Methods and Materials for Professional Development of Lecturers

Discussing Mathematical Learning and Mathematical Praxeologies from a Subject Scientific Perspective

International audience; This programmatic contribution discusses the link between concepts from Anthropological Theory of Didactics (ATD) and the “subject-scientific point of view” according to Holzkamp (1985, 1993). The main common concern of ATD and the subject-scientific approach is to conceptualize and analyse “objects” like “institutionalized mathematical knowledge” and “university” not as conditions that cause reactions but essentially as meanings in the sense of generalized societal reified action possibilities. The link of both approaches is illustrated by the issue of “real numbers” in the transition from school to university: Hypotheses are derived for further actual-empirical res…

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

International audience; 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…