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 study investigated two undergraduate mathematics students' meanings for derivatives of univariable and multivariable functions when creating linear approximations. Both participants completed multivariable calculus at least two semesters prior to participating in a sequence of four to five exploratory teaching interviews. One purpose of the…

According to commognitive conceptualization, development of mathematical thinking, whether historical or ontogenetic, requires periodic transitions to mathematical discourse "incommensurable" with the one that has been practiced so far. In this new discourse, some familiar mathematical words will be used in a new way. Historically, such…

Optimization is introduced to teaching in secondary school, focussing on functions of one variable with the first derivative criterion for critical points and monotonicity of functions. The second derivative criterion is also used to determine the nature of the critical points. Similarly, in university-level teaching, algebraic work using criteria…

This meditation on subjectivity draws on mundane and explicitly political contexts to argue for mathematics education practices that help us understand how people use mathematics to shape our world. I use two contexts to consider how to develop citizens who understand how we are subjugated by mathematical systems (designed and sustained by…

This paper contains interesting facts regarding the powers of odd ordered special circulant magic squares along with their magic constants. It is shown that we always obtain circulant semi-magic square and special circulant magic square in the case of even and odd positive integer powers of these magic squares respectively. These magic squares…

Discrete mathematics brings interesting problems for teaching and learning proof, with accessible objects such as integers (arithmetic), graphs (modeling, order) or polyominoes (geometry). Many problems that are still open can be explained to a large public. The objects can be manipulated by simple dynamic operations (removing, adding, 'gluing',…

Example-generation tasks have been suggested as an effective way to both promote students' learning of mathematics and assess students' understanding of concepts. E-assessment offers the potential to use example-generation tasks with large groups of students, but there has been little research on this approach so far. Across two studies, we…

Knowing functions and functional thinking have recently moved from just knowledge for older students to incorporating younger students, and functional thinking has been identified as one of the core competencies for algebra. Although it is significant for mathematical understanding, there is no unified view of functional thinking and how different…

Strategies are proposed that promote use of an Integrated Applied Mathematics (IAM) approach to enhance teaching of advanced problem-solving and analysis skills. Three scenarios of 1-dimensional transport processes are presented that support using Error Function analyses when considering short time/small penetration depths in finite geometries.…

The current meta-analysis investigates the longitudinal association between prior and subsequent mathematics performance, involving mathematics measured at three time points, and to identify potential factors that could moderate this association, including age, time lag, and types of mathematics. Our analysis included 105 studies, comprising 111…

This study is a contribution to efforts to promote practices for dealing with the difficulties encountered by learners in probabilistic modeling situations. We attempt to elucidate as precisely as possible the types of difficulties that secondary school students face in the process of modeling with probability tools. By referring to a large and…

Recently, the importance of statistical literacy has been stressed, and three central concepts in statistical literacy are the measures of central tendency: mean, median, and mode. This study explores aspects of statistical literacy expressed by 12-13-year-old students, focusing on mean, median, and mode. Their responses were analysed using a…

The aim of this paper is to contribute to the ongoing discussion about the role of intuition and ambiguity in doing, teaching and learning mathematics. We start by discussing the ways in which limits and continuity are presented in Calculus textbooks, to illustrate some of the ambiguities, and to contrast them with precise and rigorous definitions…

Although absolute value is of interest to mathematics teaching researchers, since many students face problems with it, there does not seem to be an integrated record of students' errors. The present study attempts to conduct a systematic review to identify and categorize errors and misconceptions of secondary school students aged 12-18 concerning…