"This book reports an outstanding piece of research. In my opinion it is up there with the best international mathematical education research. It unusually combines the highest standards of rigour with great significance for the teaching of mathematics at all ages and levels' (Professor Margaret Brown, Kings College London). 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. The book includes a CD-ROM which contains videos of classroom-based good practice and teaching resources for tutors.
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Malcolm Swan is co-director of the Shell Centre / MARS team at Nottingham University, and a lecturer in mathematics education. His research interests lie in the design of teaching and assessment for mathematics education. This includes the design of situations which foster reflection, discussion and metacognitive activity; the design of situations in which learners can construct mathematical concepts; and the design of assessment tools that enable us to evaluate learning.
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