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…

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…

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…

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…

The general perception is that high school teaching of mathematics in South Africa tends to be fairly procedural and that students that enter university are better equipped to deal with procedural problems rather than conceptual. This study compares the conceptual and procedural skills of first-year calculus students in life sciences. Also…

This paper focuses on blended learning in mathematics I module in elementary calculus, at a University of Technology. A computer laboratory was used to create a learning environment that promoted interactive learning together with traditional teaching. The interactive learning was performed using projects to optimize the discovery and error…