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A Mini-Manifesto (consistent w/ NCTM?)
Posted:
May 2, 1999 8:47 PM
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I've been browsing the NCTM 2000 documentation, plus engaging
in some threads re math curriculum on the misc.education
newsgroup (where I posted an earlier draft of the mini-
manifesto below).
I find the NCTM stuff necessarily dry, because it's written
in deliberately toned-down language, is not supposed to give
offense. The problem with such writing is it conceals
ideologies as much as reveals them. Since the internet
permits more open format debate and gives voice to
individuals (vs. committees), I'm taking the liberty of
turning up the volume a bit, making it clearer where I'm
coming from with my proposed direction for at least some
schools of thought doing the K-12 thing.
But that doesn't mean what I'm proposing is inconsistent
or entirely out of synch with what the NCTM is proposing.
Indeed, the principles of educating for participation in
democracy and accepting technology as a background premise
are very much at the heart of what I'm pushing as well.
Feedback welcome.
Kirby Urner
Curriculum writer
Oregon Curriculum Network
http://www.inetarena.com/~pdx4d/ocn/
======
Three recent threads on misc.education
a. NCTM Standards - attention Herman and Alberto (Apr 21 99)
b. Re: NCTM Standards (Apr 22 99)
c. Java as Mathematics (Apr 26 99)
initiate some useful conversations regarding the place of
computer languages in math class. From my point of view,
the perennial debate about the appropriateness of graphics
calculators in math class/on tests is a dress rehearsal for
a larger, deeper discussion involving the place/use of more
advanced technologies in general: in particular computers
and computerized simulators (VR tech).
My contention is that "math class" in K-12 was never intended
as the sole property of specialized math professionals to make
do with as they pleased, i.e. in a democratic culture, we're
not to insist that students "track" themselves too early and
study math with an eye towards becoming indoctrinated in the
same way those on a doctoral path in that subject.
A given student has x hours per week of "chair time" in which
to concentrate on a spectrum of inter-related topics. So what
do we include and what do we drop? We need to consider the
world in which the students will actually live, today and
in the future -- and not just the rarified world of an Ivory
Towerite tenured math professor (always a tiny minority and
not necessarily the cookie cutter we're using when doing our
jobs as math teachers in the earlier grades).
I've been arguing for a remix wherein computer programming
and related patterns/styles of thought be phased in much
earlier, extending a megatrend already well promulgated by
Seymour Papert and his LOGO language for kids (based on LISP).
So how does this go, beyond the early grades?
What computers do is take a lot of the drudgery out of
repetitive tasks. Exercises establish the algorithms in our
minds, give students insights into the nuts and bolts, but
the programs then reiterate these computations way more times
than we'd want to do in drills -- e.g. graph thousands and
thousands of points whereas, by hand, we'd maybe settle
for 10 and consider the skill established. So one thing
computers provide (and this is obvious) is raw computing
power. But to tap this power, you need to write in a
language those computers will understand. What's shown
in math books is two often three or four steps removed
-- so better bridges need to be built.
Why is this important?
Because a lot of the math principles become a lot more
accessible if (a) you know the algorithms which show them
off and (b) you have the computing power to drive high
powered displays of these algorithms at work, drawing from
data sets much larger than you'd want to tackle with paper
and pencil alone.
Of course fractals and strange attractors come to mind as
examples of this approach. Indeed dynamical systems theory
as a branch of mathematics owes a lot to computers for its
very existence. I also think of STRUCK, where dynamical
systems meets up with tensegrity via "elastic interval
geometry" (EIG).
Beyond points (a) and (b), computers provide useful grist
for the mill in a more philosophical context. Kids see
movies like '2001' (we're almost there), containing really
smart computers like HAL, see other AI creatures in science
fiction (most recently 'The Matrix'). A common theme in
these works is human intelligence (humint) being superceded
somehow by AI.
Stephen Hawking is one who believes that intelligence will
somehow leap across the gap, from a less biochemical to a
more electrometalic hardware, the better to probe more deeply
into space my dear. However, Stephen is also one who thinks
there's a profound difference between biochemical and electro-
metalic circuitry today, which is maybe why humint taps the
Platonic realm (outside mere rule-following) whereas computers
remain "artificial" in their intelligence (bureaucrats, good
doobies when it comes to going through the motions, but
incapable of true genius).
With this thread already prevalent in the culture (and lets
not forget this Y2K business), I believe it's essential that
computers be probed, scoped out, disassembled, programmed --
approached from many directions -- in order to remove whatever
shrouds them in mystery (e.g. ignorance and fear) and makes
them targets for phobias and paranoias of various kinds
('The Net' and 'Enemy of the State' both play up high tech-
nology as instumental to a heavy handed monitoring regime
-- and I noticed the USA State Department was quick to
reinforce those perceptions when suggesting such means were
behind Turkey's nabbing of the Kurdish resistence movement
leader (one of them)).
Sure, teachers in other classrooms will be expected to interpret
these memes-patterns of pop culture to students with eager
minds, wanting to know, but it makes sense that math teachers
especially would be looked to for insights and role model
attitudes. Math teachers should be able to carry on intell-
igent conversations around such generic topics as (examples):
* Shall we fear and/or fight and/or embrace a computerized
Big Brother?
* What is GIS/GPS and how do satellites both show me
where I'm driving (when lost) and guide B2 bombs to
their targets?
As long as both civilian and terrorist applications of the
same technologies get funding, we'll need to instruct our
students in the meaning of "dual use" -- an important concept
in all of today's negotiations about peacekeeping, sanctions
and trade. Math classes should prompt intelligent chatter
re "dual use" technologies -- don't just leave this to
science and history teachers, who maybe haven't such a
strong grasp of the basic principles driving the show.
I think math teachers need to get their heads out of their
text books, look around, realize what a scary and puzzling
world this is to children and, as Keith Devlin puts it,
"make the invisible visible" -- let kids know what's going
on under the hood, from a mathematical point of view.
Tell us about the logic of it all, the reasoning driving the
policy making, the game theories involved, the simulations
and the assumptions behind the simulations -- and do this
now, please.
So that's why I'm advocating more "Java jive" (and the like)
in our math classes today. Visit any bookstore, and you'll
see an exploding number of titles about Java, Linux, Corba,
OOP, XML... don't make kids wait until college, or make them
surf, untutored, to decipher what all this means.
Math class is the place to fit all these puzzle pieces together
(regardless of whether specialized PhD mathematicians consider
this their business or not) -- AND to do lots of exercises, AND
to write programs AND to collect lots of data in real time.
Does any one else out there share this vision?
Kirby
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