Compartmentalisation of Mathematical Sectors

The Case of Continuous Probability Distributions and Integrals

authored by

Thomas Hausberger, Charlotte Derouet, Reinhard Hochmuth, Gaetan Planchon

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.

Organisation(s)

Institute of the Teaching of Mathematics and Physics

External Organisation(s)

Université Montpellier
University of Strasbourg

Type

Article

Journal

International Journal of Research in Undergraduate Mathematics Education

Volume

7

Pages

490-518

No. of pages

29

Publication date

10.2021

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Education, Mathematics (miscellaneous)

Electronic version(s)

https://doi.org/10.1007/s40753-021-00143-y (Access: Closed)