Sunday, December 31, 2006
New Year's Eve at the Ashmont Grill and High Fidelity
After the excellent dinner we went home to watch videos. We started with High Fidelity, but Barbara had already seen it and I found it terribly boring, so we gave up on it. Oh, well.
Friday, December 29, 2006
Somebody Else's Music
Anyway, this story was clearly inspired by both Lord of the Flies and “The Lottery.” Haddam even makes the occasional explicit reference to one or the other, as well as implicit references such as memories of chanting “slit his throat.” It’s all a pretty grim picture of how teenagers (and people in general?) treat those who are different. I’m not so naive as to think that this portrayal is inaccurate — we have plenty of real-world examples that only reinforce it — but it certainly doesn’t impinge much on my everyday life. And yet... and yet... even at Weston High School one of the major social problems is bullying, according to recent surveys. But surely it is not condoned by the faculty, as it is in the present-day fictional high school of Somebody Else’s Music, where one of the alumnae of 1969 is now principal. (She explicitly blames a victim rather than the bulliers in an incident that I hope is not representative of any real high-school administration.) But then I think back to my own high-school experience, where it was absolutely clear that the faculty turned a blind eye to bullying. And what are present-day consequences of that acquiescence? Who can I remember among the students that I went to high school with in the sixties? The first one who comes to mind is George W. Bush...
Thursday, December 28, 2006
An obligation to vote?
First of all, a bit of background. An initiative petition sponsored by opponents of gay marriage was signed by enough voters to have it sent to the state legislature, commonly known as The Great and General Court of the Commonwealth of Massachusetts. The legal process in Massachusetts is that the measure will be placed on the ballot if approved by at least 25% of the legislators meeting jointly as a constitutional convention. The legislature has twice refused to vote on the measure, presumably because it is opposed by more than 50% of the members but fewer than 75%. So our esteemed governor, Mitt Romney, as part of his efforts to shore up his new-found conservative credentials, brought a case before the Supreme Judicial Court (SJC) to try to force the Great and General Court to vote. (Bear with me now about the names: the Supreme Judicial Court is truly a court; the Great and General Court is the legislature, not a court.) The SJC rightly refused to do so, unanimously declaring that it would be a violation of the separation of powers, but I am mystified by their claim that the legislature does have an obligation to vote. As I say, it all hinges on a question of mathematical logic. IANAL, of course, but the issue seems clear to me. In an article in the Boston Globe, Romney quotes a sentence from the state constitution:
Romney — weighing a run for GOP nomination for president — even sent a copy of the state constitution to all 109 lawmakers who voted to recess the special legislative session.But that’s clearly wrong! You can’t just skip over the word “only”! The Globe article goes on to quote Lawrence Friedman, a constitutional law professor at the New England School of Law, who observed that the language “dictates the form of a vote, but does not mandate a vote.” Here’s an example that shows why the word “only” is so crucial:
“The constitution quite plainly states that when a qualified petition is placed before them, the Legislature ‘shall vote.’ It does not say ‘may vote,’ or vote if procedures permit a vote, or vote if there are enough of the members in the chamber. It says, ‘shall vote.’” Romney said.
Not exactly, according to several legal experts, who say that reading of the constitution is flawed. They say that, for better or worse, lawmakers have acted within the bounds of the constitution, which stops short of ordering they vote up and down on the measure.
“That’s a nicely symbolic way of making his point, but it’s a little empty at the end of the day,” said David Yas, publisher of Massachusetts Lawyers Weekly. “The ballot initiative process is part our Democratic process, but so are the legislative tricks and treats.”
The tussle hinges on the interpretation of a single sentence in the constitution: “Final legislative action in the joint session upon any amendment shall be taken only by call of the yeas and nays.”
Supporters of the constitutional amendment, like Romney, say the sentence is a clear mandate that lawmakers must vote directly on the measure itself.
