Representing Rolling Sequences of Polyhedra to Support Mathematics Comprehension PROCEEDINGS
Jim Morey, University of Western Ontario, Canada
EdMedia + Innovate Learning, in Montreal, Canada ISBN 978-1-880094-56-3 Publisher: Association for the Advancement of Computing in Education (AACE), Waynesville, NC
CopyCat is a geometric game where the goal is to use the patterned faces of a polyhedron to create a Mosaic. The polyhedron's orientation is manipulated by rolling. Sequences of rolls can exhibit properties like non-commutativity, non-associativity, and non-closure. This paper presents visual explanations of these properties in the context of rolling polyhedra. Maps depicting the sequences of rolls use the geometric properties of the map to exhibit the regularities in the sequences. Currently, the maps can be used as tools external to the game but the ultimate goal of these visual explanations is to use them to guide the design of new CopyCat tools and interfaces that promote understanding of mathematical subtleties of rolling sequences.
Morey, J. (2005). Representing Rolling Sequences of Polyhedra to Support Mathematics Comprehension. In P. Kommers & G. Richards (Eds.), Proceedings of ED-MEDIA 2005--World Conference on Educational Multimedia, Hypermedia & Telecommunications (pp. 1279-1283). Montreal, Canada: Association for the Advancement of Computing in Education (AACE). Retrieved November 17, 2018 from https://www.learntechlib.org/primary/p/20255/.
© 2005 Association for the Advancement of Computing in Education (AACE)
- Epstein, D.B.A, Cannon, J.W., Holt, D.F., Levy, S.V.F., Paterson, M.S., Thurston, W.P. (1992)Word Processing in Groups. Jones and Barlett Publishers, Boston, London.
- Hanson, A., Munzner, T., Francis, G. (1994) Interactive methods for visualizable geometry. IEEE Computer 27,78-83.
- Hepting, D.H, Cao, W., Russell, R.D. (1998) An exploratory approach to mathematical visualization. In Western Computer Graphics Symposium ’98. Whistler, British Columbia
- Morey, J. (1997) CopyCat. Http://www.csd.uwo.ca/~morey/copycat. (last viewed December, 2004)
- Palais, R.S. (1999) The visualization of mathematics: Towards a mathematical Exploratorium. Notices of the American Mathematical Society, 46(6), 647-658.
- Peterson, D. (1996) Forms of Representation. Intellect, Exeter, United Kingdom.
- Sedig, K., Klawe, M., Westrom, M. (2001) Role of interface maniputlation style and scaffolding on cognition and concept learning in learnware. ACM Transactions on Computer-Human Interaction, 8(1),3459.
- Spence, R. (1999) A framework for navigation. International Journal of Human-Computer Studies, 51,919945.
- Tufte, E.R. (1997) Visual explanations images and quantities, evidence and narrative. Graphics Press, Cheshire, Conn.
- Tversky, B. (2000) Some ways that mpas and diagrams communicate. In Freska, C., Brauer, W., Habel, C., Wender, K.F. (eds) Spatial Cognition, Lecture Notes in Compujter Science 1849,72-80.
- West, T.G. (1995) Forward into the past: A revival of old visual talents with computer visualization. ACM SIGGRAPH Computer Graphic, 29(4),14-19.
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Hai-Ning Liang & Sedig Kamran, University of Western Ontario, Canada
EdMedia + Innovate Learning 2006 (June 2006) pp. 684–691
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