Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts
In a high-stakes assessment culture, it is clearly important that learners of mathematics develop the necessary fluency and confidence to perform well on the specific, narrowly defined techniques that will be tested. However, an overemphasis on the training of piecemeal mathematical skills at the ex...
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| Format: | Article |
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Taylor and Francis Group
2013
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| Online Access: | https://eprints.nottingham.ac.uk/2463/ |
| _version_ | 1848790791786332160 |
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| author | Foster, Colin |
| author_facet | Foster, Colin |
| author_sort | Foster, Colin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In a high-stakes assessment culture, it is clearly important that learners of mathematics develop the necessary fluency and confidence to perform well on the specific, narrowly defined techniques that will be tested. However, an overemphasis on the training of piecemeal mathematical skills at the expense of more independent engagement with richer, multifaceted tasks risks devaluing the subject and failing to give learners an authentic and enjoyable experience of being a mathematician. Thus, there is a pressing need for mathematical tasks which embed the practice of essential techniques within a richer, exploratory and investigative context. Such tasks can be justified to school management or to more traditional mathematics teachers as vital practice of important skills; at the same time, they give scope to progressive teachers who wish to work in more exploratory ways. This paper draws on the notion of a musical étude to develop a powerful and versatile approach in which these apparently contradictory aspects of teaching mathematics can be harmoniously combined. I illustrate the tactic in three central areas of the high-school mathematics curriculum: plotting Cartesian coordinates, solving linear equations and performing enlargements. In each case, extensive practice of important procedures takes place alongside more thoughtful and mathematically creative activity. |
| first_indexed | 2025-11-14T18:18:14Z |
| format | Article |
| id | nottingham-2463 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:18:14Z |
| publishDate | 2013 |
| publisher | Taylor and Francis Group |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-24632020-05-04T20:20:13Z https://eprints.nottingham.ac.uk/2463/ Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts Foster, Colin In a high-stakes assessment culture, it is clearly important that learners of mathematics develop the necessary fluency and confidence to perform well on the specific, narrowly defined techniques that will be tested. However, an overemphasis on the training of piecemeal mathematical skills at the expense of more independent engagement with richer, multifaceted tasks risks devaluing the subject and failing to give learners an authentic and enjoyable experience of being a mathematician. Thus, there is a pressing need for mathematical tasks which embed the practice of essential techniques within a richer, exploratory and investigative context. Such tasks can be justified to school management or to more traditional mathematics teachers as vital practice of important skills; at the same time, they give scope to progressive teachers who wish to work in more exploratory ways. This paper draws on the notion of a musical étude to develop a powerful and versatile approach in which these apparently contradictory aspects of teaching mathematics can be harmoniously combined. I illustrate the tactic in three central areas of the high-school mathematics curriculum: plotting Cartesian coordinates, solving linear equations and performing enlargements. In each case, extensive practice of important procedures takes place alongside more thoughtful and mathematically creative activity. Taylor and Francis Group 2013 Article PeerReviewed Foster, Colin (2013) Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts. International Journal of Mathematical Education in Science and Technology, 44 (5). pp. 765-774. ISSN 0020-739X Cartesian coordinates enlargement fluency learning for understanding practice solving equations task design traditional and progressive approaches to the teaching of mathematics http://www.tandfonline.com/doi/pdf/10.1080/0020739X.2013.770089 doi:10.1080/0020739X.2013.770089 doi:10.1080/0020739X.2013.770089 |
| spellingShingle | Cartesian coordinates enlargement fluency learning for understanding practice solving equations task design traditional and progressive approaches to the teaching of mathematics Foster, Colin Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts |
| title | Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts |
| title_full | Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts |
| title_fullStr | Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts |
| title_full_unstemmed | Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts |
| title_short | Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts |
| title_sort | mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts |
| topic | Cartesian coordinates enlargement fluency learning for understanding practice solving equations task design traditional and progressive approaches to the teaching of mathematics |
| url | https://eprints.nottingham.ac.uk/2463/ https://eprints.nottingham.ac.uk/2463/ https://eprints.nottingham.ac.uk/2463/ |