Thursday, January 31, 2008
How do you read email when there's so much spam?
I no longer trust my email. If you send me mail, I will probably receive it, but I’m far from certain that it won’t be lost in the vast deluge of spam.I definitely rely on mail.app, and mail almost never gets “lost in the vast deluge of spam.” Here’s my setup:
Meanwhile, Eudora is obviously past its sell-by date; my spam bucket overflows every month, and apparently Eudora crashes when it has more than 32,768 messages in a mailbox. With a mere thousand spam messages a day, that’s suddenly a very real possibility.
Do grownups rely on mail.app? Is there another option?
- Most spam gets caught by spamassassin on the server, which sends it on to me appropriately marked.
- I then have a mail.app Rule that puts such messages into my SPAM mailbox without ever appearing in my Inbox.
- Spam that gets through the spamassassin filter unscathed might then be caught by mail.app’s Junk Mail filter. In that case it gets automagically routed to my Junk mailbox by another mail.app Rule.
- A tiny amount of spam manages to evade both filters. I manually mark it as Junk.
- I have separate Rules that delete all mail over a week old from both the SPAM and Junk mailboxes, so that I have a chance to look them over if I wish. I have almost never had any false positives, but they do occur every once in a while.
|Spam messages caught by spamassassin on server||212|
|Spam messages caught by mail.app’s Junk Mail filter||14|
|Spam messages that avoided both filters||2|
Wednesday, January 30, 2008
How about an Obama/Bloomberg ticket?
So what’s wrong with Obama-Edwards? Personally, I think Edwards is great, but the combo would be deficient is several ways. Both of them are lawyers, both are one-term senators (well, technically, Edwards is a former senator, but still), neither has much executive experience.
The Obama-Bloomberg combination would add executive experience, business experience, a lot of money, and the totally cool idea of a ticket consisting of a black candidate and a Jewish candidate. Yes, some people would be prejudiced against this pairing, but wouldn’t such people refuse to vote for Obama anyway? And besides, Bloomberg would add the diversity of an Easterner who was a life-long Democrat, ran successfully for Mayor of New York as a Republican, and is now an Independent. Furthermore, Bloomberg is from Medford!
It’s not that I’m actually advocating such a ticket, but I wonder that no one seems to be considering it.
Monday, January 28, 2008
Courtesy: a double standard?
First of all, let me make it clear that I have no dog in this fight. Since I always bring my lunch to school, I have no need to stand in the cafeteria line and haven’t done so for about eight or nine years. When I did, I certainly wouldn’t consider it my prerogative to cut in line. But clearly some of my colleagues feel differently. After all, we have responsibilities. We’re busy and stressed and can’t afford to waste time.
So what’s going on here? My second point is that teens are exceptionally sensitive to double standards. Surely we all remember that when we were in high school and college we couldn’t abide the idea of two different moralities, one for adults and one for us. That’s why I have no trouble with the text. Yes, we should avoid cutting in line.
And yet...and yet...here is my trouble with the subtext: If people interpret it to be a claim that students and teachers should be held to the same rules, they are oversimplifying, for the situation is more nuanced than that. It’s not just a matter of morals and ethics. Yes, we “set the tone and serve as personal examples of respectful behavior,” but the specifics aren’t so simple. On the one hand, adults should live by the same broad standards as teens: no cheating, no lying, no disrespectful words or behavior. On the other hand, it would be foolish to pretend that we are in equal positions. Teachers have an authority and a responsibility that are qualitatively different from the roles of students. For example, it’s sometimes necessary for a teacher to tell kids to stop talking, but it would be inappropriate and rude for a student to tell a teacher to stop talking. The situation just isn’t reversible.
Some students at Weston are rude and presumptuous. A few treat teachers as their servants. But the majority of students are remarkably polite and respectful. I continue to be amazed at how many of my students say thank you as they leave the classroom. And a clear majority of them say thank you when I hand them a test! (It’s not that they’re truly thankful, but more that they have learned from their parents that they should say thank you when handed something. Politeness works. Courtesy helps.) Yes, it is important for us to act as models of courtesy in these regards. But we are not equals and should not pretend to be.
Finally, on a related subject — but perhaps not an identical subject — I have sometimes been told that I talk to kids in just the same way as I talk to adults. I tend to talk to 10-year-olds, 15-year-olds, and 25-year-olds in pretty much the same way. To me, that’s a matter of respect and courtesy. But I was astonished a few years ago when two of my 15-year-old students interpreted this behavior as talking down to them! I still don’t fully understand it, but apparently they thought I was being discourteous by treating them as adults.
Sunday, January 27, 2008
Surely the Globe can't be wrong! But the oldest house in Boston is actually in Dorchester, not in the North End
- A sentence begins this way in today’s Boston Globe:
The grounds of the Paul Revere House, Boston’s oldest building and a historic Colonial landmark,...
- The Paul Revere House was built in 1680 (plus or minus a year or two).
- The Blake House (in Dorchester) was built in 1648 (plus or minus a year or two).
- Ergo, the Paul Revere House is not Boston’s oldest building. The Globe was wrong.
- February 17, 11:00 AM to 1:30 PM.
- March 9, 11:00 AM to 1:30 PM.
- April 6, 11:00 AM to 1:30 PM.
- May 18, 11:00 AM to 1:30 PM.
- June 8, 11:00 AM to 3:00 PM.
- July 13, 11:00 AM to 3:00 PM.
- August 10, 11:00 AM to 3:00 PM.
Friday, January 25, 2008
The Witch of Agnesi
Well, the Witch of Agnesi is actually not the name of a witch, nor is Agnesi a town in Italy, as you might suppose. We need to digress for a moment to indulge in a brief math lesson, and then we can return to reviewing Robert Spiller’s mystery novel. Consider a curve that is described by the following equation:
If, say, we let a = 2, its graph looks like this:
And why, you may ask, is this curve called the Witch of Agnesi? Well, therein lies the solution to the mystery.
