M. Pires, M.G. Marques

Universidade do Algarve (PORTUGAL)
In the last years mathematical software has been developed, providing powerful tools for both numeric and symbolic calculations. Computer programs like Matlab, Mathematica or Maple are widely used in lab classes at the university, but they are seldom used as tools in lecture mathematical classes. Also many dynamic geometry programs, as Sketchpad, Cabri or GeoGebra, are very popular among basic and high school teachers and they help teaching geometry topics. GeoGebra is now also being widely used as a tool to help students to understand properties of function graphs. But again, at University, most of the first year teachers don’t take profit of these useful tools and keep teaching in an abstract way.
It is well known that basic and high school curriculum, in Portugal, is not designed to prepare students to University. Students finishing school are, in general, not ready to abstract studies, and this is one of the causes of failure in the first year in University, particularly in courses involving mathematics, even among students that got good marks at school.

Calculus and Linear Algebra are the most usual first year courses in engineering or economics degrees. The success in these courses often determines the success of the student in its academic career. The traditional pen and paper classes seems to be unable to attract students attention and to overcome their difficulties. Usually, students are already familiar with technologies and it is very important that university teachers use this advantage to fight against failure.

Bearing in mind all these facts, we started a project to stop failure in Linear Algebra courses. Our aim was to help students to deal with abstract concepts using an adequate syllabus, new evaluation tools and using software in lecture classes to make them understand, with simple examples, the ideas behind abstract concepts.

The project was applied for the first time in 2008/09 in a Linear Algebra and Analytical Geometry course for first year engineering students, and, since then, we have been improving it each year, with good results.
In this work we describe this experience, present the tools and strategies, characterize the target students, give account of their reactions to the classes style and, at last, we discuss the results of the experience.
keywords: linear algebra.