Close to home

Why is it that, of all of the Occupy activities that have gone on for the past two months, the pepper-spraying of peaceful UC Davis students strikes me so much more strongly than any other?

The extremity of the incident is hard to ignore: riot-geared police officers, decked in body armor and military weaponry, approach and attack unarmed and peaceful demonstrators seated in a position of pure passivity. Whether or not you agree with the reasons for the protest (I do, but I'm certain some of my readers do not), the level of force used against the sitting students is clearly out of proportion by several orders of magnitude.

The diffidence of the university administrators (in particular, UC Davis Chancellor Linda Katehi) is as striking. Afterward she is coolly dismissive of the protestors, adopting a detached and thoroughly establishmentarian "well, that's what happens when you don't do as you're told" stance in the wake of the attack.

The immediacy (and ubiquity) of the images plays a part, too: they're arresting and unavoidable...and every video of the attack clearly shows a dozen or more others actively filming the incident, a self-replicating postmodernist pastiche of views, every one showcasing unmitigated brutality.

All of these aspects of the attack factor into its effect on me, but I think what's most striking to me is how similar the students attacked are to my own. How easily those Davis kids could be the ones who come to my classes, who hang out with me in the Math Lab, who joke with me in the hall and who ride with me to conferences! How easily my kids could have been the ones writhing in agony as they gasp for breath and when they finally find it spend several hours coughing up blood! They're interchangeable. I find myself putting my students' faces over those of the kids in the video clips, and I shudder.

I wonder: how differently would my own institution have responded to actions like those of the peaceful students at UC Davis?

History lesson

Some might say this is not a "teaching" post.

They would be wrong.

I was chagrined several weeks ago when I learned how ahistorically many of my students live their lives: one of my brightest students showed her historical ignorance by not knowing, within ten years or so, when the second world war was fought.

So it is that I worry that my students might not know what's going on around them now.

I join the chorus of academic voices expressing not disappointment, not chagrin, not tut-tutting and head-shaking sadness, but rather disgust and horror at the events taking place recently at campuses in the University of California system.

All that I might say has been said more fully and more eloquently than I can here (here, for instance, and here), so I'll say little more then to say that Chancellors Linda Katehi and Robert Birgeneau must resign...as should any other academic "leader" who condones or supports the actions (or inactions) they've taken.

I cannot say more that's not been said already. I want only for my students not to miss this moment.

To them I say: this is what history looks like.

State of mind

A few months ago Zima, one of my grad school colleagues who now teaches at Kennesaw State University in Kennesaw, Georgia asked me to present at an undergraduate research conference for which she'd just received MAA funding. (Said conference is this coming weekend; it's the one Ino and Ned are presenting their findings at.) I'll be giving a run-of-the-mill plenary talk on some of the graph theory I did with a couple of REU students this past summer, and I'll be presenting in a workshop on inquiry-based learning (IBL) at the outset of the conference.

I offered Zima a title that's so generic I really could talk about anything: "Guided discovery in the mathematics classroom." I feel confined by this generality. Indeed, when I actually sat down a week or so ago to try to figure out what in the hell I needed to say about IBL, PBL (problem-based learning), Moore method, etc., I had a hard time coming up with much to say other than expressing my feeling that all too often these techniques are too "formalized." That is, I get the sense sometimes that the people who apply these techniques look on them as an all-or-nothing process: "if it ain't straight-up Moore method, it ain't anything at all" or "I use guided discovery every single day to address every one of my students' learning outcomes." So I put together a half-hour laundry list of things to say along these lines: be open to using guided discovery in moderation; it's not the be-all-end-all any more than any other pedagogical paradigm may be.

Then just now, while lying in bed unable to sleep (though admittedly probably needing to), I realized that I can say more, for I realized of a sudden why I've had such a hard time trying to come up with something practical (and original...I suspect that the folks I'll be addressing in this workshop are going to make up a choir to whom I won't really need to preach) to say about guided discovery: in my mind, guided discovery is not so much a pedagogical process as it is a state of mind.

