MOOC update #2

Uh oh.  I fell behind.  Well, really, I made a choice.  I took a vacation and even though I had occasional internet access I decided not to think about the MOOC.  This is a positive and negative thing, of course.  It's nice that there are no real deadlines associated with this MOOC (and with many online courses in general) so I can choose to take some time away.  I did take the Chapter 2 quiz before I left town, though, so I wouldn't destroy my grade (I'm joking--each quiz counts only 4%).  However, I know the material, so it was easy for me to do this.  If a student trying to learn this stuff for the first time fell this far behind, it would be difficult to catch up.  I'm back at work this week and I watched the last couple of Chapter 2 lectures yesterday.  I still have all of Chapter 3 to get to; these were released in two chunks on June 21 and June 28.  I suppose I better get cracking.

This experiment is mostly about the MOOC format for me, although I do love the material.  Calculus is still one of my favorite things to teach, and it's interesting to see how a colleague does it.  Chapter 2 was about derivatives and their applications.  Rob chose a more conceptual approach, opting not to focus on the derivative as a slope.  This is good.  Derivatives are much more than that, and I particularly like his emphasis on the fact that the derivative measures the first-order variation of a function.  Via this definition, the Leibniz rule for the derivative of a product falls out for free.  I do have one quibble, though--the discussion of the chain rule was a little hard to follow.  That is, while thinking of the derivative as first-order variation allows one to see that the derivative of a composition is a product of (some) derivatives, it's not really clear what those individual factors are.  With 25 years of calculus under my belt I was able to watch and understand, but I wonder if the typical first-year college student, even at Penn, is able to get this idea clearly.  Then, all of this goes away in the exercises when it is assumed that students will calculate derivatives using what they already learned in high school: $(f\circ g)'(x) = f'(g(x))g'(x).$

But this is nitpicking.  Overall, the presentation is still top-notch, with good examples and interesting applications.  The discussion of L'Hopital's Rule showed clearly why this result works (via Taylor series).  I especially loved the bonus material about the infinite power tower: $f(x) = x^{x^{x^{x^{x^\cdots}}}}.$  This is a tricky function, and it's not possible at this level to really treat it carefully, but using implicit differentiation we can calculate its derivative quickly.  Neat.

I'm not so sure how the UF students who are taking this course with me are doing, though.  I created a poll in our internal e-Learning site to gauge how it's going, asking questions to find out if they are still watching the lectures, doing the homework, etc.  There are more than 30 students signed up for the MOOC; I got 5 responses to my poll.  I think this says a lot, and goes to the heart of the matter for MOOCs generally at this stage--there is little incentive to keep up and complete the course.  Online courses for credit at the university are different since there is a tuition charge involved and the result goes on the student's permanent record.  If universities begin to offer credit for MOOCs, then I suspect this will change.  Rob's course has been recommended by the American Council on Education as one of five worthy of college credit.  Surely more will follow.  I don't know of any universities that have decided to offer such credit, but I suspect some will eventually.  What sort of impact will this have on higher education generally?  I'm not sure.  It could go either way, really.

For now, I'm going to get back to work and find out what Rob's take is on integration.  Personally I find much of this topic to be a bit dry and I de-emphasize the techniques portion.  Really, that is a bag of algebra tricks and I prefer to focus on applications.  More than a week of talking about techniques causes my students' eyes to glaze over, mostly because they think they mastered that in high school already.  Maybe so, maybe not.  That's the real challenge of teaching calculus at a university these days--overcoming the notion that the students think they know it all.  This is where this MOOC shines.

Another update soon.  But first, Independence Day!