Learning Strategies

New URL for this blog

2009-01-09T06:21:00.002-05:00

As of today, this blog has moved to blog.larrydavidson.com. See you there!

To Darkness and to Death

2009-01-08T17:05:00.004-05:00

I enjoyed reading To Darkness and to Death, the fourth book in Julia Spencer-Fleming’s series of upstate New York mysteries featuring a female Episcopal priest. Not that I know much about Episcopalians or their priests, but that only makes these books all the more interesting. Eco-terrorism, real estate development, church politics, and town politics all play important roles. To Darkness and to Death is definitely not one of the best in the series, but give it a try if you want a pleasant diversion in a cold climate.

The Big Ideas of Algebra, Part Two

2009-01-07T06:28:00.003-05:00

This post is a follow-up to my post of November 30, where I brought up two points that can illuminate one’s views on the big ideas of algebra:

...we discussed the assignment of partial credit for work in solving a problem — more on this later, but it definitely reflects one’s views on what the big ideas are — and whether the study of algebra is distinct from (and prior to) the study of functions...

Partial credit doesn’t sound like a deep issue, but it really is. All you have to do is gather a group of math teachers, give them a student’s solution to a problem, and ask how many points should be assigned. Regardless of whether it’s out of four (where there are only three partial-credit possibilities) or out of ten (where there are nine), there will be significant disagreements; I reached this conclusion from having participated in such activities many, many times, with various groups of colleagues. And I don’t just mean that one teacher will give two out of four and another will give three, or that one will give seven out of ten and one will give five. No, I mean that one teacher will give nine points and one will give zero! And this is in mathematics, which is supposed to be an objective discipline — unlike English, where such disparities might not be surprising.

So, what does it mean when major disagreements surface in this area?

It usually means one (or both) of the following types of differences:

differences of opinion about what the big ideas are
differences in what one values

For instance, consider these three examples of student work that we discussed in the seminar in which I participated in November:

The problem read, “The sum of three consecutive odd integers is 81. Find the integers.” One student’s solution was like this:
Let x = 1^st odd integer
x+1 = 2^nd odd integer
x+2 = 3^rd odd integer
x + x + 1 + x + 2 = 81
                 3x + 3 = 81
                       3x = 78
                         x = 26
The integers are 26, 27, 28
How many points (out of ten) is this worth? If a big idea is that odd numbers differ by 2, not by 1, then the setup at the beginning of the solution represents a significant error — especially since the student wrote the word “odd” each time, thus showing that s/he didn’t merely skip over the word “odd” in the problem statement. On the other hand, the solution is otherwise correct, the work is clearly shown, and the answers will even check, being three consecutive integers adding up to 81 (ignoring the word “odd” again). If you highly value all the skills of combining like terms, backtracking to solve an equation, and recording a solution, then the solution is worth a lot of points. But if the idea of consecutive odd integers is important, it may be worth very few points. My colleagues rated the solution all the way from one to nine; I gave it a six.
Next we have a different student’s solution to the same problem:
Finally, here’s a different problem, along with one student’s solution: “Solve 2(x – 10) &ndash (12x – 4) = 20.”

The issue here is that the student couldn’t read his own handwriting (possibly her own handwriting, but the odds are against that): “20” got transcribed sloppily and then read as 26. I gave it a nine out of ten, since that error struck me as a very minor one. But other teachers’ scores ranged all the way down to zero, on the theory that the student had nobviously never checked his answer. My own values are that checking one’s answer is a big idea of algebra, if we mean that it’s important to understand that what we mean by a solution is a number that will satisfy the equation. But failure to check, especially in a time-sensitive situation where there are no instructions to check, strikes me as a very minor offense.

Your mileage may vary.

The second point that I was intending to discuss — whether algebra is distinct from functions — will have to wait for another post. This one is already too long.

The Likeness

2009-01-05T16:02:00.003-05:00

Although it’s not quite as enthralling as her first book, Tana French’s sequel is well worth reading. In The Likeness, French continues her lyrical writing and fascinating characterization. Cassie Maddox continues from the prior novel, In the Woods, but this time she’s the clear protagonist. The beautiful writing clearly takes center stage in this book, but I also couldn’t help being captured by the interactions among two sets of characters: the police on the one hand, a group of Irish graduate students on the other. Read it for the language, for the characterization, and even for the suspense, though the plot of The Likeness is not really its strong point.

I don’t usually like to quote from Amazon reviews, since they tend to be from random amateurs. As a random amateur myself, what do I need their observations for? But in this case I really have to quote from three, even though I risk sounding like a publisher looking for blurbs:

Tana French has created another sensuous, lyrical, haunting, suspenseful story... Tana French is no lightweight, but she makes the story accessible to anyone who enjoys reading. She has that gift to appeal to a variety of readers — even readers who look for largely escape mysteries. But this is not escape reading; it is the kind of reading that makes you ponder. It is philosophical and it echoes. It has shadows, swirls, hollows, heart,humanity, tension, suspense, whispers, hawthorn, hawthorn, hawthorn... [by switterbug "laughingwild"]

It was truly an exceptional and thrilling read. The way French fleshes out Cassie Maddox, Lexie Madison and the four housemates is truly astonishing. I have always been fond of character-driven plotlines and novels, and French truly impressed me with “The Likeness”. The amount of depth present in these characters — their motivations, relationships, and personalities — was both fascinating and engrossing. This was a book difficult to put down. [by Voracious Reader 326 “College student”]

I couldn’t write a single sentence as well as Tana French if I started now and lived to be a thousand. And she wrote a whole book, two books, of them. Flawlessly. Word after word, sentence after sentence, paragraph after paragraph, until the book is as perfect as it could be. It boggles the mind, it really does... It’s a privilege to read Tana French, it really is. I feel only pity for the person who wrote of the unbelievable plot, I do. This book isn't about a plot, just as Chandler wasn’t about plot, just as we don’t read Shakespeare for the plot. Anyone can do plot; but to give feeling and life, undoubted life, to characters on paper, that is to marvel at. [by Adam Shinbrot]

The inexperienced waitress

2009-01-04T08:52:00.000-05:00

The waitress at the Legal Seafoods branch in Harvard Square was nervous and very apologetic. “This is my first time opening a bottle of wine in front of a customer,” she confessed. Of course she wasn’t allowed to rest the bottle on the table, and everything was supposed to be perfect.

We assured her that it was OK to put the bottle on the table, and we coached her through the process. The cork came out smoothly. The waitress was just so grateful: “Most people would be upset with me for not knowing how to do this.”

I replied by saying that I’m a teacher and that I believe in being patient while people learn. Doesn’t sound so unusual to me...but then again, I’m a teacher. We left a good tip.

Thesauri & The Man Who Made Lists

2009-01-03T07:10:00.004-05:00

I recently read Joshua Kendall’s biography of Peter Mark Roget, entitled The Man Who Made Lists: Love, Death, Madness, and the Creation of Roget’s Thesaurus. While this book is fascinating, it’s also deeply flawed — especially for those of us who love lists, not to mention those of us who love thesauri and other reference books.

On the plus side, Kendall teaches us a lot about Roget’s background as a scientist and physician. We learn about his compulsive list-making as a child, whether it be names of farm animals in Latin or lists of the bones in the human body. We learn about his organization of all the concepts of the English language in later life. And we learn a little — but not nearly enough — about Roget’s mental problems and how he coped with them. These problems were relevant, indeed central, to the decision to create the first thesaurus in 1852. Compiling lists of words apparently helped Roget cope with depression, anxiety, and probably Asperger’s, though Kendall only barely touches on the last of these.

On the minus side, the reader gains almost no sense (despite the subtitle) of the importance of the thesaurus to Roget’s life and to the world. It’s just one incident among many. I was looking for details — lots of details — about how the thesaurus was compiled. The lack of details is rather ironic, given the subject of the book. And it reminds me of my issues with The Professor and the Madman. The other flaw is the offhand consideration of the likelihood that Roget had Asperger’s, though of course neither the name nor the disorder was known in the 19th Century. These flaws were not enough to deter me from finishing The Man Who Made Lists, but they certainly reduced my enjoyment of the book and meant that I learned far less from it than I had hoped.