I find more and more that in teaching it's not so much what I do with my students as how I do it that matters most. Put another, perhaps more practical way, effective teaching comprises a gestalt-like complex of actions and not a single action individually. Guided discovery is what might be called an emergent operation which cannot be broken down into its constituent parts without losing much of its energy and effectiveness. So it is that I don't necessarily engage my students in singular activities, each of which forces students to lead themselves to original, new-to-them, conclusions, so much as I try to treat them in every way, in everything I do, as co-learners, co-discoverers, seekers of authentic knowledge.

Practically, this realization makes it possible to grow opportunities for genuine discovery in the most infertile academic soil, for every simple textbook problem becomes, if viewed from the right angle (like anamorphic art) a chance for authentic "research-like" engagement. Guided discovery is an "angle" from which these problems may be viewed.

I'll try to say a bit about this on Friday when I'm leading my portion of the IBL workshop. Are these views original? Meh...perhaps not. But they're more original, and, more important, more meaningful, than whatever else I will have to say. We'll see how they're received.

More big picture stuff

In regards to another recent post, it looks like we're about to beat up on the student body again. I say once more: what in the hell are we doing?

I don't usually get political here (because my pedagogy, writ small, doesn't generally intersect directly with politics outside of my own institution), but I can't help it now: if you support any leader opposed to fair taxation and rational government spending and stimulus, you support the eventual decay of our educational system. Don't re-elect these fools who are destroying our future.

Impending sense of something

Well, all my classes are prepped for a couple of days' absence from the scene. My Abstract students are hard at work on their latest problem set, and the Precalckers are plugging away at their second take-home exam.

All is calm.

Ever get that feeling that something big is about to break?

I've got that feeling right now. I can't put my finger on it. Maybe it's just that the next week and a half is frightfully busy: something's bound to happen.

We'll be ready, my friends. We'll be ready.

Big, big picture

For several years now, I've been a "big picture" kind of guy: I paint in broad strokes. I see forests and not trees. I'm more satisfied with hand-waving proofs than most of my colleagues would be. I'm more concerned that I and my students get the overall idea, the intuition, the gut-level understanding, than that we get every last detail right.

I'm not sure when I took this viewpoint on, but I think it's a relatively recent phenomenon. After all, I'm not sure you can make it through a graduate program in mathematics without punctilious attention paid to the merest minutiae of theorems and their proofs. It's come on more recently, as I've grown as a teacher and scholar, and as I've come to grips with bigger and bigger problems. It's gotten "worse" lately. I mentioned only half-jokingly to the Associate Provost for Academic Administration, with whom I've been doing a lot of work this semester for CRTF, that I'm starting to think like an administrator. For good or for ill I no longer consider curricular issues as they'll affect a single instructor or even a single department, but rather as they'll affect the school as a whole.

Perhaps the widest view one can take I took for a moment today, and it scared me: if you look at our nation's higher educational system as a whole, there are terrifying trends.

One incident: this morning I got an email from a student who's having to take a break from it all to maintain sanity. Literally. This person is going off the map for a little while and heading home to be with friends and family and to deal with mental health issues.

A second: yesterday I spent a tearful half hour with another student who's clearly dealing with stressors beyond finishing up an essay for Humanities or prepping for this week's coming Abstract Algebra exam. This is a very good student, one I know well, one whose performance this semester has declined noticeably from past semesters. There's much more going on behind the scenes.

A third: last week one student spoke of a narrow escape from dropping out and returning to military service just to make ends meet. Fortunately the financial aid office and the counseling center were able to help make an end-run around a vindictive ex-spouse whose uncooperativeness was preventing disbursement of much-needed funds.

These aren't just isolated events. Dozens of my students, in addition to managing a full load of difficult classes (often in excess of 18 hours dominated by high-level mathematics coursework) also work 20, 30, even 40 hours a week, and deal with manifold family issues (I can think of several students whose entire families depend on them for nearly everything), and still manage to keep it together...or not, as the case may be. The cracks are showing: I've had more people cry in my office than in any other semester I can remember. It ain't getting better.

