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Habilitation à diriger des recherches

QUELQUES APPORTS DE LA THEORIE DES SITUATIONS A LA DIDACTIQUE DES MATHEMATIQUES DANS L'ENSEIGNEMENT SECONDAIRE ET SUPERIEUR

Abstract : Our investigations have been developed in two directions that could seem quite opposite: first, the teaching of calculus at the transition between Upper Secondary School and University, and second, the teaching of mathematics for children with special needs, more precisely 14-15 years-old students in secondary school. The link between these two research fields is the study of the Theory of Didactical Situations (TDS); we tried to apply the TDS in these contexts which are not the original ones (originally TDS was developped for primary school) and to make theoretical concepts – as the milieu – evolve when necessary. We want to provide some relevant contribution to the TDS methodology of research in didactics, as well as to cross with other theories. This last interest leads us to use semiotic theories to analyse the mathematical signs in the situations.
We try to perform now a deeper analysis of the way signs are used by the students within the situations, and the way students succeed in linking their previous knowledge, or the knowledge they build, with the symbols they operate with in the situation. Amongst semiotic theories, Peirce's one is especially relevant for mathematics as it explores the functionality of any signs and not only of the linguistic ones. We use this semiotic analysis to build situations as well as to understand the use of mathematical symbols by the teacher and their interpretation from the students. Some research questions about the role of signs emerge from this study, in the context of the teaching of calculus – e.g. the role of the formal – as well as in the context of specialised teaching – what can be done when a mathematical interpretation is not possible?
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Habilitation à diriger des recherches
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https://tel.archives-ouvertes.fr/tel-00012153
Contributor : Isabelle Bloch <>
Submitted on : Tuesday, April 18, 2006 - 9:53:17 AM
Last modification on : Monday, October 19, 2020 - 11:12:56 AM
Long-term archiving on: : Saturday, April 3, 2010 - 10:19:07 PM

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Isabelle Bloch. QUELQUES APPORTS DE LA THEORIE DES SITUATIONS A LA DIDACTIQUE DES MATHEMATIQUES DANS L'ENSEIGNEMENT SECONDAIRE ET SUPERIEUR. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2005. ⟨tel-00012153⟩

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