Integrating Technologies in Linear Algebra Lectures

In the last years many mathematical software applications, that provide powerful tools for both numerical and symbolic calculations, have been developed. Although computer programs like Matlab, Mathematica or Maple are widely used in Lab classes at the university, they are seldom used as tools for teaching at university level. Also many dynamic geometry programs as Sketchpad or Cabri were developed and became very popular among high school teachers to help teaching geometry topics, but, again, they are usually not used for teaching at the university. It is a reality that basic and high school curricula in Portugal are not designed to prepare students to abstract studies as soon as they enter the University. Most university teachers do not take this fact into account, and this is one of the reasons that contribute to a high tax of failure in the first year courses, specially courses involving mathematics, even among students that got reasonable marks in the final high school examinations. In fact, most first year university students experience many difficulties in basic courses like Calculus or Linear Algebra, mainly because the previous math studies didn’t give them the necessary skills to deal with abstract concepts that are essential for more advanced math topics, and academic success becomes very difficult to achieve. The traditional pen and paper classes seem unable to give an answer to the students’ difficulties. Usually, students are already familiar with technologies when they arrive at the University, but very few university teachers take advantage of this. Bearing in mind all these facts we started a project to use math software applications in math lectures for university first year students, with the goal of helping them to better deal with abstract concepts when those are presented for the first time and, so, increase their academic success. The project was applied this year for the first time in a Linear Algebra and Analytical Geometry course for first year engineering students.