Suppose I put the following notice at the top of a two-part test:
Calculators shall be used only on Part A.(Yes, it’s a bit stuffy — lawyers’ language, not teachers’ language — but we’re really talking about laws here, not math tests.) If I had omitted the word “only,” it would be an injunction to use calculators on Part A, apparently requiring their use (as in Romney’s reading of the state constitution). It would be silent about Part B, which might or might not allow calculators. But the word “only” changes everything, reversing the logic to create the converse of the meaning; now it allows calculators on Part A and implicitly prohibits them on Part B. Similarly, the state constitution says “only by call of the yeas and nays,” meaning that they’re not allowed to vote by any other process, not that they must vote.
Wednesday, December 27, 2006
Tuesday, December 26, 2006
The journal Science’s “breakthrough of the year” for 2006 is the solution of a century-old math problem. The story behind the solution is quite a soap opera. It includes a Harvard math wizard, a reclusive Russian genius, a one-million-dollar prize, an award-winning journalist, and The New Yorker magazine.The New Yorker article provides a lot of mathematics and considerably more human interest; it is definitely worth reading. Also, check out the Clay Mathematics Institute’s description of the Poincaré Conjecture, a description that almost succeeds in making it understandable.
Sunday, December 24, 2006
The Lincoln Lawyer
Maybe the Globe review explained the title, but if so I didn’t remember. Is the lawyer from Nebraska? Is he somehow connected to Abraham Lincoln? No, it’s just that he drives Lincolns — and yes, that is relevant to the story. Anyway, this novel has a dramatic plot, with several major twists, which may not be as effective as Jeffery Deaver’s but are still exciting. Most important, however, is Connelly’s character development, focusing on the protagonist, who starts out seeming to be nothing but a sleazy, win-at-all-costs defense attorney.
He turns out to be much more complex than that.
You’ll have to read the book to find out how.
Saturday, December 23, 2006
Friday, December 22, 2006
Balance or integration?
We are suffering here from an “either-or” mentality. As any good K-12 teacher will tell you, to get a student enthused [sic] about learning, you need a mix of information and styles of providing that information. You need to provide traditional basics, along with more challenging concepts, as well as the ability to problem-solve, and to apply concepts in real world settings.I used to agree. But my sister, Ellen, has recently convinced me that balance is the wrong goal: what we need is integration of skills and concepts. Here are two recent true stories to illustrate the point:
- Mary buys a large rug and decides to have it shipped home, since it’s too big and too heavy for her to carry it in her car and then get it into the house. So she arranges with the store clerk to have it shipped. They roll up the rug and place it on the scale. Oh, no! It’s three pounds about the maximum weight for this shipper.
So the clerk instructs Mary to fold the rug in half and then roll it up again. “What good will that do?” asks Mary.
“It will weigh less,” replies the clerk.
Mary points out that it will indeed be smaller in one of its dimensions, but its weight won’t change. “Yes it will,” insists the clerk; “if it’s smaller, it will weigh less.”
An ill-advised attempt to explain conservation of mass turns out, of course, to be of no avail.
While the clerk’s misconception is more about physics than math, it’s surely tied in with the general belief that perimeter is always directly related to area. If you “increase” a rectangle from 6-by-8 (perimeter 28) to 3-by-12 (perimeter 30), you have surely increased its area. Right?
- On a recent test, one of my better students, whom we’ll call Matilda, consistently gets slightly incorrect answers in calculating outputs of an exponential function. The instructions said to “round off correctly to the nearest tenth of a pound,” and the calculator gave answers like 3.24312237 and 4.724646398 pounds, but this student got 3.1 and 4.6 pounds respectively. What was Matilda doing wrong? I scratched my head.
You’ve probably figured it out already, but I asked Matilda to show me her calculator work and explain her answers. She indeed got 3.24312237 and 4.724646398, and then explained that the hundredths digit was less than 5 in each case. The rule, she said, told her that when a digit is less than 5 you need to round down, so she rounded the tenths digit down...
