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ERIC Number: EJ1167544
Record Type: Journal
Publication Date: 2018-Feb
Pages: 21
Abstractor: As Provided
Reference Count: 40
ISBN: N/A
ISSN: ISSN-0013-1954
Developing Mathematical Fluency: Comparing Exercises and Rich Tasks
Foster, Colin
Educational Studies in Mathematics, v97 n2 p121-141 Feb 2018
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.
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Publication Type: Journal Articles; Reports - Research
Education Level: Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: United Kingdom (England)