Reflections, Lesson Plans, and other Artifacts
The student needs to develop an understanding, however partial and imperfect, by descriptions rather than definitions, by typical examples rather than grandiose theorems ...
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... An axiomatic presentation of a mathematical fact differs from the fact that is being presented as medicine differs from food. It is true that this particular medicine is necessary to keep mathematicians from self-delusions of the mind. Nonetheless, understanding mathematics means being able to forget the medicine and enjoy the food.
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-- Gian-Carlo Rota