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Designing online mathematical investigation
Article

, Faculty of Education, Canada ; , Department of Computer Science and Faculty of Information and Media Studies, University of Western Ontario, Canada ; , Department of Computer Science, University of Western Ontario, Canada

JCMST Volume 23, Number 3, ISSN 0731-9258 Publisher: Association for the Advancement of Computing in Education (AACE), Waynesville, NC USA

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Abstract

In this paper we focus on applets that support mathematical investigation. In the context of analyzing and redesigning an applet from NCTM’ s Illuminations Web site, we consider two interrelated issues: (1) how the pedagogy of mathematical investigation may be manifested in a mathematical applet, and (2) how interface design principles may be used to enhance an applet’ s potential for supporting mathematical investigation. Mathematical investigation, as a pedagogical tool, is not a simple undertaking. Facilitating investigation adds significantly to the complexity of instructional design. Good design becomes possible when mathematics education and human-computer interaction design experts work together, rather than in isolation, taking into account pedagogical goals and interface design principles.

Citation

Gadanidis, G., Sedig, K. & Liang, H.N. (2004). Designing online mathematical investigation. Journal of Computers in Mathematics and Science Teaching, 23(3), 275-298. Norfolk, VA: Association for the Advancement of Computing in Education (AACE). Retrieved August 11, 2024 from .

© 2004 Association for the Advancement of Computing in Education (AACE)

