A study of the computations done by grade 9 learners in a Western Cape high school when simplifying algebraic expressions involving the negative symbol

Brink, Hestia

A study of the computations done by grade 9 learners in a Western Cape high school when simplifying algebraic expressions involving the negative symbol

Thesis / Dissertation

2025

Publisher

University of Cape Town

Department

School of Education

Faculty

Faculty of Humanities

Abstract

The computations that learners do when simplifying algebraic expressions are multiple and diverse, with some determined by reasoning aligned with mathematics whilst others rely on idiosyncratic constructs like mnemonics or solution templates. Research in mathematics education highlights symbol sense and negative number concepts as persistent difficulties in learning algebra and categorises learners' errors, but it is wanting in explanations of learners' computations and how they might relate to the way learners think. This study identifies, describes and offers possible explanations for some of the computations that learners did when attempting to simplify algebraic expressions involving the negative symbol. Grade 9 learners from one class in a Western Cape high school were given a set of algebraic expressions to simplify after which interviews were conducted with some learners to discuss their solutions. In the computational analysis of the data, cognitive science and universal algebra were used as lenses for a deeper understanding of learners' mathematical (and non-mathematical) thinking. The data indicates learners' tendency to read algebraic expressions as strings of characters constituting different types of objects, classified in this study as operators, signs, numerals, letters, and superscripts. As suggested by the literature, the negative symbol presented learners with additional challenges, given its polysemic nature in mathematics. Many learners resorted to replacing standard mathematical operations with various operation-like manipulations taking different types of objects as arguments. Plausible reasons for learners' type-sensitivity and idiosyncratic computations offered by this study include: humans' innate capacity for recognising and categorising different objects and symbols; the biases produced from language; and the reliance on existing mental structures for the assimilation of new knowledge. In considering learners' computations at a fundamental level, this study contributes to a more complete view of what learners do computationally and, importantly, why.