What do you so with your AP Calculus classes after the AP exam has been given in May? There are usually 2-6 more weeks of instruction. Some of our TAHSM members have shared some ideas.
(Files are listed at the bottom of this page)
Chuck Straley has taught his students some abstract algebra.
Debbie suggests some work with non-Euclidean geometry.
Robert Rogers passed along an article from the New York State Mathematics Teacher Journal, written by Ryan Gantner.
Dan Teague shared what the North Carolina School of Science and Mathematics does during their calculus courses, emphasizing modelling and differential equations.
Cynthia Chin discusses students who prepare theatrical performances about mathematics, listen to guest speakers, and participate in a contest between the AB and BC classes.
Do some more calculus topics that were not required on the AP exam
1. My school has 160-ish school days so after the AP test I continue on with the standard integration topics typically encountered in college as well as those that appear on the BC test. I also do mathematical induction since it is not covered prior to calc at my school.
2. Topics no longer on the AP (surface area of surfaces of revolution, center of mass, work, etc.). Then we can work on error analysis for LH, RH, midpoint, trap, and Simpson's rule,
and perhaps advanced numerical methods. Now that they've just seen Taylor series, how about a quick intro to Fourier series? Or choose something and go in depth, for instance, min/max applied to economics problems.
3. I would suggest checking with the local college or university that the majority of your students will be attending. There are probably topics that they include that are not part of AP- such as, cylindrical shells, techniques of integration, integration applications like work, center of mass, fluid force, probability, etc; non-separable differential equations. I think that our job is to prepare our students to have the best chance of success at the next level, so making sure that all similar topics are covered is more important than branching out to multi-variable calculus or linear algebra.
4. My AB teacher and I (I teach BC) have done a number of different activities. One of them is having the students work in pairs to present a lesson or series of lessons (eg conic sections) to our Honors Algebra 2 kids or a lesson on limits/continuity to our Honors Precalc kids who begin calc study in 4th quarter. The students who do this have given us feedback that they not only enjoy it but also learn from it! The logistics are sometimes a problem though, in that the Calc kids must have a free period which coincides with one of these classes.
5. After the AP exam, I do one of two things. Some years, the class is assigned some of the Labs/Investigations from the Calculus for a New Century series from the MAA. These are completed in groups and somewhat independent of instruction from me. Other years, I basically continue teaching with some non-AP topics, such as linear non-separable differential equations, hyperbolic functions, surface areas of solids of revolution, and moments of inertia. I have had success and failure with both of these approaches in the past, but know I choose which to do based on the character of the class. Therefore I experienced more success than failure in recent years.