Preuve et algèbre au college: de la conception d'une séquence d'apprentissage à l'evolution du cadre théorique de référence

Abstract

The article deals with a teaching unit aimed at promoting algebra
\nas a tool for proving. The unit was carried out in two classes (Grade 7 in Italy,
\nGrade 8 in France). The aim is to show how an analytical tool (the notion of
\nrational behavior) has evolved through being tested in the post hoc analysis of
\ntwo cycles of experimentation, and how its use put in question our first
\napproach to the mathematical content at stake (algebra and proof). Besides
\ntheoretical developments, we present some advances on the pragmatic level.