Those of you who teach AP Calculus courses are wondering...what do I do? The AP Exams are over but class time remains. What can be done constructively with students during this available time?
An interesting option has been provided by Doug Shaw, a mathematics professor at the University of Northern Iowa. The materials are called *Find the Error!*.

As Doug describes his site: "I wrote most of the following problems for the *Instructor's Guide* for Stewart's *Calculus, Concepts and Contexts*... They all consist of a "proof", using calculus, that leads to a contradiction, such as 1 = 0, or that sin(x) is always positive. The student's job is to go through the proof, figure out the error, and thus confront common misconceptions about the concepts of calculus....I have used these as extra-credit problems, and my students have quite enjoyed puzzling over them. They also may be used as a final project in an AP class, assigned between the AP test and the end of the semester."

Try them...they can be fun and educational. And, if you ahev some personal time, you might browse therough items on Doug's home-page, as it is filled with some humor amongst other mathematical oddities!