Monday, July 16, 2012

A few thoughts about teaching (mostly math) as if you were not a dolt

A mathematician friend of mine–I'll call him Bob because that was his name, and maybe I'll get lucky and he'll see this and get in touch—had a passion for some really abstract, fundamental stuff: number theory and set theory. That's extremely hireable nowadays because it's used constantly in various applications to/for/of computers, so he had no real fear of unemployment, but he was also aware that a hundred years ago all those things that fascinated him had been a backwater, regarded as an odd little branch of interest only to extremely serious math people.  (He had learned this while stuck teaching math history as part of his TAship.) So he noticed that older work, the founding documents in the field, had a distinct quality of "ain't this cool?" that nowadays you have to go to web pages about obscure musical genres or visual artists to find; more contemporary papers had a whiff of engineering about them that made him uncomfortable
Every so often, this sacrifice of the spirit of play and artistic grace, for the sake of commercial and practical interests, would cause him a burst of melancholy (usually not long after he'd cashed his paycheck, particularly after he had a family to support), and he'd mutter that the terrible mistake mathematicians made was in letting people know that all that glorious and beautiful stuff was useful.
For a while I riffed on possible short stories in an alternate history in which Kepler's Music of the Spheres stuff had led to physics being done entirely in music (which is after all another elaborate system of transformations in which strings of bits become other strings of bits according to regular rules). Unfortunately, when I ran that idea past Bob, he pointed out that the density and compactness of information in math is so much higher than it could be in music that you would need symphonies to add a grocery bill, so I gave up and never returned to the idea.*
Lately, though I'm still not seeing any fiction in it, I find myself thinking about Bob's complaint from a different, teaching and learning standpoint.
For decades I've known enough business people to hear the standard grumbles about having to hire kids without skills, but in the last decade, as standardized testing has expanded, I've noticed that I hear a slightly different grumble more often: about the kid who can pass tests but doesn't seem to know how to use the information outside of that context. I also spend a fair bit of time around teachers, and hear the usual grumbles about teaching to the test, which are so familiar that I won't rehash them here. And not least, I'm occasionally around young people, many of whom appear, god save us all, to like all the testing, because it means, in effect, knowledge control: all you have to do is pass, then be forgotten with the rest. (For example, at the career college where I taught most recently there was a perpetual simmering student complaint about being expected to remember material from another course in the current one, or about having to take courses in a particular order, all tied into a kind of odd model of the universe in which if you passed enough tests you got to be an FBI agent or a brain surgeon or some such, sort of The Last Starfighter model of knowledge if you will).
It seems to me that we've got a strange model of "useful," and it's at the heart of the whole mess that surrounds standardized testing. Testing has become more and more Mandarin -- i.e. a way to find and reward people who can memorize, regurgitate, follow directions, and in general fit into the workplace in giant bureaucracies. The "use" is that finishing far enough forward in the school-race gets you into one of the slots where there's a good paycheck and benefits; it's not about being able to do the job, or only secondarily about that, it's about reserving the better slots for people who are The Right Sort.**
It's about getting the position, not doing the job. This, of course, is annoying to managers on the floor who need people that can and will do the job; it's frustrating to teachers who feel like they have been assigned to be anointers of the suitable*** rather than bringers-out and developers of abilities. It's uncomfortable for many good, thoughtful parents who see their kids becoming adroit ladder-climbers but inept makers, doers, fixers, and caretakers.
Ultimately a system built around such examinations simultaneously robs worthy students of the strength that comes from accomplishments, and gives the less worthy (and the downright shitty) an unearned and treacherous positive self-image. Like the Cowardly Lion's medal, the Tin Man's certificate of appreciation, or the Scarecrow's diploma, it's transparently awarded whether or not the person is actually brave, generous, or smart.**** The emphasis on test scores actually pushes the best to lack all conviction (because they have the wit and nerve to see and face the truth, that the congratulations and praise were bogus) and the worst to be full of passionate intensity (because the one thing that a lifetime of gulping down bogus praise will do for you is to make you really, really enthusiastic about believing lies, and insistent on being told them).
It also slowly corrodes teaching. It has long ago been demonstrated, over and over again, that the "best" teachers, the ones who consistently get high test scores from children, don't actually teach to the test much (except in the purely regurgitational materials). Rather, they teach skills and puzzle-solving, and when kid meets test, the kid solves the puzzle, using those skills.
Really crappy teachers do teach to the test, very probably because with their own limited abilities and experiences, they can't imagine any other way of passing a test. Very likely these are the same teachers who got through school themselves by loading their memories with the "just say this and you'll pass" material at the review sessions. It is sadly possible that they didn't see any point to all that stuff they were loading their memories with—perhaps there was none to see, perhaps they hadn't the ability to see it.
There's an ugly irony about standardized testing and the rotten teachers it was supposed to help us eliminate: it probably protects many more of them than it eliminates. Standardized testing may catch the completely inept teacher, who would probably be caught by any system of evaluation, but it also protects and enables lazy and mediocre ones, who can safely stop trying to teach, spend all their time drilling, and remain ensconced in the classroom for decades because they produce "acceptable results."
The teachers that standardized testing hits hardest and hurts most, though, are almost certainly the middle group: the ones who could really teach, out of genuine liking for students and learning and a desire to connect them, but who are frightened and bullied into being silly drillmasters, and neither encouraged nor enabled to do anything better. The caliber of principals and other administrators is generally lower than that of the teaching corps as a whole, and so they are even more subject to panics about whether the students are receiving enough test drill, and apt to lean on their teachers to do more of it. Thus a teacher who might have become a great math or reading teacher, or better still might have taught students to use their reading, writing, or math skills to explore the world in history, science, or a dozen other fields, is instead pressured into conducting drills and "Now on a multiple choice question, if you can eliminate one answer..." and so forth. Which is to say, it pushes all but the finest teachers to teach like the barely competent.*****
So for those of us who teach part or full time, I'd like to suggest that whenever and wherever we can, we try to slip Bob's insight into our teaching. As long as the subject is "useful" only to passing tests, it will not only have all the appeal of room-temperature overcooked vegetables, it will also accomplish nothing more than giving nothing to the Tin Man that he didn't already have.
Instead, help the students to put it to use just for pure amusement.
If it's math, show students how to play with numbers, whether it's cryptography or packing problems, calculating rocket velocities or batting averages or the number of friends who can sit at a table if frenemies don't sit next to each other or how quickly their city could deal with Godzilla. Let them see pattern and rhythm in numbers and fractions.****** Ask if they see ways to improve on the Sieve of Eratosthenes. Teach them to crack the code of the composition prompts, sure, but as a subset of cracking any text—which also means figuring out that cryptic note from the boss. If it's more interesting to have them do it as part of a game in which they are intelligence analysts trying to figure out where Agent X-12 is being held, great; but there's a surprising amount of entertainment in abstract problems.******
Most of all, recognize that the standardized tests are set up to create a safe pathway for dolts, but that is not the only safe pathway, and if by any chance you're not a dolt, it's not even the safest. Test-drilling will not protect your job in the long run as well as teaching actual skills and grasp of the subject, because the test can change instantly at the whims of several levels of authority, but the subject can't. It is also far from the best for the students; this phase of capitalism's relentless plugging and closing of upward-leading slots in the economy means there are fewer and fewer places for the well-connected and prepped "qualified" person, but the state of technology and business also means there is more room than ever for the ones who can actually do something. If you can steer them toward growing a brain rather than accepting a diploma, in the longer run, you and they will be all right.

