In this article, we explored Grade 11 learners' algebraic and geometric connections when solving Euclidean geometry riders. A qualitative interpretive case study design was followed. Thirty Grade 11 learners from a non-fee-paying secondary school in the Capricorn North district of South Africa were conveniently sampled to participate in this…

This research investigates errors and misconceptions among learners in algebraic education by utilizing Koch's error analysis method alongside the Structure of the Observed Learning Outcome (SOLO) taxonomy. The primary aim of the investigation is to discern the kinds of errors and cognitive stages demonstrated by Grade 9 students when engaged in…

South African learners' performance in mathematics, both locally and internationally, has raised significant concerns, particularly in the realm of algebra. To address this issue, a mixed-methods study was conducted to explore the effectiveness of using algebra tiles to teach algebraic expressions. The study aimed to investigate algebraic…

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…

Foundation programmes provide an alternate access route for prospective students whose prior academic results exclude direct entry to undergraduate studies. Bridging courses within foundation programmes address gaps in prior knowledge while developing content knowledge and requisite skills to equip students for the rigour of undergraduate degree…

This article revisits and expands upon a previous phenomenographic study characterising the qualitatively different ways in which South African undergraduate physics students may experience the use of +/- signs in one-dimensional kinematics (1DK). We find the original categorisation as applicable for interpreting Swedish university-level students'…

In this paper, we provide an elaboration of the notion of mathematical structure -- a term agreed upon as valuable but difficult to define. We pull apart the terminology surrounding the notion of structure in mathematics: relationship, generalising/generalisation and properties, and offer an architecture of structure that distinguishes and…

This article provides insights into Grade 11 learner understanding of the roots of quadratic equations, how learners used solution strategies to find equations with given roots, how they determine the unknown values and the other root when one root is given and how they determine the unknown values when two roots of the equation are given. The…

Responding constructively to unexpected events during a lesson is a particularly challenging facet of teaching. This study aimed to investigate how a secondary school mathematics teacher responded to learners' unexpected or unplanned offers in the teaching of algebra. A total of three sequential lessons were video recorded and the quality of the…

The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge in some branches of mathematics, the relationship between learners' procedural and conceptual knowledge of…

Despite receiving increasing attention from mathematics education scholars, there has not yet been any overall understanding of the current state of realistic mathematics education (RME). To address this gap, this study aims to provide a review of 288 studies on realistic mathematics education from the Scopus database between 1972 and 2019. Using…

Improving the strength of alignment between educational components is essential for quality assurance and to achieve learning goals. The purpose of the study was to investigate the strength of alignment between Senior Phase mathematics content standards and workbook activities on numeric and geometric patterns. The study contributes to…

This study explored the mental constructions displayed by pre-service mathematics teachers (PMTs) when applying Cramer's rule. The aim was to reveal the character of mental constructions made around the nature of the solution set of equations and the role of parameters in the solution of equations with parametric coefficients. These mental…

Concerns have been expressed that although learners may solve linear equations correctly they cannot draw on mathematically valid resources to explain their solutions or use their strategies in unfamiliar situations. This article provides a detailed qualitative analysis of the thinking of 15 Grade 8 and Grade 9 learners as they talk about their…

South African Mathematical Literacy (ML) learners are unlikely to have mastered the mathematical skills essential for undergraduate degree studies in Business Science and are most likely to commence tertiary studies in a foundation programme (FP). One such FP at one private higher education institution included an algebra course and provided an…