This morning I suggested that perhaps "underneath" low scores on
standardized tests was a vague, unarticulated student suspicion that much
of what they're being taught isn't worth knowing, hence the lack of drive.
(It certainly isn't an absence of native ability.) I'd like to elaborate a
bit.
Point to poor math performance on standardized tests or in
relation to student performance in other societies and the average
American citizen is appalled. I suspect that this reaction is a
consequence of a superficial extrapolation. Just about everybody agrees
that students ought to be able to make change, balance a checkbook,
complete an income tax short form, etc. Now for a great many people, this
is what they think of when they hear or read the term "math." And, since
this "math" is obviously a good and necessary thing, and it's hard to get
too much of a good thing, the presently required math curriculum is a good
thing.
Of course, there is in fact relatively little of this sort of
"math" in the school curriculum. If usefulness and practicality were what
math was all about, school math would surely be much concerned with
statistical description and analysis, which it isn't.
No, that isn't what most school math is all about. My friends who
teach math are, without exception, in the field not because of math's
usefulness but because of its esthetic appeal to them personally. They
don't give a hoot about practicality. (Even my engineer friends say that,
once settled into their jobs, their math needs are so circumscribed they
could have picked them up on the job.) One of my close math-teaching
friends, asked not long ago by a student in her college class to tell him
the practical uses of quadratic equations, said to the whole class, "I
don't know, but isn't working with them fun?" (She told me this herself,
with a hint of pride at her ability to deal with the question with such
finality. (She doesn't, to her credit, buy the long-discredited notion
that math is good "mental discipline.")
Now there's nothing whatsoever wrong with math as art. But to
make mandatory the heavy doses of the kind of math presently required is,
it seems to me, a serious mistake, akin to making orchestra or oil
portraiture or ballet mandatory, and then getting all upset at the failure
of some students to feel sufficient commitment to practice daily. As I
said earlier, there are no doubt cultures less pragmatic than ours where
performance can be effectively driven by certain patterns of action or
particular shared values, but that doesn't help us in our effort to
improve our own students' performance.
A great deal of human experience must be quantified in order to be
understood. If we were to revise math--at least that mathematics which is
a _required_ part of the curriculum--making it a means to the end of
making more sense of immediate experience, I haven't the slightest doubt
that student interest and performance would increase dramatically (as
would our collective ability to survive and prosper).
Incidentally, if this were done (while continuing to make present
math options available as electives) my math teacher friend would probably
be elated. She'd find herself working with students who shared with her
an appreciation of math's inherent beauty.
That said, if there's validity in what I'm arguing, is it likely
to find acceptance in the math community and begin a process that results
in a rethinking of the math curriculum and the emergence of a win-win
situation for students, teachers, and the larger society? I don't think
there's even a chance of that happening. Math scores aren't going to go
up appeciably, no matter the political push, and we're not going to see
evolution toward a curriculum that helps the average person make more
sense of life.
Marion Brady
-- mbrady@digital.net Marion<mbrady@digital.net> http://ddi.digital.net/~mbrady
Learning-org -- An Internet Dialog on Learning Organizations For info: <rkarash@karash.com> -or- <http://world.std.com/~lo/>