Didactic Engineering for the relationship between the area of plane figures (polygonal bases) and the volume of geometric solids (prisms): a preliminary analysis and a priori analysis

Abstract

The present study presents a proposal for the teaching of geometry aiming at a defragmentation of the relationship between areas of plane figures (polygonal bases) and the volume of geometric solids (prisms). In this sense, the objective of this article is to develop a study based on Didactic Engineering (DE), aiming at the construction of didactic sequence supported by the assumptions of the Theory of Didactic Situations (TDS), seeking the relationship area of plane figures (polygonal bases) and the volume of geometric solids (prisms). For this theoretical study we limit ourselves to the two initial stages of DE called Preliminary Analysis and Conceptions of didactic situations and a priori analyses. For the design of the didactic situation, in addition to the TDS, we used the GeoGebra software to support the visualization and dynamism of the figures presented. We hope that the didactic sequence allows the visualization, dynamism and the understanding of the student when it comes to the relation area of plane figures (polygonal bases) and the volume of geometric solids (prisms).