# mixedmath

Explorations in math and programming
David Lowry-Duda

I like the idea of massive online collaboration in math. For example, I am a big supporter of the ideas of the polymath projects. I contribute to wikis and to Sage (which I highly recommend to everyone as an alternative to the M's: Maple, Mathematica, MatLab, Magma). Now, there are MOOCs (Massice open online courses) in many subjects, but in particular there are a growing number of math MOOCs (a more or less complete list of MOOCs can be found here). The idea of a MOOC is to give people all over the world the opportunity to a good, diverse, and free education.

I've looked at a few MOOCs in the past. I've taken a few Coursera and Udacity courses, and I have mixed reviews. Actually, I've been very impressed with the Udacity courses I've taken. They have a good polish. But there are only a couple dozen - it takes time to get quality. There are hundreds of Coursera courses, though there is some overlap. But I've been pretty unimpressed with most of them.

But there are two calculus courses being offered this semester (right now) through Coursera. I've been a teaching assistant for calculus many times, and there are things that I like and others that I don't like about my past experiences. Perhaps the different perspective from a MOOC will lead to a better form of calculus instruction?

There will be no teaching assistant led recitation sections, as the 'standard university model' might suggest. Will there be textbooks? In both, there are textbooks, or at least lecture notes (I'm not certain of their format yet). And there will be lectures. But due to the sheer size of the class, it's much more challenging for the instructors to answer individual students' questions. There is a discussion forum which essentially means that students get to help each other (I suppose that people like me, who know calculus, can also help people through the discussion forums too). So in a few ways, this turns what I have come to think of as the traditional model of calculus instruction on its head.

And this might be a good thing! (Or it might not!) Intro calculus instruction has not really changed much in decades, since before the advent of computers and handheld calculators. It would make sense that new tools might mean that teaching methods should change. But I don't know yet.

So I'll be looking at the two courses this semester. The first is being offered by Dr. Jim Fowler and is associated with Ohio State University. It's an introductory-calculus course. The second is being offered by Dr. Robert Ghrist and is associated with the University of Pennsylvania. It's sort of a funny class - it's designed for people who already know some calculus. In particular, students should know what derivatives and integrals are. There is a diagnostic test that involves taking a limit, computing some derivatives, and computing an integral (and some precalculus problems as well). Dr. Ghrist says that his course assumes that students have taken a high school AP Calculus AB course or the equivalent. So it's not quite fair to compare the two classes, as they're not on equal footing.

But I can certainly see what I think of the MOOC model for Calculus instruction.

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