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."
