Session Information
16 SES 06 A, ICT and Curriculum Support
Paper Session
Contribution
Moreno-Armella, Hegedus, and Kaput (2008) identify a historical evolution of representation in mathematics education starting from static inert stage through static kinesthetic, static computational and discrete dynamic to continuous dynamic stage. That is, representation starts with “the inscription is ‘hardened’ or ‘fused’ with the media it is presented upon or within” (p. 102) and evolves in time. Authors claim that this evolution first starts with integrating the features of erasibility and colorability to create reusable and distinguishable representations and that innovations in technology add computational dimension to this evolution. They argue that the effect of technology on representation has not been limited with computational dimension and that technology also makes representational systems more dynamic.
Therefore, the roots of the dynamic learning environments, which are available to use intensively in mathematics education, could be considered as situated in the Kaput’s inspiring article published in 1992. In that article, Kaput envisions the use of technology to create multiple and linked representations of mathematics objects. He suggests a learning environment having mathematical objects linked each other as well as linked to other representations so that students manipulating one object in one representation could see the result in the other one.
Today’s contemporary software (i.e., GeoGebra as many others) provides this opportunity to students. For example, teachers can create mathematical objects (i.e., functions having tangents from a point on the function) by using algebraic feature of the software and illustrate the change in one of them while manipulating the other. Students can explore the effect and change algebraically on the algebra view, visually on the display view, or even numerically on the display or on the spreadsheet view. It is our assumption that students use and benefit from these different representations simultaneously. Do they really? Do they really make use them all, or at least some, of the representations? Do they have any preference in favor of one comparing to the other one?
The developers of dynamic learning environments follow what is suggested by scholars and improve their products with this assumption. For example, international GeoGebra team works hard to integrate “geometric, algebraic, and numeric representations in an interactive way… and change them dynamically afterwards.” (Hohenwarter, 2002, para. 2).
This paper has been guided by this curiosity and explored how students use various representations provided by ICT while solving their mathematics problems. Therefore, in this qualitative study, we conceptualize our research problem as “How do students use technology and various representations provided by technology while solving their mathematics problems?” Our goal guiding this qualitative research was to understand the process, to interpret reasons, and to improve the conditions for a better mathematics education. It is our assumption that the more we understand the nature of students’ mathematical thinking in technology supported environments the better we may improve learning environments and the quality of teaching and learning of mathematics.
Method
Expected Outcomes
References
Hohenwarter, M. (2002). What is GeoGebra? Retrieved from http://www.geogebra.org on January 13, 2010. Hoyles, C. and Noss, R. (2008). Next steps in implementing Kaput’s research programme. Educational Studies in Mathematics, 68, 85–97. Kaput, J. (1992). Technology and mathematics education. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning, pp. 515–556. New York: Macmillan. Moreno-Armella, L., Hegedus, S. J., & Kaput, J. J. (2008). From static to dynamic mathematics: Historical and representational perspectives. Educational Studies in Mathematics, 68, 99-111.
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