Jazz Math Ed

A lot of talented and effective lecturers prepare so carefully that every time they present a certain topic, it’s just like every other time they’ve presented that topic. So don’t get me wrong. I’ve seen it done, and done well, hundreds of times. Let’s call that “classical” style. You look at the printed score, and you pick up your instrument, and you practice like crazy until you could hardly ever miss a note except on purpose … and then, and only then, you go out in front of your audience, and, with any luck, you play your little bit and they love it.

On the other hand, there’s the “jazz” style (as I propose to call it here): you look at, not the score, but the chart: an outline of what’s supposed to go on in a given performance. Then you grab your axe and wail (and, with any luck, they love it).

Now, I have been known to prepare lectures carefully. Heck, once I even read a talk from a printed copy. Mostly, though, I won’t even think about doing things that way if I feel like I’ve thoroughly understood the material … which, since I’m mostly lecturing on subjects I’ve known pretty well for about thirty years, is most of the time. I get to have a whole lot more fun slinging the math this way … and I sincerely believe that the students (usually) get a better show. For example, I’m free to change everything around if there’s an interesting question. Moreover, since I’m working without a net, I make real mistakes in real time and have to recover somehow (just as every student will have to do before long if they’re keeping up with the homework); and more than this, I get to—have to!—model the quasi-obsessive “check it if you can think of a way to check it” behavior that typically separates the “A” students from the “B”s.

All well and good. The trouble is, it seems like whenever the subject (“how can we become better teachers”) comes up, all anybody ever wants to talk about is “classical” style. And that way madness lies. It’s possible to be too well prepared—I’ve sure as heck seen that done. There comes a point where you might as well just read the furshlugginer manual—except that that would be cheaper and more convenient. Also, quite often our bosses are enemies of the academy who would like nothing better than to find a way to eliminate their need for performing artists and replace us with canned “lectures” (or, worse yet, with computer programs) that can be paid for once and then controlled utterly. Now, I suppose I can be forced by economic pressure into training my own replacement … but I can’t be made to like it.

So: the charts don’t lie. For some reason, kids keep going to concerts. Even though the album is cheaper and you can play it again and again … heck, I don’t understand this fact myself. But record company executives seem to understand at some level that their livelihood depends on a bunch of wildly undisciplined misfits (i.e., performing artists). Wouldn’t it be nice if college administrators understood this too?

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  1. As a math prof and a bass player who’s done gigs with rock bands and jazz groups, I can say that this analogy is quite right. There’s just a couple of things I’ll add:

    – Doing things the “jazz” way doesn’t negate the need for preparation. It takes a HECK of a lot of preparation to be able to improvise well given nothing but charts; but anybody can honk and flail away without preparation.

    – Most jazz and rock songs have some sections which are scripted AND some which are improvisational. The scripted stuff has to be rehearsed to perfection ala the “classical” technique. The improv stuff is prepared for by studying the scripted parts and thinking of interesting variations on those parts. So no song is entirely just an outline; neither is any lecture.

  2. of course i quite agree.
    i have to admit: “wildly undisciplined misfits”
    was at least in part an exaggeration
    chosen for rhetorical effect.

    but not entirely: there’s a good deal of evidence
    that lots of people–including not only the bosses
    but even some of our colleagues–feel that
    “being a pro” has more to do with, for example,
    wearing expensive clothes and helping management
    pretend that their guru consultants actually have
    something useful or interesting to say.

    and, well, i guess the trouble is,
    i’ve sworn on the altar of god
    eternal hostility against every form
    of pushing people around —
    which means i consider it a *duty*
    to oppose this attitude.

    *really* being a pro is, first of all, sure:
    know the doggone math. then stuff like
    “actually listen to students and work with ’em
    based on what they can do right now and not
    what you think they *ought* to be able to do”
    (this is probably harder than it sounds …
    or maybe a lot of people just don’t even try).

    hmm. ranting again. deadline looming:
    gotta write a quiz i’ll need in 80 minutes
    (and the last 60 are booked in tutoring).
    better shut up and start improvising …

  3. Good post, Vlorbik. With the rise of IT in schools here in Scotland, a lot of teachers have been spending time putting their pre-university lessons into a powerpoint form – I suppose they like the fact that they’ll then have the resource to use over again the next year. But I think this is terrible, as the lessons then become more or less dead – how can you run with a new idea or suggestion from a student, when the slides are all stacked up and ready to reveal the “official” next line in a solution?

    Also, in my experience students don’t tend to relate well to printed matter (eg a textbook) and I do wonder if on a deeper level they see print as “dead” – this cannot be changed, it’s fixed on the page – whereas handwriting (however messy) seems more alive and is something they can relate to. Mathematics becomes more alive when you can see it developing before you, sometimes in new ways.

    I love starting with a blank board and building up whatever it is we’re going to do together. As you say, you need to know the content well to be prepared to take a few detours if suggested and still get to your destination.

    Jazz is definitely a good analogy for a good lecture. So is stand-up comedy!

  4. vlorbik

    http://larkolicio.us/blog/?p=63

    the “unfunny valley” at _point_of_inflection_.




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