If I ever try to take four concurrent math classes again, I need to remember: hitting myself over the head with a hammer every hour for 12 weeks would be less painful. This is why I put the Pushcart read on hiatus?!? (I’ll be getting back to it soon, I promise) The degree of suffering math engenders in me is well-documented in these pages, but I can’t seem to leave it alone now that free online classes are available.
These four – two of which I’ve taken before, and two of which have a couple of weeks yet to go – are all (for me) good-to-great MOOCs, but all in their own unique ways; they have different goals and atmospheres, so likely will appeal to different students for different reasons.
Calculus (Calc1, Calc2 from Ohio State via Coursera):
I took this course a year ago; it was my first MOOC, in fact, and I praised it at length at the time. I decided to repeat it to pick up some additional details. That’s the great thing about MOOCs: if you don’t quite get everything the first time around, you can take them more than once, without fighting with a Registrar and the Bursar’s Office, and without stigma; lots of people take classes more than once, and some are even designed that way.
And guess what: it only got better! While Jim Fowler’s terrific videos (they’re available to anyone via YouTube, by the way; they not only include detailed theory and examples, they’re also cute as he explains things in a variety of ways using everything from high-tech gizmos to paper cutouts) were the backbone of the course, Jenny George was now the lead instructor; her patience and talent for clear, step-by-step explanation is extraordinary, and she bravely made herself very accessible via email for questions that couldn’t be answered on the forums – not to mention, I was thrilled to (finally!) see a woman teaching math on Coursera! The division of labor worked out well, since it offers different approaches that will likely provide something for everyone. There’s one more week to go (I had a bit of a hissy fit over integration by parts the other day, in fact), but at this point I’m pretty sure I’ll get through it, and I’ve definitely strengthened my grasp of calculus – at least, as much as I can strengthen my grip of anything mathematical. One of the benefits of taking a course a second time is that what seemed so difficult before, now seems a lot easier (integration by parts notwithstanding).
I was so encouraged by the first few weeks, in fact, I decided to take a look at Jim’s Calculus 2 class – “Sequences and Series” – which was intentionally timed to coincide with Calc1. I didn’t expect to get through it all, but I figured I could get some idea of what was going on so it would look familiar when I took it “for real” later. Turns out, things went better than I’d hoped, though I left some things for my second pass. The “homework” was particularly well designed, similar to Calc1’s MOOCulus exercises but, in my opinion, even better, in that links to pertinent resources appear alongside the question. I ended up doing the full spread of six to nine homework problems per chapter nearly daily once I caught on (the questions change each time the test is reloaded), which reduced the “hey, I don’t remember this, we had this six weeks ago” confusion that usually sets in when confronted by a final exam. And, to my surprise – I like Taylor series! Who knew? Jim has a third class (multivariable calc, sounds scary) on the rotation, and I’m hoping to be up for it next time it rolls around.
Effective Thinking Through Mathematics (Utexas/Austin via edX):
I’ve admitted developing something of an attitude towards edX, but this was my favorite edX course so far. What’s interesting is that it may have been the least planned; go figure. If nothing else, it confirmed once again that putting together a MOOC, even if you’ve got a great concept and the best of intentions, isn’t easy, and it isn’t just a matter of taping what happens in the classroom.
True to the name of the course, this wasn’t, strictly speaking, a math course; the idea was to demonstrate a series of effective thinking techniques through working on mathematical problems. Some of those techniques – like “make mistakes” and “ask questions” – were familiar, and others – “understand simple things deeply” – were new. I found it a relatively easy course, partly because there was only a minimum of testing and evaluation, but mostly because I found a used copy of the non-required textbook the course is based on, and worked through it last Fall so I’d be prepared.
The topics were terrific: infinity, the fourth dimension, number theory, topology, fourth-dimensional geometry, etc. The instructional concept seemed like a great idea: instead of lectures, professor Michael Starbird sat with one or two students – not heavy-duty math students, either; these were relative neophytes – and ran through a series of concepts with them, using a more-or-less Socratic approach. He’d present a puzzle, or a question, and let the students fumble with and streamline ideas until a solution was reached.
