CyberMath: A Shared CyberMath: A Shared Virtual Environment for Virtual Environment for Mathematics ExplorationMathematics Exploration

Gustav Taxén and Ambjörn NaeveGustav Taxén and Ambjörn NaeveCenter for User Oriented IT Design, KTH, Center for User Oriented IT Design, KTH, StockholmStockholm

Current problems in Current problems in mathematics educationmathematics education• Understanding abstract concepts.Understanding abstract concepts.• Bridging related mathematical Bridging related mathematical

areas.areas.• Finding mathematics relevant.Finding mathematics relevant.

• Can we use technology to improve Can we use technology to improve this situation?this situation?

Technology requirementsTechnology requirements

• Flexible:Flexible:– Elementary, intermediate and Elementary, intermediate and

advanced subjects.advanced subjects.– Easy to provide new material.Easy to provide new material.

• Sharing of resources:Sharing of resources:– Allow physically remote teachers to Allow physically remote teachers to

offer expertise.offer expertise.– Access information ”off-line”.Access information ”off-line”.

Technology requirements Technology requirements (cont.)(cont.)• Multiple teaching strategies:Multiple teaching strategies:

– Traditional lecturing, student-driven Traditional lecturing, student-driven exploration (with guidance), student exploration (with guidance), student groups.groups.

• ””Wow” factor:Wow” factor:– Encourage exploration.Encourage exploration.

• Make use of existing hardware Make use of existing hardware available in schools.available in schools.

Constructivist learning Constructivist learning theorytheory• Students construct their own Students construct their own

understanding of the subject.understanding of the subject.• Learning is a collaborative process.Learning is a collaborative process.

Shared virtual environments (SVEs)Shared virtual environments (SVEs)

CyberMathCyberMath

Features of CyberMathFeatures of CyberMath

• Builds on DIVE: Rapid prototyping Builds on DIVE: Rapid prototyping environment for distributed environment for distributed graphics and distributed audio.graphics and distributed audio.

• Museum/exploratorium metaphor.Museum/exploratorium metaphor.• Non-trivial content.Non-trivial content.• Global illumination simulation.Global illumination simulation.

Lecture hallLecture hall

Generalized cylindersGeneralized cylinders

Cylindrical opticsCylindrical optics

Interactive Interactive transformationstransformations

DEMO

Initial usability studiesInitial usability studies

• Guided tour through generalized Guided tour through generalized cylinders exhibit.cylinders exhibit.

• Guide and students were Guide and students were physically separated.physically separated.

• Likert-scale questionnaire.Likert-scale questionnaire.

Usability studies, resultsUsability studies, results

• Favorable ratings for:Favorable ratings for:– Perceived level of immersion and Perceived level of immersion and

awareness of other users in the awareness of other users in the environment.environment.

– Feasability of CyberMath as teaching tool.Feasability of CyberMath as teaching tool.

• Average ratings for:Average ratings for:– Effectivenes of human/computer Effectivenes of human/computer

interface.interface.– Level of collaboration.Level of collaboration.

The futureThe 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 Desktop VR” vs. traditional VR

equipment (helmets, CAVEs).equipment (helmets, CAVEs).• Impact of visual richness?Impact of visual richness?