Colin Foster
The definition of the scalar product: an analysis and critique of a classroom episode
Foster, Colin; de Villiers, Michael
Authors
Michael de Villiers
Abstract
In this paper we present, analyse and critique an episode from a secondary school lesson involving an introduction to the definition of the scalar product. Although the teacher attempted to be explicit about the difference between a definition and a theorem, emphasizing that a definition was just an arbitrary assumption, a student rejected the teacher’s definition in favour of his own alternative. With reference to this particular case, we seek to explore some ways in which teachers can introduce mathematical definitions to students so as to support, rather than attempt to circumvent, their mathematical sense making. In this regard, we believe that it is important to develop learning opportunities for students that help them to gain some appreciation of important structural and historical reasons that underpin the definitional choices made.
Citation
Foster, C., & de Villiers, M. (in press). The definition of the scalar product: an analysis and critique of a classroom episode. International Journal of Mathematical Education in Science and Technology, 47(5), https://doi.org/10.1080/0020739X.2015.1117148
Journal Article Type | Article |
---|---|
Acceptance Date | Sep 3, 2015 |
Online Publication Date | Dec 9, 2015 |
Deposit Date | Nov 4, 2015 |
Publicly Available Date | Mar 29, 2024 |
Journal | International Journal of Mathematical Education in Science and Technology |
Print ISSN | 0020-739X |
Electronic ISSN | 1464-5211 |
Publisher | Taylor & Francis Open |
Peer Reviewed | Peer Reviewed |
Volume | 47 |
Issue | 5 |
DOI | https://doi.org/10.1080/0020739X.2015.1117148 |
Keywords | Definitions, scalar product, mathematics |
Public URL | https://nottingham-repository.worktribe.com/output/769679 |
Publisher URL | http://www.tandfonline.com/doi/full/10.1080/0020739X.2015.1117148 |
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