Identificación del desarrollo de habilidades visuales espaciales en representaciones y conversión entre registros para calcular volúmenes

Abstract

The study deals with the identification of the development of spatial visual skills in tasks of representation of solids of revolution and of conversion between registers to calculate their volume, carried out by engineering students. The skills studied are visual organization and scanning, and reconstruction, generation, and manipulation of the image. A predominantly qualitative mixed case study was done. The subjects were 33 second semester students taking integral calculus. GeoGebra-assisted tasks were designed based on indicators created for each skill. The results indicate a significant improvement in skills, with a significant enhancement in image generation and manipulation. These skills are of a high level since they require the visualization of three-dimensional configurations and the mental manipulation of these images. It was identified that the development of these skills contributes to the representation of solids of revolution, but for the calculation of their volume, it is necessary to convert between the verbal, graphic, symbolic, and algebraic registers, to visualize and represent the solid, determine the correct expression of the volume and calculate the definite integral obtained.