Compartmentalisation of mathematical sectors: the case of continuous probability distributions and integrals - Archives ouvertes de la Didactique des mathématiques
Journal Articles International Journal of Research in Undergraduate Mathematics Education Year : 2021

Compartmentalisation of mathematical sectors: the case of continuous probability distributions and integrals

Abstract

This paper investigates the phenomenon of compartmentalisation of knowledge in the teaching and learning of continuous probability distributions and integral calculus at the secondary-tertiary transition in France. Using the Anthropological Theory of the Didactic (ATD), and in particular the key notion of praxeology, we investigate in which sense those two sectors may be described as compartmentalised in current textbooks. We then study, by means of a questionnaire, the educational effects of the compartmentalisation: do students’ difficulties in completing ”bridging tasks” (tasks that require to relate the two sectors) reflect the partial disconnections revealed by the praxeological analyses? The key notion of ostensive, combined with the role played by the technology in the sense of ATD, is used to interpret the data. Altogether, this study sheds light on the deficit of cognitive flexibility required to change mathematical sectors, which is understood as a result of deficient praxeologies developed within the institutions.
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Dates and versions

hal-03188310 , version 1 (03-07-2024)

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Thomas Hausberger, Charlotte Derouet, Reinhard Hochmuth, Gaëtan Planchon. Compartmentalisation of mathematical sectors: the case of continuous probability distributions and integrals. International Journal of Research in Undergraduate Mathematics Education, 2021, 7 (3), pp.490-518. ⟨10.1007/s40753-021-00143-y⟩. ⟨hal-03188310⟩
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