Designing online mathematical investigation
Article
George Gadanidis, Faculty of Education, Canada ; Kamran Sedig, Department of Computer Science and Faculty of Information and Media Studies, University of Western Ontario, Canada ; HaiNing Liang, Department of Computer Science, University of Western Ontario, Canada
JCMST Volume 23, Number 3, ISSN 07319258 Publisher: Association for the Advancement of Computing in Education (AACE), Waynesville, NC USA
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 humancomputer 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), 275298. Norfolk, VA: Association for the Advancement of Computing in Education (AACE). Retrieved February 16, 2020 from https://www.learntechlib.org/primary/p/4731/.
© 2004 Association for the Advancement of Computing in Education (AACE)
Keywords
References
View References & Citations Map Arcavi, A. & Hadas, N. (2000). Computer aided learning: an example of an approach. International Journal of Computers for Mathematical Learning. 5:2545.
 Bruner, J. S. (1990). Acts of meaning. Cambridge, MA: Harvard University Press.
 Bruner, J. S. (1996). The culture of education. Cambridge, MA: Harvard University Press.
 Card, S. K., MacKinlay, J. D. & Shneiderman, B. (1999). Readings in information visualization: using vision to think. San Francisco, CA: Morgan Kaufmann Publishers.
 De Souza, C. S. & Sedig, K. (2001). Semiotic considerations on direct concept manipulation as a distinct interface style for learnware. Proceedings of the Brazilian HumanComputer Interaction Conference (IHC2001). Florianopolis, Santa Catarina. 1517 October, 229241.
 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.
 Gadanidis, G. (1994). Deconstructing constructivism. Mathematics Teacher, 87(2), 9197.
 Gadanidis, G. (2001). Webbased multimedia activities as pedagogical models. Asian Technology Conference in Mathematics, RMIT University, Melbourne, Australia, 223232.
 Gadanidis, G. & Hoogland, C. (2003). The aesthetic in mathematics as story. Canadian Journal of Science, Mathematics and Technology Education 3(4), 487498.
 Gadanidis, G., Gadanidis, J. & Schindler, K. (2003). Factors mediating the use of online applets in the lesson planning of preservice mathematics teachers. Journal of Computers in Mathematics and Science Teaching, 22(4). 323344.
 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.
 Keller, P. R. & Keller, M. M. (1993). Visual cues: Practical data visualization. Los Alamitos, CA: IEEE Computer Society Press.
 Kieran, C., Boileau, A. & Garancon, M. (1996). Introducing algebra by means of a technologysupported, functional approach. In Bednarz, N., Kieran, C, & Lee, L., (Eds.). Approaches to Algebra: Perspectives from research and teaching (pp. 257294). Dordrecht: Kluwer Academic Publishers.
 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.
 McGowen, M. A. & Davis, G. E. (2001b). Changing preservice 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
 McKee, R. (1997). Story – Substance, structure, style, and the principles of screenwriting. N.Y.: HarperCollins/Reagan Books.
 Mullet, K. & Sano, D. (1995). Designing visual interfaces: Communication oriented techniques. Prentice Hall.
 National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
 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.
 Norman, D. A. (1991). Cognitive artifacts. In J. M. Carroll (Ed.), Designing interaction: Psychology at the humancomputer interface. Cambridge, UK: Cambridge University Press.
 Norman, D. A. (1993). Things that make us smart: Deﬁ ning human attributes in the age of the machine. New York, NY: AddisonWesley Publishing Company.
 Olive, J. (2000). Computer tools for interactive mathematical activity in the elementary school. International Journal of Computers for Mathematical Learning, 5:241262.
 Ontario Ministry of Education (1997). The Ontario Curriculum, Grades 18: Mathematics. Toronto, ON: Queen’s Printer.
 Ontario Ministry of Education (1999). The Ontario Curriculum, Grades 910: Mathematics. Toronto, ON: Queen’s Printer.
 Ontario Ministry of Education (2000). The Ontario Curriculum, Grades 1112: Mathematics. Toronto, ON: Queen’s Printer.
 Preece, J., Rogers, Y., and Sharp, H. (2002). Interaction design: Beyond human computer interaction. John Wiley & Sons, Inc.
 Romberg, T. A. (1992). The scholarly basis of the school mathematics reform movement in the United States. International Journal of Educational Research, 17, 419438.
 Schank, R. (1990). Tell me a story – A new look at real and artiﬁ cial memory. N.Y.: MacMillan Publishing Company.
 Sedig, K., Klawe, M. & Westrom, M. (2001). Role of interface manipulation style and scaffolding on cognition and concept learning in learnware. ACM Transactions on ComputerHuman Interaction. No. 1, Vol. 8, pp. 3459. 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.
 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.
 Shneiderman, B. (1998). Designing the user interface (3rd ed.). Reading, Massachusetts: AddisonWesley.
 Skemp, R. R. (1986). The psychology of learning mathematics (2nd ed.). Middlesex, UK: Penguin Books.
 Spence, R. (2001). Information visualization. Harlow, England: Pearson Education Limited.
 Sternberg, R. J. (1999). Cognitive psychology. Orlando, FL: Harcourt Brace & Co.
 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.
 Surgue, B. (2000). Cognitive approaches to Webbased instruction. In Lajoie, S. P. (Ed.), Computers as cognitive tools, Volume two: No more walls (pp. 133162). Mahwah, N.J.: Lawrence Erlbaum Associates.
 Tufte, E. (1990). Envisioning information. Cheshire, CT: Graphics Press. Tufte, E. (1997). Visual explanations: Images and quantities, evidence and narrative. Cheshire, CT: Graphics Press.
 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 technologysupported learning environments. New Jersey: Lawrence Erlbaum Associates.
 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.
These references have been extracted automatically and may have some errors. Signed in users can suggest corrections to these mistakes.
Suggest Corrections to ReferencesCited By
View References & Citations Map
A multicomponent model for assessing learning objects: The learning object evaluation metric (LOEM)
Robin Kay, Liesel Knaack & Liesel Knaack
Australasian Journal of Educational Technology Vol. 24, No. 5 (Jan 01, 2008)