Wednesday, December 20, 2006
That would be a pity, because the page-turning plot, the character development, and the vivid sense of place (New York City) all turn out to be much more important than either the noirishness or the financial shenanigans. I can’t say much more without risking inadvertent spoilers. Don’t reject Black Maps because you don’t like noir. Don’t reject it because you don’t like financial mysteries. Just read it.
Monday, December 18, 2006
The Russo-Japanese War (of the condiments)
Saturday, December 16, 2006
I’m really enjoying programming in Scheme. At first I hated it, since it was so different, but now I really like it.I really did overhear that remark.
But I guess it doesn’t exactly count as a “random Chinese restaurant,” since it was at Mary Chung’s, and the table appeared to consist of ten MIT students.
Friday, December 15, 2006
Thursday, December 14, 2006
Misoverestimating minority populations
What’s wrong with this picture?
To start with, how do people think that Bush ever got elected if their perception of American demographics were even remotely accurate? And what’s more troubling is that these vastly inflated impressions of the number of Jews or the number of blacks are all too reminiscent of Nazi Germany, where Hitler played on fears that the Jews were too numerous and too powerful. In fact we have enormous white populations in the American heartland who fear the cities on the coasts and already think that Jews, blacks, and Muslims are both too numerous and too powerful.
In fact, the United States is approximately 13% black, 2% Jewish, and 1% Muslim (depending on who’s counting).
Wednesday, December 13, 2006
“We’ve collected valuable data on the issue,” [High School Principal Paul] Richards added. “One aspect of the work is to examine ways in which the school, as an institution, might contribute to student stress by its traditions, practices, and other actions. The publishing of an honor roll has been identified as a potential contributor to the focus on grades.”So why is it OK to publish athletic achievements— and music and drama — but not to publish academic ones?
Tuesday, December 12, 2006
Monday, December 11, 2006
Homework, oral traditions, and religions
In general, I observe that many students in honors courses seem to be spending too many hours of their life doing homework, whereas most students in college-prep classes seem to be spending too few. While those are overly broad generalizations, they are largely valid, at least at Weston. A majority of honors students — not all, but still a majority — are busy with lots of honors and AP courses, sports, activities, music and/or drama and/or dance. And they still want to get all their homework done. A majority of college-prep students at Weston — again not all — still have the sports, activities, and athletic endeavors, but are taking a less demanding academic load. More important, their homework load is lower and they aren’t so compulsive about getting it done. The consequence is that we end up with an inequitable quantity of homework. It would be interesting to see what would happen if we tried to reduce the homework obligations for honors classes and increase them for college-prep.
The principal timing issue is the possibility of no-homework nights. Personally, I would have no trouble with a blanket policy of not assigning homework on any weekend — how’s that for a radical proposal? — as long as it was announced a year in advance. But I have problems with the idea of proclaiming special-case no-homework nights, such as at the end of a quarter or on a Jewish holiday. Here are somes problems that can arise from prohibiting homework on any given night:
- Many teachers plan (and announce) assignments well in advance. Needing to postpone an assignment can throw a monkey-wrench into plans, especially when we're bumping up against holidays, ends of terms, etc. No matter what policy a school has, teachers need to be given notice for the following year, not the following week or even month.
- In some courses — especially high-level honors and AP classes — the calendar can be very tight, and the course can’t be completed successfully without giving daily homework.
- Schools with a complicated cycle, such as Weston’s eight-day one, have de-facto constraints on when tests can be given in certain courses. For example, Day 6 is the only day when the three sections of our Honors Precalculus all meet — and if Day 6 falls on a Wednesday, when periods are shorter, the test can’t be given until the next Day 6. So that means that it might be necessary to give an assignment on an otherwise undesirable night.