Those who know me will not be surprised that I still have an old copy of Roget’s International Thesaurus, a copy that my father gave me when I was eight years old. As I say, people won’t be surprised that I have this, though they might be surprised that I could lay my hands on it so readily. Anyway, when I was eight, this “new edition” of the thesaurus had been out for nine years, so it slightly predates my own birth. It’s instructive to contrast the arrangement and organization of this edition with the modern alphabetical lists of synonyms that still claim the name “thesaurus.” My copy, published by Crowell, contains the following remarks in the Publishers’ Preface [note the subtle placement of the apostrophe]:

The basic principle of Dr. Peter Roget’s original Thesaurus was the grouping of words according to their ideas rather than the listing of words, as dictionaries do, according to the alphabet. This principle — the secret of Roget’s success — has been scrupulously preserved in the various Crowell editions for over sixty years. [Italics as in original]

The difficulty with grouping words by ideas is that it can be very difficult to find a word, so this edition of the thesaurus contains an index that’s nearly as long as the body of the book. Be that as it may, Roget’s idiosyncratic organization of all possible concepts is a delight, as long as you don’t take it as a given truth. The schema is hierarchical and multi-level. For example, suppose you were thinking about prime numbers, but you couldn’t remember the terminology prime number. You would, of course, look under Class I (abstract relations), Section V (Number), Part 1 (Number in the Abstract), Category 84 (Number), Subcategory 2. You knew that, didn’t you?

Well, no, of course you didn’t; that’s why you needed the huge index. Anyhow, the subcategory in question reads as follows:

complement, subtrahend, multiplicand, multiplier, multiplicator, multiple, submultiple, coefficient, dividend, divisor, factor, quotient, fraction, mixed number, numerator, denominator, decimal, mixed decimal, circulating decimal, repetend, common measure, aliquot part, reciprocal, prime number, totient, quota, differential, integral, fluxion, fluent, power, root, radix, base, exponent, index, logarithm, antilogarithm, modulus.

Note that this is most definitely not a list of synonyms! It’s a list of words that are conceptually related in some way. Reading it, you spot the term you were looking for (“prime number”) and your mind is also captured by a great many other words that are closely or loosely connected. What a loss to use a modern so-called thesaurus, where you probably can’t even find “prime number” unless you already know the phrase, and then you’ll simply find that there are no synonyms.

You can browse through Roget’s Thesaurus and learn something new on any page. All you are likely to learn from a modern thesaurus is some pretentious near-synonyms that will make you a worse writer.

Juno

2009-01-01T10:42:00.005-05:00

Last night’s New Year’s Eve festivities included watching Juno, which neither Barbara nor I had seen before, even though it was released over a year ago. On the basis of reviews and personal recommendations, I had expected to like this movie. It exceeded my expectations.

I’m sure everybody knows the plot by this point, but I’ll still stay away from spoilers in these brief comments. My major observation is that all of the actors were entirely convincing in their portrayals of various teens and adults, most notably Ellen Page as Juno, who kept reminding me of various Weston students of mine. No students in particular, I hasten to add — just different generic students at different points. J.K. Simmons and Allison Janney were much more genuine than the parents in the typical movie about teenagers, although I kept being distracted because I knew I had seen Simmons before but couldn’t remember where (I’m not good at actors). When I looked him up, I discovered that he plays Dr. Skoda, who appears off and on as the consulting psychiatrist in Law and Order; the temperaments of the two characters are almost identical, thus reinforcing the distraction. Also, Jennifer Garner and Jason Bateman were effective (if a bit creepy) in their roles as the soon-to-be adoptive parents.

Early in 2008 there was some chatter about whether Juno glamorizes and therefore encourages teenager pregnancy. Frankly, I don’t see it. Admittedly, Juno isn’t portrayed as a bad kid, as the right-wingers would prefer; she doesn’t suffer much for her mistake, and her friends and family are all accepting of her. But that doesn’t mean that the movie glamorizes pregnancy, and since Juno immediately decides to have the baby adopted, it shouldn’t encourage the standard worry among adults that a girl will want to get pregnant in order to have a baby who will love her. In fact, since neither Juno nor her family is dysfunctional, what we have here is simply a straightforward tale of how a normal (if rather counterculture) teenager grows up and interacts with adults and with other kids. It’s well worth seeing, just for the quality of the acting if nothing else — but it’s also worth seeing because it’s such a refreshing and captivating story.

I’ll have to ask my student who recently moved to Weston from Minnesota about St. Cloud, where the adoptive parents live in the movie. The director portrays it as a lot like Weston.

Addendum at 8:10 PM:
I wrote the above earlier in the day. But now I’ve just finished watching the first Greater Boston of the year on WGBH, a retrospective of 2008. Emily Rooney’s guest Dan Kelly (identified just as “attorney”) made the following remarks in connection with the supposed but unproved pregnancy pact among girls at Gloucester High School:

The message of all this is not that more birth control is the answer. The message is that Time Magazine picked up on the bandwagon of sensationalizing teen pregnancy, and that bandwagon is out there because of Britney Spears’ sister pronouncing how wonderful it is to be a teen and to be pregnant... The Juno movie, the Juno effect. The Juno movie in a lot of ways was a great movie from my perspective because it showed the dignity of a human life before it’s born. It’s a pro-life movie and it sends a wonderful message to kids. But it also is a movie that glorifies teen pregnancy to some extent. To say that there will not be that many side-effects, that you can get through it, that it is not such a colossally terrible thing, and it also glorifies in some respects teen sex, although I think the message of that movie is that teens are not prepared to have sex and should not be having sex.

This analysis is just plain wrong. The movie doesn’t glorify teen pregnancy, and it doesn’t send a message. It’s not a political document. It’s a story, a work of art, which presents a group of characters and deals with the internal and external conflicts of the main one, just as stories usually do.

Wordle

2008-12-31T11:45:00.003-05:00

I just discovered a cool poster-creating applet called Wordle. In their own words:

Wordle is a toy for generating “word clouds” from text that you provide. The clouds give greater prominence to words that appear more frequently in the source text. You can tweak your clouds with different fonts, layouts, and color schemes. The images you create with Wordle are yours to use however you like. You can print them out, or save them to the Wordle gallery to share with your friends.

You can create an image from text that you type in, or from a URL of a blog with an RSS feed. In the latter case, the applet uses all the text it finds at that URL, excluding some common English words (or whatever other language you might choose).

I rather like the result I got by giving them the URL of this blog:

How many college recommendations?

2008-12-30T12:02:00.003-05:00

I just finished sending off 104 college recommendations this week.

How many?

Yes, 104. And that was in addition to 21 “early action” recommendations that I sent out earlier in the fall.

But before you conclude that that’s a ridiculously large amount of work for a teacher to have to do, especially during vacation, you need to look at the rest of the story. First of all, these 125 recommendations come from only 13 seniors (all of whom took my honors precalculus class last year), so you can see that they average nearly 10 apiece. That means writing only 13 letters (printed out many times, with each copy signed and stuffed into the appropriate stamped envelopes) and answering only 13 questionnaires (scanned in, and similarly printed out and stuffed). Actually, it’s a tad more complicated than that, since there are still a few colleges that don’t use the Common Application that makes it so easy for high-school seniors to apply to a large number of places, but it’s still basically true.

For each of these students, the total number of applications ranged from 5 to 16. This is Weston, after all. It was the total number of distinct colleges that these students applied to that surprised me a bit: 57. The reason that this surprised me wasn’t the specific number (the famous Heinz number) but the fact that it was so high. In the past, students in honors math courses at Weston tended to apply to the same relatively small number of colleges. But things have changed: it’s now much harder to get into any particular competitive college than it used to be, and as a result it’s unpredictable whether a perfectly qualified student will get admitted to his or her first choice, or second choice, or third choice...

So don’t be horrified by the task of writing 125 recommendations — just by the amount of printing, signing, and envelope-stuffing required.

In praise of Micci

2008-12-29T16:06:00.001-05:00

A completely unsolicited testimonial:

Barbara and I noticed that our 28-year-old gas furnace was behaving erratically, sometimes turning off and on in rapid intervals, and sometimes turning off altogether. We called Micci Fuel Co. to come look at it and fix whatever was wrong. They showed up on time, cleaned and vacuumed the furnace, and explained to us just what they were doing and why. If you’re in their neighborhood, we certainly recommend them!

The furnace works perfectly now.

By the way, conventional wisdom has it that young people aren’t going into businesses like this anymore, so we were pleased to see that one of the guys who showed up was in his twenties.

Dorchester Community Gardens

2008-12-28T06:10:00.004-05:00

We tend to think of Dorchester as “inner city” — which indeed it is...or not, depending on one’s definition (see below). But most of us don’t think of urban gardens in connection with Dorchester. A useful antidote is Dorchester Community Gardens. Our local community garden is on Msgr. Lydon Way. Here are a few photos, which might surprise those whose image of Dorchester is formed solely by crime reports in The Globe:

Now, as for the definition of “inner city”: Wikipedia says that it’s “the central area of a major city or metropolis,” going on to explain as follows:

the term is often applied to the poorer parts of the city centre and is sometimes used as a euphemism with the connotation of being an area, perhaps a ghetto or slum, where residents are less educated and more impoverished and where there is more crime.

Answers.com defines it like this:

The usually older, central part of a city, especially when characterized by crowded neighborhoods in which low-income, often minority groups predominate.

Whichever definition you prefer, Dorchester is certainly in part inner-city. I do tell people that I live in the inner city, but we also have community gardens and other green space.