Some students erroneously think that the name comes from the shape of the curve, which they somewhat dubiously imagine looks like a witch’s hat. Others think — and have thought over the centuries — that the curve is so-called because it was first discovered by Maria Agnesi, who was a witch.
Those people, at least, are half right, or maybe one-third right. The curve was actually discovered by Fermat, but it was published by the great Italian mathematician Maria Agnesi, who published it in 1748 in a book that MathWorld calls “the first surviving mathematical work written by a woman.” But the name of the curve — the key to solving the mystery — comes from a mistranslation, an event that warms the heart of anyone who has studied linguistics. Here we have slightly varying accounts. In the mystery novel, Spiller’s protagonist Bonnie Pinkwater (a math teacher, of course) explains the mistranslation to her precalculus class this way:
“The famous French Mathematician [sic] Pierre de Fermat...had given the curve the Italian name versiera, which simply means a curve that turns.... Maria used the same name...when she spoke of the curve in her Analytic Institutions. She embellished and extended Fermat’s ideas, making large portions of the Mathematics her own.Passing over the discrepancy between Fermat (last name) and Maria (first name) — does that remind anyone of Obama and Hillary? — and the odd capitalization of Mathematician and Mathematics, we note how a single letter can make a big difference. But it’s still surprising that a linguist would miss an initial a- of all things. MacTutor provides the explanation: just remember to quote the noun along with its preceding definite article. It’s easy to mistake la versiera for l’aversiera.
“Now the scene shifts some fifty years hence. Maria Agnesi is dead. John Colson, a British Mathematician and linguist at Cambridge University, decides to translate Analytic Institutions into English. He did an admirable job except for this one word.”
Nex to versiera she wrote aversiera and underlined the new word.... “He mistook versiera for this almost identical cousin...with disastrous results.... The word aversiera means bride of the devil.”
Unfortunately, however, Spiller himself may have gotten at least one of the words wrong. Then again, maybe not: as sources differ on the details (how appropriate that the devil is in the details in this case). The initial name for the curve is versiera according to Spiller, versiera according to the reliable website MacTutor History of Mathematics, and averisera according to the equally reliable website MathWorld. Hmmm... And the erroneous reading by Colson was aversiera according to Spiller, aversiera according to MacTutor, and avversiera according to MathWorld. So maybe Spiller is right. This bears further research; stay tuned.
Anyway, I seem to have gotten off the subject of reviewing the novel. You can see now why I just had to check the book out of the library and read it. In general it’s a competent story that fits squarely into the traditional genre of the amateur private detective with a sidekick. As is traditional, there is a series of murders (or perhaps, being a math teacher, I should call it a sequence of murders; no summation is involved). As is traditional, there is effective use of red herrings. The plot is effective, even though it slows down in the middle of the book. The account of various Wiccan characters is sympathetic without being patronizing. There is a small amount of character development and suspense; one student, in particular, turns out not to be what he first seems to be — always a useful object lesson for teachers. The sidekick is altogether too much of a Sensitive New-Age Guy; I suppose he’s just as convincing as the nerdy science teacher in Academy X, but surely it’s not realistic to have a science teacher who’s a more sympathetic character than a math teacher. :-) The setting in eastern Colorado is convincing without being obtrusive. Finally, the ending is an effective surprise.
Altogether a pleasant read, as they say — even though there isn’t nearly enough math in it.
P.S.: I suppose this seems to be yet another in my continuing series of reviews of novels that relate to high schools, but there’s an important difference between this one and the previous ones. In those earlier cases the school itself was a character in the novel, often in some sense the main character and usually an elite school. But Spiller’s novel is only incidentally school-related, and it’s clearly a very mixed-income and low-income public school, complete with students and teachers who live in trailer parks. Students are victims, and the protagonist is a teacher, and almost all of the characters are teachers, students, or parents — but it’s still not a book about a school, nor is it meant to be. Like most novels, it’s a book about people; the protagonist just happens to be a math teacher.
Thursday, January 24, 2008
“Default, dear Brutus, is not in our stars, but in ourselves...”No, that doesn’t seem quite right. I don’t think Shakespeare had Cassius talking about defaults, did he? But it’s what I think of when we just assume that defaults are somehow fated instead of being a decision that we ourselves make.
Now I’m not talking about any of the first three familiar definitions of default as given by the American Heritage Dictionary:
1. Failure to perform a task or fulfill an obligation, especially failure to meet a financial obligation: in default on a loan. 2. Law Failure to make a required court appearance. 3. The failure of one or more competitors or teams to participate in a contest: won the championship by default.No, I’m talking about the fourth definition, which is split into two specific versions:
4a. Computer Science A particular setting or value for a variable that is assigned automatically by an operating system and remains in effect unless canceled or overridden by the operator: changed the default for the font in the word processing program. b. A situation or condition that obtains in the absence of active intervention.Definition 4a, of course, is merely a recent narrowing of definition 4b, which is the more general case.
So what does all this have to do with real life? I thought about it when I listened to people describing Barack Obama as “black with one white parent.” Why not “white with one black parent”?
Perhaps it’s because white is the default in our society. If white is the absence of any other color, then a person of mixed race is automatically considered to be the non-white component. It’s not logical, but that’s how the default works. We have a fair number of mixed-race students in Weston — probably it’s a comfortable community for mixed couples — and it’s interesting to see how they are identified. For the purposes of record-keeping the idea is that people will self-identify, although it’s considerably muddied for those under 18 since it’s actually the parents who do the labeling. If a white mother and Asian father label their daughter as white, that situation is very different than if the daughter herself picks that label. My unscientific claim is that the community has a whole considers mixed-race person to be black if they’re half black and half white, Asian if they’re half Asian and half white, Latino if they’re half Latino and half white. I don’t entirely understand what happens if the default race isn’t present; a small amount of evidence suggests that a person who’s a black-Asian combination is considered black, but I don’t really know about other combinations, and I don’t have the faintest explanation for what’s going on in the completely non-white combos. In the case of white being the default, the only real explanation is racism, even though it is unconscious racism.
