Improving the learning of geometric proportionality using van Hiele’s model, mathematical visualization, and GeoGebra

Abstract

This qualitative, action research methodology study aims at the construction of a teaching unit for the development of learning processes, analyzing the learning trajectories of students around the study of geometric proportionality in topics related to similarity, homothecy, and Thales’ theorem. The didactic unit was designed under the principles of the phases of the van Hiele’s (1986) model, mathematical visualization, and the use of GeoGebra software. Among the results obtained, it can be evidenced that students went from not having a clear notion of similarity to constructing a definition for similarity, proportionality, and homothecy; from not identifying criteria for similarity to identifying and understanding the mathematical properties that remain invariant in similar figures; from not using visualization skills and not communicating their arguments using an appropriate mathematical language to using visualization skills and processes.