Archive for October, 2007

Shame Is Pride’s Cloak

\bullet The Aaronson $25 Prize.
\bulletNatalie Portman Gets Mathy (at M^3).


For seven years in grad school, more or less of course, all the classes I taught—two per semester, as regular as Homecoming—were of the “not for math or science majors” variety. The rest—Calc I and up—were almost entirely taught by the faculty (to be precise: the lectures were; grad students would very often run “recitation sections” and mark papers). Then after I graduated, I was in the show for four years. It was a small college, so the math-major stuff ran pretty seldom, but I did have a chance to teach nearly every course in the catalogue at least once. Real & Complex Analysis, ODE, Linear & Abstract Algebra, all once each; Calc I and Calc III, ditto. But as luck would have it, I was never assigned a section of Calc II: the course in integration.

Since getting sent down to the minor leagues, I’ve adjuncted at two universities and a community college. I’ve again mostly been relegated to the non-major courses, again more or less of course. It spoils the story slightly, but I’ll go ahead and admit that I’ve taught the corresponding material in the calc-for-business-majors version. But it’s just not the same. Because we don’t ask those students to do any of the stuff I considered hard as an undergraduate. And a lot of the point here is that, since I was a pretty lousy student in those days, “hard” for me meant “skip it”, and I never learned how to do the trickier problems. Until now.

Pretty much any other math-head that ever stuck with teaching for anything like this long will have done a lot of this stuff much earlier on. And, who knew. There’s a lot of wildly cool math going on here. All this time I thought I didn’t like analysis. For a long time after turning pro I felt like nobody but a blockhead would work textbook exercises, except for money (or at least some pretense of getting paid; one is allowed on this ethic to tackle problems that are obviously beyond the scope of the given class—but there must be a class). In recent years I’ve sometimes found myself doing math problems as a means of relaxation. Somewhat to my surprise.

But the real joy of this whole deal is getting to work with such talented, hardworking students. There’s a bit of a learning curve on this for me for sure. And it’s pretty clear, here at midterm, that I could have gotten quite a bit more out of this group if I hadn’t learned from a career in remediation to keep my expectations pretty low. Don’t get me wrong here: one encounters some astonishing gaps in the algebra. But it’s cluelessness at a much higher level than one is used to and I’m having a really good time. Thank god I’m a gangsta.

Nov Shmoz Ka Pop

\bullet A post about Planarity (the game), by Suresh Geomblog.

Carnival of Math


“JAWOPPA” means “Just Another Way Of Pushing People Around”—my own coinage (if I remember correctly). I’d be very pleased if this usage caught on … but what I’d really like to see is a lot more recognition of the principle it refers to. Folk wisdom has it that “I’m from the government, and I’m here to help you” means “you’re in a world of trouble now”—this idea could be restated (much less eloquently) as “nearly every government program turns out to be JAWOPPA”.

OK. The main thing was to get it on the record; I’ll link here whenever I decide to drop “JAWOPPA” into future posts. But here’s the reason this post is appearing today: somebody in a recent KTM thread linked to this outstanding source on the notorious “Delphi method”. I was Delphied at my first job in the pros (mid-90’s) and disgusted by it; I only learned its name in recent years.

Fisking Fennell

Yesterday I put up a link to Skip Fennell’s (PDF) “Addressing the Critical Needs of the U.S. Science, Technology, Engineering, and Mathematics Education System”; some remarks follow. Fennell is President of the National Council of Teachers of Mathematics; his remarks of October 10 were addressed to the (US) House Science and Technology Committee. “STEM” abbreviates the fields of study mentioned in the title.

Most of the testimony appears to have been designed to look like empty bureaucratic blather … but if you’ve learned the code words, some of it’s actually sort of horrifying. The entire document is only eight double-spaced pages, so it’s tempting to copy it out altogether. I’m going to fight this temptation, but—since it is so short—I won’t bother to cite page numbers. The passages appear in their natural order; Fennell’s stuff is (obviously) in boldface. I’m going to play it pretty fast and loose with capitalization and punctuation despite my best instincts since I don’t know how to make the WordPress editor keep from messing it up if I do it right.

