Spatial geometric thinking and its articulation with the visualization and manipulation of objects in 3D

Abstract

This paper aims to build a conceptual framework that addresses spatial geometric thinking and the respective visualization skills required at different levels of the schooling process. Studies indicate that spatial geometric sills are essential for scientific thinking. It encompasses a set of cognitive processes through which humans can construct and manipulate mental representations of objects in space and is a skill directed towards understanding objects and their relations in the 2D and 3D worlds. The use of these spatial reasoning skills involves drawing, manipulating, and explaining objects and their relationships and should be developed from the first years of schooling. Based on this theoretical context, partial research results on surface representations that can be manipulated in three dimensions (3D) and obtained through GeoGebra will be presented in this paper. The underlying theory was Duval's Theory of Registers of Semiotic Representation, which allowed the analysis of activities developed by graduate students in Mathematics Education by observing and physically manipulating such representations to obtain the respective graphic and algebraic records. The conceptual framework constructed and presented in this article contributed to identifying other skills required in this study for the development of spatial geometric thinking.