- Part of the oral culture of Weston High School is that some people think there’s such a thing as a “no-homework weekend” at the end of each quarter and over all vacations and breaks. Maybe this is true at other schools as well. Maybe other schools really do have no-homework weekends. I’ve discussed this belief with various people at Weston, and none of us can find anything in the Student or Faculty Handbooks that recognizes such an event. As far as I can tell, it arose because there really used to be no-homework weekends here — but they went away about twelve years ago. Nevertheless, they seem to linger remarkably long as part of the institutional memory here. Many kids swear that a teacher has told them that I “can’t” assign homework at certain times, though when I hand them the Student and Faculty Handbooks they are unable to find any evidence to support their claim. I think it has just become an urban legend at Weston High School. In this connection the religious holiday issue is especially troubling to me. It’s inappropriate for a public school to recognize one religion over another, and yet that’s what happens when we are told not to give homework over a Jewish holiday but it’s OK to give it over a Muslim holiday. To my mind that just promotes anti-Semitism. I recognize the necessity of the legal fiction that the reason we don’t hold school on Jewish holidays and Good Friday is that they are “days of traditionally low attendance” — for example, faculty absences would be significant on Jewish holidays but not on Muslim ones — but blanket homework prohibitions are offensive because they inevitably favor one religious group over another. Of course we need to be understanding and considerate when students have family obligations, but that should be on a case-by-case basis: a Hindu holiday here, a Jewish holiday there, a funeral in another case. Students have all sorts of family obligations, and religious ones should have neither more nor less status than others, especially when religions are treated unequally.
Sunday, December 10, 2006
End in Tears
Saturday, December 09, 2006
Thursday, December 07, 2006
DHS Open House
Wednesday, December 06, 2006
OK, I realize that that isn’t very clear. But it’s hard to be clear about The Keep without giving something away. This book is part Gothic, part mystery, part historical novel, and part dream. I suspect that it’s the sort of book that you will either love or hate, with little possibility of anything in between. If this brief description piques your curiosity, give it a try.
By the way, there are some serendipitous themes in common with The Rule of Four, which I wrote about last week. For example, both of them involve mysterious journeys through underground tunnels, beneath a university in one case and beneath a castle in the other. And both involve a book within a book. But enough said...
Monday, December 04, 2006
Two more railroad shows
In Marlborough I attended the National Model Railroad Association HUB Division, New England Model Train Expo, which had a couple of good layouts and a lot of commercial vendors. Mostly it was the same set of products over and over again, from table to table. There was almost nothing that I hadn’t seen elsewhere. There were too many commercial vendors and not enough artistry. Most disappointing was the lack of realistic detail in the layouts: while I don’t expect strict adherence to prototype (a.k.a. “rivet-counting”) in a show like this, I do think that scenery and structures should at least show a little attention to realism. We need the willing suspension of disbelief, as they say in the English classroom. And did I mention that there were too many commercial vendors?
Roslindale was a different story altogether. The Bay State Model Railroad Museum, a merger of the Massachusetts Model Railroad Society and the Bay State Society of Model Engineers, holds an open house several times a year. Packing four layouts into a small space, they are almost the opposite of what I saw in Marlborough, showing attention to detail at every level. The terrain, the scratchbuilt urban structures, the trolleys, and the weathering of all structures and railroad cars were particularly impressive. But so was everything else, really. Check out the links at the right edge of their webpage under Scale Layouts. And go visit them at the next open house, on March 3 and 4.
Labels: model railroads
Saturday, December 02, 2006
A Prairie Home Companion
Roger Ebert, as he does so often, says it best:
What a lovely film this is, so gentle and whimsical, so simple and profound. Robert Altman’s A Prairie Home Companion is faithful to the spirit of the radio program, a spirit both robust and fragile, and yet achieves something more than simply reproducing a performance of the show. It is nothing less than an elegy, a memorial to memories of times gone by, to dreams that died but left the dreamers dreaming, to appreciating what you’ve had instead of insisting on more.What’s odd is that the reviewers, including Ebert, didn’t perceive the theme of the movie to be death, but to my mind that’s clearly what the theme was. I have just learned that Robert Altman himself said that this movie was about death — shortly before his own death, hmm... — so now I’m all the more convinced.
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