A Reference Epistemological Model Regarding the Determination and Construction of Solids for Compulsory Secondary Education

Abstract

Background: The analysis of the geometric knowledge presented in the secondary education curriculum reveals phenomena such as the separation between 2D and 3D geometry and the weakening of the modelling activity in geometry. Brousseau considers that the construction of figures is a first example of geometrical modelling. Objectives: To build a reference epistemological model that clearly sets out the conditions that allow determining the shape and size of a solid and looking for possible techniques that enable constructing it. Design: theoretical research within the framework of the Anthropological Theory of the Didactic. Setting and participants: The model built is the result of several activities carried out in the last three years: an analysis of school texts, and the design, implementation, and analysis of a study and research path regarding the design of a container in two secondary schools with students aged between 14 and 17. Data collection and analysis: The model is based on the analysis of information collected from scientific texts by Pólya and other authors, from official texts and secondary education textbooks, and from the experiments carried out. Results: The model is based on the structured study of twoand three-dimensional geometry and allows guiding study processes aimed at consistently addressing the problem of determining a solid and its construction. Conclusions: The model developed includes questions regarding spatial-geometric modelling considered to be central in the introduction to geometry in secondary education.