This article traces some of the influential ideas and motivations that have shaped a large part of the research on the use of new technologies in mathematics education over the past 40 years. Particular attention is focused on Papert's legacy, Celia's Hoyles' transformation of it, and how both relate to the current research…

We consider the famous two envelope conundrum and show, in a very simple way, that there is no conundrum. Our discussion is supported by numerical simulations. We use the problem to raise the issue of disputes in mathematics, rarely touched upon in mathematics education. We suggest that it is worthwhile to expose students of mathematics to such…

Computer-aided assessment (CAA) has been used at a university with one of the largest mathematics and engineering undergraduate cohorts in the UK for more than ten years. Lecturers teaching mathematics to first year students were asked about their current use of CAA in a questionnaire and in interviews. This article presents the issues that these…

In this article we report and discuss a contextual problem solving task that was proposed to a class of 8th grade (13-14-year-old) students. These students had been developing a reasonable experience in the use of the spreadsheet to model relations within contextual problems and chose to use this tool to solve the mentioned problem, engaging in…

The purposes of an online system to auto-mark students' responses to mathematics test items are to expedite the marking process, to enhance consistency in marking and to alleviate teacher assessment workload. We propose that a semi-automatic marking and customizable feedback system better serves pedagogical objectives than a fully automatic one.…

A new application of logarithmic differentiation is presented, which provides an alternative elegant proof of two basic rules of differentiation: the product rule and the quotient rule. The proof can intrigue students, help promote their critical thinking and rigorous reasoning and deepen their understanding of previously encountered concepts. The…

In this article, we show a dynamic graphic in Excel that is used to introduce an important concept in our subject, Statistics I: the probability density function. This interactive graphic seeks to facilitate conceptual understanding of the main aspects analysed by the learners.

This article considers the role of socio-cognitive conflict in addressing students' mechanics preconceptions. A discussion problem was posed to sixth-form students taking an introductory mechanics unit. The problem involved a child choosing either to slide down a smooth slide or to jump off the top. Students were invited to predict which route…

Teaching mathematics associated with the repaying of loans has always been an awkward task--it seems superficially easy, but it contains pitfalls both for the learner and for the unwary teacher. This short article reviews some of the mathematics, and notes an interesting result.

With the London 2012 Olympics coming up, now is a good time for teachers to turn to track and field athletics for an application that has the potential to be intrinsically interesting to many pupils in schools new undergraduates. In this article, curves, well-known amongst former generations of pupils, are revisited by looking at the markings on…

Courses in mathematical modelling are always in need of simple, illustrative examples. The Michaelis-Menten reaction kinetics equations have been considered to be a basic example of scaling and singular perturbation. However, the leading order approximations do not easily show the expected behaviour, and this note proposes a different perturbation…

When one uses Google (and many people do this!), the result of the query is a list of sites that have something to do with the item one is looking for. The specific sites are always more or less on the top, so it is not necessary to have a look on hundreds of sites to read something relevant and informative. How can Google manage this? How does…

The quadratic mean, geometric mean and harmonic mean of two numbers "a" and "b" are obtained as weighted averages by using segments parallel to the bases "a" and "b" of a trapezoid.

This article describes an activity that can be carried out in one of the final classes of Italian secondary schools. The aim of the activity is to stimulate pupil curiosity, demonstrating that Mathematics is not a barren subject and allowing the students, according to an interdisciplinary point of view, to investigate some literary works and the…

Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…