Seminar by Dr Colin Foster (University of Nottingham) Developing mathematical fluency: exercises or rich tasks?

In this seminar, I will introduce the idea of mathematical etudes (Foster, 2013), which are tasks designed so as to embed extensive practice of a well-defined mathematical procedure within a rich problem-solving context. I will report on three recent 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 “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 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.

Foster, C. (2013). Mathematical études: Embedding opportunities for developing procedural fluency within rich mathematical contexts. International Journal of Mathematical Education in Science and Technology, 44(5), 765–774.

Biographical note:
Dr Colin Foster is an Assistant Professor at the Centre for Research in Mathematics Education in the School of Education at the University of Nottingham. His research interests are in the design of rich mathematical tasks and ways in which teachers can use and adapt them in the classroom to support conceptual understanding of mathematics.

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