Exploring the nature of mathematical connections in pre-university students’ triangle similarity tasks

Abstract

Triangle similarity is a mathematical concept with substantial conceptual richness; however, its teaching typically emphasizes procedural approaches over conceptual understanding, leading to a disconnect between concepts and procedures. In this context, the present study aimed to identify the mathematical connections established by a group of Mexican pre-university students while solving tasks related to triangle similarity. A conceptual framework based on the notion of mathematical connections and their typologies was adopted. The study followed a qualitative methodology with a descriptive scope, using a case study approach. Data were collected through task-based interviews. Three tasks were designed and completed by eight students, and the resulting data were analyzed using thematic analysis. The findings revealed six types of mathematical connections: procedural, feature-based, different representations, meaning, implication, and interconceptual; the part–whole connection was not observed. This absence suggests that students tend to focus on isolated properties and procedures rather than recognizing triangle similarity as part of broader mathematical structures. The results suggest the need to design instructional tasks that foster both conceptual understanding and procedural accuracy.