VECTOR SPACES DOES NOT MEAN VECTOR SETS

M. Caligaris, G. Rodríguez, M.E. Schivo, L. Laugero, M.R. Romiti

Universidad Tecnológica Nacional, Facultad Regional San Nicolás (ARGENTINA)
The topic Vector Spaces, included in the syllabus of Linear Algebra courses in engineering careers is an abstract concept that students have difficulties in understanding. Moreover, its study sometimes begins with examples of geometric vector sets, in two and three dimensions, diluting the generality of the subject.

Considering that the understanding of the concept of vector spaces is essential for the learning of others related such as subspaces, spanning sets, base, dimension, or linear transformations, the way it is presented in class is of utmost importance. However, the formal treatment with which the topic is usually approached causes students to emphasize the use of algorithmic procedures and mechanically manipulate their various semiotic representations as if they were an object in itself, without understanding the meaning of each one and without perceiving the relationships established between them. That means that students cannot understand in depth the concept of vector spaces.

Several authors recognize mathematical skills as those developed when performing mathematical activities. With these skills, students build a mode of action, inherent to a certain mathematical activity, which allows them to use concepts, properties, relationships, mathematical procedures, work strategies, and think in a logical way to solve problems.

The classification of the mathematical skills considered is that given by the revised Bloom´s taxonomy. It is an arrangement of the different objectives and skills that educators set for their students.

Taking into account that the formation of mathematical skills is a process planned and directed by faculty, technological resources and didactic sequences incorporating them were designed with the purpose that students develop different mathematical skills during the learning of the concepts addressed in the "Vector spaces" unit. The GeoGebra and SciLab programs were used to prepare those tools. These programs can be downloaded for free from the sites https://www.geogebra.org/ and https://www.scilab.org/, respectively.

This work shows the designed applications and the didactic sequences elaborated for the Algebra and Analytic Geometry courses at Facultad Regional San Nicolás, Universidad Tecnológica Nacional, Argentina. The authors of this work consider that the presented didactic proposal may help students to achieve an adequate understanding of the concepts involved in the analyzed topic.