Teaching Spatial Geometry Through 3D Visualization and Augmented Reality

Introduction

In this chapter, an experience of using Augmented Reality and 3D Visualization to teach Spatial Geometry content will be discussed. This work was carried out in part on the premises of the State University of Paraba (UEPB) and with direct support from the Educational Informatics Research Group (NIEP). The discussion starts with the presentation of the background covering related works and the concepts of augmented reality and 3D visualization. After that, there is a presentation of the methodology used in the study, followed by the presentation of the experiments conducted. Then there are discussions about what was identified as solutions and problems. After that, there is a presentation some limitations of work and future directions, ending with the conclusions.

Geometry is a branch of Mathematics that is linked to human life. From civil construction to the children delimiting a field to play soccer, we can observe the presence of figures, relationships, and geometric associations. According to (Brito, 2014) as a response to human needs, whether for land demarcation or for the development of tools and housing construction that geometric knowledge was developing.

Figure 1.

Regular tetrahedron.

For example, if a student cannot associate Figure 1 with its three-dimensional shape, he will have difficulties in identifying elements and relating the properties of this solid to the structures studied in plane geometry. The difficulty also exists in a traditional class, based on blackboard and chalk. For the teacher to draw three-dimensional elements on the two-dimensional blackboard, there are obstacles, such as:

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  The loss of information due to the lack of the third dimension.

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  The teacher's unwillingness to design these structures.

Many teachers are faced with these dilemmas in the teaching of Spatial Geometry but are not always familiar with three-dimensional visualization applications or with the use of concrete material to facilitate the understanding and assimilation of concepts by the student.

Figure 2.

Spatial geometry with straw concrete material.

Concrete material for teaching Spatial Geometry is quite common and ranges from the construction of solids by the students themselves (Fanelli, 2013) to the use of commercial materials (Moraes, 2014). The use of applications for viewing in three dimensions, seeks to incorporate innovative technologies, such as computers, tablets, or smartphones (Pereira, 2014). For the teaching of spatial geometry, there are several methodologies to help teaching and learning, among which we can mention:

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  Blackboard (and chalk): most used by teachers. Its use in the teaching of Spatial Geometry requires considerable skill in drawing on the part of the teacher. The observation of the three-dimensional object depends on the student’s perception, and it is not possible to manipulate the object (for example, rotate), which consequently tends to hinder student learning.

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  Concrete material: these are usually solids built from planned models. Most of the time, they are built with straw (Figure 2) paper (Figure 3) or acrylic pieces (Figure 4).

Figure 3.

Spatial geometry with paper concrete material.

Figure 4.

Spatial geometry with acrylic concrete material.