Please use this identifier to cite or link to this item:
Title: Developing mathematical fluency: comparing exercises and rich tasks
Authors: Foster, Colin
First Published: 26-Sep-2017
Publisher: Springer Verlag
Citation: Educational Studies in Mathematics, 2018, 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.
DOI Link: 10.1007/s10649-017-9788-x
ISSN: 0013-1954
eISSN: 1573-0816
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © the authors, 2017. This is an open-access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Appears in Collections:Published Articles, School of Education

Files in This Item:
File Description SizeFormat 
10.1007%2Fs10649-017-9788-x.pdfPublished (publisher PDF)1.32 MBAdobe PDFView/Open

Items in LRA are protected by copyright, with all rights reserved, unless otherwise indicated.