Studies related to school mathematics have shown that students who scored well on standardized tests often are unable to successfully use memorized facts and formulae in real-life application outside the classroom. The outcome of TIMSS and PISA studies further emphasizes the importance of mathematics teaching and learning in the Malaysian…

This study aims to analyse university level mathematics education students' perceptions on conceptual understanding of trigonometry and trigonometric functions and their content development of these concepts. A case study was conducted with 90 freshman students of Elementary Mathematics Department. The data were gathered via a scale; they included…

Martin Gardner's "The Annotated Alice," and Robin Wilson's "Lewis Carroll in Numberland" led the authors to put this article in a fantasy setting. Alice, the March Hare, the Hatter, and the Dormouse describe a straightforward, elementary algorithm for counting the number of ways to fit "n" identical objects into "k" cups arranged in a circle. The…

The hyperbolic function sinh(x)/x receives scant attention in the literature. We show that it admits a clear geometric interpretation as the ratio between length and chord of a symmetric catenary segment. The inverse, together with the use of dimensionless parameters, furnishes a compact, explicit construction of a general catenary segment of…

In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of…

Concept-focused quiz questions required College Algebra students to write about their understanding. The questions can be viewed in three broad categories: a focus on sense-making, a focus on describing a mathematical object such as a graph or an equation, and a focus on understanding vocabulary. Student responses from 10 classes were analyzed.…

In a developmental research approach, from a sociocultural position, we address the meanings students make of mathematics in teaching sessions and how this relates to the intentions of the teacher and approaches to teaching. Analyses of data come from small group tutorials of one tutor with first year university mathematics students (n=5). We…

The aim of this paper is to report early findings from university mathematics teaching in the tutorial setting. The study addresses characteristics of the teaching of an experienced research mathematician and through interviews, her underlying considerations. An analysis of a teaching episode illuminates her use of generic examples to reveal…

"Instant Insanity II" is a sliding mechanical puzzle whose solution requires the special alignment of 16 colored tiles. We count the number of solutions of the puzzle's classic challenge and show that the more difficult ultimate challenge has, up to row permutation, exactly two solutions, and further show that no…

A deeper learning of the properties and applications of the derivative for the study of functions may be achieved when teachers present lessons within a highly graphic context, linking the geometric illustrations to formal proofs. Each concept is better understood and more easily retained when it is presented and explained visually using graphs.…

Traditional definitions, language, and visualizations of convergence and the Cauchy property of sequences convey a sense of the sequence as a potentially infinite process rather than an actually infinite object. This has a deep-rooted influence on how we think about and teach concepts on sequences, particularly in undergraduate calculus and…

Most students thinking mathematics is a difficult subject. This study aims to enhance students' motivation and efficiency in learning mathematics. This study developed 3D animation on the binomial theorem with historical stories of mathematics as the plot. It also examined the effect of animation on students' learning willingness and…

The research relates to undergraduate students' understanding of mathematical concepts that relate to the conceptualisation of the continuous such as the notion of limit. The cognitive difficulties that accompany the learning of these concepts at the different stages of the mathematics education are well reported in the literature. I analyse the…

Instructors in higher education are very familiar with the Likert scale Students' Evaluation of Teaching (SET) used to evaluate teaching. Researchers have raised concerns about biases affecting the results of SET surveys, as well as their validity and reliability and use in high-stakes decision making. Here, we demonstrate that Q methodology,…

We analysed multivariable calculus students' meanings for domain and range and their generalisation of that meaning as they reasoned about the domain and range of multivariable functions. We found that students' thinking about domain and range fell into three broad categories: input/output, independence/dependence, and/or as attached to specific…