Fred the Footrest

2008-12-27T09:35:00.008-05:00

My major Hanukkah present from Barbara was a footstool in the shape of a genuine replica of a stuffed bear:

We named him Fred the Footrest. You have noticed that William is loyally guarding Fred in case any hunters should come near.

The manufacturers (or their lawyers) are really unclear about the status of this product. It came with two tags. Note the last three words of the safety warning:

In contrast, here is the tag below the safety warning:

So...is it a toy, or isn’t it? Inquiring minds want to know.

Chinese food in Elmira

2008-12-26T15:55:00.002-05:00

We had lunch today at Beijing Garden, a reasonably good Chinese restaurant in Elmira. Why were we the only customers using chopsticks? Why was everybody covertly looking at us?

And why wasn’t this restaurant open yesterday (Christmas Day)? I guess there isn’t much of a Jewish population in Elmira anymore.

What do I need to do to get an A?

2008-12-24T21:02:00.001-05:00

“What do I need to do to get an A?” asks one of my students in an honors math course.

I wish I had a magic recipe. I can say with reasonable confidence that it’s possible to get a B by studying hard, by studying smart, by working hard to understand concepts, by getting enough practice in math skills. But an A? Every student sees some classmates getting A’s by some mysterious method, in some cases working very hard and in other cases magically earning the A with seemingly little effort. Surely there must be a secret recipe that the teacher isn’t revealing.

Of course there isn’t such a recipe. Think of some non-academic endeavors. What can you do to gain a place on the varsity basketball team or the Greater Boston Youth Symphony Orchestra? Sure, working hard is important and necessary (think of the old joke about how to get to Carnegie Hall: “practice, practice, practice”), but unfortunately it’s not sufficient. There’s no way that I’m going to be a top-ranked musician or a top-ranked athlete, no matter how hard I try. And yet, as a teacher, I definitely don’t want to be the bearer of discouraging news. I want my students to work hard, to do their best. But their best might or might not match their hopes. There’s nothing wrong with a B in an honors math course at Weston High School — in fact, I have a couple of students who work very hard and are delighted when they achieve B’s. But, in Lake Wobegon and similar communities, nothing less than an A will do.

So here’s the dilemma: how do I motivate students to achieve their personal best — which, after all, is the aim in music and athletics and other endeavors — without telling them that their personal best might not be good enough? I know how to help students get B’s, but after 34 years of teaching I don’t know how to help them get A’s, at least in honors courses. Some do, most don’t, but it’s not clear what effect I can have on the outcome. I can help a willing, able, and motivated student get an A in a college-prep course, but such a student might well try his or her best and only get a B in an honors course. As I say, there’s nothing wrong with that, but in today’s world of competitive parents and even more competitive college admissions, my point of view won’t be compelling. This is discouraging. The last thing I would do is say ahead of time that any given student is incapable of earning an A. And yet, at some point, one is forced to admit that a particular student is trying as hard as any reasonable person could expect and is earning a B. I don’t know what to say, except to repeat that there’s nothing wrong with that.

More about the Ashmont Grill and Tavolo

2008-12-23T20:34:00.003-05:00

I’ve written a couple of previous posts about the Ashmont Grill — two years ago and five months ago. Since the latter post, Barbara and I have visited several times, mostly for the Monday Night wine club, which I highly recommend (though not, of course, for my under-21 readers). Each evening features a four-course dinner (admittedly of four small plates), with wines paired with each course, for an amazing $30 per person. The food is almost uniformly excellent, though occasionally the restaurant takes this opportunity to try out new dishes which of course aren’t necessarily successful. (Presumably the reason that they can achieve the $30 price point is that the wines are donated by a winery or retail outlet each time.) Here are four recent examples to whet your appetite:

From September 8

From October 27

From November 3

From December 22

I’m looking forward to Tuscany! (Who wouldn’t?)

A related event was a wine tasting benefit on August 4 at the Ashmont Grill for the St. Marks Area Civic Association, featuring wines from Albert Winestein, a retail wine-and-cheese store in Hyde Park.

Perhaps the most interesting feature of the Wine Club is not the wine nor even the food, but the fact that guests are arranged family style at tables that seat four to eight. As a couple, Barbara and I are always seated with strangers, something that would usually have a high probability of making me uncomfortable. I’m not particularly extraverted, and I tend not to be very sociable with people I don’t know yet. But the fact is that we’ve met lots of interesting people with a surprising number of things in common with us — not just providing the obvious conversation topics such as food, wine, and Dorchester. We’ve met a manager at a local independent bookstore (one of the few that remain), a physics professor, an architect from a neighboring town, and a woman who knew one of the very few Weston families to be distinctly countercultural.

So, if you live anywhere near Dorchester, try it out! Reservations are advised; you can call the restaurant (617-825-4300) to make inquiries and to be put on their email list. They usually don’t know the menus until a few days in advance, so don’t expect a lot of notice.

As locals know, the current incarnation of the Ashmont Grill is the creation of Chris Douglass, a neighborhood resident who is best known for his South End restaurant, Icarus. Barbara and I usually go to Icarus only once a year (for our anniversary), since it’s extremely expensive. The Ashmont Grill is still a bit overpriced, and not in the same league as Icarus in terms of cuisine and service, but at least it’s the sort of place that one could go to once a month, even without the exceptional value of the Wine Club. Read my July 19 review for more of my point of view, or check out the many reviews on Yelp for a variety of opinions, some reasonable and some wrong-headed. (I’m reminded of Tom Lehrer’s remark that the trouble with folk music is that it’s written by the people, and my friend Brian’s observation that you have to be wary of the general public’s opinions of restaurants, since McDonald’s is the most popular restaurant in the world.)

Before we leave the subject of the Ashmont Grill, I need to write a bit about Tavolo, Chris Douglass’s latest restaurant, catty-corner from the Ashmont Grill and right at the Ashmont Station on the Red Line. The theory was that this would be a third price point, with Icarus at the very high end, Ashmont Grill in the Middle, and Tavolo at the low end. As a pizza-and-pasta joint, Tavolo should be informal and inexpensive, while still serving high-quality food. Barbara and I have been there a couple of times, and we’re not impressed, though we really, really want to like it. The food is perfectly OK (nothing to write home about, but then again that’s not what you would expect), though there were a few flaws. For instance, while Barbara’s salad came with the dressing on the side, as she had requested, it was so heavily pre-salted that she couldn’t eat it. (Why pre-salt a salad at all?) And the carbonara was a bit too eggy, at least for our taste. We really liked the mushroom pizza. Service was fine, including cheerfully willing replacement of the salted salad. But our big problem was the wine prices. For a purportedly inexpensive restaurant with a $40 ceiling on wine, why does the lowest-price red go for $32? (My friends who are beer drinkers don’t have similar complaints.) For instance, a nice Sicilian Nero d’Avola that can be purchased retail for ten dollars is priced at $36 at Tavolo! I know that there are lots of reason for significant mark-ups, but if the otherwise pricey Birch Street Bistro in Roslindale can charge $24 for similar wines, why can’t Tavolo?

Donovan's in Savin Hill over the Bridge (well...almost over the bridge)

2008-12-22T05:52:00.002-05:00

The Savin Hill neighborhood in Dorchester is conventionally divided into two parts, at least by real estate agents. The “better” half, according to some, is “Savin Hill over the Bridge,” namely the portion to the east of the bridge that crosses the Southeast Expressway. Dorchester is changing so rapidly that this decades-only terminology may now be out of date; read what people have to say on Yelp if you want some local opinions on the subject.

Anyway, immediately to the west of the bridge — practically on the bridge itself, but not quite “over the bridge” — is C.F. Donovan’s Restaurant, one of our favorites in Dorchester. Simple, unpretentious, not trying to be upscale or too gourmet, Donovan’s is where Barbara and I go when we’re driving home and it’s too late to start cooking dinner. Always reliable, Donovan’s has a large menu, prices are good, the food is always of high quality, the service is friendly and accurate, the portions are large, and the wine list is both decent and reasonably priced. What more could one ask for?

Try the Savin Hill scallops (“Jumbo Sea Scallops sautéed with sage butter, served over baby spinach and garlic mashed potatoes”), the French onion soup, the prime rib, the onion rings, the chicken bella boca, the grilled asparagus, and the burgers. In our experience, you can’t go wrong.

David Handler's Berger & Mitry series

2008-12-21T05:49:00.001-05:00

David Handler, best known for this Stewart Hoag series and other novels, has also written six books (so far) in his Berger and Mitry series:

The Cold Blue Blood (2001)
The Hot Pink Farmhouse (2002)
The Bright Silver Star (2003)
The Burnt Orange Sunrise (2004)
The Sweet Golden Parachute (2006)
The Sour Cherry Surprise (2008)

If you’re exceptionally observant, you’ll notice a certain pattern to those titles.

