Abstract
The history of mathematics education provides ample evidence of the dichotomous distinction that has been made over the years between concepts and procedures, between concepts and skills, and between “knowing that” and “knowing how.” In no field of school mathematics learning has this dichotomy been so damaging as in algebra. While reform efforts of the past decade have attempted to imbue algebra learning with meaning by focusing on “real-life” problems and their various representations, these efforts have missed the main point with respect to the literal-symbolic: that is, that conceptual aspects of algebra abound within the literal-symbolic and that these are integral to most of the so-called procedures of algebra. Both theoretical and empirical arguments will be used to make the point for adopting a different vision of the literal-symbolic domain, in which the procedural is so permeated with the conceptual as to render obsolete a primarily procedure-based view of algebra in school mathematics.
The research presented in this article was made possible by a grant from the Social Sciences and Humanities Research Council of Canada (Grant # 410-2007-1485). I also express my appreciation to research colleagues, as well as to the students and their mathematics teacher who participated in the research.
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Notes
- 1.
Lagrange, J.-B. (2000, p. 16).
- 2.
Lagrange, J.-B. (2003, p. 271).
- 3.
Donald, M. (2001, pp. 52–57).
- 4.
Please note that, henceforth in this chapter, the terms procedure and technique will be used synonymously, except in those cases where the context clearly indicates otherwise.
- 5.
Our research team has included over various periods of this program of research André Boileau, Caroline Damboise, Paul Drijvers, José Guzmán, Fernando Hitt, Ana Isabel Sacristán, Luis Saldanha, Armando Solares, and Denis Tanguay—as well as our project consultant, Michèle Artigue.
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Kieran, C. (2013). The False Dichotomy in Mathematics Education Between Conceptual Understanding and Procedural Skills: An Example from Algebra. In: Leatham, K. (eds) Vital Directions for Mathematics Education Research. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6977-3_7
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