1. CyberMath: A Shared Virtual Environment for Mathematics Exploration Gustav Taxén and Ambjörn Naeve Center for User Oriented IT Design, KTH, Stockholm

2. Current problems in mathematics education Understanding abstract concepts.Understanding abstract concepts. Bridging related mathematical areas.Bridging related mathematical areas. Finding mathematics relevant.Finding mathematics relevant. Can we use technology to improve this situation?Can we use technology to improve this situation?

3. Technology requirements Flexible:Flexible: –Elementary, intermediate and advanced subjects. –Easy to provide new material. Sharing of resources:Sharing of resources: –Allow physically remote teachers to offer expertise. –Access information ”off-line”.

4. Technology requirements (cont.) Multiple teaching strategies:Multiple teaching strategies: –Traditional lecturing, student-driven exploration (with guidance), student groups. ”Wow” factor:”Wow” factor: –Encourage exploration. Make use of existing hardware available in schools.Make use of existing hardware available in schools.

5. Constructivist learning theory Students construct their own understanding of the subject.Students construct their own understanding of the subject. Learning is a collaborative process.Learning is a collaborative process. Shared virtual environments (SVEs) CyberMath

6. Features of CyberMath Builds on DIVE: Rapid prototyping environment for distributed graphics and distributed audio.Builds on DIVE: Rapid prototyping environment for distributed graphics and distributed audio. Museum/exploratorium metaphor.Museum/exploratorium metaphor. Non-trivial content.Non-trivial content. Global illumination simulation.Global illumination simulation.

7. Lecture hall

8. Generalized cylinders

9. Cylindrical optics

10. Interactive transformations DEMO

11. Initial usability studies Guided tour through generalized cylinders exhibit.Guided tour through generalized cylinders exhibit. Guide and students were physically separated.Guide and students were physically separated. Likert-scale questionnaire.Likert-scale questionnaire.

12. Usability studies, results Favorable ratings for:Favorable ratings for: –Perceived level of immersion and awareness of other users in the environment. –Feasability of CyberMath as teaching tool. Average ratings for:Average ratings for: –Effectivenes of human/computer interface. –Level of collaboration.

13. The future Collaboration issues.Collaboration issues. Teaching strategies.Teaching strategies. School integration issues.School integration issues. Easy content creation.Easy content creation. ”Desktop VR” vs. traditional VR equipment (helmets, CAVEs).”Desktop VR” vs. traditional VR equipment (helmets, CAVEs). Impact of visual richness?Impact of visual richness?