This article focuses on first-year university students' understanding of concepts related to third-degree polynomial and trigonometric functions that they encountered during their study of Grade 12 mathematics. In this study three online questions from two first-year mathematics quizzes at the University of KwaZulu-Natal were analysed. The first…

This case study explored Grade 12 learners' misconceptions in limits of functions. The study aimed at understanding problems that learners face in learning the concepts of limit by analyzing misconceptions that learners have and identifying the possible sources of these misconceptions to take remedial action. An exploratory research design was…

The concept of the limit is often experienced as a very abstract concept. In this study we explore the understanding of the concept of the limit with 74 students who are prospective high school mathematics teachers. The study is located within the first of three calculus courses which they study as part of their bachelor's degree in education at a…

The literature describes different stances concerning the focus on how mathematics should be taught, with some preferring a conceptual knowledge approach and others a procedural knowledge approach. The current study investigated the relationship between students' conceptual and procedural knowledge in a calculus context. To better understand the…

The outbreak of COVID-19 and the consequent lockdown took the world by surprise, forcing the trimming of the school curriculum and institutions of higher learning to urgently adopt online platforms to continue teaching and learning. This article is a case study that explores the use of a social media platform, WhatsApp, to improve peer learning…

Recreating the social aspects of face-to-face teaching in an online environment became more challenging in the midst of the COVID-19 pandemic. With limited or no face-to-face interaction with students, lecturers had to explore alternative ways to recreate aspects of an engaging and supportive face-to-face learning environment. This article focuses…

This paper seeks to explore the nature of dialogue within calculus lecture rooms. This paper reports on part of a larger study, in which the participants were two lecturers lecturing to 198 third year pre-service teachers at a University in South Africa. This qualitative interpretive study was framed within the ambits of social constructivism and…

Dynamic visual tools such as MATLAB have inbuilt features which are believed to be able to empower students to learn through the visualisation of three-dimensional objects. While student learning through MATLAB has been investigated regarding students in urban settings, only a handful of studies have investigated how MATLAB can assist students in…

This study focuses on the mathematics department at a South African university and in particular on teaching of calculus to first year engineering students. The paper reports on a cause-effect analysis, often used for business improvement. The cause-effect analysis indicates that there are many factors that impact on secondary school teaching of…

This paper presents an enrichment case study to showcase a possible avenue for attending to the needs of academically strong mathematics students. We report on a group of university students who were presented with the opportunity of exploring a specific first year mathematics topic deeper, using an inquiry-based learning approach as part of an…

This article reports on a study which used the APOS (action-process-object-schema) Theory framework and a classification of errors to investigate university students' understanding of the integration concept and its applications. Research was done at the Westville Campus of the University of KwaZulu-Natal in South Africa. The relevant rules for…

In this article I use Sfard's theory of commognition to examine the surprising activities of a pair of in-service mathematics teachers in South Africa as they engaged in a particular mathematical task which allowed for, but did not prescribe, the use of GeoGebra. The (pre-calculus) task required students to examine a function at an undefined point…

This article reports on a study which investigated first year university engineering students' construction of the definition of the concept of the chain rule in differential calculus at a University of Technology in South Africa. An APOS (Action-Process-Objects-Schema) approach was used to explore conceptual understanding displayed by students in…

This qualitative case study in a rural school in Umgungundlovu District in KwaZulu-Natal, South Africa, explored Grade 12 learners' mental constructions of mathematical knowledge during engagement with optimisation problems. Ten Grade 12 learners who do pure Mathemat-ics participated, and data were collected through structured activity sheets and…

Many studies point to the problem of poor mathematics content knowledge of mathematics teachers in South Africa. The purpose of this study was to investigate teachers' knowledge of the mathematics they are themselves teaching. Data was generated from the teachers' (n = 253) written responses to test that was a shortened form of a previous Grade 12…