Bridging probability and calculus: the case of continuous distributions and integrals at the secondary-tertiary transition

Charlotte Derouet (1) , Gaëtan Planchon (2) , Thomas Hausberger (2) , Reinhard Hochmuth (3)

1 LISEC - Laboratoire Interuniversitaire des Sciences de l'Education et de la Communication
2 IMAG - Institut Montpelliérain Alexander Grothendieck
3 Leibniz Universität Hannover=Leibniz University Hannover

This paper focuses on two mathematical topics, namely continuous probability distributions (CPD) and integral calculus (IC). These two sectors that are linked by the formula P(a<=X<=b)=int_a^b f(x)dx are quite compartmented in teaching classes in France. The main objective is to study whether French students can mobilize the sector of IC to solve tasks in CPD and vice versa at the transition from high school to higher education. Applying the theoretical framework of the Anthropological Theory of the Didactic (ATD), we describe a reference epistemological model (REM) and use it to elaborate a questionnaire in order to test the capacity of students to bridge CPD and IC at the onset of university. The analysis of the data essentially confirms the compartmentalisation of CPD and IC.

Mots clés: Anthropological Theory of the Didactic; Transition to and across university mathematics; Teaching and learning of analysis and calculus; Teaching and learning of probability

Domaines: Education; Histoire et perspectives sur les mathématiques [math.HO]

Charlotte Derouet, Gaëtan Planchon, Thomas Hausberger, Reinhard Hochmuth. Bridging probability and calculus: the case of continuous distributions and integrals at the secondary-tertiary transition. INDRUM 2018, INDRUM Network, University of Agder, Apr 2018, Kristiansand, Norway. pp.497-506. ⟨hal-01849962⟩