Course: Calculus 1A: Differentiation

Length: 13 weeks,6-10 hrs/wk

School/platform: MIT/edX

Instructor: David Jerison, Jen French, Stephen Wang

Quote:How does the final velocity on a zip line change when the starting point is raised or lowered by a matter of centimeters? What is the accuracy of a GPS position measurement? How fast should an airplane travel to minimize fuel consumption? The answers to all of these questions involve the derivative.

I’ve taken three different calculus moocs in the past few years, and they’re all terrific in their own way. This was my second time through this one; I didn’t pass last time so I wanted to try again.

What I particularly like about the MIT courses is how they set up each topic with a series of lead-in questions. By the time you get to the actual instruction video, you’ve already seen a lot of what goes into the process, so it’s a natural extension of what they keep calling “intuition”. I’m not sure I’d call it that; I don’t think I have that much intuition about math, certainly not about calculus. There’s probably a sophisticated pedagogical term for this. Whatever it is, it helps. And yes, I managed a solid passing score this time.

It also helps that the two most frequently heard (if rarely seen) instructors, Jen and Steve, have a speaking style I like: calm, just the right speed, and with enough personality to forestall the “audio textbook” aura so many moocs have. I got to know Jen a little on the forums last time, and was very impressed with her patience and willingness to help us through questions. This time, the forums were primarily handled by a different instructor, Hanson, who was equally great to work with. Good people + good material = great class (some math is easy).

Though it’s 12 weeks long, this is only the first part of a series of three moocs designed to prep high schoolers for the AP Calculus exam. Integration starts in November, and Series/Sequences in the Spring.

The course starts with Week 0, a sort of optional orientation/prep week. No grades are recorded. There’s a set of prereq exams to gauge readiness, and a unit on limits for anyone who wants to get back into gear, as well as the opportunity for new users to get used to the platform.

The four content units are released every three weeks, a nice compromise between self-paced and scheduled; a missed week isn’t a catastrophe (and every deadline ended up extended anyway). Lots of questions and practice exercises are scattered in with the videos, and each unit has a final quiz with a part A – “nuts and bolts”, they call it – and part B, more application oriented. The timed final exam had a 48 hour window, which is a lot less stressful than requiring it all be done in one sitting. Each of these elements has a different impact on the ultimate grade.

The material consists of introductory intuition questions, videos by Jen and Steve, and occasional in-class lectures by Dr. Jerison. He’s a lot less warm and fuzzy about it all, but I’ve come to appreciate his style. After he goes through a step, he’ll pause, move to the side, and look around the room at the in-class students. I’m not sure if he’s checking for blank WTF faces, or just to see if most of them are done writing things down (or, for that matter, just catching his breath and finding his place in his notes), but it makes a nice rhythm that helps me to keep up. In terms of filming, I greatly appreciate that he gets out of the way of the board, allowing the live camera holder to adjust angles and zoom to incorporate everything. These are silly little logistical details that have nothing to do with math, but make it so much easier to follow.

I found the course far easier this second time around. I really don’t know if that’s because it was modified, or if something sank in over the past two years. I haven’t been working on calculus at all (though I do some math every day and have taken several math moocs and science moocs involving significant math, including just a whiff of calculus) , so I’m not sure what that would’ve been. One thing I’m pretty sure they added this time are “Recitation videos” explaining individual problems in great detail. These are part of the older OCW series; I found them extremely helpful, particularly those by Christine Breiner. They’re all available on Youtube or through the OCW site.

Though I’m feeling pretty good about doing so well, I realize that by this time I should be able to do this stuff in my sleep. The next course on integration will be a real challenge, since I’ve never been that comfortable with it and it was extremely difficult last time. IIRC, It’s also a lot less hand-holdy, with a lot more reliance on the in-class lectures by Dr. Jerison. But’s what’s next, so I’d best get to it. I did some review before this section, using Khan to refresh my memory on certain points; that’s probably more important for the integration course, so I should get started. I should. I should.