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The definition of the scalar product: an analysis and critique of a classroom episode
journal contribution
posted on 2019-02-07, 17:03 authored by Colin FosterColin Foster, Michael De VilliersIn 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 which help them to gain some appreciation of important structural and historical reasons that underpin the definitional choices made.
History
School
- Science
Department
- Mathematics Education Centre
Published in
International Journal of Mathematical Education in Science and TechnologyVolume
47Issue
5Pages
750 - 761Citation
FOSTER, C. and DE VILLIERS, M., 2015. 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), pp.750-761.Publisher
© Taylor & FrancisVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2015Notes
This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Mathematical Education in Science and Technology on 9 December 2015, available online: http://www.tandfonline.com/10.1080/0020739X.2015.1117148.ISSN
0020-739XeISSN
1464-5211Publisher version
Language
- en
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