MOOCs are all the rage

 MOOCs (Massive Open Online Courses) are all the rage. Tom Friedman (NYT, Jan 27), the perennially uncritical purveyor of modernity, loves it.  Coursera loves the free publicity. And we old-school professors are supposed to be worried about something that has the potential to take our lunch. Should we be worried?

One thing MOOCs are likely to do is sort out the difference between "certification" and "learning". There is a misconception that learning consists of the transmission and absorption of facts, but like certification this particular function of universities is sort of trivial, and can easily be taken over by an online conglomerate. How are MOOCs different from giving somebody a reading list, testing them on what they've read and handing them a piece of paper as a result? What can anyone do with that? Also, MOOCs perpetuate (and profit from) the myths of the "star professor" and the "prestigious university" as critical factors in learning. They're not; the critical factor is the mind doing the learning. Learning is primarily participatory.

Teaching (beyond mere certification for an entry-level job) includes instilling in someone the ability and desire to form original connections, to go further, to question foundations. This is partly innate, but can be fostered by socialization, by hanging out (physically) with others in the same frame of mind. It requires long-term immersion in a subject, to the point of developing a sort of love for it, and a social environment (including exchanging ideas beyond the confines of the subject itself.) I guess MOOCs are OK for mass learning (and to broaden access to current developments), but they're a long way from being able to recreate, say, the atmosphere of a mathematics research institute.

The full sweep of a career

I hadn't been to one of the giant national meetings since back when I was a postdoc and on the job market, many years ago. Which is one of two reasons why people go to these things, the other being  you have some sort of `chair' position (of a committee, maybe).  And then there's `general schmoozing and networking' (my reason); but that has limited reach, since it's not a research meeting, and hardly anyone from my area is here.

So I'm free to observe the full sweep of a career path, from high-school students and undergraduates to eminent people in retirement age; and also alternative histories: editors, government and industry people, faculty at small schools, mathematical artists and writers. In common just love of the enterprise, expressed in many different ways. And that makes its special, since out there `the enterprise' inspires fear, awe or contempt, but rarely love.

First stop: the employment center. It's a strange setup, reminiscent of a Civil War field hospital: white curtains separate small interview areas. Young men and women sit nervously in the waiting area, in business wear they're clearly not accustomed to, until an employer (wearing `casual academic') calls their name. These aren't the people getting high-powered research postdocs; on the other hand, they're fairly lucky ones, having nailed a preliminary interview. I sit there for a while, thinking that unlikely as it may seem to them, they'll never have as much `power' (to write their life histories) as at this very point. Half-embarrassed at lurking among kids, I don't linger.

The best place to hang out and meet people is the exhibit area, which for me amounts to a giant, mouthwatering math bookstore. Mathematicians love math books, but I take that to extremes...so many interesting, beautiful things I absolutely must learn more about. It's dangerous, but each time I go there I run into somebody I know, and chat for a while. At one point I spot, standing by himself, a man who ten years ago held a tremendous amount of power in the profession. Even back then he was a gentle, approachable guy with a broad vision of things. We start talking, and he says to me: `when one is old, one becomes invisible; it is very interesting'. He believes the economics of higher education in America is close to a breaking point, and a phase transition will soon happen.

I find the time and energy to go to a few plenary talks, and they are all interesting in their fallibility. The applied mathematician, whose work sounds original and useful, but perhaps not very deep. The combinatorialist who started by singing a song and knows how to structure a plenary talk, but finally couldn't help getting technical. The `rising star' probabilist, who got so technical so fast that in the end was talking to a nearly empty auditorium. The young dynamicist who explained an interesting connection understandably, but gave no idea of the broader interest of her line of work. The best was the Fields medalist, who didn't get technical, described lots of deep connections and even a little fact I'll have fun explaining to my partner (whether she'll `get' how wonderful it is, I don't know).

I skip the topologist's talk to visit the `math in industry' panel, standing room only. Filled with eager new PhDs, who've seen the writing on the wall and are pondering a jump while they can. The compensation difference is lopsided, as the consulting guy eloquently describes, his arms mimicking a scale. The panelists were well chosen: men in consulting, government and finance, women from the automotive, information and software industries. They give good practical advice, by turns encouraging or skeptical; there are a few of us mid-career people in the room, and we get the message: you're too old, too set in your ways; do you want to have people half your age as peers? But for young, generalist problem-solvers, doing this makes sense, though most of them are not yet in a position to understand why. (You'll work on their problems, but it's non-trivial, motivated, and with lots of room for creative input and expansion.)

