Abstract:

Geometry, as an area of knowledge that studies the general spatial structure, includes both bidimensional and three-dimensional shapes, requiring a set of spatial abilities (i..e spatial orientation and visualization) to understand spatial objects and the relationship between them and its one- and two-dimensional elements. Understanding these concepts is crucial to bridging spatial abilities into the real world. In fact, three-dimensional spatial abilities impact the acquisition of high-level mathematical concepts, such as problem-solving (a fundamental human cognitive process), and reasoning.

Teachers must be concerned with providing students with the adequate tools to develop their spatial abilities as soon as they start to integrate abstract thinking. Nonetheless, teachers sometimes lack the resources to do so. Textual books are the traditional documents in a classroom setting, however, these do not (always) motivate the interaction between teachers and students. Information and Communication Technologies (ICT), specifically Augmented Reality (AR), on the other hand, aid the interaction between them, and also benefit from both virtual and physical learning experiences.

The capability of superimposing virtual objects onto the real world gave rise to research lines where several studies are being developed. In the Mathematics field, AR presents itself as an asset in developing several specific skills, namely spatial abilities. Nowadays, there is a whole range of Augmented Reality applications integrating the visualization of geometric solids. Nevertheless, the research that goes beyond visualization is quite limited, if not non-existent. From the analyzed research literature, available applications only allow to visualize and rotate geometric solids, with no predisposition to explore the relationship between volume variables (i.e. solid base’s area, and solid’s height) and the solid’s volumetry.

In this sense, a team of the GEOMETRIX thematic line has in-development a digital educational resource making use of AR functionalities, held on its website, providing teachers with a resource to integrate into their classes.

This AR application, available on the website, has several components:
(a) augmented visualization of geometric solids;
(b) direct manipulation of volume variables to visualize the impact on the solid’s shape;
(c) detachment of the one- and two-dimensional elements that make up the three-dimensional solid.

For teachers, this open-source resource enables them to easily integrate an ICT-based resource into their classes without requiring additional training. For students, it assists them in developing crucial mathematical skills, namely spatial abilities. This pedagogical resource offers, among others, diversified strategies to discern one-, two- and three-dimensional shapes, using augmented visualization to the manipulation of volume variables.

Keywords:

Spatial Abilities, 3D Geometry, Augmented Reality.