*For a pretty cool take on the same basic idea you might see Melissa Scott's classic Five-Twelfths of Heaven, which was considerably better than any idea I ever had about music-to-math.
**Notice the etymology here; it's not unlike the Sorting Hat at Hogwarts, ne?
***Perhaps even in the sense of "able to become a suit in some large office block."
****That's what makes the scene in the movie such a classic, because "Oz never did give nothing to the Tin Man that he didn't already have." They all deserve the awards and recognition they are receiving, as outward signs of the brain, heart, and courage they were ostensibly questing for, and actually had all along. But they are receiving them from a charlatan who has no idea what what they actually did, and wouldn't care if they did know, and who means to cheat them. You don't get irony better than that.
***** This is another effect of the systematization that divides the highly and the less skilled more deeply and completely every year. If you remember the Lopez lifeguard case, this is another way of making the good-potentially-excellent function like the marginal-potentially-adequate, as Whatzisname points out.
******I don't mean "instead of" (in the way that  some teachers have turned math class into group drumming); I mean that a kid who has a grasp of a time signature is only a short step from understanding quantum numbers and suborbitals. Maybe I gave up on that short story idea too easily.
******* Here's one I've used on just barely or just recently literate/numerate students: given a particular dictionary, how would you find the two words in it which are adjoining but farthest apart alphabetically? (There are dozens of ways). Now is there any way of deciding which way would be fastest without actually trying them against each other? And how sure could you be of your answer? Does it depend on how you define "farthest apart alphabetically?" I've seen a bright eight year old spend most of a day on that problem ... and I guarantee she learned a lot more doing that than she ever would have memorizing "first try to eliminate answers that include the words always and never."