DIGITAL TECHNOLOGIES: A WINDOW ON THEORETICAL ISSUES IN MATHEMATICS EDUCATION

In this lecture, I use digital technologies as a window on theoretical issues in mathematics education. More precisely I address the issue of the theoretical fragmentation of the field. After setting the problem in an introductory part, I successively use two dimensions of my research activity with digital technologies for approaching this issue. The first one corresponds to the development of the instrumental approach, the second one to the on-going research work on the integration of theoretical frames carried out within the European projects TELMA and ReMath. I. Introduction Researchers in the field of mathematics education seem more and more sensitive to the difficulties generated by the diversity and fragmentation of existing theoretical frames in the field 1 . Why so many theories and constructs? What exact needs do these constructions try to respond to? How many different constructs do we have for expressing more or less the same concerns, for fulfilling the same goals? What do they have in common and what exactly differentiates them? How do they respectively shape our research and design practices and more globally our vision of didactical action? How can we coherently and productively behave as researchers and as practitioners in such a world? Is it possible to reduce the increasing theoretical load of the field and, if so, how could this goal be better achieved? In the lecture, I address these issues, using as a filter the research developed on the design and educational use of digital technologies, and relying on my personal research experience. I specially use as examples the development of the so-called "Instrumental approach" from the mid nineties, and the research work I am currently involved in the frame of two European projects: TELMA and ReMath 2 with the aim of developing tools for connecting and integrating different theoretical approaches. I.1. Why approaching theoretical issues through digital technologies? I have chosen in this lecture to focus on theoretical issues in mathematics education, and to use research on teaching and learning with digital technologies: calculators, mathematics software or any kind of digital resources, as a window for looking at these issues.

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