Topology is considered an advanced field in mathematics, and it might seem off-putting to people with no previous experience in mathematics. The classification theorem, which lies within the field of algebraic topology, is fascinating, but understanding it requires extensive mathematical knowledge. In this manuscript, we present a modular object…

In this article, ambiguous street and park signs are analysed and deciphered using symbolic logic. These examples showcase the ways in which instructors of undergraduate mathematics courses can blend their students' everyday exposure to logical reasoning with classroom experiences. (Contains 4 tables and 6 figures.)

The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical…

The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We…

In this article, we present the results from a qualitative study on students' initial reactions to the use of structured derivations in mathematics education. Our findings suggest that the approach increases the clarity of solutions and facilitates debugging of proofs. It also has potential to increase students' self-perceived level of…

The current study compared the effects of technological environments with that of the paper-and-pencil environment on reasoning about the concept of derivatives in the context of maximum and minimum problems. The data consisted of clinical interviews conducted with three pre-service secondary mathematics teachers and a newly registered graduate…

With Simson's 1753 paper as a starting point, the current paper reports investigations of Simson's identity (also known as Cassini's) for the Fibonacci sequence as a means to explore some fundamental ideas about recursion. Simple algebraic operations allow one to reduce the standard linear Fibonacci recursion to the nonlinear Simon's recursion…

The use of short assessment tasks can provide valuable information about undergraduates' knowledge and understanding. However, it is known that there are gender-related differences in performance on certain types of objective tests, both among school pupils and university undergraduates. This article focuses on undergraduate learning, using a…