Visual Immersive Haptic Mathematics in Shared Virtual Spaces

  • Alexei Sourin
  • Olga Sourina
  • Lei Wei
  • Paul Gagnon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5300)


When teaching subjects richly infused with mathematics, in particular geometry, topology and shape modeling, there is a frequent problem that the learners are not able to “visualize” the attendant theoretical concepts. It is important, therefore, to constantly illustrate the associated theories with practical visual exercises, which are preferably to be done in collaboration with other learners to allow them to discuss possible approaches to the problem and to consult with the instructor, virtually or face-to-face. We have proposed an approach that would allow for solving mathematical problems while being immersed within shared virtual 3D collaborative environments. Only mathematical formulas are used by the learners for immediate interactive definition of geometry, appearance and physical property of the shapes being created in the virtual environment. We target learners and educators who are studying subjects rich in mathematics and geometry, or teaching them at the secondary or tertiary level or doing research on these topics. The process allows the learners to see and feel the geometric meaning of mathematics, thus making it less abstract and more perceptual and tangible. We also see ways of incorporating beneficial uses of immersive virtual environments into traditional courses at Universities which might benefit from 3D visualization.


Web Technologies Networked Learning Distance Education Virtual Campus Virtual Classroom Virtual Learning Web-Based Learning Shape Modeling Haptic Collaboration Shared Virtual Spaces 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kunimune, S., Nagasaki, E.: Curriculum Changes on Lower Secondary School Mathematics of Japan - Focused on Geometry. In: 8th International Congress on Mathematical Education (1996) (retrieved January 8, 2008),
  2. 2.
    Mathematics Syllabus Primary. Ministry of Education Singapore (2007) (retrieved January 8, 2008),
  3. 3.
    Secondary Mathematics Syllabuses. Ministry of Education Singapore (2007) (retrieved January 8, 2008),
  4. 4.
    TSG 16: Visualisation in the teaching and learning of mathematics, 10th International Congress of Mathematical Education, Copenhagen, Denmark, July 4-11 (2004),
  5. 5.
    Gibson, W.: Neuromancer. Ace (1984) ISBN-13: 978-0441569595Google Scholar
  6. 6.
    Prasolova-Førland, E., Sourin, A., Sourina, O.: Cyber-campuses: Design Issues and Future Directions. The Visual Computer 22(12), 1015–1028 (2006)CrossRefGoogle Scholar
  7. 7.
    Sourin, A.: Nanyang Technological University Virtual Campus. IEEE Computer Graphics & Applications 24(6), 6–8 (2004)CrossRefGoogle Scholar
  8. 8.
    Kaufmann, H., Schmalstieg, D.: Designing Immersive Virtual Reality for Geometry Education. In: IEEE Virtual Reality Conference, VR 2006, pp. 51–58. IEEE CS Press, Los Alamitos (2006)Google Scholar
  9. 9.
    Song, K.S., Lee, W.Y.: A virtual reality application for geometry classes. Journal of Computer Assisted Learning 18, 149–156 (2002)CrossRefGoogle Scholar
  10. 10.
    Pasqualotti, A., Dal Sasso Freitas, C.M.: MAT3D: A Virtual Reality Modeling Language Environment for the Teaching and Learning of Mathematics. Cyber Psychology & Behavior 5(5), 409–422 (2002)CrossRefGoogle Scholar
  11. 11.
    Liu, Q., Sourin, A.: Function-based shape modelling extension of the Virtual Reality Modelling Language. Computers & Graphics 30(4), 629–645 (2006)CrossRefGoogle Scholar
  12. 12.
    Liu, Q., Sourin, A.: Function-defined Shape Metamorphoses in Visual Cyberworlds. The Visual Computer 22(12), 977–990 (2006)CrossRefGoogle Scholar
  13. 13.
    Wei, L., Sourin, A., Sourina, O.: Function-based Haptic Interaction in Cyberworlds. In: 2007 International Conference on Cyberworlds, pp. 225–232. IEEE CS Press, Los Alamitos (2007)CrossRefGoogle Scholar
  14. 14.
    Pasko, A., Adzhiev, V., Sourin, A., Savchenko, V.: Function Representation in Geometric Modeling: Concepts, Implementations and Applications. The Visual Computer 11(8), 429–446 (1995)CrossRefGoogle Scholar
  15. 15.
    Chickering, A.W., Gamson, Z.F.: Seven principles for good practice in undergraduate education. American Association of Higher Education Bulletin, 3–7 (1987)Google Scholar
  16. 16.
    Hawkins, J.: On Intelligence. Owl Books, New York (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Alexei Sourin
    • 1
  • Olga Sourina
    • 1
  • Lei Wei
    • 1
  • Paul Gagnon
    • 1
  1. 1.Nanyang Technological UniversitySingapore

Personalised recommendations