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Developing mathematical fluency: comparing exercises and rich tasks

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journal contribution
posted on 27.04.2018, 08:55 by Colin Foster
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.

History

Citation

Educational Studies in Mathematics, 2018, 97 (2), pp. 121-141

Author affiliation

/Organisation/COLLEGE OF SOCIAL SCIENCES, ARTS AND HUMANITIES/School of Education

Version

VoR (Version of Record)

Published in

Educational Studies in Mathematics

Publisher

Springer Verlag

issn

0013-1954

eissn

1573-0816

Copyright date

2017

Available date

27/04/2018

Publisher version

https://link.springer.com/article/10.1007/s10649-017-9788-x

Language

en