Exploration and Visualization of Solids through Cross-Sections: An Approach with GeoGebra

Abstract

In integral calculus, we find that understanding three-dimensional solids defined by cross sections is a significant challenge for university students. This difficulty is related to limitations in spatial visualization, in the articulation of different registers of representation, in determining the function that corresponds to the cross-sectional area, among others. One of the main cognitive barriers identified in the specialized literature is the difficulty in imagining the solid generated by cross sections, which makes it difficult to have a deep understanding of the calculation of the volume of said solid. The aim of this workshop is to use the GeoGebra software as a tool to facilitate the construction, exploration, and analysis of solids generated by elementary cross sections. The workshop is aimed at higher education professors or future secondary school teachers with a minor in Mathematics. Activities are proposed so that, by manipulating the tools offered by both GeoGebra 2D and 3D, participants can dynamically construct and visualize the generation of solids and, at the same time, establish meaningful links between the algebraic, geometric, and graphical aspects involved in volume calculation. A relevant result is to manage to understand the solid generated by cross sections, clearly differentiating the shape of the base of the solid and the cross section, correctly determining the area of the cross section, and identifying the limits of integration to calculate its volume, which promotes learning in students.