It may be the best way to present material when you’ve got a one-to-two teacher/student ratio, or in a physical classroom, but I’m not sure it quite translated to MOOCland. The problem, for me, was: this can get a little frustrating when you’ve got different questions, ideas, and solutions than the participants. I was bored when they were struggling with something I understood, and never found out the flaws in some of my own ideas. A strong self-motivation is part and parcel of the MOOC process, but here, it was nearly impossible NOT to sit back and let the students in the videos do all the work, since after the first few minutes, our paths of reasoning typically diverged in some important aspect. Still, I’m intrigued by the concept, and I wonder if there isn’t a way to make it work better – perhaps via a “choose-your-own-adventure” based approach (which might be overly complicated for a MOOC), or by requiring more participation at the initial stages of a problem before the “answers” are released (which would require a better communication system than what they laughingly refer to as discussion boards). But I have to remember, again, that this isn’t primarily a math course; the idea was to show the five elements of effective thinking in action.
The logistical organization seemed to disintegrate a bit in later weeks (we’re in the last week now), with weekly lessons released later and later; I got the impression they were taped week to week, which seems pretty risky to me. In one case, an introduction segment wasn’t released at all so things started in the middle, leaving me (and some others in the class) perplexed – how did the featured participants know those particular features were salient? Am I really so stupid that it’s obvious and I don’t see it when they do? Turns out, the initial part of the discussion hadn’t been included in the material released. This was fixed within a couple of days (days?!?), but for me, already highly insecure about math, it created unwelcome tension. But it’s one of my primary tenets of MOOCs: technical sh*t happens; deal with it and move on.
I still think Prof. Starbird has a great idea here, but there might be a better way to translate it to work better within the inherent limitations and advantages of the MOOC format. Still, I’d recommend it to anyone who wants a gentle, low-pressure introduction to a variety of heavy-duty mathematical concepts. If a new crop of topics were introduced, I’d take it again myself.
Introduction to Mathematical Thinking (Stanford via Coursera):
“I have lost my faith, Josephus.” That’s the opening line in a favorite quasi-literary-historical mystery of mine (no, not that one), and it’s the refrain that started running through my head around the dreaded Week 6 of Stanford’s Intro to Mathematical Thinking (my second time through) when I again failed to grasp induction. The premises of the class – of the general philosophy of mathematical pedagogy Prof. Keith Devlin advocates – are that 1) we are all capable of learning basic math; there is no such thing as a “math person” and 2) we learn more from our failures than our successes, so struggle is to be cultivated; if the class is easy, you need a harder class. Compelling ideas, especially to someone (like me) who equates math with failure. But: though I’m the Fox Mulder of the math world – I want to believe – this is Kool-Aid I just can’t drink. I have yet to find a limit to my capacity for learning-less failure, and at some point, you need to be able to come up with a correct answer. It may be it’s simply too late for me, for a variety of reasons. I still haven’t had the fortitude to look at my scores; the only score I need to know is the one I gave my own final as part of the self-grading requirement: 14 out of 40. Not as bad as last time, when I couldn’t even attempt about half the questions, but a pretty poor showing still.
That said –while I do pretty horribly in this class, it’s been extremely helpful with other classes. Both Calculus sessions were far more understandable because of it, both from the general caveat to take the time I need to figure something out, to the advantage of having seen some things (like the definition of limits, and summation signs) often enough that I could pay attention to what was actually happening when those things were used. It’s the most instructive class I’ve ever sucked at.
Perhaps the greatest benefits of the first run of this class (which I talked about at length last year, calling it “ModPo for Math”) was that, between repeats, I tried to get better prepared for this second pass through a variety of avenues. Any course that can get me to do a couple of hours of math a day, when I’m not even enrolled in a math class, is a big deal, whether I do well in it or not. And just doing that much work every day has to have some effect. But I doubt I’ll take it again in the Fall; it just takes too much out of me.
By the way, I lied about that line from the novel. It’s actually in the past perfect tense: “I had lost my faith, Josephus.” The novel is the story of reclamation of faith, in various things, through various means, by each of the three characters. This explains – it must explain – why, even having lost my faith, I’ve signed up for How to Learn Math: For Students – a course based on the premise: “Everyone can learn math well. There is no such thing as a ‘math person’….evidence shows the value of students working on challenging work and even making mistakes….” Sound familiar? No wonder – Dr. Jo Boaler, the instructor, is a Stanford colleague of Dr. Devlin.
Turns out it’s not all that easy to lose one’s faith. I guess I’ll have to keep trying.
To be continued…