Mathematics Support Centres are to be found in various forms in the majority of UK higher education institutions. They have been established in order to ease widespread and serious difficulties that a significant number of students have with mathematics, particularly at the school-university transition. They usually offer mathematics and/or…

Here, we investigate what loci are produced when a square of side-length one is allowed to rotate around a square of side-length n, where n is a whole number. We find that if i = 1, 2, 3 or 4 (mod 4), the loci obtained for n [congruent to] i (mod 4) all have the same symmetry and we show how the perimeter of each class can be determined. We also…

Mechanics has never been the most popular subject in A-level mathematics, the UK's public examination for 16-18-year olds, either with students, teachers or educators. The attempts to popularize mechanics have failed and it is conceivable that the subject will be dropped from the A-level syllabus in the foreseeable future. This article argues the…

In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…

To help students view mathematics in a more favourable light, a number of former pupils were contacted and asked to give details of how they use mathematics in their daily lives. This information was gathered through an online questionnaire or visits to the school to talk to pupils--a booklet of responses was also given to students. Attitudinally…

We present a pictorial proof of the inequation (1 + 1/n)[superscript n] less than e less than (1 + 1/n)[superscript n+1]. The inequation is also confirmed through the Taylor expansion and alternating series theorem.

Many reasons have been documented about the need for more effective teaching of mathematics in universities. These include changes in the level of mathematical skills of new students; changes in society, particularly technological ones, which have led to a strong preference for visual presentation of information; and new students lacking the…

This article presents the results of two studies on using an innovative pedagogical strategy in teaching mathematical modelling and applications to engineering students. Both studies are dealing with introducing non-traditional contexts for engineering students in teaching/learning of mathematical modelling and applications: environment and…

A common problem in learning mathematics concerns the gap between, on the one hand, doing the formalisms and calculations of abstract mathematics and, on the other hand, applying these in a specific contextualized setting for example the engineering world. The skills acquired through problem-based learning (PBL), in the special model used at…

This article reports the findings of qualitative research undertaken to seek to identify the key reasons why some students are not engaging with mathematics support provided by Loughborough University. The research involved a number of focus groups and "on the spot" interviews with "non-users" from across the campus. Barriers identified include a…

While many engineering educators have proposed changes to the way that mathematics is taught to engineers, the focus has often been on mathematical content knowledge. Work from the mathematics education community suggests that it may be beneficial to consider a broader notion of mathematics: mathematical thinking. Schoenfeld identifies five…

A mathematics module in the undergraduate programme for first year engineers aims to enable those with low mathematical qualifications to understand and use efficiently calculus and related topics. The teaching approach is designed to develop student's fluency, understanding and responsibility through creating an inquiry community, encouraging…

Shows how integer-sided triangles can be nested, each nest having a single enclosing isosceles triangle. Brings to light what can be seen as a relatively simple generalization of Pythagoras' theorem, a result that should be readily accessible to many secondary school pupils. (Author/KHR)

Investigates the use of mathematical modeling tasks in 11- and 12-year-old students and the development of mathematical thinking skills using practical modeling activities. Analyzes the development of students' mathematical thinking with interviews of a form of dynamic assessment. Reports that some students proved to be naturally mindful and…

Considers the impact of the introduction of graphic calculators into assessment within the International Baccalaureate Diploma. Discusses difficulties that arise in the development of practice questions, how these difficulties were resolved in the questions that appeared on the examinations, and problems of different calculator syntax. (Author/KHR)