Working with, working on the notion of mathematical praxeology to describe the learning needs ignored by educational institutions
Travailler avec, travailler sur la notion de praxéologie mathématique pour décrire les besoins d'apprentissage ignorés par les institutions d'enseignement
Abstract
Essentially using tools proposed by the Anthropological Theory of Didactics, in this paper we deal with the institutionally ignored learning that students must carry out to be successful in the French mathematics teaching system.
Borrowing from Aline Robert’s work, we define analysis tools which differentiate several contribution levels of a punctual Mathematical Organization in a problem. From this we introduce the idea of praxical curriculum in a teaching institution: mainly ignored by the official texts, the stages of the praxical curriculum are established from a study of the exercises and problems students actually face to; they are described in terms of MOs and contribution levels of these MOs. We use again punctual MOs to describe the learning a praxical curriculum calls for. This leads us to develop the notion of technology where we distinguish a theoretical component and a practical one. Furthermore we introduce what we call a complex punctual Mathematical Organization related to a type of problems T; this structure integrates in a common organization the different one technique punctual MOs concerning T. These complex MOs supply us with a model for the learning required by the upper MO contribution levels. At last, we wonder whether a rather progressive praxical curriculum could live in the French mathematics educational system.