Beyond Row-by-Column: An Intervention using GeoGebra and MWS in the Learning of Matrix Multiplication in Secondary Education

Abstract

Teaching matrix products in secondary school tends to focus on the row × column algorithmic rule, leaving aside its interpretation as a geometric transformation. This study analyzes the impact of a didactic sequence based on the Mathematical Workspace (MWS) and mediated by GeoGebra on the learning of matrix products. Ten senior students participated from a school in Lima. The intervention included two induction sessions and two implementation sessions, combining manual and digital activities. The results show significant progress in semiotic (coordination between algebraic, graphical, and numerical registers), instrumental (meaningful use of GeoGebra), and discursive geneses (argumentation about the geometric effect of matrices). A transition from mechanical execution to a richer conceptual understanding was evident. The study proposes implications for the design of visual tasks and the reflective use of technology in school linear algebra.