An Instrumental Approach to Mathematics Learning in Symbolic Calculator Environments

Luc Trouche (1, 2)

1 LIRDEF - Laboratoire Interdisciplinaire de Recherche en Didactique, Éducation et Formation
2 LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier

A rapid technological evolution (Chapter 1), linked to profound changes within the professional field of mathematics (Chapter 3), brings into question the place of techniques in mathematics teaching (Chapter 5). These changes have created serious difficulties for teachers; obliged to question their professional practices, they make different choices regarding integration of new technologies and techniques (Chapter 4), choices that are linked to their mathematical conceptions and to their teaching styles. In this chapter, we place ourselves on the side of the students. We have already seen (Chapter 1) that they seem to adopt the new computing tools faster than the institution. In this chapter, we study more precisely their learning processes related to their use of symbolic calculators. First of all, we pinpoint the didactic phenomena taking place in the experiments; subsequently, we suggest a new theoretical approach aimed at giving a better description, for each student, of the transformation of a technical tool into an instrument for mathematical work.

Mots clés: Computational transposition; Instrumentation; instrumentalization; Instrumented technique; Operational invariants; Schemes

Domaines: Histoire et perspectives sur les mathématiques [math.HO]; Education

Luc Trouche. An Instrumental Approach to Mathematics Learning in Symbolic Calculator Environments. Dominique Guin, Kenneth Ruthven, Luc Trouche. The didactical challenge of symbolic calculators: turning a computational device into a mathematical instrument , 36, Springer, pp.137-162, 2005, Mathematics education library, ⟨10.1007/0-387-23435-7_7⟩. ⟨hal-01557242⟩