Anyway, I’ve recently read the first four novels in the list above, and I highly recommend them, both individually and as a series. Reading them in chronological order would make sense, as the characters develop satisfactorily from one book to the next.

The premise behind the series is a simple one. Handler delivers on it. In the small town of Dorset, Connecticut, two unlikely detectives have come together both professionally and romantically: Mitch Berger, a Jewish film critic who writes for the New York Times, and Desiree Mitry, an African-American cop who has become the “resident trooper” for Dorset (a thinly veiled version of Old Saybrook). That’s it. But out of this premise Handler weaves a series of truly entertaining mysteries with appealing characters, interesting plots, and a great sense of place. Do read them!

Kindle for textbooks?

2008-12-20T16:17:00.002-05:00

One of my students asked me why his textbooks aren’t available for Kindle. Currently the typical Weston student’s backpack weighs 42 pounds*; Kindle weighs only ten ounces! Aside from everything else that’s available for it, imagine replacing your math book, your English book, your science book, your history book, and your Latin book (not to mention the extra book for the student taking two math courses or two sciences or two languages...) with a single light-weight device. It would be much cheaper for the publishers, too.

So why hasn’t anyone jumped on this opportunity? Save our students’ backs!
________
*Actually, I made this figure up. But the reality is probably all too close to that.

Obedience

2008-12-19T06:00:00.002-05:00

Obedience, by Will Lavender, is a fascinating but flawed novel. Not flawed like Strip Search, which I reviewed the other day; this novel is worth reading. But it’s flawed nevertheless. It shares with Strip Search the characteristic of a great premise that the author can’t quite deliver on.

Reviewers on Amazon and elsewhere have commented on the difficulty of suspending disbelief when faced with an implausible plot and implausible characters, but I didn’t have that particular problem. As an academic mystery with a title and plot based on Stanley Milgram’s famous experiment, there was plenty to hold my interest, and I was actually able to buy into Lavender’s peculiar world. But here’s how a Massachusetts reviewer named Winter began his review that you should read:

Great idea. Mediocre book. That’s all you need to know.

Maybe that is all we need to know, but Winter goes on for eight more paragraphs anyway.

I will do likewise.

Well, maybe just four more.

The main characters are a group of college students in the fictional Winchester University. Although the students and their university are painted in fairly broad strokes, I found them plausible enough and wasn’t nearly as bothered by Lavender’s descriptions of them in “overwrought prose” as Winter was. I can’t comment on Winter’s analysis of the likely effect of reality TV on today’s college students, since I don’t know anything about the four shows he mentions. I do like Winter’s phrase that the three students are “less stable than Microsoft Windows,” but I don’t understand what’s wrong with that.

Most of the mainstream (professional) reviewers were positive about Obedience. Most of the Amazon (amateur) reviewers were quite negative. I’m not sure what to make of this split. My feeling is that the latter group wanted a real-life novel that could be believed on the face of it, whereas the professionals were willing to look for metaphor and even fantasy. If you can live with something less than realism in an apparently realistic story, give Obedience a try. But don’t say you weren’t warned.

Where are my model railroad pix?

2008-12-18T05:51:00.003-05:00

One of my students asked me why I haven’t yet posted any photos of the model railroad I’m building. One answer is that it’s still in such an early stage that I don’t have much to show yet. Another answer is that I’m intimidated by videos like the stunning Route 6 HO Scale Model K-Car Trip around Philadelphia, which is so much like the urban, transit-oriented layout I am trying to accomplish (except for being Philadelphia rather than Boston) and yet so far from what I am really going to achieve.

But I’ll bite the bullet soon and will show some of my progress.

Strip Search

2008-12-17T20:38:00.006-05:00

Strip Search, by William Bernhardt, is an irritating novel.

Why do I say that? Well, it’s not just because Bernhardt portrays math teachers as weird and psychotic, though that’s certainly a major part of it. And it’s not just because the plot is so implausible, though that too is part of it. And it’s not just that the book is riddled with mathematical errors, though of course that definitely bothered me. And it’s not just that the amount of violence is excessive and unnecessarily explicit, though that would certainly put off many readers. No, the most irritating characteristic of Strip Search is that it reads like a “good idea” that someone had. My impression is that someone said to the author, “Here’s a proposal for a novel. Go write it.” Not surprisingly, a coherent novel was not the result.

You may wonder why I started reading this book. In the past I’ve found Bernhardt to be a competent and engaging writer, even if not a memorable one. And I had heard that Strip Search featured a combination of mathematics (equations left as clues at each crime scene) and a major character (Darcy) who’s an autistic savant. No math teacher could resist that enticing combination. Some readers (in customer reviews on Amazon, for instance) were annoyed by the characters and found none of them likeable. Personally I didn’t have that problem, although I can see why others might. But anyone who has taught students who have Asperger’s or autism will find Darcy likeable enough, to coin a phrase. And the detective is no more unlikeable than many a highly flawed protagonist.

You may also wonder why I bothered finishing Strip Search if I was so irritated by it; I’m not one of those people who feel compelled to finish a book once they’ve started it. But I kept irrationally hoping that things would get better, that there would be a good reason for all the flaws. Unfortunately I was wrong, so here is your warning. Don’t read this post any further if you’re intending to read Strip Search, as I can’t write what I need to write without introducing spoilers.

*** SPOILER ALERT*** SPOILER ALERT *** SPOILER ALERT ***

OK, so we have a detective who’s actually a police psychologist (the protagonist) and fits into the genre stereotypes of being insubordinate and an alcoholic. Later she turns to pills. She is a psychologist without a doctorate, and she reaches most of her conclusions by intuition and guesswork. Since she’s also the first-person narrator, I’ve forgotten her name. Oh, that’s right, it’s Susan.

But don’t think that Bernhardt extends genre stereotypes to gender stereotypes. No, we also have Esther Goldstein, a female mathematician who not only teaches math but also has apparently solved the Riemann Hypothesis (misspelled “Reimann” throughout the book). For reasons that apparently stem in some undefined way from an unhappy childhood, she is also reviving the ancient Pythagorean religion, the Brethren of Purity. Unfortunately she also turns out to be a psychotic mass murderer. But then again she is a math teacher, so you can’t expect her to be normal, can you? “Math has been riddled with positively brilliant madmen,” as she explains at one point.

The sympathetic characters, such as police lab technician Amelia, say things like, “I gave up on math after my second semester of algebra.”
Susan, even though she presumably has at least a master’s degree in psychology, says, “I hadn’t taken a math class since junior high school.”
The puzzle expert says, “I’m a word boy. Left brain. Math freaks are a whole different breed. And this doesn’t look like a real puzzle anyway. How can you solve an equation if you don’t have any of the numbers?

Bernhardt’s mathematical errors include confusing variables with unknowns and referring to expressions as equations. For example, on page 161, we have this excerpt:

It was another equation:

Bernhardt’s account of the Pythagoreans’ attitude toward the irrationality of the square root of 2 is also muddled. For instance, Esther, the professional mathematician who’s an expert on the Pythagoreans, says, “The square root of two was a problem with no solution.”

OK. That’s enough. Don’t bother reading the book.

Misreading Larry Summers

2008-12-16T16:04:00.002-05:00

Continuing yesterday’s theme... There has been renewed interest in Larry Summers’s supposed sexist remarks. When Senator Obama (I almost said “President Obama”) announced that he would appoint Summers to be his senior White House economic advisor, bloggers and others revived the old canard that Summers believed that women were deficient in their math and science abilities. For instance, Wendy Hansen in the LA Times wrote as follows:

The notion that boys are better than girls at math simply doesn’t add up, according to a study being published Friday in the journal Science. An analysis of standardized test scores from more than 7.2 million students in grades 2 through 11 found no difference in math scores for girls and boys, contradicting the pervasive belief that most women aren’t hard-wired for careers in science and technology.it

The study also undermined the assumption — infamously espoused by former Harvard University President Lawrence Summers in 2005 — that boys are more likely than girls to be math geniuses. Girls scored in the top 5% almost as often as boys, the data showed.

The trouble, of course, is that Summers did not espouse that position. Summers did observe that there is a gender disparity among the very top mathematicians and scientists (as no one could deny) and proposed that it would be helpful to investigate why: to what extent is it genetic, and to what extent is it societal?

Although this question is precisely what a scientist in a research university should ask, it created great controversy. The very act of asking the question suggested to many people that Summers was assuming that women are less capable than men in math and science.

Summers had great strengths as President of Harvard, especially in his sponsorship of the Crimson Summer Academy (where I teach in the summers, so I can’t claim objectivity) and in his insistence on huge scholarships for low- and moderate-income students. Unfortunately his lack of social skills caused him to lose support in the Faculty of Arts & Sciences (though not in Harvard’s ten other schools), and he was forced to resign. Some say he has Asperger’s Syndrome; he might well, but who knows? Anyway, he has returned to being a professor of Economics at Harvard, and now he is a top advisor to Obama. I don’t believe that he’s sexist, but he clearly has some problems communicating his ideas; nevertheless, he is a distinguished economist with a lot to contribute, and he is an excellent pick for the Obama administration.

