Didactic proposal based on mathematical modeling for the multigrade classroom. The case of topography

Abstract

This research is focused on the design and implementation of a didactic device known as Research and Study Route (REI), based on the paradigm of questioning the world and the Anthropological Theory of Didactics, for a rural multigrade classroom in a Colombian high school. The objective of the REI is to investigate a main question, how to raise a field for planting? This makes it possible to generate relations between school mathematics and topography. In particular, it considers the topographic survey of land for cultivation, an activity that is of interest to the community in which the school is located. The researchmethodology is inspired by Didactic Engineering (Artigue, 2020), adapting the preliminary analysis to the study of the topographic survey and elucidating a praxeological model of reference, fundamental in the determination of the generating question and in the design of the REI. The preliminary analysis of topography allows generating a didactic design in which mathematical and topographic justifications are related to bring to the classroom with a non-school activity such as the topographic survey with tape.