math game(s) -- an alternative (approach) to teaching math?

Anton Eliëns, Zsofia Ruttkay


Creative Technology / University Twente
multimedia @ VU / Amsterdam

student(s)


taxonomy of math games


  1. games to practice routine tasks
  2. manipulative virtual environments for try-out
  3. simulations for making conjectures
  4. strategic games -- manipulative & combinatorial
  5. visualization of structure(s) -- patterns of nature
  6. explorations in 2D and 3D geometry
  7. generative (visual) art

Mr. E's knapsack


Mathematician Mr. E is traveling the world with his knapsack full of (mathematical) knowledge. Exploring the world, he meets famous colleagues like Euclid, Euler, Gauss, Newton, Einstein, Gödel, Leibniz, etc. He has to collaborate - learning as well as teaching - to proceed, get goods, get a regenerating cup of coffee, and sometimes a place to stay. He uses his problem solving skills to discover the world, and to unravel it's Big Mystery. Mr. E's journey is taking him around the globe and through the history of science and mathematics.

An adventure game, that we take as a convenient metaphor for an online mathematics textbook, provides flexible access to a variety of illustrations and exercises dependent on the skill level of the students, and allows for extensions by student-created content both visual (e.g. generated plants) and intellectual (e.g. a question raised for the future players). In addition interactive video may be used to provide the necessary historical and societal context,  [XIMPEL].

MATHS ON THE WEB -- FRAMEWORKS AND TOOLS

 When Java applets were introduced about a decade ago, there was a general enthusiasm among educators, at least in CS departments, that their topics - mathematics, programming languages - could be presented in an interactive way. However, although Java has been adopted as the programming language of choice at many universities, the early vision(s) of interactive education has not been realized, despite the increasingly large collection of interactive examples of mathematics, physics, and related disciplines on the Web.

When we look at how, for example, Wikipedia has become a trusted source of information on mathematics, we may attribute this to the lack of a coherent framework for incorporating interactive math examples. Such a framework, apparently, is more easily provided for (hyper) textual information, or images and video, as testified by the large amounts of user-contributed content in sites such as flickr and youtube.

Is it possible to create a similar repository for samples of interactive mathematics, and, on a more modest scale, to formulate guidelines to enforce a coherent approach in both (visual) style and (mathematical) content?

In developing our Creative Technology curriculum, we discussed computer programming platform options ranging over C++, flash/actionscript and, of course, Java. Finally, as indicated before, we have chosen for processing, as a language to teach programming, but foremost as a platform for exploring both mathematical and visual ideas in an exploratory fashion using computational means, suited for educating creative engineers.

CONCLUSIONS AND FUTURE WORK

 It is apparent, when browsing through resources, how many applications lack aesthetic appeal and design wit, usually because the author is a computer scientists or mathematician not equipped with the skills, or the environment he/she used to create the content does not provide good support for the visual design.

From an educational, or if you will, methodological point of view, games and interactive CG may be used:

methodology


[Bourbaki] Aubin D. (1997),
The Withering Immortality of Nicolas Bourbaki: A Cultural Connector at the Confluence of Mathematics, Science in Context, 10. 1997, pp. 297-342.
[Patterns] Björk S. and Holopainen J. (2005),
Patterns in Game Design, Charles River Media
[Education] Chalmers A. and Cunningham S. 92002),
New Media and Future Education, Proc. East-West-Vision 2002. pp. 67-74.
[Teaching] Duchowski A.T. and Davis T.A. (2007),
Teaching Algorithms and Data Structures through Graphics, Proc. of Eurographics 2007, Education Papers.
[XIMPEL] Eliens A., Huurdeman H., van de Watering M.,
Bhikharie S.V. (2008), XIMPEL Interactive Video -- between narrative(s) and game play, In Proc. GAME-ON 2008, Valencia, Spain
[Replay] Eliens A. and Ruttkay Zs. (2009),
Record, Replay & Reflect -- a framework for serious gameplay, In Proc. EUROMEDIA 2009, Brugge (Belgium)
[VideoGame] Gee J.P. (2003),
What video games have to teach us about learning and literacy, Palgrave Macmillan
[Fun] Lundgren S. (2006),
Facets of Fun -- On the Design of Computer Augmented Entertainment Artifacts, Dissertation: Chalmers University of Technology
[Animation] Peters K. (2006),
Animation: Making Things Move!, Foundation Actionscript 3.0, Wrox Press
[Processing] Reas C. and Fry B. (2008),
Processing: A Programming Handbook for Visual Designers and Artists, MIT Press
[Sangaku] Ruttkay Zs. (2008),
A Sangaku Revived, BRIDGES 2008, Leeuwarden, Tarquin Books, UK, 2008. pp. 155-162
[Math] Ruttkay Zs. and Eliens A. (2009),
From Puzzles to Interactive Textbooks -- CG in Maths Education, in preparation
[Visual] Terzidis K. (2008),
Algorithms for Visual Design Using the Processing Language, MIT Press