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

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journal contribution
posted on 07.02.2019 by Colin Foster, Michael De Villiers
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 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 Technology

Volume

47

Issue

5

Pages

750 - 761

Citation

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 & Francis

Version

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

2015

Notes

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

0020-739X

eISSN

1464-5211

Language

en

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