Foreshadowing the MVT

The Mean Value Theorem (MVT) is proved by writing the equation of a function giving the (directed) length of a segment from the given function to the line between the endpoints as you can see here. Since the function and the line intersect at the endpoints of the interval this function satisfies the hypotheses of Rolle’s…

Starting the Year

As you get ready to start school, here are some thoughts on the first week in AP Calculus. I looked back recently at some of the “first week of school” advice I offered in the past. Here’s a quick (actually, a bit longer then I planned) summary with some new ideas. The last time I…

On Scaling

Why “scaling” is necessary No teacher can make two tests on the same topics equal in difficulty. No two teachers, even if they collaborate, can make two tests on the same topic equal in difficulty. No two teachers in different schools, districts, or states can make two tests on the same subject equal in difficulty.…

On Grading

I got to thinking about grading the other day after seeing a question on Facebook. We’ll get to that question in a minute, but first I want to try to outline a grading scheme I used towards the end of my teaching career. It is based on how free-response question on AP Calculus exams are…

Pacing for AP Calculus

Some thoughts on pacing and planning your year’s work for AP Calculus AB or BC.  The ideas are my own and are only suggestions for you to consider. Almost all textbooks provide an AP pacing guide among their ancillary material. You can consult the guide for your book for specific suggestions for the number of days…