We’ve just started the fourth quarter of school, and I’m starting to see some of my kids slip away from me, getting farther and farther out to sea — little bobbing dots in the distance.

In multivariable calculus, I’ve designed the course to prevent that from happening. I have a serious fourth quarter project for them — totally designed and executed by them. (They have to make a prospectus, they come up with a concrete and reasonable timeline, they troubleshoot problems that arise, and they even come up with the grading rubric.)

But I do something else to change things up, which actually is pretty neat.

We watch videos.

These multivariable kids will soon be off to college and will likely take tough, lecture-based math classes, where you don’t get the individualized attention you get in high school. My kids have never been exposed to college lectures, have never learned to taking solid math lecture notes, and have never learned to work through the difficulties that the lectures might pose.

So in the fourth quarter, I teach about 1/3 of the final unit… and then I hand the class over to Denis Auroux of MIT. Yup, I download a bunch of MIT OpenCourseWare 18.02 lectures and we watch them together in class.

Today, we watched Lecture 19 on vector fields and line integrals in the plane.

After we get to harder lectures, we’ll get in the habit of spending a day watching a lecture, followed by spending a day going over questions, tying the lecture to the book, and doing problems.

I feel like part of me is lying to ’em, though, because Denis Auroux is such a clear expositor with amazing board technique. Not standard, by any means. (But why burst their bubble now?)

If you were teaching an AP Calculus course, I would definitely have my kids watch an 18.01 (single variable calculus) lecture at least a few times after the AP test.

PS. I should really show them something like this — which I got exposed two a few times as an undergrad. Not horrible, but you really have to be focused.