And they say that girls can't do math...

2008-12-15T06:57:00.001-05:00

So why is it that the top two mathletes on Weston High School’s Math Team are freshmen girls? And a year young for their grade, at that?

Check out the situation from ten months ago. But it’s only two data points.

Obama and the Achievement Gap

2008-12-13T16:10:00.002-05:00

Now that we’ve elected an African-American intellectual to the highest office in the land, can a reduction in the achievement gap be far behind? For many years we’ve been observing that black male students see very few role models for high academic success. Honors courses are for geeks; so are A’s. If you try for either, you’re “acting white.” After all, look at the successful African-American males in the media: we see athletes and entertainers — both groups neatly conforming to prevailing stereotypes — but not a geek among them.

Until now.

That’s change we can believe in.

iPhone games

2008-12-12T06:15:00.003-05:00

Having been an enthusiastic iPhone user for the past four months, I’m not surprised that many of my students want to play games on it (at least those students who don’t have iPhones themselves; this is Weston, after all). That’s a good excuse for installing games, isn’t it? Or do I just want to play them myself?

Maybe so, but at least the recommendations still came from the students.

Here’s what I have, in alphabetical order:

First is Dactyl, a game of hand-eye coordination. Not unexpectedly, I’m terrible at Dactyl and can’t possibly compete with my freshmen and sophomores on the math team.
Then comes Enigmo, which I haven’t learned yet, so I have no opinion on it. But my students tell me that it involves physics and problem solving, so it must be good.
Then we have Labyrinth Lite, an astonishingly faithful reproduction of the classic wooden labyrinth game. Tilting the iPhone backward and forward in two directions exactly mimics the physical game, even to the point of accurately reproducing the momentum and sounds of the real-life steel ball.
The silliest game that used to be on my iPhone is Scoops. Scoops of ice cream fall from the sky, and you move your cone left and right in order to catch the scoops while you avoid onions. Onions? Yes, onions. I’ve removed Scoops, even though a certain sophomore disapproves of my doing so.
Then there’s Tetris, though I’m currently using the unauthorized knock-off called Tris, which I installed shortly before it got kicked off the Apple Store. Maybe I’ll get the real thing, as Tris rotates the tetrominoes counterclockwise rather than clockwise as nature intended.
Finally we have my current favorite, Trace. It’s hard to describe this one, but it’s addictive and not time-pressured, so try it yourself!

Of course I also play Sudoku a lot, but that’s really a puzzle, not a game.

What’s next? Scrabble, perhaps? Or SimCity? Is the screen big enough for either of them?

Turn your iPhone into an ocarina.

2008-12-04T15:26:00.001-05:00

I recently installed an unusual application on my iPhone: Ocarina. This program turns your iPhone into a four-hole ocarina, with the holes outlined on the iPhone’s touch-sensitive screen. But the really cool thing is that you actually blow into your iPhone to simulate blowing into the ocarina! Try it: it really works!

Many of my students agree that this is really cool, although some adults think that it’s a waste of time. I don’t really understand their point of view, since they are likely to spend their time on useless things like watching football games, but anyway....

The reason that I had to demo this product for my precalculus class is that we have just finished studying the use of trigonometric and exponential functions to model musical sounds, and one of the issues that arose is what the dependent variable represents when graphing an oscilloscopic rendering of a tone. Sure, if Middle C is 262 Hz, we notice that the frequency is 262 cycles per second since the period of the independent variable is 1/262 of a second. But what does the y-axis represent? We say pressure, and we may measure it in pascals or mV, but what does this have to do with the loudness of a sign? The direct analog construction of the iPhone ocarina application — with no intermediate abstractions of digital software — provides a clear understanding of this phenomenon, since the user’s breath blowing into the iPhone moves the membrane of the microphone, illustrating pressure in a literal way.

Teaching spreadsheets in high school math classes

2008-12-02T20:20:00.002-05:00

Should high-school math classes be teaching Excel? Or, more generally, should we be teaching spreadsheet use — and Excel just happens to dominate the market? We have been exploring these issues at Weston High School.

Certainly the right point of view is to teach spreadsheets rather than Excel, although the dominance of Excel means that it will inevitably be hard to distinguish it from spreadsheets in general. Anyway, I think the real questions are the following:

What can spreadsheets add to high-school math?
When and in what order should we teach various spreadsheet techniques?
Should we teach non-mathematical skills such as formatting cells, creating headers, etc.?

A side point is that knowledge of Excel will be very helpful to our students in college courses and in a great many job situations, so somebody should teach it in high school. I suppose the responsibility falls to the math department by default, even if it isn’t really math, though that conclusion makes me uncomfortable. The only other likely places are the science department — since science courses also do a fair amount with Excel — and the business department, though that wouldn’t touch all students by any means.

There are a lot of issues, large and small, in using Excel. The notion of a variable is quite different from that of a variable in mathematics. Order of operations is important, and that’s almost identical to what we do in math and can therefore reinforce it. Sorting becomes important, and that’s a mathematical concept that comes up a lot in computer science courses but rarely in pure math. Graphing and regression are possible in Excel, but both are clumsy. Sometimes the syntax can be confusing, such as beginning a formula with an equals sign, but getting used to different syntactic conventions is a useful mathematical skill. A great many mathematical functions are built into Excel and can therefore be reinforced when we use spreadsheets. Perhaps most important is the level of abstraction involved in creating formulas that can be dragged vertically or horizontally independent of pre-existing data.

We’ve just completed an Excel activity in my college-prep Algebra II class: Saving for College. My hope is that this activity will not only give some experience with spreadsheets (that’s the secondary goal) but will also reinforce some of the important concepts in exponential functions (that’s the primary goal).

Incidentally, it turns out that many of those who teach Excel only have a very narrow view of this powerful piece of software. (As much as I don’t like Microsoft, I do have to admit that Excel has a great many excellent features and has an enormous number of useful options, many of which I barely know myself.) So I wonder if Weston needs to have a workshop in which we try to plumb the depths of Excel and figure out which aspects of this software will be most useful in teaching high-school math.

"Everyone else does it."

2008-12-01T15:04:00.003-05:00

The Josephson Institute Study of the Ethics of American Youth has been widely reported on such widely varied outlets as National Public Radio, Fox News, and Yahoo News. They report “a troubling picture of our future politicians and parents, cops and corporate executives, and journalists and generals.”

I do agree that their picture is troubling, but something about their analysis makes me uneasy. First let’s look at their results:

More than one in three boys (35 percent) and one-fourth of the girls (26 percent)...admitted stealing from a store within the past year.

...

A substantial majority (64 percent) cheated on a test during the past year (38 percent did so two or more times).

...

As bad as these numbers are, it appears they understate the level of dishonesty exhibited by America’s youth. More than one in four (26 percent) confessed they lied on at least one or two questions on the survey. Experts agree that dishonesty on surveys usually is an attempt to conceal misconduct.

The justification, of course, is that “everyone else does it.” That may explain the cognitive dissonance:

Despite these high levels of dishonesty, the respondents have a high self-image when it comes to ethics. A whopping 93 percent said they were satisfied with their personal ethics and character and 77 percent said that when it comes to doing what is right, I am better than most people I know.

So, how do we interpret all of this? As a teacher of teens, I have to be troubled by these results. (I’m ignoring the self-reported accounts of using the Internet to cheat, as that’s a remarkably gray area.) But the report doesn’t quite ring true, despite the assurance that “These statistics have been verified by the Department Chair, Decision Sciences & Marketing, Graziadio School of Business & Management, Pepperdine University.” Maybe I’m in an atypical situation, but I just can’t believe that over half of my students have cheated on a test during the past year. I don’t want to be flippant, but maybe it depends on what the definition of “cheat” is. Maybe I’m just unobservant, but I don’t see students using notes on a no-notes section of a test, and I don’t see them texting on their cell phones, and it’s hard for me to figure out other ways in which they might be cheating. I do hear of the occasional student in other classes who texts during a test or sneaks in notes, but I just don’t see it, and it seems rare and exceptional. I guess I have to look into this matter further.

