Abstract
This research aims at studying the place and role of magnitudes in the development of different mathematics fields and in their interrelations at school. Our perspective is that of the Anthropological Theory of the Didactic developed by Yves Chevallard. An epistemological analysis of the mathematical knowledge related to magnitudes allowed us to examine certain institutional choices and their impact on teaching. This work is complemented by an ecological and praxeological study of the curricula, school textbooks and corporate documents to characterize the institutions' relations to magnitudes. A clinical type methodology was used to analyze the knowledge concerning magnitudes taught in grade 6 and 7 in France. This study was inspired by Bronner's work about the numeric to develop a tool - a magnitudes filter - which is used to describe and analyze the practices related to magnitudes at school. In particular, this research focused on the interrelations between the magnitudes, the functional and the numeric in the case of proportionality and on the internal functioning of magnitudes in the case of the area magnitude. As a result, this research shows that the introduction of magnitudes as a study domain in school programs of 2005 creates difficulties among professors in integrating new technologies and theories for an adequate teaching of magnitudes. Moreover, it shows a certain stabilization of the place and role of magnitudes in the development of different mathematics fields, but difficulties concerning the interrelations between these areas.