The definition of the scalar product: an analysis and critique of a classroom episode
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...
| Main Authors: | , |
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| Format: | Article |
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Taylor and Francis
2015
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| Online Access: | https://eprints.nottingham.ac.uk/30635/ |
| _version_ | 1848794028309479424 |
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| author | Foster, Colin de Villiers, Michael |
| author_facet | Foster, Colin de Villiers, Michael |
| author_sort | Foster, Colin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:09:41Z |
| format | Article |
| id | nottingham-30635 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:09:41Z |
| publishDate | 2015 |
| publisher | Taylor and Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-306352020-05-04T17:27:24Z https://eprints.nottingham.ac.uk/30635/ The definition of the scalar product: an analysis and critique of a classroom episode Foster, Colin de Villiers, Michael 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. Taylor and Francis 2015-12-09 Article PeerReviewed Foster, Colin and de Villiers, Michael (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. ISSN 1464-5211 Definitions scalar product mathematics http://www.tandfonline.com/doi/full/10.1080/0020739X.2015.1117148 doi:10.1080/0020739X.2015.1117148 doi:10.1080/0020739X.2015.1117148 |
| spellingShingle | Definitions scalar product mathematics Foster, Colin de Villiers, Michael The definition of the scalar product: an analysis and critique of a classroom episode |
| title | The definition of the scalar product: an analysis and critique of a classroom episode |
| title_full | The definition of the scalar product: an analysis and critique of a classroom episode |
| title_fullStr | The definition of the scalar product: an analysis and critique of a classroom episode |
| title_full_unstemmed | The definition of the scalar product: an analysis and critique of a classroom episode |
| title_short | The definition of the scalar product: an analysis and critique of a classroom episode |
| title_sort | definition of the scalar product: an analysis and critique of a classroom episode |
| topic | Definitions scalar product mathematics |
| url | https://eprints.nottingham.ac.uk/30635/ https://eprints.nottingham.ac.uk/30635/ https://eprints.nottingham.ac.uk/30635/ |