A sensible approach to teaching mathematics: In many math courses, such as calculus, the majority are engineering students but the instructors, consciously or unconsciously, present the subject as if they were planning a career in pure mathematics

We teach Mathematics at a Big Ten school with a large and selective engineering college. In the beginning of our careers, we too stated careful definitions and proved theorems, but found that our formal mathematical language which was intended to prevent misunderstanding had precisely the opposite effect. It obscured ideas that students would otherwise find straightforward. For example the formalism