Interactive Media Systems, TU Vienna

Construct3D - An Augmented Reality System for Mathematics and Geometry Education

Research project in the area of Virtual and Augmented Reality.

Keywords: Studierstube, Augmented Reality, Applications.

About this Project

Construct3D is a three dimensional geometric construction tool based on the collaborative augmented reality system "Studierstube". Our setup uses a stereoscopic head mounted display (HMD) and the Personal Interaction Panel (PIP) - a two-handed 3D interaction tool that simplifies 3D model interaction. Means of application in mathematics and geometry education at high school as well as university level are being discussed. A pilot study summarizes the strengths and possible extensions of our system. Anecdotal evidence supports our claim that the use of Construct3D is easy to learn and encourages experimentation with geometric constructions.

Additional Information

Spatial abilities present an important component of human intelligence. The term spatial abilities covers five components, spatial perception, spatial visualization, mental rotations, spatial relations and spatial orientation [Maier 1994]. Generally, one goal of geometry education is to improve these spatial skills. In a long term study by Gittler and Glück [1998], the positive effects of geometry education on the improvement of spatial intelligence have been verified. Various other studies [Osberg 1997; Rizzo et al. 1998] conclude that spatial abilities can also be improved by virtual reality (VR) technology. However, little to no work has been done towards systematic development of VR applications for practical education purposes in this field.

Using Augmented Reality in Education

To fill the gap of next-generation virtual reality interfaces for mathematics and geometry education we are developing a three dimensional geometric construction tool called Construct3D that can be used in high school and university education. Our system uses Augmented Reality (AR) [Azuma 1997] to provide a natural setting for face-to-face collaboration of teachers and students. The main advantage of using AR is that students actually see three dimensional objects which they until now had to calculate and construct with traditional (mostly pen and paper) methods. We speculate that by working directly in 3D space, complex spatial problems and spatial relationships can be comprehended better and faster than with traditional methods.

Supporting different learning styles & providing multimodal/hybrid hardware setups for classroom use

For productive use in the classroom, a number of circumstances must be accommodated: Support for a variety of social settings including students working alone and together, a teacher working with a student or teaching a whole class, a student or the whole class taking an exam, etc. Collaboration in these situations is largely determined by roles, and the teacher should be able to retain control over the activities. Moreover, it is not realistic to expect that schools can afford extensive installations of expensive equipment such as used in our lab, and therefore the software must run on a variety of immersive and non-immersive hardware platforms including heterogeneous and hybrid setups.

Differences of educational geometry software to Computer-Aided Design (CAD) packages

It is important to note that while geometry education software shares many aspects with conventional 3D computer-aided design (CAD) software at a first glance, its aims and goals are fundamentally different. Geometry education software is not intended for generating polished results, but puts an emphasis on the construction process itself. While relatively simple geometric primitives and operations will suffice for the intended audience of age 10 to 20, the user interface must be both intuitive and instructive in terms of the provided visualizations and tools. Commercial CAD software offers an overwhelming variety of complex features and often has a step learning curve. In contrast, geometry educators are interested in simple construction tools that expose the underlying process in a comprehensive way.

Construct3D represents our current prototype of such an AR based geometry education tool, including hard- and software, user interface design, and initial experiences.

Videos of Construct3D in Action