Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…

We consider how the arc length integral of the graph of a function in the plane is connected with the hyperbola and its rational parameterization.

The article presents a demonstration of the converse of the Pythagorean Theorem based on the "reductio ad absurdum". This is necessary to overcome the discrepancy, noticed by pupils, between the Euclidean purpose to demonstrate that the given triangle is right-angled and the auxiliary figure by which the given triangle is drawn as if it were…

A practical and technological application of calculus problem is posed to motivate freshman students or junior high school students. A variable coefficient of friction is used in modelling air friction. The case in which the coefficient of friction is a decreasing function of altitude is considered. The optimum parabolic path for a flying object…

We developed four separate scenarios focusing on the connections between mathematics, biology, and social sciences. This structure facilitated the coordination of faculty from seven academic departments on campus. Each scenario had students from different majors build mathematical models, gather information from their respective disciplines, and…

We present the topic of graph connectivity along with a famous theorem of Menger in the real-world setting of the national computer network infrastructure of "National LambdaRail". We include a set of exercises where students reinforce their understanding of graph connectivity by analysing the "National LambdaRail" network. Finally, we give…

Promoting student understanding for transfer is an illusive hallmark of effective mathematics instruction. While much research has shown the necessity of promoting understanding for transfer, less attention has been paid to actual pedagogical strategies that can be used to promote transfer of mathematical ideas. Using Fogarty et al. (1992, "How to…

In this article we consider, via a specific modelling example, the educational benefits to be gained from running mathematical activities with our sixth-form and undergraduate students that, in modern parlance, might be termed "rich tasks". The idea for this modelling activity arose while the author was reading a popular-science book on cosmology…

In this article, we consider the mathematics grades of first year students at the National University of Ireland Maynooth and the influence that the Mathematics Support Centre (MSC) has on these grades. We will consider the evidence to suggest that the MSC has a positive effect on the grades of the students who attend the centre. It seems to be…

The study reported in this article deals with the observed actions of Turkish pre-service mathematics teachers in dynamic geometry environment (DGE) as they were learning Khayyam's method for solving cubic equations formed as x[superscript 3] + ax = b. Having learned the method, modelled it in DGE and verified the correctness of the solution,…

A problem is discussed which is generated by shadows and which is a generalization of simple harmonic motion.

In this article, we give a brief history of the Feynman's Triangle problem and describe a simple method to solve a general version of this problem, which is called the Routh Theorem. This method could be found useful to school teachers, instructors or lecturers who are involved in teaching geometry.

This article describes one type of mathematical problem, open-start problems, and discusses their potential for use in assessment. In open-start problems how one starts to address the problem can vary but they have a correct answer. We argue that the use of open-start problems in assessment could positively influence classroom mathematics…

In Volume 26, Number 2, we reported on a group case study run for level 3 mathematics students at the University of Brighton. At the core of the study was a quadratic assignment problem, and we reported on attempts by students to use Excel to solve the problem, and on the attendant difficulties. We provided an elegant solution. In this article, we…

Vehicles holding at traffic lights is a typical queuing problem. At crossings the vehicles experience delay in both directions. Longer periods with green lights in one direction are disadvantageous for the vehicles coming from the other direction. The total delay for getting through the traffic point is what counts. This article presents an…