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References

View References & Citations Map
  1. Arcavi, A. & Hadas, N. (2000). Computer aided learning: an example of an approach. International Journal of Computers for Mathematical Learning. 5:25-45.
  2. Bruner, J. S. (1990). Acts of meaning. Cambridge, MA: Harvard University Press.
  3. Bruner, J. S. (1996). The culture of education. Cambridge, MA: Harvard University Press.
  4. Card, S. K., MacKinlay, J. D. & Shneiderman, B. (1999). Readings in information visualization: using vision to think. San Francisco, CA: Morgan Kaufmann Publishers.
  5. De Souza, C. S. & Sedig, K. (2001). Semiotic considerations on direct concept manipulation as a distinct interface style for learnware. Proceedings of the Brazilian Human-Computer Interaction Conference (IHC2001). Florianopolis, Santa Catarina. 15-17 October, 229-241.
  6. Fleming, M. & Levie, W. H. (Eds.) (1993). Instructional message design: Principles from the behavioral and cognitive sciences (2nd ed.). Englewood Cliffs, NJ: Educational Technology Publications.
  7. Gadanidis, G. (1994). Deconstructing constructivism. Mathematics Teacher, 87(2), 91-97.
  8. Gadanidis, G. (2001). Web-based multimedia activities as pedagogical models. Asian Technology Conference in Mathematics, RMIT University, Melbourne, Australia, 223-232.
  9. Gadanidis, G. & Hoogland, C. (2003). The aesthetic in mathematics as story. Canadian Journal of Science, Mathematics and Technology Education 3(4), 487-498.
  10. Gadanidis, G., Gadanidis, J. & Schindler, K. (2003). Factors mediating the use of online applets in the lesson planning of pre-service mathematics teachers. Journal of Computers in Mathematics and Science Teaching, 22(4). 323-344.
  11. Gadanidis, G. & Rich, S. (2002). From large lectures to online modules and discussion: Issues in the development of online teacher education. The Technology Source, July/August.
  12. Keller, P. R. & Keller, M. M. (1993). Visual cues: Practical data visualization. Los Alamitos, CA: IEEE Computer Society Press.
  13. Kieran, C., Boileau, A. & Garancon, M. (1996). Introducing algebra by means of a technology-supported, functional approach. In Bednarz, N., Kieran, C, & Lee, L., (Eds.). Approaches to Algebra: Perspectives from research and teaching (pp. 257-294). Dordrecht: Kluwer Academic Publishers.
  14. Lajoie, S. P. (1993). Computer environments as tools for enhancing learning. I. Lajoie, S. P. & Derry, S. J. (Eds.), Computers as cognitive tools (pp. 261288). Hillsdale, N.J.: Lawrence Erlbaum Associates.
  15. McGowen, M. A. & Davis, G. E. (2001b). Changing pre-service elementary teachers’ attitudes to algebra. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (eds.) Proceedings of the 12th ICMI Study Conference: The future of
  16. McKee, R. (1997). Story – Substance, structure, style, and the principles of screenwriting. N.Y.: Harper-Collins/Reagan Books.
  17. Mullet, K. & Sano, D. (1995). Designing visual interfaces: Communication oriented techniques. Prentice Hall.
  18. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  19. National Council of Teachers of Mathematics (2003). Side length, volume, and surface area of similar solids. Reston, VA: National Council of Teachers of Mathematics. Retrieved 02/2003 from http://standards.nctm.org/document/eexamples/chap6/6.3/part2.htm.
  20. Norman, D. A. (1991). Cognitive artifacts. In J. M. Carroll (Ed.), Designing interaction: Psychology at the human-computer interface. Cambridge, UK: Cambridge University Press.
  21. Norman, D. A. (1993). Things that make us smart: Defi ning human attributes in the age of the machine. New York, NY: Addison-Wesley Publishing Company.
  22. Olive, J. (2000). Computer tools for interactive mathematical activity in the elementary school. International Journal of Computers for Mathematical Learning, 5:241-262.
  23. Ontario Ministry of Education (1997). The Ontario Curriculum, Grades 1-8: Mathematics. Toronto, ON: Queen’s Printer.
  24. Ontario Ministry of Education (1999). The Ontario Curriculum, Grades 9-10: Mathematics. Toronto, ON: Queen’s Printer.
  25. Ontario Ministry of Education (2000). The Ontario Curriculum, Grades 11-12: Mathematics. Toronto, ON: Queen’s Printer.
  26. Preece, J., Rogers, Y., and Sharp, H. (2002). Interaction design: Beyond human computer interaction. John Wiley & Sons, Inc.
  27. Romberg, T. A. (1992). The scholarly basis of the school mathematics reform movement in the United States. International Journal of Educational Research, 17, 419-438.
  28. Schank, R. (1990). Tell me a story – A new look at real and artifi cial memory. N.Y.: MacMillan Publishing Company.
  29. Sedig, K., Klawe, M. & Westrom, M. (2001). Role of interface manipulation style and scaffolding on cognition and concept learning in learnware. ACM Transactions on Computer-Human Interaction. No. 1, Vol. 8, pp. 34-59. Sedig, K. & Morey, J. (2003, in press). A descriptive framework for designing interaction for visual abstractions. 2nd International Conference on Visual Representations and Interpretations, VRI’2002, September, 2000, Liverpool, UK.
  30. Sedig, K., Rowhani, S., Morey, J. & Liang, H. (2003, in press). Application of information visualization techniques to the design of a mathematical mindtool: A usability study. Journal of Information Visualization.
  31. Shneiderman, B. (1998). Designing the user interface (3rd ed.). Reading, Massachusetts: Addison-Wesley.
  32. Skemp, R. R. (1986). The psychology of learning mathematics (2nd ed.). Middlesex, UK: Penguin Books.
  33. Spence, R. (2001). Information visualization. Harlow, England: Pearson Education Limited.
  34. Sternberg, R. J. (1999). Cognitive psychology. Orlando, FL: Harcourt Brace & Co.
  35. Stylianou, D. A. (2002). On the interaction of visualization and analysis: the negotiation of a visual representation in expert problem solving. Journal of Mathematical Behavior, 21, 303–317.
  36. Surgue, B. (2000). Cognitive approaches to Web-based instruction. In Lajoie, S. P. (Ed.), Computers as cognitive tools, Volume two: No more walls (pp. 133162). Mahwah, N.J.: Lawrence Erlbaum Associates.
  37. Tufte, E. (1990). Envisioning information. Cheshire, CT: Graphics Press. Tufte, E. (1997). Visual explanations: Images and quantities, evidence and narrative. Cheshire, CT: Graphics Press.
  38. Vosniadou, S. (1996). Learning environments for representational growth and cognitive fl exibility. In Vosniadou, S., De Corte, E., Glaser, R., & Mandl, H. (Eds.), International perspectives on the design of technology-supported learning environments. New Jersey: Lawrence Erlbaum Associates.
  39. Winn, W. (1993). Perception principles. In M. Fleming & W. H. Levie (Eds.), Instructional message design: Principles from the behavioral and cognitive sciences (2nd ed.). Englewood Cliffs, NJ: Educational Technology Publications.

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