Theoretical foundations of the investigation on the learning of the mathematics in classroom: first elements of didactics of the mathematics

Abstract

Current research in disciplinary didactics is directed to focus attention on the phenomenon of learning, but from a foundational point of view and in any way not accepting a single model of learning theory (even if cognitive psychology at this time seems the most authorized to give interesting foundations for many research experiences). Facing disciplinary didactics as epistemology of learning, I will make examples only in the field that concerns me, that is to say in Mathematics. But, discussions with colleagues, didacts of other disciplines and occasional readings, have confirmed to me the fact that the general problems seem to be the same, even in the different specificities. Therefore, even not wishing (being able) to leave the narrow scope said, I am convinced that not very diverse will be the possible analogous critical analyzes that belong to other research sectors. What I will do here will be quickly clarified. I will analyze some of the problems that seem to emerge more strongly in recent years, which have been consolidated as research elements in Mathematics Didactics, and which I think provide a solid and meaningful basis for a possible generalization. I will refrain from presentations that are too technical and therefore I will limit myself to the position of each one of the proposed problems, presenting, in summary, in the following sections, some rather diffuse techniques in the research environment that seem to be of particular interest, especially for teachers. I will do, as far as possible, reference to research, to give the reader an idea of what the researchers, some researchers, do in Didactics of Mathematics.