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I hope that you find this book useful and have a good time reading!
Collaborative Learning in Mathematics: A Challenge to Our Beliefs and Practices
By Malcolm Swan
Synopsis
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. About Malcolm Swan
Malcolm Swan is a lecturer in Mathematics Education at University of Nottingham and is a leading designer on the MARS team. His research interests lie in the design of teaching and assessment. He has worked for many years on research and development projects concerning diagnostic teaching (including ways of using misconceptions to promote long term learning), reflection and metacognition and the assessment of problem solving. For five years he was Chief Examiner for one of the largest examination boards in England. He is also interested in teacher development and has produced many courses and resources for the inservice training of teachers.Most assessment practices seem to emphasise the reproduction of imitative, standardised techniques. I want something different for my students. I want them to become mathematicians - not rehearse and reproduce bits of mathematics.I use the five 'mathematical thinking' tasks to stimulate discussion between students. They share solutions, argue in more logical, reasoned ways and begin to see mathematics as a powerful, creative subject to which they can contribute. Its much more fun to try to think and reach solutions collaboratively. Assessment doesn't have to be an isolated, threatening business.Not just answers, but approaches.
Related links
Thinking Through Mathematics was a design-based research project which studied the impact on teachers and learners of the introduction of teachign approaches and resources which emphasised 'connected' and 'challenging' ways of teachign mathematics to post-16 learners.
Read the 50 page booklet by Malcolm Swan which describes the Thinking Through Mathematics approaches. Improving learning in mathematics: challenges and strategies
Improving learning in mathematics: challenges and strategies
