Didactics of linear transformations: between mathematical abstraction and meaningful teaching

Abstract

This article analyzes the teaching of linear transformations in university mathematics education and the question of balancing rigor or formality with meaningful teaching. The mathematical foundations are analyzed in terms of their definition and properties. Furthermore, this study examines concepts, highlighting their theoretical and pedagogical importance. Similarly, at the didactic level, the use of interactive digital resources (GeoGebra, Python, MATLAB) and constructivist approaches is encouraged to facilitate contextualization and the solution of real-life problems. Finally, the article proposes strategies for linking theory and practice and emphasizes the importance of linking these abstract concepts with more functional means through the use of other visual representations.