ALGORITHMIC MATHEMATICS IN LINEAR ALGEBRA APPLICATIONS

The aim of this paper is to provide a computational approach to Linear Algebra (AL) in order to tackle the conceptual difficulties that this field of mathematics presents to students. Also, AL is considered difficult in the curricula due to the high level of abstraction of the concepts involved. In the first-year courses of Mathematics there are different issues which hinder the teaching-learning process, being the most notorious the lack of basic knowledge which students who start university have. Therefore it is essential to present simple models which can encourage students to develop new ways of thinking and reasoning while triggering motivating teaching situations.

This experience is introduced in Algebra and Analytical Geometry subject with the purpose of integrating linear transformation concepts and the use of mathematical software tools. The activities presented aim at developing algorithms procedures so as to relate theoretical knowledge with interesting engineering applications.

The methodology adopted to carry out the experience was carried out through theoretical lessons with technology practice, where the contents of the linear algebra were given to develop simple geometric models that would lead to a meaningful conceptualization of the topic. Students conducted an exploratory activity by using and matching the theoretical concepts; from related transformations different models, curves and surfaces were developed in 2D and 3D, looking for patterns of behavior and their relationship with various applications. To address the methodological innovations described above, curriculum adaptation to fit the generation of new learning systems cannot be postponed.