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Compartmentalisation of Mathematical Sectors: The Case of Continuous Probability Distributions and Integrals

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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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Notes

  1. This theoretical framework puts into the fore the notion of institution and its consequences on teaching and learning.

  2. https://cache.media.education.gouv.fr/file/special_8_men/98/4/mathematiques_S_195984.pdf

  3. The syllabus makes the distinction between “fluctuation” and confidence intervals. In the former, the frequency is to be estimated from the probability which is given; in the latter, the situation is reversed.

  4. Centre National de la Recherche Scientifique; https://www.insmi.cnrs.fr/

  5. Didactique et Épistémologie des Mathématiques, liens avec l’Informatique et la Physique, dans le Supérieur; https://demips.math.cnrs.fr/

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Acknowledgements

This research grew out of a project initiated within a thematic working group of the CNRSFootnote 4 consortium DEMIPSFootnote 5 that federates university mathematics education research in France.

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Authors and Affiliations

  1. Institut Montpelliérain Alexander Grothendieck, Univ. Montpellier, CNRS, Montpellier, France

    Thomas Hausberger & Gaetan Planchon

  2. LISEC, Université de Strasbourg, Strasbourg, France

    Charlotte Derouet

  3. Faculty for Mathematics and Physics, Leibniz University Hannover, Hannover, Germany

    Reinhard Hochmuth

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  1. Thomas Hausberger
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  2. Charlotte Derouet
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  3. Reinhard Hochmuth
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  4. Gaetan Planchon
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Correspondence to Thomas Hausberger.

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Hausberger, T., Derouet, C., Hochmuth, R. et al. Compartmentalisation of Mathematical Sectors: The Case of Continuous Probability Distributions and Integrals. Int. J. Res. Undergrad. Math. Ed. 7, 490–518 (2021). https://doi.org/10.1007/s40753-021-00143-y

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