Suppose you are assigned to teach a college-level first-semester calculus class (including a properly-taught AP Calculus class in high school) and you are given the following parameters to follow:

- The course actually needs to be a course in first-semester calculus and not some related field;
- It is to be the equivalent of a 4-credit hour college class (four 50-minute meetings per week for 14 weeks);
- The students in the course need to be prepared to enter a second-semester calculus course that starts with techniques of integration (i.e., you should cover basic integration concepts and u-substitution); and
- The audience is a general audience of students needing calculus — i.e. not just engineers and scientists.

But apart from those parameters, *you may do whatever you want in the course, in whatever way you see fit*.

What would your course do, or look like? Especially, what departures would you make from the “standard” calculus course? Anything really radical you have in mind?

Technorati Tags: Calculus, Curriculum, Math, Student engagement, Teaching

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Off the top of my head, I would put a lot more emphasis on (manual) curve sketching, and include a lot of examples of graphs that have features that can be missed using a calculator (such as the inflection point of y=e^(-1/x), if I recall correctly).