The Big Ideas of Algebra, Part One

2008-11-30T16:01:00.002-05:00

Earlier this month I participated in a fascinating two-day seminar on The Big Ideas of Algebra, taught by Deborah Hughes-Hallett and sponsored by Teachers as Scholars. Although I undoubtedly talked too much, I figure that that was because I had a lot to contribute. Nevertheless, I learned a number of valuable things from the seminar, and they will be as useful both at Weston High School and at the Crimson Summer Academy. Mostly this was a matter of focusing my attention on things I already knew and believed but wasn’t thinking much about. In particular, I am now convinced than ever that we need to pay a lot more attention to symbolic literacy (understanding the symbols and combinations of symbols used in algebraic expressions) and to the distinctions among expressions, equations, and functions. Because of my linguistics background I have always believed that one important way to look at mathematics is that it is a language — in fact, that’s probably what got me to make a smooth transition from linguistics to math — but I hadn’t thought enough about the implications of that point of view when teaching math.

In addition, among the other matters we talked about in the seminar, we discussed the assignment of partial credit for work in solving a problem — more on this later, but it definitely reflects one’s views on what the big ideas are — and whether the study of algebra is distinct from (and prior to) the study of functions. More on that later as well.

"Opportunity, compassion, honor, excellence, Davidson"

2008-11-28T11:56:00.001-05:00

I saw this catalog the other day, and I found the cover strangely appealing:

I’m not sure which part I liked better: the “Davidson Bill of Rights” at the bottom, or the list of words at the top, terminating in “Davidson.”

(It was actually a Davidson College catalog, BTW.)

The Girl of His Dreams

2008-11-27T07:01:00.003-05:00

If you can’t travel to Venice in the real world, the next best thing is to travel vicariously in the novels of Donna Leon. Formally speaking, these novels are squarely in the mystery genre, but Leon devotes as much attention to her locale (Venice, of course) and her characters (primarily Commissario Guido Brunetti and his family) as she does to the plot of the mystery. Some readers might find this balance disappointing, but the books are much the richer for it.

The Girl of His Dreams is the latest in Leon’s Brunetti series. The characters continue from Blood from a Stone and Death at La Fenice, both of which I read last year; the stories are independent. This time we have a lot about religion: the Roman Catholic church, Catholic priests, and a somewhat vague alternative but Christian religion that might be a cult or at least a scam. The teenagers are a little less stereotypical now, perhaps because they’re older. There is also a continuation of two themes from Blood from a Stone, ethnic prejudice and the presence of foreigners in Venice. This time the foreign group is Gypsies, who have fled from the former Yugoslavia during the conflicts there. Political issues infuse the novel, ranging from the treatment of Gypsies to the word itself to the Venetians’ attitude toward the Church. Leon’s pace is fairly slow and deliberate, but the book is never boring. Do read it.

A small linguistic note:
Leon is an American living in Venice, so she wrote the book in English, though Italian and Venetian are sprinkled lightly throughout to add an air of authenticity. The linguistic issue arises when two characters decide whether to call each other by the familiar or the polite second-person pronoun. I’m familiar with this issue in French and German, and I’ve asked Spanish-speakers about it in Spanish, but I don’t know much about it in Italian. Nevertheless, I understand that an Italian author could simply make a point by having a character say “tu” or “voi.” This distinction is nearly impossible to translate into English, thereby requiring some sort of circumlocation or paraphrase. But the English-speaking writer can simply have her characters say something like, “Shall we call each other tu?” or even “Shall we use the familiar form of the pronoun?” The latter, of course, would be unbearably pedantic and implausible, so we have to assume that the reader will understand “tu” from context or from familiarity with other Romance languages.

Meme abuse

2008-11-26T05:54:00.001-05:00

What’s a meme? Well, those of us who have spent too many years on the Internet (from its inception in 1969, actually, when it was called the ARPAnet) and those of us who have read The Selfish Gene, by Richard Dawkins, know what a meme is. Although the Wikipedia article on memes is far too long and leaves a lot to be desired, it definitely includes the correct definition:

A meme...comprises any idea or behavior that can pass from one person to another by learning or imitation. Examples include thoughts, ideas, theories, gestures, practices, fashions, habits, songs, and dances. Memes propagate themselves and can move through the cultural sociosphere in a manner similar to the contagious behavior of a virus.

That’s clear enough, so why is the word used incorrectly these days by so many people, some of whom should definitely know better but most of whom have never learned what a meme really is? Many writers seem to think that a meme is an informal quiz or questionnaire that is passed around by email or by the Web, often of the “you are a _____” variety. Now you can see both the similarities and the differences here: Do they propagate themselves, or do users intentionally transmit them? Are they cultural ideas and behaviors, or are they questionnaires? The word is definitely losing most of its import these days!

As a teacher, I suppose I’d better cite some sources for this claim. I’m sure that some of my colleagues would be aghast that I cited Wikipedia as my source for the correct use of a word, but so be it. As for the current incorrect use, I am reluctant to cite either email messages or websites of friends — for obvious reasons — but I can probably find similar use by strangers without much effort. Let’s see... most of the initial hits from a Google search actually lead to the correct usage (much to my surprise), but I’m sure I can also find the usage I object to... OK, here are a few:

That’s enough. You get the idea. What’s up here?

Reading the OED and The Professor and the Madman

2008-11-25T06:03:00.002-05:00

I have recently read two unconnected but closely related non-fiction books: Reading the OED: One Man, One Year, 21,730 Pages, by Ammon Shea, and The Professor and the Madman, by Simon Winchester. Probably I should have read them in the reverse order, but it was Shea’s 2008 book that impelled me to go back and read Winchester’s, which was written ten years earlier.

As the subtitle to Shea’s book suggests, he successfully took on the self-assigned task of reading the entire Oxford English Dictionary in a year. You may wonder why anyone would do such a thing — one of my colleagues would uncharitably claim that Shea must have too muich time on his hands — but never mind, the book is well worth reading on several counts even without a compelling answer to that question. First of all, any reader has to be simply astounded that anyone could accomplish such a feat: it has a fascination similar to any story of the accomplishment of a long-lasting unlikely challenge. Second, the details surrounding the endeavor are of interest to any compulsive reader (not that I would know anyone in that category), ranging from Shea’s physical arrangements for the effort to the effects on his eyes, his body, and his relationships. Third, Reading the OED does not merely recount the story of what Shea did but also includes lots of notes on many interesting words that he encountered along the way. Definitely a niche book, I suppose, but go read it if you’re a lover of words and dictionaries. And if you didn’t grow up with a dictionary in every room, it’s never too late to start.

Winchester’s book is much more of a popularization. Basically it tells the tale of two men in Victorian England: James Murray, “the professor” and the principal editor of the OED for decades during the creation of its first edition; and Dr. William Chester Minor, “the madman” and the most prolific contributor of source material to the OED over the same decades. I wish this book had been around during my father’s life, not only because he was a lover of words and dictionaries but also because of one of the stories he used to tell as a psychiatrist. It concerned a visitor to the large mental hospital where my father was the director; the visitor stopped to ask for directions from the first person he saw, and the reply turned out to be detailed, complex, and accurate. It turned out that the person giving directions was a patient in the hospital. When the visitor expressed surprise, the reply was, “I may be crazy, but I’m not stupid.”

I’m sure you’ve heard that line before in other contexts, but this (probably apocryphal) story is the context for it that always sticks in my mind. It continued to resonate for me in The Professor and the Madman, where Minor is portrayed as a deeply paranoid schizophrenic who spent most of his adult life confined to the Broadmoor Asylum for the Criminally Insane, as a sentence for shooting a man whom he had mistakenly believed to have broken into his apartment. Winchester tells the entwined stories of Murray and Minor, but mostly Minor’s, which is the more fascinating or the more sensationalistic one, depending on your view of such things. In any case, I did find it fascinating, but I wish there had been more details of the lexicographic procedures used for researching a writing a gigantic dictionary in pre-computer days. If you’re not a dictionary lover, read it for the story of Minor’s life and mind; if you are a dictionary lover, read it not only for that story but also for the account of how the OED was constructed. And, in either case, read it as intellectual history: Winchester’s portrait of the times provides more than just a glimpse of what was happening in Britain then.

Spanish foods?

2008-11-24T15:53:00.002-05:00

Following up on yesterday’s footnote, I need to mention another linguistic annoyance: the misuse of the word “Spanish.” Yes, it correctly describes the language that is spoken not only in Spain but also in much of Central and South America, but it’s not the right word for the culture, the food, or the people — unless, of course, you’re talking about Spain itself. For the Western Hemisphere we have the perfectly good words “Hispanic” and “Latino.” Anyway, my local neighborhood convenience store changed owners recently, and now it advertises “Spanish & American Foods,” as you can see in this picture. (I couldn’t find an angle that would avoid the intrusive stop sign, but you can still read it pretty well.)

Needless to say, I found lot of Latin American items inside the store but very little food from Spain. They do, however, primarily carry the Goya Foods brand, and it’s of interest that Goya was indeed founded by a couple from Spain. Goya, however, clearly uses the words “Spanish,” “Hispanic,” and “Latino” correctly on their website.

