Sébastien Jolivet - A model for the didactic description of mathematical learning objects, for indexing and services in TEL environments

In a context where digital tools and the WEB allow for the diffusion and massive sharing of resources, the current challenge is to find the right resource at the right time. Current description standards (e. g. LOM or ScoLOMFr) do not allow the description of the didactic dimensions of a learning object. Our thesis is a contribution to fill this gap from the Technology-Enhanced Learning (TEL) field point of view. We were particularly interested in the description of mathematics exercises. We conducted our work within the Anthropological Theory of Didactics (ATD) framework. More specifically, we have exploited the formalization of the praxeological approach proposed by the T4TEL framework. Our findings and propositions are four-fold. First, we proposed a didactic resource description model (M2DR) that allows the description of a mathematics exercises based on didactic criteria and determines its suitability for a curriculum. This model is based on the use of a reference epistemological model (REM). The second result is the modeling of didactic intentions, used for searching for mathematics exercises described with the M2DR model. The third result is an enhancement of the T4TEL framework defining a task model and introducing the notion of optimal types of tasks. The fourth result is the definition of a process for implementing an ontological representation of a REM described in T4TEL using types of tasks generators. This process allows the model to be used in a computerized environment. It has been applied to different REMs in the fields of elementary algebra and numeracy. That fostered the use of the M2DR model to describe different mathematics exercises.