Original Research

Simplifying algebraic expressions with brackets: Insights into Grade 10 learners’ structure sense through a study of their errors

Nadia M. Theba, Craig Pournara, Shikha Takker
Pythagoras | Vol 45, No 1 | a783 | DOI: https://doi.org/10.4102/pythagoras.v45i1.783 | © 2024 Nadia M. Theba, Craig Pournara, Shikha Takker | This work is licensed under CC Attribution 4.0
Submitted: 19 September 2023 | Published: 13 May 2024

About the author(s)

Nadia M. Theba, School of Education, Faculty of Humanities, University of the Witwatersrand, Johannesburg, South Africa, South Africa
Craig Pournara, School of Education, Faculty of Humanities, University of the Witwatersrand, Johannesburg, South Africa, South Africa
Shikha Takker, School of Education, Faculty of Humanities, University of the Witwatersrand, Johannesburg, South Africa; and, School of Education, Faculty of Humanities and Social Sciences, Mahindra University, Hyderabad, India

Abstract

Developing structure sense is an important part of learning algebra. We investigated learners’ structure sense of algebraic expressions involving brackets. This led us to propose the constructs surface structure sense and systemic structure sense. Using a random sample of 58 Grade 10 learners scoring above 40% in a test, we coded incorrect responses for surface and systemic structure errors. The initial analysis revealed that the presence of more brackets supports surface structure sense. However, learners overgeneralised the presence of brackets to represent multiplication in situations involving subtraction. The arrangement of brackets also led to errors in the order of operations. Further analysis suggested that regular application of procedures on familiar algebraic structures may give the illusion of systemic structure sense. We recommend that the teaching of algebraic expressions must emphasise what the arrangement of an expression means before focusing on how to operate on the expression.

Contribution: The research contributes to mathematics teaching by suggesting teaching strategies to improve on learners’ understanding of the role of brackets in algebraic expressions, by considering the arrangement of the components in structures.


Keywords

structure sense; algebraic expressions; brackets; Grade 10; algebra.

Sustainable Development Goal

Goal 4: Quality education

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