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Title: Developing mathematical fluency: comparing exercises and rich tasks
Authors: Foster, Colin
Keywords: Bayesian hypothesis testing
Enlargements
Linear equations
Fluency
Practice
Mastery
Mathematics education
Procedures
Rich tasks
Issue Date: 2017
Publisher: Springer © The Author
Citation: FOSTER, C., 2017. Developing mathematical fluency: comparing exercises and rich tasks. Educational Studies in Mathematics, 97 (2), pp.121-141.
Abstract: Achieving fluency in important mathematical procedures is fundamental to students’ mathematical development. The usual way to develop procedural fluency is to practise repetitive exercises, but is this the only effective way? This paper reports three quasi-experimental studies carried out in a total of 11 secondary schools involving altogether 528 students aged 12–15. In each study, parallel classes were taught the same mathematical procedure before one class undertook traditional exercises while the other worked on a “mathematical etude” (Foster International Journal of Mathematical Education in Science and Technology, 44(5), 765–774, 2013b), designed to be a richer task involving extensive opportunities for practice of the relevant procedure. Bayesian t tests on the gain scores between pre- and post-tests in each study provided evidence of no difference between the two conditions. A Bayesian meta-analysis of the three studies gave a combined Bayes factor of 5.83, constituting “substantial” evidence (Jeffreys, 1961) in favour of the null hypothesis that etudes and exercises were equally effective, relative to the alternative hypothesis that they were not. These data support the conclusion that the mathematical etudes trialled are comparable to traditional exercises in their effects on procedural fluency. This could make etudes a viable alternative to exercises, since they offer the possibility of richer, more creative problem-solving activity, with comparable effectiveness in developing procedural fluency.
Description: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Version: Published
DOI: 10.1007/s10649-017-9788-x
URI: https://dspace.lboro.ac.uk/2134/36824
Publisher Link: https://doi.org/10.1007/s10649-017-9788-x
ISSN: 0013-1954
Appears in Collections:Published Articles (Mathematics Education Centre)

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