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…

The purpose of this article is to conduct a mathematical and phenomenological comparison of three concepts: (1) the finite limit of a function at a point, (2) the finite limit of a sequence, and (3) the infinite limit of a sequence. Additionally, we aim to analyse the presence of these concepts in Spanish textbooks. The methodology employed is…

Error analysis is an instructional strategy that can assist teachers to identify learners' areas of weakness in mathematics and that can point to remediation of those errors. This article explores the errors learners exhibit when solving quadratic equations by completing the square using Newman's Error Analysis Model. A research study explored the…

Mathematics achievement is core to South Africa's readiness for digital innovation, yet current pass rates in this subject are below the global average. Simply attributing mathematics performance to intelligence does not fully account for the multifaceted reality of achievement in the subject. The current study investigated the value of both…

Possessing mathematical competence is a pre requisite for independently comprehending, understanding and applying all features of mathematical modelling in a particular setting. This research study thus explores the mathematical modelling competencies that Grade 10 learners exhibit while solving contextual problems in a mathematics learning and…

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…

The teaching and learning of mathematics in sub-Saharan African countries is dominated by teacher-centred pedagogies rather than student-centred ones. Observations of mathematics teachers at two private schools in South Sudan confirmed such practices. This inspired the researchers to design an intervention to help six primary mathematics teachers…

Flexible teaching of mathematics word problems is essential to improve learning. Flexible teaching is vital in terms of providing meaningful learning, creating inclusive learning spaces and making content accessible. As such, teachers need to strive to provide flexible teaching of mathematics word problems in order to optimise and maximise…

A cohort of pre-service mathematics students was exposed to a teaching strategy based on retrieval practice and test-potentiated learning. The aim of the study was to determine how high and low prior topic knowledge study participants compare in terms of their procedural fluency and conceptual understanding after exposure to the teaching strategy.…

This article is an advanced theoretical study as a result of a chapter from the first author's PhD study. The aim of the article is to discuss the relationship between commognition and the Van Hiele theory for studying discourse during Euclidean geometry problem-solving. Commognition is a theoretical framework that can be used in mathematics…

Problem-solving is of importance in the teaching and learning of mathematics. Nevertheless, a baseline investigation conducted in 2016 revealed that mathematical problem-solving is virtually missing in South African classrooms. In this regard, a two-cycle design-based research project was conducted to develop a professional development (PD)…

This article explores a conceptual relationship between learner choice and mathematical sense-making. It argues that when learners can exercise choice in their mathematical activities, mathematical sense-making can be enhanced. The literature around mathematical modelling suggests a link between sense-making and learner choice. A three-tiered…

The purpose of the reported study was to investigate the social science students' concept images and concept definitions of anti-derivatives. Data were collected through asking students to answer 10 questions related to anti-derivatives and also by interviewing them. The theory of concept image and concept definition was used for data analysis.…

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…

The purpose of this mixed methods study was to investigate the effect of a graphing calculator (GC) intervention on Grade 11 learners' achievement in quadratic inequality problem solving. The quantitative aspects of the study involved an experimental and control group design in which the experimental group received instruction using the GC…