Saturday, February 21, 2009

How I'd Rewrite the Syllabus for the Calculus Circus

Everyone knows that it's not real calculus. This is the class that you get credit for if you scored a 3 on AB calculus.

First off, I'd take out every calculation dealing with limits. I'd talk about continuity in pretty vague terms -- warning students that stupid things can happen if the function is undefined at a point (division by zero) or if the pieces of a piecewise-defined function don't line up.

None of that definition of the derivative, either. We'd talk about the derivative as a slope, sure, but we wouldn't delve into the nitty gritty of it. Certainly no calculations that require tedious algebra. From there, once we hit max/min, we would skip everything about local max / local min and only deal with global max / global min.

And then in the integration chapter, we'd leave out the part where they actually calculate Riemann sums.

Now that is a calculus course that I could successfully teach in one semester to the students who I have.