3. Presence Production in a Distributed Shared Virtual Environment for Exploring Mathematics web-site: http://kmr.nada.kth.se Claus Knudsen Ambjörn Naeve Division of Media Technology and Graphic Arts Dept. of Numerical Analysis and Computing Science clausk@gt.kth.se Centre for user-oriented IT Design Dept. of Numerical Analysis and Computing Science amb@nada.kth.se

4. Centre for user-oriented IT-Design (CID) CID is a competence centre at KTH that provides an interdisciplinary environment for applied research on design of human-computer interaction. CID is engaged in 4 different areas of research: Connected Communities (Digital Worlds). Interactive Learning Environments. New forms of Interaction. User orientation.

5. Goals and characteristics of CID integrate usability with technical and aesthetic aspects. create an attractive environment at KTH for strong cooperation between academy, industry and users. produce “pre-competitive” results in the form of prototypes, demonstrators and user studies. strong international collaboration.

6. A Knowledge Manifold is a conceptual framework for designing interactive learning environments that support Inquiry Based Learning. can be regarded as a Knowledge Patchwork, with a number of linked Knowledge Patches, each with its own Knowledge Gardener. gives the users the opportunity to ask questions and search for certified human Knowledge Sources.

7. A Knowledge Manifold (cont.) has access to distributed archives of resource components. allows teachers to compose components and construct customized learning environments. makes use of conceptual modeling to support separation of content from context. contains a conceptual exploration tool (Conzilla) that supports these principles and activites.

8. Structure of today’s math education system Closed layered architecture based on: lack of subject understanding in the early layers. minimization of teaching duties in the final layers. life long teaching with: curricular-oriented ”knowledge pushing”.

9. Problems with today’s math education It does not: promote understanding. support personalization. integrate mathematics with human culture. stimulate interest. integrate abstractions with applications. support transition between the different layers.

10. Possibilities for improving math education visualizing the concepts. interacting with the formulas. using ICT to increase the ”cognitive contact” by: personalizing the presentation. Promoting life-long learning based on interest by: improving the narrative by: showing before proving. focusing on the evolutional history. routing the questions to live resources. proving only when the need is evident.

11. Ongoing Mathematical KM work at CID Dynamically uploadable math component archives Interactive geometrical constructions with PDB Interacting with mathematical formulas CyberMath: a shared 3D ILE for exploring math using LiveGraphics3D / Graphing Calculator Virtual Mathematics Exploratorium with Conzilla

12. CyberMath: A Shared Virtual Environment for the Interactive Exploration of Mathematics teaching of both elementary, intermediate and advanced mathematics and geometry. Goals: The CyberMath system should allow: Means: Making use of advanced VR technology (e.g. DIVE). global sharing of resources. the teacher to teach in a direct manner. students to work together in groups. teachers to present material that is hard to visualize using standard teaching tools.

13. CyberMath: An Avatar Using a Laser Pointer

14. CyberMath: Finding the Kernel of a Linear Map

15. CyberMath: Importing a Mathematica Object

16. CyberMath: The Cylindrical Exhibition Hall

17. CyberMath: Experimental Lecture Connectivity

18. Definition of Presence at a Distance Presence at a distance is defined as the subjective experience of being in one place or environment, even when one is physically situated in another. Presence journal 2000

19. Factors creating a sense of presence and reality sensory environment individual preconditions content characteristics vividness interactivity and control company of others depth & breadth imagination emotional state associative context suspension of disbelief plot and story narration and dramaturgy presentation and execution

20. CyberMath: The Teacher in Stockholm

21. CyberMath: 1:st Group of Students in Uppsala

22. CyberMath: 2:nd Group of Students in Uppsala

23. CyberMath: Changing the Learning Mode

24. CyberMath: Social Mingling in Cyberspace

25. CyberMath: Transforming a Set of Planes

26. CyberMath: The Virtual Museum Mode

27. CyberMath: The Solar Energy Exhibit

28. CyberMath: The Cooperative Learning Mode

29. CyberMath: The WASA Platform

30. Ongoing Knowledge Manifold projects at CID e-Learninge-Commerce Archives Portfolios Environments e-StandardsResearch Partner Wallenberg Global Learning Network Stanford-LLAcademicL3Se-Accessibility IMS / RDF ISO / WG36 CyberMath Conceptual Math-modeling Mathematics Exploratorium MicrosoftWorldCom Hewlett Packard Industrial WebGiro CEN/ISSS/WS/EC Electronic Commerce Integration Meta-Framework Accessing the Printed Word FMLS HI Swedish Learning Lab VWE

31. Emerging Knowledge Manifold projects at CID WGLNe-Learninge-Commercee-AdministrationResearch PartnerAcademic Personalized Access to Distributed Learning Resources Administrativee-Accessibilitye-Europe User-oriented Mathematics Learning Environment ethical Multi-lingual Upper Level Electronic Commerce Ontology Edutella Mathemagic Mathematical Courselets National Research School in Mathematical Didactics L3SSLL Authority Handbook 24/7/365 Authority ÖCBVINNOVA... UKLA STEM

32. References Naeve, A., The Garden of Knowledge as a Knowledge Manifold - a conceptual framework for computer supported subjective education, CID-17, KTH, 1997. Naeve, A., Conceptual Navigation and Multiple Scale Narration in a Knowledge Manifold, CID-52, KTH, 1999. Nilsson, M. & Palmér M., Conzilla - Towards a Concept Browser, (CID-53), KTH, 1999. Nilsson, M., The Conzilla design - the definitive reference, CID/NADAKTH, 2000. Naeve, A., The Concept Browser, a New Form of Knowledge Management Tool, Proc. of the 2:nd european conference on Web Based Learning Environments (WBLE-2001), Lund, Sweden, Oct. 24-26, 2001.

33. Naeve, A., The Knowledge Manifold – an educational architecture that supports inquiry based customizable forms of e-learning, WBLE-2001. [ Reports are available in PDF at http://kmr.nada.kth.se ] Naeve, A. & Nilsson, M. & Palmér, M., The Conceptual Web - Our Research Vision, Proceedings of the First Semantic Web Working Symposium, Stanford, July 30 - Aug 2, 2001. Naeve, A. & Nilsson, M. & Palmér, M., E-learning in the Semantic Age, WBLE-2001. References (cont)

34. Taxén G., & Naeve, A. CyberMath - A Shared 3D Virtual Environment for Exploring Mathematics, presented within Course-31, Geometric Algebra, Siggraph 2000, New Orleans, July 2000. Taxén G., & Naeve, A. CyberMath - A Shared 3D Virtual Environment for Exploring Mathematics, the 20:th ICDE world conference, Düsseldorf, April 2001, on Compact Disc. References (cont) Taxén G., & Naeve, A. CyberMath - Exploring Open Issues in VR-based Learning, SIGGRAPH 2001, Educators Program, SIGGRAPH 2001 Conference Abstracts and Applications, pp. 49-51. [ Quicktime demos of lectures in CyberMath are available at http://cid.nada.kth.se/il ]