Mathematics and geometry education with collaborative augmented reality
Section snippets
Motivation
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 [1]. Generally, the main goal of geometry education is to improve these spatial skills. In a long-term study by Gittler and Glück [2], the positive effects of geometry education on the improvement of spatial intelligence have been verified. Various other studies [3], [4]
Related work
Construct3D combines four research areas: geometry, pedagogy, psychology and AR. We will give a short overview of closely related work in these areas.
A large body of work has been done on 3D modeling in general. However, although 3D input devices with six degrees of freedom (6DOF) have been used to enhance modelers, little modeling has been done in immersive VR systems. A good overview of 3D modeling systems with 6DOF input devices can be found in the work of Mine [7]. Mine's CHIMP [8] was used
Basic construction functions
Construct3D is based on the Studierstube system recently described by Schmalstieg et al. [25]. Studierstube uses AR to allow multiple users to share a virtual space. We use see-through HMDs capable of overlaying computer-generated images onto the real world, thereby achieving a combination of virtual and real world, allowing natural communication among users. The latest version of Studierstube allows the mix and match of heterogeneous output devices such as personal HMD, virtual workbench,
Hybrid hardware setups
To complement the diverse teacher–student interaction scenarios that are possible on the software side with practical hardware solutions for an educational environment we created various hybrid hardware setups. Realistically not all scenarios can be done in schools with equipment similar to our standard lab equipment of rather expensive tracking systems, head mounted displays and stereoscopic video projections. However, many components such as PC workstations with accelerated graphics and
Evaluations
The key hypothesis—that actually seeing things in 3D and interacting with them can enhance a student's understanding of 3D geometry—were supported by the anecdotal evidence we have gathered from trial runs with real students. In our first evaluation [5] with 14 students we got very positive and encouraging results and some problems were pointed out. During the evaluation it was gratifying for us to see users work with Construct3D in a very constructive manner. It was obvious that they did not
Conclusions and future work
In this paper, we present a fully functional educational AR application for mathematics and geometry education. We implemented flexible methods to support various teacher–student interaction scenarios. Hybrid hardware setups allow the use of Construct3D in today's classrooms and provide a testbed for these scenarios. Initial evaluations of the concept are encouraging, and our mid- to long-term plans are to integrate it in Austrian high school and higher education curricula. We have established
Acknowledgments
The authors would like to thank Gerhard Reitmayr for his ongoing support, Klaus Feiler and Reinhard Steiner for integrating Boolean operations, Florian Ledermann for his work on the Augmented Classroom and all of the Studierstube team. We also thank all participants in our pilot studies for their time. This work is sponsored in part by the Austrian Science Fund FWF under contract number P14470-INF and the EC under project number IST-2001-34204 (Lab@Future).
References (28)
ISAACa meta-cad system for virtual environments
Computer-Aided Design.
(1997)- Maier PH. Räumliches Vorstellungsvermögen. Peter Lang GmbH, Europäische Hochschulschriften: Reihe 6, Bd. 493, Frankfurt...
- et al.
Differential transfer of learningeffects of instruction in descriptive geometry on spatial test performance
Journal of Geometry and Graphics,
(1998) - Osberg K. Spatial cognition in the virtual environment, Technical R-97-18. Seattle: Human Interface Technology Lab,...
- et al.
The virtual reality mental rotation spatial skills project
CyberPsychology and Behavior,
(1998) - et al.
Construct3Da virtual reality application for mathematics and geometry education
Education and Information Technologies
(2000) - Azuma R. A survey of augmented reality. In: PRESENCE: Teleoperators and Virtual Environments, vol. 6(4). Cambridge, MA:...
- Mine M. Working in a Virtual World: Interaction Techniques Used in the Chapel Hill Immersive Modeling Program. UNC...
- Chapin WL, Lacey TA, Leifer L. DesignSpace: A manual interaction environment of computer aided design. In: Proceedings...
Conceptual design space—beyond walk-through to immersive design
SeamlessDesign for 3D Object Creation
IEEE MultiMedia Magazine,
Summer students in virtual realitya pilot study on educational applications of VR technology
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