Transformaciones lineales en un ambiente de geometría dinámica.

This paper reports the presence or absence of a systemic thinking in students, when they solve the linear extension problem, which consists of determining a linear transformation through the images of the vectors of a basis. The problem is formulated geometrically, making use of the tools of the Cabri-géomètre II software. The difficulties that students present when face this problem, probably are due to that they do not carry out the adequate connections among the concepts involved. This phenomenon can be studied from the point of view of the theoretical approximation the theoretical thinking versus the practical thinking (Sierpinska, 2000). One of the characteristics of the theoretical thinking is that tries to be focused in the establishment and study of the relations between the concepts and its characterization inside a system that also contains other concepts (Sierpinska, et al. 2002). [ABSTRACT FROM AUTHOR]