Analyse du déploiement d’un raisonnement covariationnel en situation chez des élèves de 15 à 18 ans

Abstract

Many researchers accept that working on covariation helps to construct the notion of functions and promotes comprehension of concepts in differential calculus. However, no study has yet defined the characteristics of the situations that allow this work to take place. We therefore propose a reflection on these characteristics with the assistance of applied covariational reasoning. Based on the Covariation Framework generated by Carlson and her colleagues (Carlson et al., 2001, 2002, 2003, 2015), we describe 13 units of reasoning, a priori, that are applied during functional modeling situations in real learning contexts. Through the creation of four situations and an analysis of data collected during a study among students aged 15 to 18 years, we have refined the descriptions of the units of reasoning and identified the actual reasoning skills used by students in each situation. In this article, we present some of the results—particularly how these units of reasoning manifest in the students’ descriptions of the behaviours of quantities and their growth. We also show the effects that a situation’s written and induced forms of questioning have on the dynamic of reasoning.