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
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."