A didactic sequence in the teaching of linear transformation: Unification of methods and problems, modeling and explanation of learning

Abstract

This work contributes, on the one hand, to determine the didactic implications of an epistemological analysis on the generality of economic and analogous methods in the resolution of problems of linear carácter. On the other hand, to construct and to evaluate a didactic sequence that makes the students understand better the meaning of a unifying concept and to help to the spontaneous mobilization of its properties by the exposure to a series of problems that resort to different mathematical frameworks (numerical, geometric, physical and analytical). The theoretical articulation concerns the Modelling and process/object duality in the formation of the concept. We are inspire by a didactic engineering to present a part of the results of our research. These results refer to the levels of explicitness and to the competences developed in the use of technical skills and mathematical methods that help to make explicit the process of formation of the notion.