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Reconstruction of Meanings for Function Approximation

Reconstruction of Meanings for Function Approximation 94 TOMMY DREYFUS AND JOEL HILLEL Figure 1. will argue that the software plays a more subtle, covert role in these instances. The constructed shared meaning of a particular piece of mathematics by a group of students can be seen as being triggered by a multiplicity of “agents of communication” (Sierpinska et al., 1995). In our particu- lar study, the agents included Maple as well the students themselves, an observer, the classroom teacher (who was not physically present), class- room notes, and the text. Elsewhere, we have examined how the roles of these different agents changed as the session progressed, and how they contributed to the meaning shared by the students (Hillel and Dreyfus, 1995). We therefore want to emphasize that our more narrow focus on Maple in this paper does not mean that we consider that in computer based environments the computer/software system is the sole agent which affects students’ learning processes. THE MATHEMATICAL CONTEXT The topic under consideration was Inner Product Spaces (IPS) in general and orthogonal projections and approximations in particular. Here, a more- or-less familiar geometric concept is recast within a more general theory of IPS. In its geometric setting projections are related to the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Technology, Knowledge and Learning" Springer Journals

Reconstruction of Meanings for Function Approximation

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Publisher
Springer Journals
Copyright
Copyright © 1998 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/A:1009783831945
Publisher site
See Article on Publisher Site

Abstract

94 TOMMY DREYFUS AND JOEL HILLEL Figure 1. will argue that the software plays a more subtle, covert role in these instances. The constructed shared meaning of a particular piece of mathematics by a group of students can be seen as being triggered by a multiplicity of “agents of communication” (Sierpinska et al., 1995). In our particu- lar study, the agents included Maple as well the students themselves, an observer, the classroom teacher (who was not physically present), class- room notes, and the text. Elsewhere, we have examined how the roles of these different agents changed as the session progressed, and how they contributed to the meaning shared by the students (Hillel and Dreyfus, 1995). We therefore want to emphasize that our more narrow focus on Maple in this paper does not mean that we consider that in computer based environments the computer/software system is the sole agent which affects students’ learning processes. THE MATHEMATICAL CONTEXT The topic under consideration was Inner Product Spaces (IPS) in general and orthogonal projections and approximations in particular. Here, a more- or-less familiar geometric concept is recast within a more general theory of IPS. In its geometric setting projections are related to the

Journal

"Technology, Knowledge and Learning"Springer Journals

Published: Oct 5, 2004

References