Archive for the ‘Education’ Category

I’ve recently had a series of discussions with a friend of mine who is an advisor on education policy to a member of Congress and a TFA alum (from a particularly hard-scrabble school in Philadelphia), and in general has an extremely good sense of what is possible both in schools — classrooms and administrations alike — and in the federal government.

I will say right now that this post could’ve been shorter if it simply reported the conclusions to which it eventually comes. I am instead presenting it in a more historically accurate sequence because I believe that the process of reconciling the two views below gets at the real work to be done in education policy.

In our discussions, we have disagreed about the appropriate focus for education reform  — and for the purpose of this note, I’ll restrict myself to mathematics education, both for concreteness and because it is arguably the biggest challenge.

My position in these discussions is related to the fact that effective mathematics teaching requires an actual interest and yes, academic preparation, in mathematics — one cannot effectively teach what one does not thoroughly understand. Such preparation is so sorely lacking in public American mathematics classrooms that it could make you depressed if you didn’t know that wouldn’t do you any good.

There is a whole host of studies involving value-added data — eg. the citations in this extraordinarily clear report [pdf] from the Education Trust — that support teacher effectiveness as the single biggest determinant of student achievement, especially in previously academically struggling students. I concluded that nothing less than a renewal of the mathematics teaching force will provide the mathematics education American students deserve.

My friend, who understands the teacher union side of education policy very well, responded that any such proposal will be viewed as unmitigated antagonism by the unions; furthermore, and more importantly, that the current teaching force — even the part that is demonstrably ineffective — has something valuable to contribute: namely, the willingness to show up. She points out that teachers in low-income, low-performing (and evidently hard-to-staff) schools have in that way demonstrated a key requirement of their very difficult job.

This might sound like the kind of false praise with which a fellow at the American Enterprise Institute might begin a hilariously Ayn Rand-ish attack on teachers unions, but if you think about it for a second, showing up at some of our worst schools is not at all trivial.

Will finish this soon (have to run now)…


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This [pdf] is the note on that remarkable series of lessons I mentioned – it has pictures, which is why it’s not posted directly here. The link takes you to the draft currently under review for publication in The Mathematics Teacher.

Update (3/16/10): The Mathematics Teacher inexplicably did not accept the note for publication. In my view, this is just evidence of how revolutionary and ahead of its time the piece is, so it should just make you want to read it more.

Here are the first two of its three concluding paragraphs, not so much as a spoiler as for a sense of the article’s substance and approach (a sort of abstract/excerpt hybrid):

“…the students had the exhilarating and empowering experience of really doing mathematics – of stepping outside the realm of formulaic exercises with pre-ordained answers, to the dark rooms Andrew Wiles described in recounting his work on Fermat’s Last Theorem, where one has no idea where the furniture is, let alone the light switch, until one feels his way around.

I believe it is extremely valuable for students to see the role that creativity plays in mathematics; pursuing open problems allows the special brand of creativity that is the mathematician’s trade to step into the classroom, something that happens less often than it might. But there is also a more pedestrian benefit to these open problems, one perhaps even more important: seeing mathematics’ influence on creativity. Yes, students are asked to be creative in most of their classes; but the rigor and discipline imposed in a well-defined open problem demands intense creativity within a precisely-defined structure. The skills required to formulate creative solutions in a world ruled by highly precise definitions are invaluable in science, history, and the ability to write cogent and incisive arguments. Exposing students to open problems makes them better not just at mathematics, but all subjects with an analytical component.”

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