Mathematics and E-learning: a Conceptual Framework

This paper starts from the study of the epistemological statute of the didactics of the mathematics (Henry, 1991; D’Amore, 1999), which faces the phenomenon of learning from the point of view of fundaments, in order to give useful and specific considerations for e-learning environments. Investigations on how the triangle teacher-pupil-knowledge changes are presented. Then the model of a-didactic situations (Brousseau, 1997) is analysed in the context of e-learning platforms. 1. The triangle “pupil-teacher-knowledge” in didactics During last twenty years the research in didactics of mathematics has analysed in various modes and with accurate details, what it is beyond the triangle whose “vertices” are the pupil, the teacher and the knowledge (Chevallard e Joshua, 1982; Chevallard, 1985; D’Amore e Fandiño, 2002): According to didactics, it represents a systemic model useful to situate and analyze the multiple relations among the three “figures” representing the “vertices” of the triangle. The complex nature of the systemic model comes from considering at the same time all the mutue relations among the vertices, including various implications of different nature. For an accurate deepening of such topic we cite the synthesis in D’Amore e Fandiño (2002). In such analysis, the triangle has not an explicative and descriptive function of the education experience but, above all, methodological: each vertex of the system is the observer from which we look at the relations betweens the others, even if we are conscious that none of the involved figures can be considered totally separated by the others. Moreover the implicit effort is to render such scheme as more comprehensible as possible of the multiplicity of variables involved on the educational experience intended as problematic experience. In such systemic model we can distinguish at least three categories of incident bodies: teacher