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Mavrikis , Manolis; Noss , Richard; Hoyles , Celia; Geraniou , Eirini (2012)
Publisher: Wiley
Languages: English
Types: Article
Subjects: [SHS.EDU] Humanities and Social Sciences/Education, epistemic affordance, [ INFO.EIAH ] Computer Science [cs]/Technology for Human Learning, [ SHS.EDU ] Humanities and Social Sciences/Education, [INFO.EIAH] Computer Science [cs]/Technology for Human Learning
This is the preprint. The final version is available from the publisher : http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2729.2011.00469.x/pdf; This paper describes the design of a mathematical microworld to tackle the persistent difficulties that secondary school students have with the idea of algebraic generalization, which is a key stumbling block in secondary-school mathematics classrooms. Our focus is to characterize algebraic ways of thinking and to design both affordances of the system as well as suitable tasks and pedagogies that provide a substrate of activity and experience for the teaching and learning of algebraic generalizations. Using as reference illustrative cases of 12 to 13-year-old students' interaction with the microworld, we demonstrate the strong interplay between epistemology and the design of the microworld and draw conclusions regarding its potential to support the development of algebraic ways of thinking.
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    • Becker J. & Rivera F. (2008) Nature and content of generalization of 7th- and 8th-graders on a task that involves free construction of patterns. In Proceedings of the Joint Meeting of PME 32 and PMENA, Vol. 4 (eds O. Figueras, J. Cortina, S. Alatorre, T. Rojano & A. Sepulveda), pp. 201-208. Cinvestav-UMSNH, Morelia, Mexico.
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    • Chua B., Hoyles C., Mavrikis M. & Geraniou E. (2009) Exploring the link between task features and generalisation. Research in Mathematics Education 11, 73-74.
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    • Dörfler W. (2008) En route from patterns to algebra: comments and reflections. ZDM 40, 143-160.
    • Geraniou E., Mavrikis M., Kahn K., Hoyles C. & Noss R. (2009a) Developing a microworld to support mathematical generalisation. In PME 33: International Group for the Psychology of Mathematics Education, Vol. 3 (eds M. Tzekaki, M. Kaldrimidou & H. Kaldrimidou), pp. 49-56. Thessaloniki, Greece.
    • Geraniou E., Mavrikis M., Hoyles C. & Noss R. (2009b) A learning environment to support mathematical generalisation in the classroom. In CERME 6, Sixth Conference of European Research in Mathematics Education (ed. Weigand), 28 January - 1 February, 2009. Lyon, Frankreich.
    • Geraniou G., Mavrikis M., Hoyles C. & Noss R. (2010) Students' justification strategies on equivalence of quasi-algebraic expressions. In Proceedings of the International Conference on Psychology of Mathematics Education, Vol.2 (ed. B. Ubuz), pp. 393-400. Ancara, Turkey.
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