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…

This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further…

An investigation into prospective mathematics/statistics teachers' (n = 134) conceptual understanding of statistics and attitudes to statistics carried out at the University of Limerick revealed an overall positive attitude to statistics but a perception that it can be a difficult subject, in particular that it requires a great deal of…

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…