Mathematics education research

Collaborative Learning in Mathematics:
A Challenge to Our Beliefs and Practices

Malcolm Swan; National Institute of Adult Continuing Education (niace), 2006.
ISBN 186201311X.
Price in UK pounds: £24.95

"I think Swan’s work is exemplary and that it should be widely known" - Professor Alan Schoenfeld, University of California at Berkeley

"(it) is in my opinion up there with the best applied educational research in the UK, and the best international mathematical education research" - Professor Margaret Brown, King’s College London

"a major contribution to mathematics education literature ... outstanding example of design research" - Dr Anne Watson, Oxford University

Many people find mathematics an impenetrable subject. It is a subject where it seems possible to spend many years practising skills and notations without having any substantial understanding of the underlying concepts. This book describes one systematic attempt to intervene and transform this situation. It documents the difficulties experienced by teachers and students as they attempt to adopt new approaches to teaching and learning - approaches based on collaborative discussion and reflection.

The book describes an iterative design approach to research and development in which theoretical arguments and reviews of existing research studies are brought together in the design of innovative teaching approaches. These are evaluated in typical classrooms and the outcomes lead to the further refinement of the theories and approaches. Revised approaches are then tested further on a wider scale. The emerging results reveal ways in which teaching methods in mathematics may be designed to become more effective.

Part 1 Eliciting design principles
Chapter 1 Purposes of learning and teaching mathematics
Chapter 2 Theories/metaphors for learning mathematics
Chapter 3 Building conceptual structures
Part 2 Implementing design principles
Chapter 4 Initial study: a two-year study of four FE classrooms
Chapter 5 Teachers’ beliefs and practices
Chapter 6 The design tools for the research
Chapter 7 Main study: the programme and its effects
Chapter 8 Challenging beliefs and practices
Chapter 9 A qualitative comparison of two teachers
Chapter 10 Summary and conclusions