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The definition of the scalar product: an analysis and critique of a classroom episode

Foster, Colin; de Villiers, Michael

Authors

Colin Foster

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 Dec 9, 2015
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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