A few pedagogical designs in linear algebra with Cabri and Maple

Since the 90’s, with the creation of new electronic environments for learning and teaching, several research groups in Mathematics Education have been emerging and developing. This article elaborates few pedagogical designs in Linear Algebra supported by both the geometrical micro-world Cabri and the computer algebra system Maple. Stumbling blocks in the learning of Linear Algebra are examined, more exactly linear transformations, eigenvectors, quadratic forms, conics with changes of bases and finally singular values. Encountering a special group of students very eager to explore the world of linear algebra, we initiated a classification of linear transformations of the Euclidean plane R² via ellipses.