Returning for a moment to the question of Barack Obama... here is a pair of questions and answers from an interesting interview in this past Sunday’s New York Times Magazine featured Obama’s half-sister, Maya Soetoro-Ng, who is half white and half Indonesian:
Do you think of your brother as black? Yes, because that is how he has named himself. Each of us has a right to name ourselves as we will.
Do you think of yourself as white? No. I’m half white, half Asian. I think of myself as hybrid.
Wednesday, January 23, 2008
Collaborating with colleagues
- For many years now in Weston we have had regular team meetings of teachers who teach the same content. For example, everyone who teaches college-prep Algebra II meets once every eight days for an hour. But we haven’t made one of Saphier’s suggestions part of our regular MO, probably because nobody had ever articulated it for us:
Come into a meeting prepared to present what the cognitive confusions are.This idea is much more useful than simply saying, “Too many kids don’t understand logarithms; we should give them more practice and then schedule a retake.” (This is, in fact, what we actually said.)
- One difficulty in combining EA with DI is how to handle the logistics when you have to pull six kids aside to work on reteaching logarithms. The rest of the class needs to be productive during this time. Saphier had several suggestions for letting this happen.
- According to Saphier’s research:
The most successful schools are deeply collaborative; the prime place for our own learning is the workplace.Contrast this POV with what my colleagues and I believed when I was teaching back in the ’70s: you shut the door and are in solitary control of your own classroom.
- Combining these two previous thoughts, we have the following observation:
Error analysis and collaboration can seal the cracks through which a lot of our kids fall.Too often we pay lip service to the idea that we want all students to succeed, but we don’t know how to get that to happen. Maybe EA and collaboration will be the key.
- In team meetings, according to Saphier, members show the following characteristics:
Makes sense to me.
- They are non-defensive.
- They have open, strong, debate.
- They hold each other accountable for important norms.
We then split up into multi-school teams, the same groups of a dozen or so teachers in which we had been meeting on previous PD days. It’s always refreshing to exchange ideas with colleagues whom we never otherwise see, such as a reading recovery teacher from the primary grades, a regular fifth-grade teacher, and the Metco liaison from the middle school.
After lunch we met by department. The math department split up into groups of five (each group containing both middle- and high-school teachers), in which we did EA by examining student work in a variety of a courses. By looking at the same problem as attempted by a few dozen students, we can learn something about their apparent misconceptions. The most striking observation was that students in grades 8, 10, and 12 can be making exactly the same mistake. It all reminded me of something I learned from a teacher with many years of experience back when I was a new teacher in my first semester:
Don’t just look at the question that a student is answering incorrectly; figure out what question the student is answering correctly, even though it’s not what you were asking.P.S.: Today’s quiz: Without looking back, how many two-letter acronyms appeared in this post?
Tuesday, January 22, 2008
Firing a teacher, part two
One of his students wrote this:
The parents just wanted the teacher to be warned not to do something like that again.Another wrote the following [please pay no attentioin to the texting abbreviations and seventh-grade version of English]:
i think every single person in our grade needs to stand up for themselves and share our feelings about our teacher leaving. DUCT TAPE?! puhlease. it wasnt duct tape. everyone is just making a big deal but no one knows what rly went down unless you are us.. so stop making guessess and learn to be a news team. HUGGINS FOREVER!
Labels: teaching and learning
Monday, January 21, 2008
I'm delighted to learn that I was wrong
I have to admit that it will appeal strongly only to readers who are fascinated both by cartography and by railroads, and mostly to those whose railroad interests are focused on urban transit. I am a member of that small band.I’m delighted to learn that I was wrong about the narrowness of the audience. The author has written to me from across the Pond and has let me know that “it reached number 110 on the general Amazon Sales Ranking and as high as Number 1, 2 and 5 in categories like Mass Transit, Atlases and Travel books.” That’s wonderful!
Sunday, January 20, 2008
Adults and math: Who needs a formula?
A participant in the HO Railroading Yahoo newsgroup asks the following:
Is there any known formula for converting a N-Scale track layout to a HO track layout?Where do I begin in explaining why this question bothers me so much? The most obvious reason is the writer’s inability to deal with fractions, even when he has a computer and therefore a calculator; he clearly can’t figure out what operation to perform on 1/87 and 1/160. Some of my ninth-graders in Weston couldn’t do that either, so I suppose it should neither surprise me nor bother me. But the main reason the query upsets me is the opening five words. “Is there any known formula?” Most formulas are the wrong way to go, as they tend to replace thinking with algorithms. Sometimes we do need formulas, but why look for one here? Surely an experienced model railroader knows that multiplying N-scale lengths by 160 gives you real-life scale (prototype, as we call it). And then dividing the real-life lengths by 87 gives you HO scale. Who needs a formula?
Saturday, January 19, 2008
Transit Maps of the World
The full title of the book is Transit Maps of the World: The World’s First Collection of Every Urban Train Map on Earth. Wow! Author Mark Ovenden and editor Mike Ashworth have done an amazing job of compiling the comprehensive collection described in the subtitle. The frontispiece promises beautiful cartography within, and the book delivers on the promise. (But there is one small glitch. What the frontispiece shows is a stylized map that at first glance looks like the London Underground, but a second glance shows that the “stations” are really cities. These are all the cities represented by maps in the book, and they’re linked together by fanciful subway lines. The commentary says this:
This captivating diagrammatic view of the cities included in this book is in the style of Harry Beck’s classic London Underground diagram. It was conceived by the author and executed at LS London by Alan Foale, who is responsible for updating the London diagram. It is also available as a full-size wall poster from London’s Transport Museum shop or online.But, alas, I searched through the London [no “’s”] Transport Museum site to no avail.)
