I really tried to hit the ground running with this one: “Introduction to Mathematical Thinking, taught by Dr. Keith Devlin at Stanford. I didn’t just show up for the game; I worked out beforehand at Khan. Before the start of the race, I backed up to get some momentum by watching a series of prior public lectures by the instructor, a total of about nine hours of very cool stuff (shhh, nobody tell the Right that the word “algebra” is derived from Arabic, or they’ll outlaw it) and grubbed up a used copy of the not-required textbook to play around with. And once things started, I hammered in a variety of pitons (that’s a mixture of three metaphors, shall I go for four?), to hold me securely when things got rough.
And yes, I fell off the cliff anyway. But you know, while some cliffs were mistakes in the first place, there are some cliffs that are worth falling off, even worth trying again. This cliff, painful as it was, was very worth it.
True to the course title, the emphasis throughout was on reasoning rather than computation, on understanding and constructing proofs for mathematical statements rather than solving problems. That at least gave me a shot. Still, a certain amount of mathiness was necessary, and my threshold for mathiness is extremely low.
I had no reason to take this course, other than mathematical masochism; it’s intended primarily, though not exclusively, for 17-year-olds about to start a university degree in a STEM field. It’s hard to tell from message boards where anyone can be anything, but I don’t think I met any 17-year-olds in the class; maybe they didn’t need the message boards, maybe they just cranked out the work in a couple of hours and went partying. Maybe they were very mature or just didn’t seem like my idea of 17-year-olds. I met a lot of STEM people, elhi math teachers, and, yes, a few from my natural peer group, middle-aged mathtastrophes trying for a second (or third, or seventh) chance: splendid pitons, all. It’s amazing the affection you can feel for someone with whom your only conversation has been along the lines of, “there is an even number x greater than 2 , which is not a prime, so the contradictive assumption made in the beginning is False so the problem statement is correct, is that right?” Especially when s/he helps you figure it out. Then there were the Community TAs, fellow students who “got” it and helped us all. Most Coursera courses have CTAs, but in this one, they were exceptionally effective.
I felt good the first couple of weeks, when the focus was language. Language? I can do language; I did pretty well, all things considered, though I’d prefer to never hear about melanoma again. Then I faded a bit for a couple of weeks, until week 6, when the Induction Bomb hit and I just dissolved into a puddle of goo. I picked up some of the last two weeks, but I never really recovered. The good news is that I may have gleaned enough background to build back up for next time. Yes, next time: it’s not just ok to take this course more than once, it’s encouraged, even expected. So it’s less like “oh, gee, I flunked out” and more like, “End semester 1, semester 2 starts next Spring.”
In spite of myself, I genuinely came away from this with a lot. I didn’t even realize it, until, near the end of the class, I went through some old lecture questions out of curiosity, as a review; I was amazed at how easy some things were that weeks before had me dripping tears on my keyboard (that’s not a metaphor; seriously, I worried about shorting something out at one point). Seems grasp lags a couple of weeks behind exposure, but while I was perpetually in a state of WTF, I did in fact learn something.
So what did I learn:
I learned enough about implication, conjunction, disjunction, negation, and sets to be willing to go back and try Intro to Mathematical Philosophy when it runs again. I wiped out of that this summer in W1, stomped to death by Achilles’ Tortoise. I understand logic a lot better now. And – wow – I kinda sorta vaguely get converging sequences. Maybe I can get to W2, where, IIRC, Hilbert’s Hotel awaits (and I kinda, sorta vaguely get that, too). Lesson: there’s a benefit to coming at things from different angles.
I learned that a writing technique might just be valuable in math as well. A few years ago, when I still had pretentions about being a “real” fiction writer, I read From Where You Dream, Robert Olen Butler’s writing process book that advised getting new writing (not revision) done first thing in the morning, before you encountered other language at all – just pee, switch on the coffee maker, and write, don’t look at the newspaper or CNN (good advice no matter what, IMHO), and let your new writing be your first linguistic engagement with the world following sleep. Back then I modified that and used it for a couple of scenes I was struggling with: I literally got into bed, covers over my head and cat next to my pillow (oh, Lucy; another raw, fresh ghost of you I find) and hovered between sleep and wake, imagining myself as the point-of-view character. That got a little rough sometimes, especially when the kid got beat up in the boys’ room at school, but I got the gritty dirt on the floor getting into his mouth, the hexagonal tiles, I got the pier scene right, too, the wet hands slipping, the different tones of voice, so it was worth it. I transferred that to math by accident with the last equation of the course – insomnia can be your friend – and kinda sorta ended up understanding what the epsilon and the a and the m and the n all had to do with each other (maybe). I wish I’d thought of using this technique earlier in the course. It requires a certain degree of memorization, but I seem to grasp things better when I can visualize, even “feel” myself pointing at and moving the symbols around in an immersed state, as opposed to staring at my computer screen, crying. Lesson: try this again. Try this for everything. Try things that work, in different areas when you need something that works.
I learned, for the 27,364,582nd time this year, that I am still my own worst enemy. I completely skipped a question because I saw a summation sign, and I panicked. In my defense, I was having a horrible week for a variety of reasons (that was the Friday LDM came to town, an interlude I badly needed). But when I saw the solution, I realized I actually had the skills do interpret and even answer the question, if I’d just put the effort into remembering what I knew about summation signs, maybe with a quick refresher (and what’s the good of having an internet if you’re just going to use it for hilarious South American men’s underwear commercials). Lesson: I need to get out of my own way.
