How can research be used to inform and improve mathematics teaching practice?

Abstract

Every year there is a substantial investment in educational research and a wealth of high quality and informative material is produced. The articles in this volume are no exception. Megan Staples reports on an intriguing study––Promoting student collaboration in a detracked, heterogeneous secondary mathematics classroom. She explains how students worked together productively when their teacher used a range of strategies to encourage students to focus on their own and their colleagues’ acquisition of mathematical understanding. For example, she would set a group a problem and, when they indicated they were ready to report back, the teacher would ask one of the children to explain how the group had solved the problem. The group received points depending on the individual’s response both to the problem and the teacher’s follow-up questions. Not surprisingly, members of each group worked hard to ensure that all their team mates had a good understanding of the mathematics involved as they could never be sure who would be picked to represent the group. Mathematical problems also feature in the work of Sandra Crespo and Nathalie Sinclair. In their article––What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems––they point out that, although problems are a central feature of the mathematics curriculum in schools, many teachers are ill-equipped to select, let alone write, the most appropriate problems for their students. Working with prospective elementary teachers, Sandra and Nathalie describe the difficulties and tensions faced when devising problems that were suitably challenging mathematically and yet, at the same time, pedagogically appropriate. Encouraging prospective and practising teachers to reflect on the quality of their work is an important and arduous undertaking as discussed by Shari Stockero. In her article, however, she explains how using a video-based curriculum as part of a university