These students shouldn't have to deal with all they're dealing with today. They should be free to be students, to be free from having to support themselves with back-breaking (or at least time-sucking) labor.

It hasn't always been like this. I speak from experience.

I had it far easier than these folks, barely more than a decade ago. I had student loans and a scholarship, and my family'd done well in socking some away to help me go to school, so the only work I needed to find to get me through my college years was as a work-study assistant in the Math and C&S Department's computer lab. Big. Deal. This was a sinecure. I "worked" 10, maybe 20, hours a week, passing out boot-up disks (yes, we still used those back then), trouble-shooting simple software problems (usually involving nothing harder than MS Excel), and shooting the shit with my geeky friends. Most of the time I got paid to do my homework. The rest of my time (that not devoted to hanging out, eating pizza, running, and annoying the crap out of my dorm mates by playing Pink Floyd's "One of These Days" really frickin' loudly on my monster tower speakers) was spent on schoolwork. I managed to make straight As (aside from a couple of stray minuses) and learn a lot. I was a slacker my first year of college, because I could afford to be: I quickly learned that I didn't need to put too much effort in in order to do well, so I took it easy. My second year I started taking courses that offered legitimate challenge, so I buckled down. That's also when I first realized that I could teach myself as much as anyone else could teach me, so I started studying on my own, everything from additional math and physics and computer science to philosophy, literature, languages, and history. On my free time. (Holy crap...free time! What's that, again?)

I could reminisce forever, but let me get to my point: I'd love to launch into a cliché and crotchety "kids these days" diatribe, but I can't. I had it easier than these kids. Far easier. I didn't have to work my ass off just to stay warm and well-fed, let alone well-educated, and I had time enough (and more) to do well in and learn from all of my classes.

Many of my students have no such luxury. They have to work, and often work hard, just to afford the modest cost of the education my public school provides to them. (It may be worth noting that I went to a pricey private school for college.) If they don't work (and often even if they do) they have to go into debt up to their eyeballs to pay the bills, for they cannot always rely on family to help them out (many of these students are first-generation college students and come from families who can ill-afford to give financial aid). Moreover, they face dim job prospects on graduation, with the economy lagging the way it is. There are no sure signs of long-term improvement. Thus many of my students are going to saddled with crushing student-loan debt and little opportunity to find the work they'll need to get to help pay it back.

Do you think a student with 18 hours a week of coursework and a 40-hour-a-week job who's drawing several hundred dollars per term in student loans and trying her best to hold her family together really has time to learn (or care) what a derivative is? Do you think such a student is going to be completing her homework in full, passing her exams, and finishing her oral presentation on subgroups of groups of symmetry? Even if she's meeting these superficial measures of academic achievement, do you really think she's going to be getting much meaningful out of it?

It's become cliché to put someone in "The 99%," but my students, almost every last one of them, belong there. Bless 'em all, they belong there.

And my students amaze me. Even with 18 hours of coursework and 40 hours on midnight shifts at motel desks and family foibles and student loans and squabbles with landlords over week-late rent checks, they do still learn what a derivative is. And they do still care. They don't just finish their homework, they polish it to perfection. They don't just pass their exams, they ace them. They do incredible work, and they do it without complaint. Somehow, despite having to do everything else we demand that they do, they're learning, and they're helping each other to learn. They're there for each other, even when the system's left them behind.

But this can't go on forever. A college education can't be what it used to be if we don't give these people a bit more breathing room. What in the hell are we doing to them?

The system needs to change. Otherwise, in ten or twenty years we'll look back and notice that though we've stocked our universities with the brightest scholars and the best teachers, and though we've built the shiniest classroom buildings and equipped them with the sleekest high-tech gadgetry, we've miseducated an entire generation simply because we asked too much of them while they were trying to do what we want them to be doing before they do anything else. We just wanted them to learn.

Well...I'll keep doing all that I can, and I'm sure I can count on my students and colleagues (some of the most admirable people on Earth) to do the same. It's a mountain we've got to move, and the only way we're going to move it is if we all get behind it together.