Abstract
This brief commentary chapter devoted to issues suggested by the Mason and Lee chapters raises a number of fundamental questions concerning generalization: the epistemological status of generalization and the nature and complexities of generalization as it is manifested in the didactic context of the algebra classroom.
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There is another element that points to this same conclusion. If we look at the emergence of symbolism from a historical perspective, we notice that the use of the unknown in problem solving has often led to the development of different algebraic languages (Diophantus, Chuquet, Viète, etc.). However, the symbolic representations for the concept of variable came much later: Historically, the mathematical objects of variable and equation come from different conceptualizations (see The Roles of Geometry and Arithmetic in the Development of Algebra: Historical Remarks from a Didactic Perspective in this volume).
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© 1996 Kluwer Academic Publishers
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Radford, L. (1996). Some Reflections on Teaching Algebra through Generalization. In: Bernarz, N., Kieran, C., Lee, L. (eds) Approaches to Algebra. Mathematics Education Library, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1732-3_7
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DOI: https://doi.org/10.1007/978-94-009-1732-3_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-4168-0
Online ISBN: 978-94-009-1732-3
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