I learned that I’m learning; yes, me, I’m learning more about math. Things most fourteen-year-olds know, maybe; things maybe I knew when I was fourteen (then again…). Ridiculously small things, like what an even number or a rational number really is. Some of what I learned was even more basic, grade school level, and had nothing to do with this course – all those elhi math teachers, talking about something called math talks and number sense, which I realize now I lack completely, but now that I understand what it is I lack, I can do something about it. Lesson: Progress, even very slow and minor progress, is progress.
I learned about a next step. One of the other ancillary benefits of the huge population of MOOCs and the chatter that goes on in the discussion forums is that you find out about other classes; it’s how I originally found out about this one, in fact, back when I was in MOOCulus last Spring. Some of us are signed up for Effective Thinking Through Mathematics starting in January through EdX (I’m really nervous about EdX, I’m in my first class there now and I’m not too comfy with the platform, though I didn’t understand Coursera at first, either, and now it’s like home). I’m getting a running start on it as well; I found a cheap used copy of the not-required textbook (for the first time in my life, I have more math books on my Read Next shelf than fiction). I was looking through it the other night. I came across the “genie” problem – you’ve probably seen variations of it, it’s a pretty standard logic puzzle. Nine stones, one’s a diamond and is heavier than the glass, but you don’t know which, and you can only use a balance scale twice; how do you figure out which is the diamond? I’ve never been good at these things. I tend to skip over them, leave them for the smart people to play with. But because it’s part of this upcoming course, I took a crack at it, and… I knew what to do almost immediately! It was the same thing as some proof we did somewhere in the last eight weeks where you show that a number is either even or odd, and you go from there. It’s a bit embarrassing to be so psyched (I was pacing in circles for fifteen minutes) over something a clever eight-year-old has learned how to do, but it’s better than not knowing, right? Lesson: Come at things from as many angles as possible, until something somewhere coalesces.
I’ve added Keith Devlin to my Pantheon of Mathematical Heroes (it’s a very small pantheon: Jim Fowler, Vi Hart, and now Keith. But I’m working on adding a few more). He’s kind of Mr. MOOC; before I started this course I came across his blog, MOOCtalk (there’s a lot more to this than just filming a few lectures lifted from the classroom – at least there is when you do it right), and he’s in considerable demand as a speaker on the topic. At one point, he posted: “When you are teaching a real class, you put effort into accelerating students who show promise and trying to rescue those that are struggling. Situations like this show up some of the things that are lost when you go to a MOOC…” It wasn’t that lost this time, at least not on me. I was rescued, very specifically. He didn’t even answer my question; he told me to figure it out and gave me a general sense of how, and then sent me to see the “What it Feels Like to be Bad at Math” by the Math with Bad Drawings guy (a great site I now follow). A world-class Stanford mathematician rescued me, the middle-aged mathtastrophe. So now, like Private Ryan, I need to earn this.
So the next time someone tells you there’s no way you can learn anything in a MOOC with 80,000 students, send them to me and I’ll tell them a few things. It does take a Teacher (and some day I’ll post my definition of that word; like Mel Gibson said in Man Without a Face, it’s not about a piece of paper, it’s about a moment of grace. Mel may have fallen off his own cliff, but at least he got that much right). And, of course, a Student has to show up, too. My Student doesn’t always show up for every MOOC I take, but she does when she finds a Teacher. Keith Devlin’s a Teacher. A great deal of care went into designing a MOOC that would approach the effectiveness of an in-person class, and it showed. I’ve said before that not all MOOCs work (“just like real college!”), but when they do – when I’m excited about a math class I really have no business taking – they’re pretty extraordinary
I wish I could’ve been a success story, but if I can get this much out of a course when I do so horribly (score-wise, at least), imagine what I can get out of it when I do well.
So goes another chapter in my lifelong love-hate relationship with math (it’s a source of some amusement that I actually have a “math” tag on this blog). Some day I have to figure out where this comes from, this insistence on banging myself over the head with a hammer for months on end. And make no mistake about it: math, even the conceptual math used here, is psychically painful for me, something that’s a little different from anxiety. Anxiety I take for granted.
I have yet to cry because I can’t understand a Gertrude Stein poem, and lord knows, I haven’t understood any of them (but I’m getting there, thanks, ModPo (the other day I called this course “ModPo for math” since they both found ways to transcend the innate limitations of a MOOC); I don’t feel like a waste of oxygen when I don’t see the point of a Pushcart story, and puzzling over TNY stories is practically a team sport in the blogosphere. But I’ll cry if I can’t figure out how old Ben is if he’s 3 times as old as Omar and 16 years ago he was 7 times as old as Omar (that’s an actual Khan question… when was the last time you asked a question like this? Say “Hey, Ma, 12 years ago I was 4 times older than Bob and now I’m 3 times older, how old are we?” and Ma is likely to slap you upside the head). Maybe because even ten-year-olds figure out how old Ben is, but there are MFAs and PhDs who throw up their hands at Gertrude Stein.
There must be some very deep Freudian stuff going on here, since I have an obsession with this particular mountain range called Math. When I’m not watching insane Rube Goldberg pop music videos (89 devices, 85 takes; if they can do that, I can do this), that is.
Next chapter, in January.