This paper summarizes work done within the previous 6 years to integrate and implement Virtual and Augmented Reality (VR/AR) technologies in geometry education. A VR/AR application supporting dynamic 3D geometry is presented, intended for real use in high school and university geometry education. Related areas such as dynamic three-dimensional geometry, usability and user interface design, spatial abilities, pedagogy and low-cost VR systems influenced our work and the development of the educational geometry application Construct3D. After describing the design of Construct3D, the strengths of this learning environment for geometry education are investigated. Dynamic three-dimensional geometric content is depicted that fully benefits from the advantages provided by the application. In order to adapt software and hardware to users´ needs, user interfaces were redesigned and in depth research was done on usability design. Very positive and useful feedback from teachers and students, who are excited by the possibilities, was collected in three evaluations with more than 100 students in over 500 teaching lessons. Results from these 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. Various hardware setups have been studied that are suitable for educational purposes. 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. Regarding spatial ability research, a currently running project for training spatial abilities with more than 300 participants is outlined. A review of shortcomings of existing spatial ability tests concludes with ideas to conduct future testings directly in VR/AR. Finally the recent development of a low cost optical tracking system, that allows to build affordable, immersive VR systems is described. Our work enables teaching of three-dimensional dynamic geometry in an interactive, immersive learning environment, therefore offers new possibilities to modern geometry education. Despite the findings mentioned in this paper, many more research questions have emerged during the development of Construct3D. According to each of the related areas we indicate interesting topics that might require future work. By summarizing our work, which aims to establish Augmented Reality in geometry education, and by providing insight into the problems and future challenges in each of the related areas, we want to highlight and advert the full potential of Augmented Reality in geometry education.
H. Kaufmann: "The Potential of Augmented Reality in Dynamic Geometry Education"; Keynote Lecture: 12th International Conference on Geometry and Graphics, Salvador, Brasilien (invited); 08-06-2006 - 08-10-2006; in: "Proceedings of the 12th International Conference on Geometry and Graphics (ICGG) 2006", (2006).
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