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Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts

Foster, Colin

Authors

Colin Foster



Abstract

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.

Journal Article Type Article
Publication Date Jan 1, 2013
Journal International Journal of Mathematical Education in Science and Technology
Print ISSN 0020-739X
Electronic ISSN 0020-739X
Publisher Taylor & Francis
Peer Reviewed Peer Reviewed
Volume 44
Issue 5
APA6 Citation Foster, C. (2013). Mathematical ├ętudes: embedding opportunities for developing procedural fluency within rich mathematical contexts. International Journal of Mathematical Education in Science and Technology, 44(5), doi:10.1080/0020739X.2013.770089
DOI https://doi.org/10.1080/0020739X.2013.770089
Keywords Cartesian coordinates, enlargement, fluency, learning for understanding, practice, solving equations, task design, traditional and progressive approaches to the teaching of mathematics
Publisher URL http://www.tandfonline.com/doi/pdf/10.1080/0020739X.2013.770089
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0





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