NCTM believes that creating a coherent STEM curriculum and placing a well-qualified, highly effective teacher in every STEM classroom are critical goals[.] “Coherent” is the big idea here: the current incoherence is widely blamed on local control by school boards. “Every…classroom” is the type of wild exaggeration one learns to expect; apparently this kind of thing annoys only me. But I’ll mention “highly effective teacher”: it’s the famous Lake Wobegon effect. If “highly” is to mean anything at all, then only a minority of teachers can be “highly qualified”. In a national system where every local school board is empowered to decide what is taught and who does the teaching in every classroom, there are daunting, but not insurmountable, challenges to achieving these goals. I believe Fennell is pre-emptively excusing the inevitable failure of the Council (whose creation he’s advocating) to bring about any substantial change in (what all sides seem to agree is) the disaster that is American Math Ed. Moreover, I believe that he doesn’t even really want to bring such changes about; the status quo is working perfectly well for him (and NCTM).

As members of the National Science Board … have noted, a child’s first—and perhaps most—infulential teacher is a parent. Any call to action—small or large—must recognize the crucial role that parents play … Without parental support and involvement, it will be very difficult to convince young people of the urgency and importance of STEM literacy … This might look like empty piety, or just another pre-emptive excuse for “failing” at making changes, but this post in KTM nails it: the current system, by design, fails to instill basic math skills in most of the victims students; parents who are determined to have educated children must resort to other resources to accomplish what is ostensibly the mission of the public schools. Let me qualify that; “by design” is my interpolation and shouldn’t be attributed to Barry G. or anyone else at KTM; most of ’em probably don’t even believe it [yet]. Anyhow, it appears that Mr. Fennell likes having things this way and isn’t even going to pretend to try to change it.

Just as parents must do their part, educators and lawmakers must do what we can to reach beyond the “best and “brightest” students … it is important that we truly reach all students and meaningfully address the persistent problem of achievement gaps in education. Addressing “achievement gaps” sounds like a good thing until one comes to find out that the approach favored by “reformers” like Fennell is to lower the high end of achievement rather than raising the low end.

(…The “National Action Plan” is introduced…) Implementing all aspects of the plan could produce significant—and, more important—enduring, change in STEM education … Wow. Does he mean to have admitted that he’d rather have enduring but insignificant change than significant but fleeting change? Probably not; usually in politics you have to look at the opposite of what somebody says to find out what they really think … Time and again, research has shown that the most important factor in student achievement is the quality of the teacher. “Research” presumably deserves the usual squarequotes (I used to subscribe to the NCTM’s Journal for Research in Mathematics Education, so I know what I’m talking about here). We endorse all efforts to ensure that students are taught by well-qualified and highly effective teachers. While working tirelessly to ensure that teachers continue to be pushed around by clueless timeservers to ensure that most of the best will soon quit. Thanks for your endorsement.

All teachers must understand how students learn mathematics. The must know how to plan, conduct, and assess the effectiveness of mathematics lessons … invest in the particular culture of their students and school … dedicate time and energy both inside and outside the classroom .. are adept at actively engaging students of diverse backgrounds and strengths … I don’t tell you what to invest in, buddy. More to the point, the “diversity” card here refers to the technique of forbidding schools to separate out the better-prepared students for higher-level lessons. My sources tell me that this strategy (for learning-prevention) is working quite well. This seems like as good a time as any to mention that setting up high ideals as if they were actually part of one’s job description is a classic management technique for blaming workers when the system fails. The “best” examples occur when ideals are in conflict; for example,
“grade inflation is bad” but “low pass rates are worse”. Damned if you do, damned if you don’t.

OK. Burning out. The rest, for now anyhow, is left as an exercise. Back to reading everybody’s else’s stuff.

She Loves You Yeah Yeah Yeah