Anyway, among the treats awaiting the specialized reader are beautiful contemporary maps from hundreds of cities, historical maps for many of them, great photographs of stations and transit vehicles, and crisp explanatory text. Among the most attractive maps are those of obvious cities (e.g. London, New York, Boston, San Francisco, Montreal), those of less obvious cities (e.g. Madrid, Budapest, Barcelona, Hamburg, Hong Kong, Osaka), and those of thoroughly unobvious cities (e.g. Bucharest, Kiev, Prague, Cairo, Stuttgart). The blurb from The Guardian points out that the explanatory text provides a lot of background on the history of mass transit and remarks that this book is “the ideal gift for the most challenging relative.” Well, I suppose...as long as your most challenging relative is an urban-transit-and-cartography enthusiast.
Unfortunately a few of the maps did not scan well and are decidedly fuzzy. If they were printed in a larger size they might have been easier to read, but then I suppose the fuzziness would have been more obvious.
Finally, as I observed in a much earlier post (two and a half years ago in fact), my interests in cartography and model railroading share something with my interests in certain parts of mathematics: representation. Although Transit Maps of the World doesn’t deal with model railroading per se, the two topics are deeply intertwingled for those of us who model urban transit. And transit maps are especially interesting for math teachers and mathematicians, not because they are scale model of reality (similar, as we say in geometry) but precisely because they are not scale models. Riders almost always want a map to be topographically correct, but they don’t want it to be made to scale. Indeed a scale map of an urban transit system would be nearly impossible to use: either it would be much too tightly crammed together in the downtown area, or the entire map would need to be much too big. Applied geometry isn’t as simple as they taught you back in ninth grade (or tenth grade, if you’re above a certain age).
Thursday, January 17, 2008
Mathematicians are Platonists
From time to time, some of my students object when I say that the Pythagorean Theorem or prime numbers or the quadratic formula or whatever was discovered. They want me to say that it was invented. And there’s a profound philosophical disagreement buried in that distinction. Here’s an excerpt from Holt’s review:
Mathematicians believe in God at a rate two and a half times that of biologists, a survey of members of the National Academy of Sciences a decade ago revealed. Admittedly, this rate is not very high in absolute terms. Only 14.6 percent of the mathematicians embraced the God hypothesis (versus 5.5 percent of the biologists).Perhaps the reason that a majority of students view mathematics as a meaningless game is that they don’t believe in its reality: if you’re inventing a formula or a theorem, you could just as well invent a different formula or theorem. But those of us who are Platonists believe that mathematical objects are truly out there, waiting to be discovered. If and when another intelligent species is discovered on another planet, they too will have the same prime numbers, an equivalent quadratic formula, and so forth. (Of course it’s likely that they will have discovered things that we haven’t, and vice versa, but they won’t have contradictory findings; 42 won’t turn out to be prime on Gliese 581c.)
But here is something you probably didn’t know. Most mathematicians believe in heaven. Not a heaven with angels, but one populated by the abstract objects they devote themselves to studying: perfect spheres, infinite numbers, the square root of minus one and the like. Moreover, they believe they commune with this realm of timeless entities through a sort of extrasensory perception. Mathematicians who buy into this fantasy are called “Platonists,” since their mathematical heaven resembles the realm of the Good and the True described in Plato’s Republic. Some years ago, while giving a lecture to an international audience of elite mathematicians in Berkeley, I asked how many of them were Platonists. About three-quarters raised their hands. So you might say that mathematicians are no strangers to belief in the unseen.
There’s a slight twist to this issue, apparent to anyone who has explored non-Euclidean geometry. Isn’t there a contradiction between Platonism and the knowledge that other valid geometries can be formed by varying the Euclidean postulates? Anyone who has studied enough math knows that the conclusions of math are contingent: the Pythagorean Theorem and other familiar theorems of Euclidean geometry will change if the postulates change. More on this apparent contradiction later on...
Wednesday, January 16, 2008
Life imitating art: Academy X & Firing a teacher, part one
The big advantage of being learning disabled was extra time — twice the time to take all of your tests, including, most importantly, the SATs. The Educational Testing Service, gatekeeper to the promised land, had decided to stop reporting which students received extra time, setting off a mad rush by students to have themselves classified as learning disabled. All it took was several thousand dollars and compliant testers. In the past few years, almost one third of the school had developed some sort of learning disability. Considering that roughly half the students at Academy X went to an Ivy League school, one way of looking at it was as an inspiring story of kids overcoming their handicap to achieve success. I myself wouldn’t have minded being designated learning disabled if that allowed me to take twice as long to return papers.The details are different — for instance, we have very few kids with 100% extra time (but a great many with 50% extra), and we certainly don’t have half of our kids going to Ivy League colleges — but otherwise it definitely applies to Weston.
