Reports from 13 Further Mathematics Knowledge Networks supported by the National Centre for Excellence in the Teaching of Mathematics [NCETM] are analysed. After summarizing basic characteristics of the networks regarding leadership, composition and pattern of activity, each of the following aspects is examined in greater depth: Developmental aims…

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…

The integration of digital tools in mathematics education is considered both promising and problematic. To deal with this issue, notions of "webbing" and "instrumental orchestration" are developed. However, the two seemed to be disconnected, and having different cultural and theoretical roots. In this article, we investigate…

This article focusses on a programme of research into the teaching and learning of proof inspired by Celia Hoyles. By revisiting the first of a series of projects into justifying and proving in school mathematics developed by Celia in the 1990s and by considering how the innovative research methods adopted as well as the results obtained impacted…

For more than 10 years, I had the honour and pleasure to work with Celia Hoyles and Richard Noss. We share a common concern for more learnable mathematics, especially in algebra, and for the need to build new representational infrastructures taking advantage of technology. Beyond this common concern, my choice to work in the French institutional…

Some mathematical activities and investigations for the classroom or the lecture theatre can appear rather contrived. This cannot, however, be levelled at the idea given here, since it is based on a perfectly sensible question concerning distributional approximations that was posed by an undergraduate student. Out of this simple question, and…

As mathematicians, we assign rigid meanings to words that may have a variety of interpretations in common language. This article considers meanings of "if" and "or" from everyday English that have caused students to misinterpret mathematical statements, and that are consistently overlooked by instructional materials in addressing students'…

Teachers of mathematics recognize the difficulty of reaching every student when the range of student abilities puts a considerable strain on the classroom discussion and time. In a response to the problem, students are grouped so that those with greater mathematical aptitude help those who have difficulties. While this approach is to be…

In this research we present the use of some technologies in problem solving activities (at different secondary school grades), aimed at finding a model for a geometric configuration, and representing this model in various ways: through a construction, through a Cartesian graph, etc. The task is part of a teaching experiment, in which students used…

When a Computer Algebra System (CAS) is used as a pedagogical and functional tool in class and as a functional tool in exams, its effect on student achievement can be quite profound. The timing of when students are first introduced to a CAS has an impact on gains in student achievement. In this action research project, the CAS calculator was…

This theoretical study is an attempt to explore the potential of the dynamic and interactive mathematics learning environments (DIMLE) in relation to the technological pedagogical content knowledge (TPACK) framework. DIMLE are developed with intent to support learning mathematics through free exploration in a less constrained environment. A…

The present article reports a study concerning the analysis of 19 activity plans (we call them "scenarios") developed by mathematics teacher educators-in-training for the pedagogical use of digital tools. The development of these scenarios took place during their training program and was designed as an activity for increasing reflection, for…

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.…

No risk, no fun--betting on sports events costs the gamblers a lot of money and brings excellent profits to those who offer the bets. Among the people who bet on a regular basis, the proportion of young adults is frighteningly high. We now suggest a concept (as part of a basic mathematics course) for acquiring the necessary mathematical knowledge…

Based on the results of a survey of the science and mathematics students at our university, we observed that students do not consider mathematics and science to be creative endeavors, though the traditional artistic disciplines rank high in this regard. To address this problem in perception, the authors used photography as a means to encourage…