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Re: Op-Ed by W.Schmid in Harvard Crimson
Posted:
May 12, 2000 11:45 AM
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Regarding the opinion piece by Harvard mathematician Wilfried Schmid,
see the interesting letter to the editor (immediately
below) from a Harvard alumnus who is now a 6th grade math teacher.
Eric
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To the editors,
Given the usual trajectories of my classmates' careers, I realize that
The Crimson will probably not be overwhelmed with a flood of responses
from honest-to-goodness math teachers reacting to Wilfried Schmid's
opinion pieceof 5/4 ("New Battles in the Math Wars"). Nevertheless,
here I am, an alumnus and an actual, practicing sixth-grade math
teacher, whose experience of the ongoing efforts at and the need for
reforms in math education hasbeen significantly different from that of
Dr. Schmid.
Right from the martial headline - "Math Wars" indeed - it was
clear that the piece, and The Crimson, would plow worn fields with an
already-dull blade. But both seem to have come quickly up to speed in
enlisting the inflammatory rhetoric and hackneyed themes and "spin
bites" that have been at the core of the angry critiques of reform
mathematics education for the past 2-3 years. Coming only a few days
after the The New York Times fronteda similar piece, your publication
of this "opinion" raises disturbing but long-standing questions about
The Crimson's and The University's roles asorgans of apprenticeship
and servitude to the institutional elites of ourculture. It is frankly
a little sad to realize that you had to wait on "TheTimes" to
establish the developing "spin" on math reform, and only then look
into your own backyard to shake loose a supporting "opinion."
Along with tens of thousands of other practicing elementary and
secondary math teachers, I would dispute many of the claims that
Schmid and others have laid against "reform" mathematics - but what
are they ? Where does he actually say anything of substance ? Shall I
stoop to remind your readers of the actual "reform" timelines in
Massachusetts and the nation which create a much more real, but
complex context for the Professor's lead-in factoid , and for his
narrow slices from the "international comparisons" pie? Shall I
attempt to discover his "proverbial man on the street", or search
amongst the rather bland, but thoughtful and concerned math educators
with whom I have worked, for his "avant-garde reformers"? Is it
possible that
"proof by insinuation and innuendo" have replaced deduction and
induction in the higher reaches of mathematics ?
There is little of substance in the Professor's rambling discourse
except a discordance that is manifest in the simple fact that he, as a
professionalmathematician, has no better sense of how 95% of children
encounter mathematics in school -- and no more standing from which to
launch critiques of curriculum reforms -- than his colleagues in the
School of Education would have to question his recent work on
"nilpotent orbits." We can recall that the last Harvard Mathematician
to express rambling opinions on matters extra-numeric was Theodore
Kaczynski. Quite the wordsmith, Ted, but hardly aman I'd set loose on
my curriculum or my children.
Call it opinion, sure... but I'll bet lots of parents in
Cambridgeport and Fields Corner, and lots of Professors of European
Literature for that matter, have opinions about public school math.
Needless to say, the former are silenced in this debate by parents of
privilege who lobby so vigorouslyfor a return to curricula that
demonstrably serve the social-filtering
functions they need to pass-on their privilege. The latter are
apparently just more self-conscious of the deep hubris of presuming
their talents to extend to the noisy and fascinating world of
11-year-old minds. Not so Dr.Schmid ! Shall only the Doctor of
Mathematics speak on this matter? Will he help us to cast off any
nagging notion that there are contexts that surround his broad sweeps
of rhetoric, that there might be a history and a research
base and a broad experience base and an actual profession of education
(gasp!) that can, and has, and does inform these issues? Will the
Professor make it all simple for us ?
To put it succinctly - Dr. Schmid is confused on so-called "invented
algorithms", simplistic on calculators, incorrect on "downgrading
skills", hyperbolic on the "avant garde reformers" (I just cut my
hair yesterday!), incorrect on the stance of and efforts of NCTM,
irrational on textbookeconomics, ill-informed on "statistical studies
and anecdotal evidence", inverted on the role of "understanding" in
the "New Math " of the 60's (except that it was, indeed, "the
mathematicians" who pushed that misguided effort into our schools) and
tangential about "textbooks", in Singapore or
the U.S. He is quite correct to call for continuing improvement in
teacher education to support more challenging mathematics in every
classroom, but dangerously wrong to downplay the central role of
pedagogy in pre-college math classrooms.
It is quite clear whose prerogatives and perks would be threatened
over time by reforms in education which redefined achievement, and
even intelligence, beyond the narrowed confines which brought Dr.
Schmid and his peers to their positions of privilege. I don't
begrudge them their finely-honed proofs, their sub-sub-fields and
corollaries, - I admire the abstract beauty of
mathematics and the doing of it at that level. But please lets not
strew mathematics professors and long-division worksheets in the path
of my students and millions of others who only in the past decade have
been offered a glimpse of math classrooms in which they can honestly
perceive themselves as thinkers, as problem-solvers, and as active
participants in their new millennium.
-Daryl Anderson '76
Daryl Anderson, '76 is a former high-school science teacher who
stepped-out to run a small software company and later to become a
full-time parent. He has recently returned to education (Syracuse,
M.Ed '98) and has been a sixth grade math teacher for 2 years. One of
his sixth grade classes last year welcomed a local mathematics
professor for a 3-day series talking about "orbits" and modular
arithmetic in a card-shuffling model. It remains to be established if
those orbits were "nilpotent."
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