PROPUESTA DIDÁCTICA PARA LA ENSEÑANZA DE LAS RAZONES TRIGONOMÉTRICAS DESDE EL MODELO DEL TRIÁNGULO SEMÁNTICO

Abstract

This article presents a didactic proposal for teaching trigonometric ratios based on the semantic triangle model of mathematical meaning, as proposed by Rico and Moreno (2016). The aim of the study is to analyze the meaning that students attribute to the content of trigonometric ratios through the design and implementation of an educational intervention based on this model. The proposal was developed within the framework of a qualitative research study with an interpretative approach, targeting first-year students in the Mathematics Teaching program at the University of Costa Rica. Through the design of a four-lesson intervention, the potential of the semantic triad—conceptual structure, representation systems, and senses and modes of use—as an organizing axis for lesson planning was explored. The results show that this model supports a more coherent and meaningful approach to teaching by integrating different levels of conceptual complexity, various representations, and contextualized applications. Additionally, emergent elements were identified, suggesting a deeper appropriation of the content by students, particularly in their use of graphic representations and conceptual reasoning. It is concluded that the semantic triangle constitutes a valuable theoretical and methodological tool for both mathematics teaching and teacher education.