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Title: The definition of the scalar product: an analysis and critique of a classroom episode
Authors: Foster, Colin
De Villiers, Michael
Keywords: Definitions
Scalar product
Sense making
Issue Date: 2015
Publisher: © Taylor & Francis
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.
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 which help them to gain some appreciation of important structural and historical reasons that underpin the definitional choices made.
Description: 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.
Version: Accepted for publication
DOI: 10.1080/0020739X.2015.1117148
URI: https://dspace.lboro.ac.uk/2134/36827
Publisher Link: https://doi.org/10.1080/0020739X.2015.1117148
ISSN: 0020-739X
Appears in Collections:Published Articles (Mathematics Education Centre)

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