LearnerInformation Interaction: A MacroLevel Framework Characterizing Visual Cognitive Tools
Kamran Sedig & HaiNing Liang, The University of Western Ontario, Canada
Journal of Interactive Learning Research Vol. 19, No. 1 (January 2008) pp. 147–173

Macrolevel characterization of mathematical cognitive tools
Kamran Sedig & HaiNing Liang, University of Western Ontario, Canada
EdMedia + Innovate Learning 2006 (June 2006) pp. 712–719

A survey of navigation interaction in computerbased learning environments
HaiNing Liang & Sedig Kamran, University of Western Ontario, Canada
EdMedia + Innovate Learning 2006 (June 2006) pp. 684–691

Interactivity of Visual Mathematical Representations: Factors Affecting Learning and Cognitive Processes
Kamran Sedig & HaiNing Liang, The University of Western Ontario, Canada
Journal of Interactive Learning Research Vol. 17, No. 2 (April 2006) pp. 179–212

Interaction and Interactivity in Online Mathematical Applets: Two Sides of the Same Coin
Parul Nanda, HaiNing Liang & Kamran Sedig, The University of Western Ontario, Canada
EdMedia + Innovate Learning 2005 (Jun 27, 2005) pp. 1284–1290

MicroLevel Design of Interactive Visual Learning Environments
Kamran Sedig & Sonja Rowhani, University of Western Ontario, Canada
EdMedia + Innovate Learning 2005 (Jun 27, 2005) pp. 1050–1057
These links are based on references which have been extracted automatically and may have some errors. If you see a mistake, please contact info@learntechlib.org.