Midsummer Night's Dream

2008-11-23T11:55:00.008-05:00

Kudos* to the Weston High School Theater Company for its outstanding production of Midsummer Night’s Dream the past three nights. Among the excellent cast, I first want to mention Katherine Donahue (Helena) and Anna Been (Hermia), who were exceptionally effective against each other (and sometimes against the male leads) portraying convincingly fierce women. You’ll say that of course girls are always stronger than the guys in high school drama productions, but in this case that wasn’t quite true: far and away the best performance was given by Brian Cowe in his amazingly intense, madcap rendition of Puck. All I can say is, “Wow!”

*I can’t refrain from observing that “kudos” is a singular noun, and it irritates me when I hear or see a reference to “another kudo” or the like. If only more people studied Greek, they would know that of course κυδος is simply a third-declension neuter noun in its nominative singular form. Now I know that it actually looks misleadingly like a second-declension masculine, but... OK, OK, end of rant.

Teaching RSA in high school

2008-07-25T06:10:00.001-04:00

By this point I’ve taught simplified versions of the RSA algorithm to ten different cohorts of teens: four years’ worth of Honors Algebra II students at Weston High School, juniors for four summers at Crimson Summer Academy, and two years’ worth of college-prep Algebra II students at Weston. Tweaking the details as I’ve gone along, and benefitting from changes in technology, I’ve learned a lot from these experiences.

There are several types of benefits for the students. Some benefits are conceptual, involving understanding ideas about public-key cryptography, ranging from technical questions like how a cryptosystem can use a public key, why that’s necessary, and why it’s secure, to public-interest issues like whether we can trust so-called “secure” financial transactions on the Internet. I could have predicted these benefits; the unit was designed to try to achieve them, after all. And I could have predicted the success of some of the more concrete mathematical benefits as well, since RSA involves exponentiation, prime numbers, modular arithmetic, factoring, representation of characters as integers, and other operations with numbers. But a third type of benefit is more of a surprise: because the technical details are complicated, and even a single mistake can doom the effort to failure, most of my students have been doggedly persistent in paying attention to details and getting them right. Too often we can fall into the trap parodied by Tom Lehrer: “The important thing is to understand what you’re doing rather than to get the right answer.” We give so much partial credit that a student can get a B without ever producing a correct result. Part of the way that my colleagues and I have avoided this trap with RSA is that our sequence of activities and assignments concludes with a two-way exchange of messages: each student sends me a message using my public key, and I reply with a message using the student’s public key. This gives everyone practice in figuring out their private and public keys, enciphering, and deciphering. But fewer than half the kids get it right the first time, since there are so many opportunities to make mistakes. Unlike the usual math problem, they can’t settle for having a couple of points taken off; the message simply won’t work. So they try over and over again — sometimes four or five times — in order to get it right. If they don’t, I can’t read their message, or they can’t read mine.

If you’re interested in checking out how I’ve simplified RSA so it can be studied at the level of Algebra II, take a look at my worksheets, starting at RSA Phase One. (If you keep incrementing the “1” in that URL, you’ll find the next three worksheets at the expected URLs.)

Dim Sum at Chau Chow

2008-07-23T17:14:00.002-04:00

Two years ago I promised a review of the dim sum at the then-new branch of Chau Chow in Dorchester, but I don’t think I ever wrote one. So here, at long last, is that review.

Barbara and I ate dim sum there this morning (for what must be at least the sixth time — so you can see that we like it). Chau Chow serves traditional dim sum, where the servers roll carts around the restaurant and you order small quantities (Chinese tapas?) by pointing, not from a menu. There are, of course, both advantages and disadvantages to this system: aside from being authentic and just generally cool, the rolling-cart method has the advantage that you can see what you’re getting; it has the disadvantages that the food can sometimes come in very rapid succession, and you don’t always know what you’re getting, especially when the server speaks little English or very heavily accented English. At Chau Chow there are several servers in this category, but they’re all friendly and willing to try. The food is quite delicious, at least to these moderately educated Western palates. I don’t know what customers at the extremes would think — either the extreme of wanting totally Americanized food or the extreme of wanting nothing familiar. Perhaps both of those groups would be disappointed.

There are several dishes about which Barbara and I can agree: we’re both very fond of them. This morning we had scrumptious pork-and-shrimp shumai, unctuous eggplant that’s probably bad for us, yummy ground pork dumplings, the always delicious fried taro cakes (with a bit of shrimp in them), two different kinds of lovely shrimp-and-scallion dumplings, some not-to-be-missed lobster dumplings (yum!) — all of those were items we both loved. Do you begin to detect any themes there? In addition, we had scallion dumplings (which Barbara liked more than I did, since I’m put off by the flavor that steaming imparts to scallions) and stuffed mushrooms (which I love, but which have a texture that doesn’t appeal to Barbara). Needless to say, this was too much food, so we took quite a bit home to reheat for breakfast and/or lunch tomorrow. The entire bill came to $42.00 including tax and tip, which sounds like a lot for breakfast or brunch but was actually quite reasonable when you consider all the leftovers it provided.

So go to Chau Chow, especially if you have a group of more than two people, so you can sample more choices. Maybe you’ll try the chicken feet.

Do I look Russian?

2008-07-22T20:54:00.002-04:00

One day I walk into a Russian grocery store in Watertown, and the owner starts speaking to me in Russian; I don’t understand a word. Another day I walk into a Russian grocery store in Waban, and the employee at the register starts speaking to me in Russian. Waiting to check out a book at the Boston Public Public Library, I can’t understand a question from the next patron in line, because — you guessed it — the question is in Russian. Buying new glasses at LensCrafters, I remark to the optician that I assume from his name that he must be Russian, and he says yes and that it’s clear that I am too.

Do I look Russian? Apparently I do, though I never thought so. I suppose it isn’t surprising, since that’s what most of my ancestry is. But I speak only about 20 words of Russian, and the only phrase that’s really useful to me is, “Я не понимаю.”

Interpreting political data

2008-07-21T16:01:00.003-04:00

I want my CSA sophomores to understand many sorts of visual representations of data — tables, charts, graphs, etc. — especially in the context of elections, since we’re applying mathematics to models of voting. This summer, of course, we have a wealth of material to choose from, both prospective (polling data) and retrospective (historical data). Perhaps the best source for both is FiveThirtyEight; Electoral Projections done right; the only downside is the complexity of their representations. Being a teacher, I try to turn this complexity into a teachable moment, but it’s still necessary to figure out how to help kids digest and understand the representations. Here are two examples:

One day we looked at FiveThirtyEight’s Electoral History Charts. Here's a small part of one chart, so you can see what I mean about complexity:

This is pretty overwhelming even for college students, so it certainly can’t simply be thrown without explanation at kids who’ve just finished their freshman year in high school. After digging into it, you realize that it’s a wonderful (and almost successful) attempt at representing several different dimensions of information in one two-dimensional table — but it does take some work:
- It’s clear what’s going on horizontally. Each row represents one state.
- The vertical axis is almost as clear; one realizes from context that each column is a presidential election fro 1948 through 2004.
- By now we’re all familiar with the symbolism of red states and blue states, so of course the red cells show elections where the state voted for the Republican presidential candidate, and the blue cells where the state voted for the Democratic candidate.
- But there are different shades of red and blue: the darker and more saturated colors (such as Maine in 1956 or Massachusetts in 1996) represent landslides. The lighter or less saturated the color, the closer the election was (in that state); really pale colors, almost indistinguishable from white, show races that were so close that they were almost a tie.
- Finally, there’s a letter and a number in each cell. These show the winning party and the margin by which it won. For example, in 1984 the Republican candidate (Reagan) took Connecticut by a 22-point margin.
The class is already divided into six groups, each with five students. To get them to dig into the data and to understand the interpretations, I assigned each group a region of the country and asked them four questions:
- For each of your states, figure out the average margin by which the Republicans won those states in the past ten elections (1968–2004). One way to do this is to count the “r” numbers as positive, the “d” numbers as negative, and average them. Do this separately for each state in your region(s), and list the results.
- If your region(s) contained both positive and negative averages, find the state with the most positive average and the state with the most negative average. List them, along with their averages. If your region(s) contained only positive or only negative averages, find the states with the smallest and largest averages, and list them, along with their averages.
- In which year did your region(s) vote most heavily Republican? Find out who the presidential candidates were in that year.
- In which year did your region(s) vote most heavily Democratic? Find out who the presidential candidates were in that year.
This all took a long time, but it worked out well. Each group then reported their findings back to the whole class, after which we were able to make some horizontal and vertical generalizations: What happened (nationwide) in 1984, where we see a sea of red? What happened (chronologically) to Vermont? And so forth.

I hear you asking what the chart does when a state votes for a third-party candidate. Using the RGB principle, the site colors the cell green. For example:

This, of course, gave us an opportunity to talk about third-party candidates. Students were suitably amazed when they learned how a segregationist candidate (Strom Thurmond) could have won Alabama by a huge margin in 1948, despite what should have been a large number of black voters.

