keywords

• mathematical equivalence
• the equals sign
• early algebra
• operational view
• relational view