Resumen

FONSECA, Cecilio. Trajectories of Study and Research: A proposal within anthropological theory of the didactic for the creation of teaching and learning sequence. Paradígma [online]. 2011, vol.32, n.1, pp.55-70. ISSN 1011-2251.

In this work we progress, extend and complete a new didactical device: the Trajectories of Study and Research (TSR) that we are designing and experimenting inside the Anthropological Theory of the Didactics (ATD). The TSR appear as a new strategy that wants to contribute with the development of sequences of teaching and learning which can be applied in the scholar institution. They put the focus of the process of study of the mathematical activity in its instrumental character and the computer tool (symbolic calculator) is designed to help this process of study. The TSR recover the “raison d’ètre” of the mathematical activity and try to walk towards a convergence between the knowledge given at school and the society. After to precise the notion of TSR, we’ll use it to create a sequence of teaching and learning around the matrices diagonalization from a powerful extramathematical problematic question, rich and very versatile that goes from the Secondary School to the University.

Palabras clave : Trajectory of Study and Research; sequence of teaching and learning; mathematical modeling; convergency between school and society; raison d’ètre; matrices diagonalization.