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Calculus Second Edition

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Calculus Second Edition, 9781429263740 (1429263741), W. H. Freeman, 2012
On Teaching Mathematics

As a young instructor, I enjoyed teaching but I didn’t appreciate how difficult it is to communicate mathematics effectively. Early in my teaching career, I was confronted with a student rebellion when my efforts to explain epsilon-delta proofs were not greeted with the enthusiasm I anticipated. Experiences of this type taught me two basic principles:

1. We should try to teach students as much as possible, but not more.

2. As math teachers, how we say it is as important as what we say.

The formal language of mathematics is intimidating to the uninitiated. By presenting concepts in everyday language, which is more familiar but not less precise, we open the way for students to understand the underlying ideas and integrate them into their way of thinking. Students are then in a better position to appreciate the need for formal definitions and proofs and to grasp their logic.
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