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Text identical to archival version, embedded hyperlinks
activated. Note that I've used NCMT throughout, but it should be
NCTM (National Council of Teachers of Mathematics)
MEMORANDUM
October 30, 1997
TO: Kenneth Ross, Department of Mathematics,
University of Oregon
FR: Kirby Urner, 4D Solutions
RE: NCMT Standards, Geometry, 1999
Dear Sir --
I am exploring the MAA website and learning about the
connections between MAA and NCMT at the level of providing
endorsements, sharing minutes of proceedings and so on,
and decided to send you a background memo re my own attempts
to engage the NCMT in productive discussions.
As a recent workshop presenter and participant at the Oregon
Math Summit organized by Norma Paulus and Maggie Niess at OSU,
I discovered a lot of professional math people were advocating
bold, new experimental approaches designed to galvanize student
interest, while the rank and file were more concerned about
the looming prospect of harder standardized tests, drilling
for which would leave little room for any radical departures
from the norm. For me, this was the central tension in the
conference.
Ralph Abraham, one of the invited superstars, was especially
aware of the dichotomy between those who see mastery in
mathematics as an ability to pass a set of standardized
tests, versus those such as himself who have waged career-
long battles to bring new thinking into the curriculum --
a battle which Dr. Abraham said often put him at odds with
more conservative collegues, who were also many times those
for whom he had the most professional respect.
My angle on this situation, an analysis I shared with a
number of teachers at this symposium, is that those with a
commitment to the advance of mathematics have an advantage
over those more interested in consolidating past gains, in
the following sense: the Platonic Realm (as Sir Penrose
called it -- another invited superstar) is always a source
of fresh material, some of which will be of relevance to
students in K-12, and, simply by virture of its being new,
will not be a part of the current standard.
In other words, people who source the curriculum have the
ability to stay one step ahead of those who wish to codify
the subject into a set of standardized tests (in actual
practice, the same person may perform both roles, wear
two hats, as I suspect is the case with many professionals
in orbit around the NCMT).
Ralph Abraham, for example, had recently returned from Italy
where he's been working with folks on a calculus text which
will segue into dynamical systems theory (e.g. chaos math and
fractal geometry) far more effectively than what currently
passes for a standard calc text today. This new text will
then set new standards (Ralph has also migrated all of
Euclid's constructions onto the web, complete with explicit
step-by-step graphics).
I think the first objection to my thesis that will pop into
a lot of minds is that fresh material only shows up at the
'frontier' in any discipline, and in mathematics that frontier
is a territory which only PhDs are qualified to pioneer. As
far as K-12 is concerned, this model suggests, the curriculum
is more or less set in stone, with the main challenges having
to do with fine tuning within broad brush parameters that are
unlikely to change in the foreseeable future.
But I'd argue a different model, and invoke historical evidence
that the curriculum is vulnerable to suprising changes at all
levels: in my own short lifetime, the K-12 curriculum has
already changed considerably, in many ways in response to
changes in technology and expectations about the future of the
econosphere -- i.e. changes of a kind that are only accelerating.
We have good reason to expect that geometry in the 21st century,
for example, will not be studied in K-12 just the way it is
today -- which brings me to the title of my Math Summit
workshop: 'Beyond Flatland: Geometry for the 21st Century'.
Finally, I come back around to the topic at hand: my interest
in engaging the NCMT more specifically about changes in
curriculum standards we probably should be anticipating
and starting to codify for the benefit of tomorrow's test
makers and exercise framers. Back in February of this year,
I sent a memo to the NCMT, which I then enhanced with a few
graphics and uploaded to my website as well (the trajectory
followed by several of my memos). It featured some background
thinking about how curricula change over time (as here, but
more briefly expressed) and went on to hypothesize what a
typical 1999 geometry exercise might look like (on CDROM).
The memo is at http://www.teleport.com/~pdx4d/ncmtmemo.html
and is one of the web pages I use to provide introductory
level access to the synergetic geometry shared via my own
website and a host of others. Since 1999 is only just a
little more than a year away, it seems not too early to start
drafting some of the new curriculum essentials and getting
feedback from professionals, both inside and outside the
classroom, regarding the most effective, student-friendly,
and technology-leveraging approaches we might take with an
eye towards overhauling some aspects of K-12, in the arena
of spatial geometry in particular.
Thank you for you attention to this matter and I hope you will
let me know of any NCMT professionals in your sphere with
special expertise in spatial geometry who might be willing to
share with me any early drafts of 1999 curriculum standards
materials.
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