And then there’s this paragraph:
So many parents were willing to let their children call in sick on days when they were supposed to take tests or hand in papers that it often seemed as if the plague swept the school at the end of each term. And it was an open secret that, in addition to the usual recreational drug use, many students took drugs to boost their academic performance. The lucky ones had Ritalin prescriptiions, but it wasn’t too difficult to find a friend who could provide one of the variety of pills that helped you concentrate better for a test or stay up all night to finish a paper.... And for many of the girls, the pills had the added benefit of acting as an appetite suppressant, thus killing two birds with one stone.Many of us here refer to Weston as Lake Wobegon; I’ve even done so myself in this blog. So I was not surprised to read this description of Academy X:
The whole system was geared toward a constant adjustment upward, a New York version of Garrison Keillor’s Lake Wobegon where all children were above average. When the school gave out prizes at the end of the year, a virtual army of students stood in line to receive them. It took the sort of persistent lack of effort that was itself an achievement to stay off the awards platform.Some excerpts don’t apply here quite so literally but still evoke the right flavor. For example, I’ve heard the following sentiments in the Weston Public Schools, all except the nursery-school reference:
I am part of an elaborate system designed to ensure that children end up in the right nursery school so that they can attend the right elementary school so that they can gain entrance to the high school Ivy League so that they can win admission to the actual Ivy League. What happens after that seems to be superfluous.Certainly the religious issues are different:
Religion still counts here, although not in the mushy way of Protestant denominationalism. Harder, deeper divisions. Jew or Gentile. The problem is that these categories quickly subdivide, creating added complexities. Are you a practicing Jew, proud of your cultural heritage, perhaps even Orthodox? Or a self-hating Jew who does everything but hide the menorah behind the couch?But then there are the signs of wealth, which are probably comparable:
A family portrait from last Christmas will impress only your aunt Millie. But a family portrait from at least three generations back shows an admirable grip on the top rung of society. A home in the Hamptons is good. A compound on Martha’s Vineyard is better.Some descriptions are clearly not meant to be taking literally — at least I think not, since Academy X is definitely a satire. For instance, the spirit of the following paragraph rings true at Weston, even though the specifics don’t apply here:
Many teachers at Academy X played the game. Some recommended poorly performing students to their colleagues for tutoring at one hundred dollars or more an hour and then found remarkable levels of improvement in their work. Others gave all As, unless a student was really awful and insulted the teacher, in which case he or she was punished with an A–. These teachers were then rewarded with awards, endowed chairs, yearbook dedications, not to mention a whole array of end-of-the-year “gifts” from grateful parents — box seats to ball games, weekends in the Hamptons — the list was limited only by the ethical code of the teacher, which is to say that it was hardly limited at all. Those who did not play the game were earned or threatened in a variety of ways — perhaps a meeting with a dean to remind the teacher of a student’s “special needs” or a letter from a parent on the legal stationery of the parent’s firm warning vaguely of “further action.”Like all stories, Academy X has a beginning, a middle, and an end. I was grabbed by the beginning, which proceeds quickly and amusingly. The story then slows down in the middle and threatens to bog down in a subplot about the narrator’s love life. Some other subplots are too predictable in this section of the book, making the slow pace even slower. But after that the book picks up with a rousing and unpredictable ending, which illustrates why you should fight false accusations rather than quietly resigning. (In this case, the accusation is a male teacher’s worst nightmore: a female student puts on a torn shirt and accuses the teacher of sexual harassment, all because he discovered that she had plagiarized an important paper.) I have no hesitation recommending this book.
So why does the title of this review refer to “life imitating art”? So far it looks like an ordinary case of art imitating life, doesn’t it? It appears to be somewhat like those Law & Order shows where they claim that the story isn’t based on real events even though the viewers know that it is (for example, the recent “Dr. Death” episode, officially named “Called Home”). But there’s a twist here: soon after the book came out, Trees was fired from his job at Horace Mann. Was it because of the novel? Who knows? Trees has now sued the school, and his suit includes the same phrase that I used (too hard to resist, I guess). His lawyer asserts that the headmaster actually admitted that the firing was because of the book, not because of job performance. Let’s see how this plays out. (Private schools have a lot of leeway in firing teachers, as long as it’s not based on a prohibited category, such as race or religion.)
As a footnote, it’s interesting to see the reactions to this satire inside and outside of Horace Mann. The headmaster refused to allow the student newspaper to publish two letters of support for Trees (even though New York’s Governor Spitzer’s daughter is the editor of the paper, and his wife is on the Board of Trustees). And there was the following reaction from another school:
“I think this is the biggest self-righteous, arrogant traitor walking the face of the earth,” a member of the board of trustees at the nearby Riverdale Country School, Victoria Goldman, said. “He's sending up the entire community that he works with, and that takes nerve.”By the way, the chapter titles of Academy X make an amusing list:
- Brave New World
- Great Expectations
- All the King’s Men
- Breakfast at Tiffany’s etc.
Tuesday, January 15, 2008
I have comments turned off because they tend to generate flame wars and spam. Adam’s blog is meant for general discussion, but as a public-school teacher I can’t be in that position. You can imagine what would happen if somebody posted something inappropriate and it appeared on my blog (even though I wasn’t the author of the comment). No schoolteacher can allow his or her blog to become a public forum.Coincidentally, I received an interesting rant by email in response to my post from yesterday concerning Huckabee’s so-called Fair Tax. My point had simply been that I wanted to illustrate one of the widespread errors that adults make in applying middle-school math, but it engendered a long rant from one of Mike Gravel’s campaign directors. [How weird is that? Politics makes strange bedfellows, including the two Mikes.] He had a point, at least a political and economic point, but it had little to do with the math, which, as he himself pointed out, he apparently understood. My point was simply that an n% tax is a standard concept from a mathematical standpoint, even if there might be motivation for redefining it for political reasons. While this writer’s rant wouldn’t have been unacceptable on the “public school teacher” grounds that I cited above, I still can’t open my blog to unmoderated comments, and I don’t have time to moderate.
Monday, January 14, 2008
The fuzzy math of Huckabee's FairTax
On Friday, the first of two days of campaigning in Michigan, Huckabee used the Detroit Economic Club as a platform to push his support for the so-called fair tax that would replace the income tax with a 23 percent national sales tax.This figure of 23% is being thrown around a lot — you’ll find it all over the Web — so you may wonder how 30% magically became 23%. Here’s how:
Let’s suppose you buy a product for $100.00 and pay a $30.00 tax; that would be a 30% tax rate, wouldn’t it? Well, it would be 30% in my classroom, and even on the MCAS, so where does 23% come from? It’s simple: $30.00 is 23% of $130.00. Let’s apply that same theory to discounts: Apple offers a 10% discount on a new iPod if you recycle your old one, so they charge you $134.10 for a $149.00 model. But under the Huckabee model they should be allowed to call it an 11.1% discount, since you saved $14.90 out of an eventual price of $134.10. It’s nice how percents can be slippery, isn’t it?
