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Teaching and learning mathematics by abstraction. (English)
Tall, David et al., Intelligence, learning and understanding in mathematics. Post Pressed, Flaxton, Qld. (ISBN 1-876682-32-9). 235-255 (2002).
From the conclusion: The notions of abstract-apart and abstract-general ideas, derived from Skemp’s abstraction theory, have considerable potential for clarifying the interpretation and planning of research and practice in mathematics teaching and learning. There is a great deal of misunderstanding about the nature of abstraction in mathematics. Mathematical ideas are not abstract because they are not concrete; they are abstract because they are general. Also, mathematical ideas are not difficult because they are abstract; they are difficult because they are often taught as abstract apart when their understanding requires abstract-general thinking. We have identified aspects of traditional mathematics teaching which contribute to the development of abstract-apart concepts, and proposed teaching strategies (“teaching for abstraction”) which would be more likely to lead to abstract-general-concepts.
Classification: C30
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