CyberMathA Shared Virtual Environment for Exploring Mathematics Gustav Taxén, Ambjörn Naeve, Olle Sundblad, Pär Bäckström and Sören Lenman. 
A public demonstration of CyberMath is now available. See bottom of this page for more information. 
It is well known that the current state of mathematics education is problematic in many countires. The Interactive Learning Environments group at CID is developing an avatarbased shared virtual environment called CyberMath, aimed at improving this situation through the presentation of mathematics in a new and exciting way. CyberMath is suitable for exploring and teaching mathematics in situations where both the teacher and the students are copresent and physically separated. Our first prototype environment was built on top of DIVE, a toolkit for building interactive shared distributed virtual environments that support multiple simultaneous participants. However, due to problems with instability and usability, we are now migrating to an inhouse platform, Wasa. 
In the CyberMath environment, people (represented by avatars) can gather and share their experience of mathematical objects. When a person points to an object with the mouse, a red beam running from his avatar to the object appears in the 3D environment, similar to a laser pointer. Objects can easily be manipulated (rotated and translated) using the mouse. Since live audio is distributed as well, a person can point, act and talk  much as he/she would do in real reality  as if the mathematical objects were hanging there in front of him/her. Hence, mathematics teachers are provided with a tool that integrates the best of both the virtual and the real world: virtual (mathematical) objects can be manipulated and discussed in a realistic way. 
An avatar is using the laser pointer to point to a geometric object in the DIVE version of CyberMath. 
CyberMath is built like a museum with a virtual lecture hall in its center. Special care has been taken to make the environment as inviting as possible. The lecture hall contains a virtual slide projector and can be used to hold traditional PowerPointbased presentations. The lecture hall is surrounded by a number of different exhibition galleries, each of which contains a collection of mathematical components expressing a common theme. In the lecture hall the overall theory can be presented and then the participants can move into the surrounding exhibition halls and study the mathematical objects in practice. 
The lecture hall in CyberMath can be used for traditional PowerPointbased presentations (DIVE version). 
Two usability studies of the DIVE version of CyberMath have been performed, one smallscale test in August '00 with 2 subjects (both teacher and students located in Stockholm) and a larger study in October '00 with 13 subjects (teacher located in Stockholm and the students in Uppsala). These studies were aimed at evaluating the DIVE version of CyberMath and provide feedback for further enhancement. We can also run CyberMath in the sixwalled CAVE at KTH and we are investigating the possibility of connecting different CAVEbased CyberMath sites through the Internet. We believe that CyberMath in a networked cave environment holds the potential to provide a hightech front end which is interesting enough to create public interest and contribute to a more positive attitude towards mathematics  especially among young people. It could also provide a useful platform for developing various forms of interactive problem solving games  where the present violenceorientation of the gaming industry can be shifted towards an emphasis on cooperative problem solving skills, leading to future knowledge games that are designed to stimulate the learning interest of the gamers. 
The exhibit hall (Wasa version). 
CyberMath was introduced at SIGGRAPH 2000, New Orleans as part of the Geometric Algebra Course. It was also presented at SIGGRAPH 2001, Los Angeles, as an Educators Program Paper. 


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Gustav Taxén, gustavt@nada.kth.se Ambjörn Naeve, amb@nada.kth.se Olle Sundblad, osu@nada.kth.se Pär Bäckström, paer@nada.kth.se Sören Lenman, lenman@nada.kth.se (C) Copyright 20002001 The Center for User Oriented IT Design. None of the material on this page may be reproduced without permission. 