Developing secondary school students’ procedural fluency with cover, copy and compare

The aim of this thesis is to establish the efficacy of Cover, Copy and Compare (CCC) for improving secondary-level mathematical procedures. CCC is a well-established method for enhancing the computational fluency of primary school students (ages 6-11) and students with special educational needs. Despite extensive research on the utility of CCC for primary-level mathematics, there exists no published empirical work that considers CCC as a method for developing mainstream secondary school students’ (ages 11-16) procedural fluency. To address this limitation, I created a CCC mobile application (app) that has secondary school students practise finding the equation of a straight line given the Cartesian coordinates of two points. In this thesis, I describe the complete processes of designing, developing, testing, refining and ultimately evaluating this app.

In a randomised controlled trial, I showed that secondary school students using the CCC app make significantly greater improvements in their procedural fluency with finding the equation of a straight line given two points than students using an app comprising typical classroom exercises. Furthermore, by quantitatively exploring the app’s event logs, I identified an association between class membership and fluency gains made using the app, suggesting that classroom-level factors influence procedural fluency outcomes when implementing CCC in secondary mathematics classrooms. The overall findings of this thesis imply that CCC may be beneficial for developing secondary mathematics students’ procedural fluency and informs our understanding of what effective procedural fluency practise entails.