And then there are the math Oscars, including a well-deserved career achievement award. In the category `achievement in undergraduate teaching', three faculty from selective liberal-arts schools. The citation gives no idea of what's special about them, especially given their student population; so I decide to go to their talks, in the hope of maybe learning something useful about teaching. That's also standing-room only. There are only two talks, and I do hear something useful. One guy talks about `grace', and I have to force myself to get past the religious overtones to understand his surprising observation: `grace', gifts not justified by merit, does play a role in an academia. I think it's hard to recognize because it's so rare; nobody expects miracles in a mathematical career, and indeed they don't happen.

Post-Tenure Review and Me

The envelope from the provost's office has an ominous confidential stamp, so I just set it down on my desk and go about my business, avoiding the distraction of dealing with its contents. When I do open it, it's the expected: the provost concurs with the head that my performance `needs improvement', so I'm facing `post-tenure review'. And by the way, your sabbatical is canceled until you're again a faculty member in good standing.

Post-tenure review arose in academia in the 1990s; in the USA first, where tenured faculty have no class consciousness, and you can change any rule of engagement as long as it only affects new people. It is part a result of `business values' worship in American culture, part resentment at the only profession with essentially guaranteed long-term employment, in a country where most employees are treated as serfs with no job security. It was harder to do in Europe, but gradually introduced there too, through the back door of `America worship' by euro-academic bureaucrats.

PTR was sold as a way to get rid of tenured `dead wood', or of people who spend all their time on outside consulting. So it still carries an imputation of `serious misdeed', incompetence even. Sorry, that's not me, not by a long stretch. My research `exceeds expectations', my lectures are clear, my class interaction with students completely normal, graduate students ask me to guide their work.  And yet, it can be done. The mechanism is there, and all it takes is a committed department head.

For these reviews have become something entirely different: a mechanism for the expression of power, one of the few in unhierarchical tenure-track academia. You might think it means your colleagues don't like you, but really all it takes is a couple of determined people with a grudge, and access to the head's ear. Or a head with an agenda, who feels a sense of mission in `doing something about people who can't adapt to where they are'. Or a naive head, an insecure newbie struggling with the job, believing this kind of action will make his faculty take him seriously. Then it moves to the dean, and the provost. To them it's all about sending a message  to the faculty: `yes, as a matter of fact we can use this mechanism to enforce our current policy priorities, even if you're doing your job just fine'.

So this spring term, in addition to my regular teaching and advising and (hopefully) research, I'll have to deal with this nonsense. The head tries to pass the process as `advisory', when in reality it's adversarial and very personal, a wasteful game involving a few men in their early fifties who should have more useful things to do with their time: the head, the dean, the provost and myself. At some point a mea culpa, an act of contrition will be expected from me. If at all possible, I want to deny them that pleasure, to leave in the written record, as clearly as possible, the many reasons why they're wrong. (Or to make sure they know it's given grudgingly; just what it takes to keep the job and no more). This will take some willingness from colleagues who don't know me to stick their necks out and support my position, which at the moment seems like a tall order; why should they?

First Day (Part II)

In the afternoon, it’s time to meet the graduate students. I walk into class…and count nine people there (all men). That’s good, since only six are enrolled in the course. My graduate student is among them, sitting in the front row. I recognize a couple of faces from last year’s graduate course; also good. This is a Ph.D-level course (second-year graduate), so nine is a very decent number.

The focus of the course is a “hot topic” in my field. Ten years ago, a program to solve a famous problem in one area of mathematics using techniques from another area was brought to fruition in unexpected and spectacular fashion, by a brilliant individual working alone (the kind of thing that only happens in math, I think.) The techniques involved in proving that theorem are very powerful, not fully developed, and still have the potential to prove interesting results in both fields; it’s the kind of topic where a beginner can still find a good problem and make a contribution.  “Regardless of what your main field of interest is, having a paper in this area would be a good thing”, I tell them. 

On the other hand…since the topic bridges two areas, having some knowledge of both at the beginning graduate level would be highly desirable, right? So I ask for a show of hands. How many have taken a basic course in area A? Three hands shoot up. A fourth student says `I took it in the Physics Department, does that count?’ Now, that could take us far afield; but I just smile and say, `sure’. How many have a basic course in area B behind them? Four hands (different ones). Okay, so my first mission here is not to scare them away. When I was a student, if something was new and difficult it was impossible so scare me off; mastering new things is what it’s all about, even if it’s hard work. But by now I know from experience that not everyone is like that.  I tell them “well, you’ll have to do some independent reading of background material.” And I promise I won’t get too technical regarding area B.

In fact, the requirement for a grade is minimal: I want them to give a talk on the topic of the course—either present a result found in one of several monographs in this area, or one from a recent paper. On the other hand (I tell them) the more ambitious students should be thinking in terms of finding a good research problem in this area by the end of the year. “You’re graduate students, and what do graduate students do? They ask questions” (hint, hint).  “Some of them will be good questions” (they smile). “And, since you have no experience, they’re not likely to be questions that would occur to me, or to someone already working in the area”.  That’s their edge: being able to ask new questions, out of sheer ignorance.