Percents are always calculated on the original amount, regardless of whether we’re talking about taxes or discounts.
Sunday, January 13, 2008
Stay off the main drag
This was not a random shooting.But surely if you want to get people scared and worked up, it would be much scarier if it really were a random shooting. Nobody is safe when violence is random. If it’s targeted, it’s less likely to affect the general public.
In any case, the remedy is supposed to be to stick to our safe residential streets and not venture out onto big, bad Dot Ave. In reply, a calmer community activist pointed out that that’s the worst possible way to keep Dot Ave safe: if we cede it to the gangs, if good people stay away, then it will become the territory of the violent. We need more sunshine, not more hiding.
Saturday, January 12, 2008
Can a middle-aged professional become a math teacher?
Not that Weston is in any sense typical, but it was a good experience both for him and for us. He got to talk with me and also with a colleague who has successfully made such a mid-career switch (from engineering, not accounting, but the issues are the same). He visited one of my colleague’s classes and two of mine (one at each level), including a precalculus section where I let the students interview him for about 12 minutes; the idea had been to limit it to five minutes, but their questions turned out to be too good for that. Several questions concerned the Enron scandal (these kids were ten years old at the time; how do they know about Enron?), but my favorite questions were two that couldn’t have been further apart. One student asked the visitor how he has used the math he learned in high school; I loved his answer, which was something to the effect that he loved his high-school math classes and that he hasn't used the details, like the definition of cosine, but he most definitely has used the analytical skills that he learned in those classes. That’s exactly what I want my students to understand. A totally different question was, “What have you done to benefit humanity?” Perhaps not the question you would expect from Weston, but all the better for that.
In my Algebra II class, the students were working on projects, so my visitor walked around, listened to the students, and talked with them. At one point, a group of three sophomore girls asked me for some help on Excel, but I was trying to answer other students’ questions at the time, so I suggested that they should ask our visitor instead. They cheerfully did so, he responded in a helpful manner at an appropriate level, and they later expressed satisfaction with the outcome (and with the visitor as a potential teacher). This led to a brief conversation about the usefulness of having students interview teacher candidates, and I told them that one of the reasons I accepted the job offer from Weston eleven years ago was my positive reaction to a group of students who had interviewed me at the time.
It still isn’t easy to switch into teaching mid-career. Not that it’s easy to become a teacher fresh out of college either, but at least you haven’t become accustomed to the rhythms and demands of the office world in that case. Facing four groups of 20–24 teenagers each day — or five groups of 30 in some schools — is not the least like working with a group of adults on accounting or engineering problems. It’s far more exciting for most of us, but it brings its own challenges every day that aren’t dreamed of in the world of the office. We desperately need qualified math teachers, so we’re happy to have new recruits!
Friday, January 11, 2008
What does this have to do with math?
- Sometimes very little (if any) actual math is learned. It happens too often that kids devote most of their attention to how the project looks or to ancillary materials, rather than to learning mathematics.
- Sometimes, as suggested in my earlier post on homework, the bulk of the work on a project is actually done by a parent, a friend, or a tutor, not by the student who is receiving credit for the work.
- Sometimes I have very little control over the structure and content of the math that is learned, so it seems less valuable than the tightly organized material of regular worksheets, assignments, and related activities.
So what happened today? The first experience concerned our recent test rather than the project that the students are currently pursuing. I quote a question here in its entirety:
ABC News reported that “Australian polar scientist Professor Patrick Quilty thinks he has a pretty cool idea. He wants to move Antarctic icebergs around the world for use as a source of water... Professor Quilty reckons it can be done by wrapping icebergs in huge, and he means huge, plastic bags and towing them to places like Africa where water is a scarce commodity.”Two different students asked, “What does this have to do with math?” (I’m sure many more than two were thinking the same thing, but were reluctant to verbalize the question.)
The bags are useful because the iceberg would start melting on its way from Antarctica to Africa, and the towing would take a long time. (Icebergs are very heavy!)
Suppose the amount of water in an iceberg decays exponentially at the rate of 4% per month, so that the volume is always 96% of the previous month’s volume.
- You need to tow a small iceberg, with a volume of one million cubic meters, from Antarctica to Mali. You have decided not to use Quilty’s bagging idea; you’re just going to accept the loss
of the melted water. The journey will take eleven months. How many cubic meters of water will remain in the iceberg when it arrives in Mali? [Be sure to show all your work clearly.]
- Why is it unrealistic to assume that there’s a constant decay rate all the way from Antarctica to Africa?
- One-point extra-credit question for those who are good at geography: Why will you have particular difficulty towing an iceberg to Mali (rather than, say, to Morocco)?
My response was that one of our main concerns in math is making mathematical models of real-world phenomena, and it’s impossible to judge the accuracy of the model unless you understand the real-world constraints. I don’t know whether this satisfied anyone, but IMHO it’s clearly correct.
The second experience also came from the test rather than the project. Many students (not all, but a clear majority) found the test unreasonably difficult. They were made very uneasy about questions that required them to think differently (or is it “think different”?), such as one where they had to find the half-life of a radioactive substance based on a couple of data points. It’s not at all surprising that they are far happier when given a worksheet that contains 12 equations, where they are explicitly told to solve the first four by Method A, the next four by Method B, and the next four by the method of their choice (though that last part makes some people nervous, especially since a couple required Method C).
