Mathematics As A Constructive Activity Learners Generating Examples
This book explains and demonstrates the teaching strategy of asking learners to construct their own examples of mathematical objects. The authors show that the creation of examples can involve transforming and reorganizing knowledge and that, although this is usually done by authors and teachers, if the responsibility for making examples is transferred to learners, their knowledge structures can be developed and extended. A multitude of examples to illustrate this is provided, spanning...
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Watson (Oxford U.) and Mason (Open U.) examine teaching techniques which actively engage learners, enhancing their sophistication and deepening their understanding, revealing their depths, making them accept initiative in finding and applying deeper concepts, and enriching enjoyment of mathematical structures and connections. They give examples used in classrooms, then "example spaces" specifically for learners to explore, then the tools teachers need to help learners develop those "example spaces" and strategies for prompting learners to generate them. They close with a very useful chapter for those seeking to justify expansion of programs that examines the constructive activities of mathematics, including its ability to teach how to learn, how to build evidence, and construct outcomes. Annotation ©2005 Book News, Inc., Portland, OR
1Introduction to exemplification in mathematics12Learner-generated examples in classrooms103From examples to example spaces334The development of learners' example spaces595Pedagogical tools for developing example spaces926Strategies for prompting and using learner-generated examples1337Mathematics as a constructive activity160App. ASome historical remarks on teaching by examples197
