Skip to Main content Skip to Navigation
Theses

La fonction de densité au carrefour entre probabilités et analyse en terminale S. Etude de la conception et de la mise en œuvre de tâches d’introduction articulant lois à densité et calcul intégral.

Abstract : This thesis focuses on the connections between probability and analysis (calculus) in the scientific track of Grade 12 (French baccalaureate program). We explored the ways in which links between the mathematics subfields of continuous probability and integral calculus are created and explored, through a research focused on the concept of density function. Using the Mathematical Working Space model and some elements of Activity Theory, we sought to identify tasks that would allow introducing this concept and building the semiotic relationship between probability and integral. In order to address this issue, we began with an epistemological and historical study of the birth of the concept of density function, which enabled us to identify the important role of statistics in this genesis. Then, an analysis of institutional documents and textbooks showed that the link between continuous probability and integral calculus is imposed on students and rarely exploited in the different tasks given to them. Finally, we studied the design and implementation of original introductory tasks through a research methodology that we call “collaborative didactic engineering”. The goal of these tasks is to get the class “collective” to construct the concept of density function and trigger the need for calculating areas under a curve. We highlighted the activities of the class “collective” in the construction of this notion by analyzing articulations between the three subfields: continuous probability, descriptive statistics and integral calculus.
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-01431913
Contributor : Jérôme Barberon <>
Submitted on : Wednesday, January 11, 2017 - 1:24:49 PM
Last modification on : Monday, November 30, 2020 - 3:10:20 PM
Long-term archiving on: : Friday, April 14, 2017 - 4:14:15 PM

Identifiers

  • HAL Id : tel-01431913, version 1

Citation

Charlotte Derouet. La fonction de densité au carrefour entre probabilités et analyse en terminale S. Etude de la conception et de la mise en œuvre de tâches d’introduction articulant lois à densité et calcul intégral. . Histoire et perspectives sur les mathématiques [math.HO]. Université Paris Diderot (Paris 7) Sorbonne Paris Cité, 2016. Français. ⟨tel-01431913⟩

Share

Metrics

Record views

1391

Files downloads

766