Abstract
This paper describes a series of ‘intellectual mirror’ software environments for the teaching and learning of algebra. These environments are distinguished by the fact that they allow users to manipulate the symbolic representation of functions symbolically and the graphical representation of functions graphically, thus leading to a deeper understanding of the concept of function both as process and as entity.
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Note and References
Schwartz, J.L., Intellectual Mirrors: A Step in the Direction of Making Schools Knowledge-Making Places, In: Harvard Educational Review, Vol. 59, No. 1, February 1989.
This is not the place to document the parlous state of secondary mathematics teaching and learning the US (or elsewhere). Nor is this the place to talk about the mathematical and pedagogic flaws with current curricula in algebra, and thus the need for a new curriculum.
There is a particular kind of ‘number recipe’ that requires special mention, i.e. the constant function. The number recipe F(x)= 1 is a recipe that produces the value 1 no matter what value of x you supply it with. This number recipe is different from and should be distinguished from the number 1.
The VISUALIZING ALGEBRA series of software environments was developed at Education Development Center by Judah L. Schwartz and Michal Yerushalmy under the direction of Wayne Harvey. The series is published by Sunburst Communications, Pleasantville, NY 10570 to whom inquiries may be addressed. The series consists of The Function Analyzer - published 1989 The Function Supposer - published 1990 The Function Comparator(functions of one variable) - in press
The Function Comparator(functions of two variables) - in press
In addition, the following software environments also embody the approach to algebra described in this paper.
un*SOLVING Linear Quadratic Equations Inequalities, by Judah L. Schwartz, Sunburst Communications, 1990.
The Function Family Register, by Judah L. Schwartz, Sunburst Communications, 1990.
The Algebraic Proposer, by Judah L. Schwartz, True BASIC, West Lebanon, NH 03784, published 1987.
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© 1993 Springer-Verlag Berlin Heidelberg
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Schwartz, J.L. (1993). Software to Think With: The Case of Algebra. In: Ferguson, D.L. (eds) Advanced Educational Technologies for Mathematics and Science. NATO ASI Series, vol 107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02938-1_17
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DOI: https://doi.org/10.1007/978-3-662-02938-1_17
Publisher Name: Springer, Berlin, Heidelberg
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