3. The Knowledge Manifold web-site: http://kmr.nada.kth.se Speaker: Ambjörn Naeve an educational architecture that supports inquiry-based customizable forms of e-learning

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. Fundamental principles of the KM architecture Nobody can teach you anything. A good teacher can inspire you to learn. Your learning is enhanced by taking control of your own learning process. Your learning motivation is based on the experience of subject exitement and faith in your learning capacity from a live teacher. No ”problematic” questions can be answered in an automated way. Respect for ignorance can only be upheld when the ignorant person is uneducated.

6. A traditional educational design pattern (Tenured Preacher / Learner Duty) School Duties Course Preacher Prisoner Employee TeacherLearner Life-long teaching: Minimal learning efforts Security Doing time in return for a degree Pupil Confinement Tenure Agent 007 with a right to kill interest **

7. An emerging educational design pattern (Requested Preacher / Learner Rights) School RightsResource SeekerLearner Student Knowledge Life-long TeacherConsultant learning: Pedagogical Interest Developing your interests Requested teaching: You teach as long as somebody is learning Course * *

8. A Knowledge Manifold is designed in a way that reflects a strong effort to comply with emerging international IT standards. 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 live certified Knowledge Sources. has access to distributed archives of resource components.

9. A Knowledge Manifold (cont.) allows teachers to compose components and construct customized learning environments. makes use of conceptual modeling to support the separation of content from context. contains a conceptual exploration tool (concept browser) that supports these principles.

10. Resource Components / Learning Modules Learning Environment Learning Module What to Teach Resource Component * * What to Learn separating connecting from with through Multiple NarrationComponent Composition through

11. The seven different knowledge roles The knowledge cartographer The knowledge composer The knowledge librarian The knowledge coach The knowledge preacher The knowledge plumber The knowledge mentor

12. QBL: the 3 performing knowledge roles Preacher Knowledge CoachPlumber Master GardenerBroker you teach as long as somebody is learning you assist in developing each indidual learning strategy you find someone to discuss the question ´ ´ ´

13. QBL: 3 dimensions of the knowledge role (cont) Source Strategist OpportunistKnowledge fascinationmethodologyopportunity quality measured by given answers quality measured by lost questions quality measured by raised questions

14. Taking a walk in the Garden of Knowledge What follows are some snapshots from the first KM prototype called the Garden of Knowledge. The prototype is available on CD-rom and part of it is accessible on the web at the address: http://cid.nada.kth.se/il/kt/ktproto This prototype was developed at CID during 1996/97 in collaboration with the Royal College of Music and the Shift New Media Group. The program focuses on symmetry in order to illuminate some of the structural connections between mathematics and music.

15. The entrance to the Garden of Knowledge

16. The overall subject patch Clicking ”geometri” opens the geometry patch.

17. Browsing the geometry patch Clicking the left margin returns to the overall subject patch.

18. Pointing to ”symmetri” produces a definition Symmetry = invariance under motion.

19. Clicking ”symmetri” opens a new sublevel Pointing to ”rosetter” shows preview of content.

20. Pointing to ”band” shows preview of content

21. Clicking ”band” opens a new sublevel

22. Clicking ”make your own bands” brings up a tool which lets you create bands according to the 7 different symmetry types.

23. 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

24. 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

25. 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”.

26. 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.

27. 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.

28. 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

29. Virtual Mathematics Exploratorium-1

30. Virtual Mathematics Exploratorium-2

31. Virtual Mathematics Exploratorium-3

32. CyberMath: The Virtual Museum Mode

33. CyberMath: The Solar Energy Exhibit

34. 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.

35. 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://cid.nada.kth.se/il ] 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)

36. 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 ]