Michèle Artigue

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.

Le Logiciel ‘Derive’ comme revelateur de phenomenes didactiques lies a l'utilisation d'environnements informatiques pour l'apprentissage

In this article, we address the issue of integration of computer environments in the mathematics secondary curriculum, by referring to the results of a research project carried out with the software DERIVE. Firstly, we present the research project and its theoretical framework, secondly, we evidence some didactical phenomenas linked to the DERIVE transposition of mathematical knowledge and learning processes in this environment which, in our opinion, play a crucial role in integration issues.

The Integration of Symbolic Calculators into Secondary Education: Some Lessons from Didactical Engineering

In this chapter, we approach the question of the integration of symbolic calculators into education, through the analysis of two didactic engineering projects developed and experimented by the research teams ERES (Universite Montpellier II) and DIDIREM (Universite Paris VII). The first project concerns exact and approximate computation, and the equivalence of algebraic expressions; it was planned for grade 10 students (15–16 year-old students); the second project concerns the teaching of the derivative to grade 11 scientific students. Through retrospective analysis of these two experiments, and by using the theoretical frames and approaches developed in the previous chapters, we investigate the problems raised by the integration of symbolic calculators into secondary mathematics education. This leads us, in the last part of this chapter, to discuss the viability of such an integration.

Teacher training as a key issue for the integration of computer technologies

In spite of many institutional actions, and the enthusiasm and militancy of pioneers, the integration of computer technologies into secondary mathematics teaching develops very slowly in France. In this text we point out some obstacles to integration which seem specially resistant—the limited ‘educational legitimacy’ of computer technologies, the underestimation of computer transpositive processes, the opposition between the technical and conceptual dimensions of mathematical activity, the relationship to instrumentation—and defend the thesis that the poor sensitivity of the usual teacher training to these obstacles partially explains its poor efficiency.

Numeration a l'ecole elementaire

This paper presents results of research concerning the construction of the concept of natural integers by children. By testing the same children, whose school history was known with accuracy, at one year in tervals, we have sought to determine:— How their competence in counting and numeration evolved during this period.— What the mechanisms of this evolution were.— What role school learning played.