The third experience did come from the project and relates to the first. You’ll see if you look at the project description (as I said earlier, I cannot take credit for writing this scenario) that the requirements are slightly fanciful but still are most definitely a combination of pure math, applied math, and non-math. Even the fanciful parts definitely qualify as “real world.” Some students enjoy working on this (in their groups of three), others want more direction (“answer these questions by Method B...”), and some just grumble and put up with it. But the same issue arises here as happened with the melting iceberg: what does this have to do with math? A couple of students verbalized this question explicitly.
I guess the reason I find this so frustrating is that the very same students also ask, “When will I ever use this in real life?” Apparently we can’t win. If we just give them an algorithm to carry out, they will do it cheerfully, but then they think it’s irrelevant. If we give them something relevant to think through, they complain that it’s not math.
Nevertheless, I have been extremely pleased with the way almost all of my students have been grappling with the challenging questions of the project. We have been devoting a lot of classtime and a little bit of homework time to this endeavor, and it’s clearly making most of these Algebra II students think much more deeply about exponential functions, decay, logarithms, and so forth. I have absolutely no doubt that the activity is a worth-while learning experience, well worth the amount of time devoted to it. That eliminates concern #1 listed above. Doing the work mostly in class eliminates concern #2. And having a tightly structured list of requirements for the project eliminates concern #3.
I think I’m going to go further in this direction.
Thursday, January 10, 2008
Those of us who went to high school in the ’60s and ’70s never heard of rubrics until well into our teaching careers. If anyone used them when I was a student, I certainly never noticed. But now rubrics are not merely a common vehicle for assessment, they are a standard piece of standards-based education — so much so that it’s not unusual for students to ask for one, as happened in my class. That makes sense: isn’t it reasonable to expect to know the basis on which you will be graded? This story won’t sound at all remarkable to current students and younger teachers, but it represents quite a change in my history of learning and teaching.
So I quickly posted the rubric and put a link to it in the assignment.
Wednesday, January 09, 2008
Hell for the Holidays
Tuesday, January 08, 2008
Why do homework?
It’s tough to give a convincing answer to that question. Typically we point out that homework helps you learn, but that answer goes only so far. We may observe that you’ll do better on tests and quizzes if you do the homework, but most kids need the more immediate motivation of a check mark on the assignment. Some will simply deny the connection, considering their assignments to be busy work; others will say they have too much on their plate and will do triage, finding time for the high-stakes work and not for the low-stakes work. So most of us give in and calculate some sort of homework grade, perhaps with a check mark or with a 0–4 system, which is what I use. Usually we base the grade purely on “sincere effort,” not on correctness of answers.
But that’s not really the subject of this post. Most of my students do their homework — though significantly more in my honors class than in my non-honors ones. (In Weston, being WestonLake Wobegon, there are only two levels of math classes, so the lower level is called “college prep.” Everyone is above average.) What I’ve been thinking about is not how many students do their homework, nor what motivates them to do it, but what they’re learning from it when they make a “since effort.” And here is the enormous difference between the two levels of classes:
- The large majority of students in an honors class (admittedly not all, but definitely a large majority) consider that it’s their responsibility to understand the material, even if they can’t answer all the questions that very day. It might not be fair to ask a quiz question relating to new concepts presented on the homework due that very day, but it’s certainly fair to ask it on a subsequent day. Students expect to learn from doing their homework.
- The large majority of students in a college-prep class (admittedly not all, but again definitely a large majority) consider that they have met their responsibility as long as they have put in enough effort to earn their check mark or their 4 out of 4. They do not expect to learn from doing their homework. If they go through through the motions, they’ve done enough. If several assignments in a row use the word logarithm, they feel no obligation to know what a logarithm is. This is very frustrating, both for me and for them.
Sunday, January 06, 2008
Saturday, January 05, 2008
The Yiddish Policeman's Union
Anyway, I’ll stay away from giving any details, lest I inadvertently include any spoilers. Let’s just say that the beginning is a little slow, especially as the reader/listener has the task of figuring out what’s going on in this world. That task, of course, is common in science fiction, but science fiction rarely has the attention to character that The Yiddish Policeman’s Union has. So you have to learn about the fictional world, get to know the characters, and understand the plot, which is initially confusing and contains a surprising amount about chess, not to mention a bit about Esperanto and other apparent irrelevancies. But it’s well worth persevering, since the initial difficulties start to fade away to reveal a fascinating integration of all three — the alternative history, the characters, and the story line. Do read it, or listen to Peter Riegert’s captivating performance as an audiobook narrator. (The audiobook concludes with a fascinating interview with Chabon, in which he actually gives a compelling answer to that horrible question all authors dread: Where do you get your ideas?)
Friday, January 04, 2008
There's nothing like promoting stereotypes
Thursday, January 03, 2008
Achilles and Odysseus
One was the psychological reality of fictional characters. Some readers challenge the appropriateness of discussing the sexual orientation of Dumbledore, on the grounds that he is a fictional character so it doesn’t make sense to talk about anything that’s not in Rowling’s writings. But that seems to me to be missing the point. If writing is compelling enough to encourage the willing suspension of disbelief, then the characters take on a life of their own. It’s not unusual for an author to say that s/he writes in order to find out what happens to his or her characters. If a reader can believe in a character’s life outside of a work of fiction, then it certainly makes sense to consider that character’s sexual orientation and everything else about his or her life. I don’t know whether Dumbledore was gay, but I think it’s highly probable based on Book 7.
