Interactive Media Systems, TU Vienna

Geometry Education with Augmented Reality

Thesis by Hannes Kaufmann

Supervision by Dieter Schmalstieg, Michael Wagner, and Mark Billinghurst


To fill the gap of next-generation user interfaces for mathematics and geometry education Construct3D is introduced a three-dimensional dynamic geometry construction tool that can be used in high school and university education. This system uses Augmented Reality (AR) 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. By working directly in 3D space, complex spatial problems and spatial relationships may be comprehended better and faster than with traditional methods. After a description of Construct3D´s design various hardware setups are presented that are suitable for educational purposes. Immersive, semi-immersive, mobile and hybrid setups are studied for their applicability to geometry education. An immersive setup that uses head mounted displays is most favored by teachers and students. It allows users to actually "walk around" geometric objects which are fixed in space. In order to adapt software and hardware to users´ needs user interfaces were redesigned and in depth research was done on usability design. Development steps and results present how Construct3D´s look and feel was considerably improved. A wide range of selected geometric content from basic and advanced high school geometry to university education is presented. Diverse examples demonstrate the potential and robust constructive apabilities of the dynamic geometry application. Finally results from two evaluations show that Construct3D is easy to use, requires little time to learn, encourages learners to explore geometry and can be used in a consistent way. At the end an outlook is given on ongoing and future work and basic guidelines to developers of educational VR/AR applications are summarized.


H. Kaufmann: "Geometry Education with Augmented Reality"; Supervisor, Reviewer: D. Schmalstieg, M. Wagner, M. Billinghurst; Institut für Softwartechnik und Interaktive Systeme, 2004.


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