I start slowly, with a survey of the main results I would like to focus on during the course, including simple examples one can do “with bare hands” (that is, on the back of an envelope).  I get one good, creative question (from the guy who took it in Physics). “No, I don’t think this has been done”, is the answer. Then I move on to a very simple result that can be proved in the same spirit as more difficult theorems, and where the techniques appear in their most basic form. This is standard “area A” material. Unfortunately area A can get technical very quickly, and in the back of my mind is the fear of discouraging those who are just planning to sit in to get informed. I could do the “big ideas” thing, and never get technical; but that would be cheating them of any chance to work in this area. The right balance between ``technical” and “big ideas” (in lecture) is not a trivial one to find.

When the lecture is over, I chat with my student for a few minutes. He tells me he has a new job, as an instructor at a local community college. That’s good, but it means he won’t have time to take any graduate courses for a grade. He is at the thesis-writing stage, anyway (Master’s degree). He tells me he is “just about finished” with writing up the derivation I asked him to do.

First Day

It’s the perfect day.  Pleasantly warm, comfortably dry. The students are back, scurrying about campus looking for their classrooms; rested, happy, excited, expectant. Lots of skimpy shorts and tight-fitting t-shirts (they clearly had a fun summer), so the professors are in a good mood, too. Sure, it is mildly annoying to get to the campus at 9 and have to look for a spot on the staff lot (must be the graduate students), or to deal with long waits at the coffee shop. But it’s good to see them back, they’re our raison d’etre, after all. Not to mention that some of that sexual energy can’t help but radiate to the environment.

I love the first day of classes. I’ve written my syllabi, posted them on the web site. I checked that my textbooks are already at the bookstore (not always the case). I’ve written down notes for my first few lectures. Not too detailed—you have to leave room for spontaneity in the delivery; just enough to give the impression of flowing naturally, without embarrassing moments of hesitation. I rarely have to look at my notes, and students are strangely impressed by that. I’ve secured a set of brand new markers (hate the damn glass boards). About ten minutes before class starts, I close the laptop to collect my thoughts. This will be the term when I’ll be less professorial and more ``approachable”; when I’ll just talk to them, and they’ll respond as curious students of the Academy.  Shouldn’t be hard, it’s a small class.  Fortified by optimistic thoughts, I walk into the classroom two minutes early…

And sitting there are six students; another walks in a moment later. I wonder if my face betrays my feelings, and just in case, I casually move to the business at hand. I introduce myself, and using the online roster (they look like their pictures) try to learn their names.  I knew the enrollment was nine, so seven on the first day is not unreasonable. Still, it is hard not to be taken aback by the reality of it. Mind you, this is not a graduate seminar. It is “Introduction to Advanced Mathematics”, meant for sophomores and juniors who want to learn any math beyond Calculus; our “proofs course”.  I taught it last fall to a class of twenty-four, and it went well. There are two other sections of the course this fall, and both are full, with enrollments of thirty.

I can only conjecture as to the reason, and it goes like this. The science-motivated math majors take the honors section. The other sections are populated by teaching-oriented majors, computer science majors, and engineers for whom this class is a requirement. In practice, most are seniors, trying to clear this last, pesky obstacle to graduation. For somebody like that, the guy with a reputation like “you learn a lot, and he’s friendly; but he expects you to work really hard” would hardly be a first choice. Better take the section where you can reliably expect a B for going through the motions. Math isn’t their interest, after all; so one can’t blame them for optimizing their use of time. Now, the natural question is: why do these majors require students to take the “proofs course” designed for mathematicians? It makes no sense, but that will be for a future post. Today I’m teaching.

And it goes well. I’m not doing anything hard: logical connectives, truth tables, equivalent propositional forms, tautologies.  I tell them about Godel’s Incompleteness Theorem, twin primes, and the conjectures of Goldbach, Catalan, and Collatz. (All this to illustrate the difference between “truth” and “provability”).  To another audience this might seem mysterious, intriguing, or fascinating. Maybe to some of these students, too. But surely some of the engineers are thinking “and this is good for…?”  And they don’t ask, unfortunately.  But I did point out that the text includes discussions of Turing machines, P vs. NP and RSA cryptography. (Some of them have heard about those, so maybe I have a `hook’ there to draw them in.)  They all seem engaged (it’s a small room), sometimes nodding or smiling. I ask them to work on a problem on the spot, and they do it. I ask questions, and get intelligent answers. It’s a good start.

I always get a `high’ from teaching, and it can take half an hour or more to `come down’ enough to be able to think about anything else. Knowing this, I walk out of the building, into the beautiful sunny day and the scurrying half-dressed students, headed for the coffee line.