The second issue is more specific: the claim by Bill Mullen that people tend to identify with either Achilles or Odysseus. Even though the NPR show cited above strongly suggests an orientation with Achilles, I have long felt much closer to Odysseus. This started in 11th grade, when I read the Iliad in Greek and the Odyssey in English. Just to be sure, I then read the Iliad in English and parts of the Odyssey in Greek — and sure enough, I’m clearly an Odyssey person. Odysseus speaks to me, but Achilles leaves me cold. Not surprisingly, Tennyson’s great poem “Ulysses” and Joyce’s great novel Ulysses have meant a lot to me. From Tennyson:
’Tis not too late to seek a newer world.(Note, despite the dichotomy proposed by Mullen, that Tennyson explicitly refers to “the great Achilles.”)
Push off, and sitting well in order smite
The sounding furrows; for my purpose holds
To sail beyond the sunset, and the baths
Of all the western stars, until I die.
It may be that the gulfs will wash us down:
It may be we shall touch the Happy Isles,
And see the great Achilles, whom we knew
Tho’ much is taken, much abides; and though
We are not now that strength which in old days
Moved earth and heaven; that which we are, we are;
One equal temper of heroic hearts,
Made weak by time and fate, but strong in will
To strive, to seek, to find, and not to yield.
And from Joyce:
Sitting at his side Stephen solved out the problem. He proves by algebra that Shakespeare's ghost is Hamlet’s grandfather. Sargent peered askance through his slanted glasses. Hockeysticks rattled in the lumberroom: the hollow knock of a ball and calls from the field.Ah! I don’t feel like downloading the 93-hour audiobook version for my iPod, but it’s tempting...
Across the page the symbols moved in grave morrice, in the mummery of their letters, wearing quaint caps of squares and cubes. Give hands, traverse, bow to partner: so: imps of fancy of the Moors. Gone too from the world, Averroes and Moses Maimonides, dark men in mien and movement, flashing in their mocking mirrors the obscure soul of the world, a darkness shining in brightness which brightness could not comprehend.
— Do you understand now? Can you work the second for yourself?
— Yes, sir.
In long shady strokes Sargent copied the data. Waiting always for a word of help his hand moved faithfully the unsteady symbols, a faint hue of shame flickering behind his dull skin. Amor matris: subjective and objective genitive. With her weak blood and wheysour milk she had fed him and hid from sight of others his swaddling bands.
Like him was I, these sloping shoulders, this gracelessness. My childhood bends beside me. Too far for me to lay a hand there once or lightly. Mine is far and his secret as our eyes. Secrets, silent, stony sit in the dark palaces of both our hearts: secrets weary of their tyranny: tyrants willing to be dethroned.
The sum was done.
— It is very simple, Stephen said as he stood up.
— Yes, sir. Thanks, Sargent answered.
He dried the page with a sheet of thin blottingpaper and carried his copybook back to his desk.
— You had better get your stick and go out to the others, Stephen said as he followed towards the door the boy's graceless form.
— Yes, sir.
Wednesday, January 02, 2008
Cheating and imaginary property, Part Two
- Has there been a decline in ethical attitudes and behavior among students in recent years?
- Are some lines that used to be bright now in fact just shades of gray?
The children now love luxury; they have bad manners, contempt for authority; they show disrespect for elders and love chatter in place of exercise. Children are now tyrants, not the servants of their households. They no longer rise when elders enter the room. They contradict their parents, chatter before company, gobble up dainties at the table, cross their legs, and tyrannize their teachers.What a great example! But apparently it doesn’t actually come from Plato, even though it has been floating around the Internet for years. Oh, well.
Despite quotations that might be spurious, it is hard to believe that there has been a recent decline. We usually view the past through rosy glasses. I just wish there were more actual evidence.
The second issue is probably more telling. Bright lines are easy when cheating is difficult. They become gray when cheating is easy. Not very many students are likely to go to the trouble of writing illegal notes on the back of a label affixed to a water bottle, though that kind of cheating is not unheard-of. But downloading a verboten copy of a song or a video is all too easy. As is making photocopies of copyrighted text. (Do you know any teachers who have done that?) Ease of cheating doesn’t make an act any more or less unethical, but it certainly makes it more likely. And the lines have become grayer. What is “fair use”? Can I photocopy some material for a class when I don’t have time to get permission? Can I do so when I am unlikely to get permission? What if it’s a single paragraph? What if it’s a whole chapter? What if the book is out-of-print? What if a student doesn’t cite a source for “commonly known” facts? What if a teacher copies a problem? What if s/he copies a problem and makes a small change? The lines aren’t so bright now that we have the technology to copy material off the Internet and to make photocopies of printed matter. Let him who is without sin...
Tuesday, January 01, 2008
New Year's Eve at Brasserie Jo
First of all, as the name tells you, Brasserie Jo is a brasserie, not a classy French restaurant like L’Espalier (which offers “sophisticated and modern New England-French cuisine”). Brasserie Jo offers exactly what the name promises: a huge menu of French classics, primarily peasant dishes. We were initially served a crusty, thin loaf of French bread (in a paper bag, as from a French bakery) and a plate of carrot sticks (overly seasoned with horseradish and some unidentified herb). Barbara had crab cakes (small but tasty); short ribs (cooked just right and also tasty), served with assorted root vegetables; and haricot verts (nicely seasoned and sufficiently cooked). I had lobster bisque (adequate, but with no lobster meat and almost completely devoid of lobster taste); an interesting salad of bibb lettuce, goat cheese, and roasted pear (fresh and delicious, though both the cheese and the pear were too mild, even the roasting not giving much flavor to the pear); and duck confit with braised lentils (both flavorful, though both slighly overcooked).
So, overall it was fine (“definitely OK,” as I said above), but nothing special. It certainly didn’t reach the near-perfection of Icarus or Sel de la Terre. That wouldn’t matter if the price had been more reasonable. But, for the two of us, a bill of $180.00 (including tax, a “moderately priced” bottle of wine, and tip) places Brasserie Jo in the “not worth it” category. For that price, I’d much rather go to Sel de la Terre. For slightly more, I’d much rather go to Icarus.
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