Conclusion
The crucial point is the power of algebra to gain insight into something that you could not do without it: Algebraic symbolism ⋯ introduced from the very beginning in situations in which students can appreciate how empowering symbols can be in expressing generalities and justifications of arithmetical phenomena ⋯ in tasks of this nature manipulations are at the service of structure and meanings. (Arcavi, 1994, p. 33) Arcavi’s point applies not only with arithmetical phenomena, but with any phenomena of objects and relationships between them. The different frameworks proposed by various authors to define the core of what algebra is, can each be used to give perspectives on algebraic activity. Sometimes these activities will be generational, sometimes transformational, sometimes functional, and sometimes involving generalised arithmetic, but all are encompassed by the global/meta-level activities that give purpose for algebra.
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3.1.6 References
Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24–35.
Brown, L., & Coles, A. (1999). Needing to use algebra-A case study. In O. Zaslavsky (Ed.), Proceedings of the 23rdannual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 153–160). Haifa, Israel: Program Committee.
Coles, A. & Brown, L. (2001). Needing to use algebra. In C. Morgan and K. Jones (Eds.), Research in Mathematics Education (Vol. 3, pp. 23–36). Hampshire: British Society for Research into Learning Mathematics.
Kieran, C. (1996). The changing face of school algebra. In C. Alsina, J. Alvarez, B. Hodgson, C. Laborde, & A. Pérserez (Eds.), 8th International Congress on Mathematical Education: Selected lectures (pp. 271–290). Sevilla, Spain: S.A.E.M. Thales.
3.2.6 References
Dahan-Dalmedico, A., & Peiffer, J. (1986). Une histoire des mathérsematiques, routes et dédales. Coll. Points Sciences, Paris: Le Seuil.
Drouhard, J-Ph., & Panizza, M. (2003). What do the students need to know, in order to be able to actually do algebra? The three orders of knowledge. Paper presented to the 3rd European Conference on Research on Mathematics Education (CERME3), Bellaria, Italy. To appear in the Proceedings of CERME3.
Gray, E., & Tall, D. (1994). Duality, ambiguity, and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 25(2), 116–140.
Gould, S. J. (1980). The panda’s thumb. New York: W. W. Norton.
Kuhn, T. (1970). The structure of scientific revolutions. Chicago: The University of Chicago Press.
Kieran, C. (1991). A procedural-structural perspective on algebra research. In F. Furinghetti (Ed.), Proceedings of the 15thannual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 245–253). Assisi, Italy: Program Committee.
Lee, L. (1997). Algebraic understanding: The search for a model in the mathematics education community. Unpublished doctoral dissertation. Université du Québec à Montréal.
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Brown, L., Drouhard, JP. (2004). Responses to ‘The Core of Algebra’. In: Stacey, K., Chick, H., Kendal, M. (eds) The Future of the Teaching and Learning of Algebra The 12th ICMI Study. New ICMI Study Series, vol 8. Springer, Dordrecht. https://doi.org/10.1007/1-4020-8131-6_3
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