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Polynomial Approximation of Functions: Historical Perspective and New Tools

Polynomial Approximation of Functions: Historical Perspective and New Tools This paper examines the effect of applying symbolic computation and graphics to enhance students' ability to move from a visual interpretation of mathematical concepts to formal reasoning. The mathematics topics involved, Approximation and Interpolation, were taught according to their historical development, and the students tried to follow the thinking process of the creators of the theory. They used a Computer Algebra System to manipulate algebraic expressions and generate a wide variety of dynamic graphics; thus21st century technology was applied in order to “walk” with the students from the period of Euler in 1748 to the period of Runge in 1901. We describe some situations in which the combination of dynamic graphics,algorithms, and historical perspective enabled the students to improve their understanding of concepts such as limit, convergence, and the quality of approximation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Technology, Knowledge and Learning" Springer Journals

Polynomial Approximation of Functions: Historical Perspective and New Tools

"Technology, Knowledge and Learning" , Volume 8 (3) – Oct 11, 2004

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Publisher
Springer Journals
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Education; Learning and Instruction; Mathematics Education; Educational Technology; Science Education; Creativity and Arts Education
ISSN
2211-1662
eISSN
1573-1766
DOI
10.1023/B:IJCO.0000021793.71677.cd
Publisher site
See Article on Publisher Site

Abstract

This paper examines the effect of applying symbolic computation and graphics to enhance students' ability to move from a visual interpretation of mathematical concepts to formal reasoning. The mathematics topics involved, Approximation and Interpolation, were taught according to their historical development, and the students tried to follow the thinking process of the creators of the theory. They used a Computer Algebra System to manipulate algebraic expressions and generate a wide variety of dynamic graphics; thus21st century technology was applied in order to “walk” with the students from the period of Euler in 1748 to the period of Runge in 1901. We describe some situations in which the combination of dynamic graphics,algorithms, and historical perspective enabled the students to improve their understanding of concepts such as limit, convergence, and the quality of approximation.

Journal

"Technology, Knowledge and Learning"Springer Journals

Published: Oct 11, 2004

References