Alternatives to exercises for developing procedural fluency


The event is taking part on the Tuesday, May 21st 2019 at 15.30
Theme/s: Pure Maths
Location of Event: 306 Alan Turing
This event is a: Public Seminar

Achieving fluency in key mathematical procedures is essential to students’ mathematical development. The dominant approach to addressing procedural fluency is through repetitive practice of routine exercises, but is this the only effective way? In this seminar, I will introduce the idea of ‘mathematical etudes’ (Foster, 2013, 2018), which are tasks designed to embed extensive practice of a well-defined mathematical procedure within a rich, problem-solving context. I will report on three quasi-experimental studies carried out across 11 secondary schools, involving altogether over 500 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. 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 evidence in favour of the null hypothesis that etudes and exercises were equally effective, relative to the alternative hypothesis that they were not. These data suggest that the mathematical etudes trialled are comparable to traditional exercises in their effectiveness in developing procedural fluency, which could make etudes a viable alternative to exercises. I will discuss some possible implications of this for students’ learning of mathematics.

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