An Analysis of the Influences of a Hybrid Learning Environment in the Solution of Vector Tasks according to the Anthropological Theory of the Didactic (ATD)

This paper discusses a part of a doctoral study based on the theoretical pillars of the Anthropological Theory of the Didactic (ATD). Supported by this theory, our research interest followed a path that led us to the teaching of the mathematical object vector and its institutional configuration in a Mathematics Teaching course at Universidade Estadual de Feira de Santana (UEFS), in the state of Bahia, Brazil, centered on two dichotomous aspects. The first one refers to the possibility of application and institutional relevance of this mathematical object. The second aspect is related to the obstacles encountered in the didactical scope, which have impact on the teaching/learning of this mathematical object. In this discussion, the question that guided our investigation emerged: how to harness praxeological recombinations that can promote mediation between personal and institutional relationships in the scope of vector knowledge in the Mathematics Teaching course at UEFS? Based on this context, we aim at analyzing students’ productions in terms of solution paths to a vector task in a Hybrid Learning Environment (HLE), from a developmental perspective based on the T4TEL didactical framework (Chaachoua, 2018). With regard to methodological support, Didactical Engineering provided directions that enabled us to make a comparison between a priori and a posteriori analyses, resulting in the identification of the reach of the techniques that were developed in contrast to the naturalized techniques that are part of this context.