A Praxeological Model for teaching triangle construction: a look at the relationship between praxeological blocks

Abstract

The purpose of this article is to present the structure of , which aims to integrate praxeological blocks into triangle-construction tasks within a Dynamic Geometry environment. This model emerged from a doctoral dissertation and was grounded theoretically and methodologically in the Anthropological Theory of Didactics and its assumptions, with the intention of contributing to the training of teachers who teach geometry using a graphical approach. We began with the problem related to the teaching of geometric constructions, which is still based on the description of procedures disconnected from their theoretical justifications. Methodologically, the structure of the  model presented here was based on three previous studies focused on analyzing instructional materials that included triangle-construction tasks and, subsequently, on the resolution and study of techniques in GeoGebra. Based on the data obtained from these studies, it was possible to design the model, considering stages such as: (i) pedagogical choices; (ii) description of the praxeological blocks and the nature of the tasks envisaged for the model; and (iii) presentation of the types of tasks incorporated into the .  The structuring of the model demonstrated that, by adopting theoretical and methodological assumptions—such as the praxeological quadruple and the notion of a praxeological reference model—it was possible to develop a robust praxeological framework that integrates practical and theoretical knowledge through the nature of the proposed tasks, which explore the capabilities of the GeoGebra software. We thus aim to address gaps such as the disjointed teaching of geometric constructions and their mathematical justifications, which persist in the instruction of these concepts when using a graphical approach.