Travail mathématique et domaines mathématiques

Abstract

In the Geometrical Working Space (GWS) theoretical framework, the differentiation of geometrical approaches is based on the geometrical paradigms notion. Due to this notion, it is possible not only to point out the epistemological differences in the test approaches, but also to understand and explain variations in the instrumental and figural geneses. The extension of the GWS’s theoretical framework to the Mathematical Working Spaces draws attention on the simultaneous use of several domains of mathematics in the mathematical work. We analyze the problems initially lying on a geometrical support, but which solution can be expressed in another mathematical domain that, form a educational point of view, is not, thus, necessarily situated neither to the same paradigmatic level, nor to the same didactical or pedagogical level of elaboration. These differences in level can be source of misunderstandings and dysfunction in the academic practice.