Jean-Baptiste Lagrange

Technology and Mathematics Education: A Multidimensional Study of the Evolution of Research and Innovation

This chapter will highlight the interest and necessity of considering a plurality of perspectives (or dimensions) when addressing the issue of the integration of information and communication technologies (JCT) into the teaching and learning of mathematics. It will also show how this multidimensional perspective can be efficient for an analysis of the existing literature.

Curriculum, Classroom Practices, and Tool Design in the Learning of Functions through Technology-Aided Experimental Approaches.

The paper starts from classroom situations about the study of a functional relationship with help of technological tools as a ‘transposition’ of experimental approaches from research mathematical practices. It considers the limitation of this transposition in existing curricula and practices based on the use of non-symbolic software like dynamic geometry and spreadsheets. The paper focuses then on the potentialities of classroom use of computer algebra packages that could help to go beyond this shortcoming. It looks at a contradiction: while symbolic calculation is a basic tool for mathematicians, curricula and teachers are very cautious regarding their use by students. The rest of the paper considers the design and experiment of a computer environment Casyopée as means to contribute to an evolution of curricula and classroom practices to achieve the transposition in the domain of algebraic activities linked to functions.

Design for Transformative Practices

Software design is a crucial dimension in the educational use of technology and a key for transformative practices. The choice for this chapter, issued of a plenary panel at the study conference, has been to ask creators and designers of well established and widely used environments to contribute from his/her own unique expertise. After introductory remarks by the coordinator of the panel, each contributor exposes what visions drive his/her work and how.

Introduction: Perspectives on Didactics of Mathematics through Michèle Artigue’s Contributions

Since the early 1970s and up to the present day, Michele Artigue has been closely linked to the emergence and the development of the didactics of mathematics. By observing her exemplary professional history, one can witness a new and specific research domain taking form, as well as see the difficulties that accompanied its recognition by both the academic community and, more generally, the whole education community. Following this notion of recognition, we have organised this opening chapter around some of the major issues related to the past, the present, and the future of the didactics of mathematics, and more generally of mathematics education: didactics as a specific research domain, the role of theoretical frameworks, the relationship to connected fields of research, and finally, the way didactics considers its relationship with the outside world of mathematics teaching and learning.