These charts are abstract and difficult, partly because they’re so textual. So what about a more visual representation, such as a map? Maps are a great way of presenting this sort of information, though they really have to be snapshots in time and are therefore not suitable for longitudinal historical data. It turned out that the maps we used had a great side benefit: students learned a bit about geography (which isn’t much taught these days), since most of the maps omit the names of the states. Here were two of the maps we used, the one on the left showing the current polls for the upcoming election, and the one on the right showing the results of the 2004 election:

These maps let me ask questions like these:
- Of the states that Kerry won in 2004, which ones are now likely to switch to the Republican candidate (McCain) according to the map? What is the total of their electoral votes?
- Of the states that Bush won in 2004, which ones are now likely to switch to the Democratic candidate (Obama)? What is the total of their electoral votes?

More on simulations later. Stay tuned...

Zakiyyah's Concert

2008-07-20T18:05:00.009-04:00

Instead of being out in the thunderstorm this afternoon, I attended a beautiful concert performance by my fellow Dorchesterite and former student, coloratura soprano Zakiyyah Sutton. (Yes, I had to look it up too. I used to know what coloratura meant, but I had forgotten.) The concert was held at the mostly white Old South Church in Copley Square, but was actually sponsored by the Concert Committee for Young People’s Artistry and Education of their sister UCC Church, the predominantly black Eliot Congregational Church in Roxbury. As you’ll see, this racial distinction turned out to be relevant.

Zakiyyah, who just graduated from the Boston Arts Academy, was a student of mine for two summers at Crimson Summer Academy and will be attending Wellesley College in the fall. She sang an amazing 14 numbers in this concert: ten as solos and four as duets with fellow performer Jamal Hoskins, a tenor, who performed five solos (and, of course, four duets). The Eliot Studio Singers accompanied a few of the songs as well.

By far the best performance was Zakiyyah’s rendition of the aria “Der Hölle Rache” from Mozart’s Magic Flute. This was actually her second song in German, since she had opened the concert with “Bist Du Bei Mir,” attributed to J.S. Bach in the program but apparently actually written by Gottfried Heinrich Stölzel, or so they say. Zakiyyah’s other two pre-intermission solos were Scarlatti songs, both beautifully sung in Italian; she was so convincing in both languages that it was only afterwards that I found out that she actually doesn’t speak either of them.

The second half of the concert was less familiar to me, including a song from Aladdin, one by Stevie Wonder, and several gospel numbers, only two of which I knew. Culturally speaking, I found the performance eye-opening in several ways, starting with the fact that I was in a small minority in the audience (there were probably only six or seven whites there) and I have very little familiarity with the traditions of the black church, both for racial and religious reasons. Sure, I know about them second-hand from books, plays, and movies, but it’s something quite different to be immersed in the black church in person. The differences became vividly evident when Zakiyyah movingly dedicated a song (“His eye is on the sparrow”) to her ailing father and then broke down when she started to sing it. The audience was just so supportive of her, and in a way that no white audience could have been. I don’t meant to suggest that a white audience wouldn’t have been equally supportive, because of course they would have tried to be — they just wouldn’t have been able to show it very well. The interaction between performer and audience was just so meaningful and effective in this context.

About ten minutes later, Zakiyyah got back up and said that she had recovered and wanted to sing the song the way it should be done. Actually, I thought she had sung it perfectly well the first time — she did manage to get through it successfully with the aid of the audience — but I have to admit that the second rendition was truly beautiful, and I’m glad she decided to do it.

In general, the solos were much more effective than the duets, perhaps because Zakiyyah was definitely the stronger performer. But their closing number, a duet version of “Amazing Grace,” was moving and perfect.

I’ll close with a couple of non-musical notes: the opening remarks by Old South Church Associate Minister Quinn Caldwell included an African proverb that definitely resonated with me: “If you want to walk fast, walk alone; if you want to walk far, walk together.” This speaks to me in part because of what it says about teaching. (More about that in a later post.) Also, I was struck by the explicit recognition of two judges in the audience: Judge Leslie E. Harris and Judge Milton L. Wright, Jr.; the latter turns out to be “a gifted singer and writer of a musical production as well as a lawyer.” The musical director from the Eliot Church pointed out that performances like this one show “Roxbury on the good side,” in contrast to what they usually see in court. While Zakiyyah is from Dorchester, the point is still completely valid and contrasts with what we usually hear on the news. Crime is news; music isn’t.

Ashmont Grill revisited

2008-07-19T21:16:00.002-04:00

It was too hot to cook today, so Barbara and I went to the Ashmont Grill, along with our friend Cheri. This was our third dinner visit there in the past six months or so (in addition to a couple of brunches). I didn’t post anything about the previous two dinners, since I was waiting for a tie-breaker, and now we have one.

First of all, what happened two visits ago? We had been disappointed at that time, because earlier experiences at the Ashmont Grill had all been wonderful; but that time everything was mediocre. Vegetables were somewhat overcooked, meat was a bit dry and not hot enough, and service was haphazard. Next time would be better, we hoped. And indeed it was. So which was the real Ashmont Grill? I am pleased to report that the one disappointing experience was an anomaly, and all seems to be well. The three of us sampled a variety of items on the menu, and there wasn’t a false step among them: crisp, light calamari, whisked to us from the fryer without spending time under a heat lamp; plump, fresh, garlicky mussels in a red pepper sauce; a top-quality hamburger cooked exactly to order; fall-off-the-bone short ribs in not too much sauce; excellent home-made cole slaw; hot, thick, sinfully rich home-made onion rings; hot, fresh, cornbread; and a nice bottle of Côtes du Rousillon.

The prices, of course, are significantly lower than those at Chris Douglass’s other restaurant, his flagship Icarus, which is one of the very best restaurants in Boston. But it still seems a bit expensive for an informal, low-key, neighborhood-type place. Oh, it’s still definitely worth it, but don’t expect cheap. The food and service are great; now if only the prices were a little lower...

What kids call their parents...and their parents' friends

2008-07-17T07:53:00.003-04:00

Just getting around to blogging this, but there was a fascinating article a few weeks ago in the Boston Globe, made all the more relevant to me because it mentioned several of my Weston students and was written by the mother of one of those students. Ellen Freeman Roth’s article, headlined “Not your father’s nicknames when teens talk to parents,” explored what kids call their parents and their parents’ friends:

Lisa and Michael Josephson of Old Greenwich, Conn., are Mama Jo and Papa Jo, names coined by their daughter’s friend. Timothy Sweet of Watertown began calling his father “Sweet Man” a dozen years ago on a Boy Scout trip. Sweet likewise has nicknames for his friends’ parents, including “Glenzo” for Glen and “Pina” for Patricia.

Sarah Switlik, 18, a Babson College student from Princeton, N.J., said her mother, Pam, wasn’t thrilled at first when Sarah called her P-Money. “Initially my mom said, ‘Really, Sarah,’ exasperatedly. Now when she’s texting she signs off, ‘Love, P$.’ It makes her feel like one of the girls.”

...

Caroline Gaulin, 22, of Greenwich, Conn., yelled “My bad, G-Dog!” to her father, Dan, during a basketball game to make light of an error she'd made. “After that we started calling him G-Dog,” she said. “Now he loves it.”

Teachers are almost always called by title and surname at Weston, but at CSA we’re all on a first-name basis. These customs run counter to expectations and fly in the face of the customs for naming of parents and parents’ friends, at least based on my predictions. There are probably some interesting class issues here. Although I grew up calling my parents “Mom” and “Dad,” I called all my other relatives and my parents’s friends by their first names: it was Lillian and Leonard, not Aunt Lillian and Uncle Leonard; Luke and Gen, not Mr. and Mrs. Garner. But Barbara grew up more formally, with Aunts and Uncles and surnames with titles. I’ll have to ask my CSA students what they do; I’ll predict big differences between Weston and Dorchester.

Supreme Musical Artists of the Past Fifty Years

2008-07-16T07:50:00.003-04:00

As I mentioned in my post of four days ago, my sophomores at Crimson Summer Academy (CSA) are currently studying models of voting. While I’m trying to move them away from cuteness as a criterion and toward serious consideration of candidates, my mission is more mathematical than political. So I want my students to learn about the mathematical methods involved in various answers to our Big Question for the summer: “What if nobody gets a majority?” We’re a democracy (more or less), which means that the majority should rule (more or less) except where minority rights are involved. So we study all sorts of real-life voting methods that soon-to-be voters will have to confront:

simple plurality, as in elections for Massachusetts governor
two-round runoff, used in much of the South and elsewhere
preliminary-and-final (very close to two-round runoff), used in elections for Mayor and City Council in Boston
Plan E Proportional Representation, used in elections for City Council in Cambridge
the Electoral College, used in elections for president of the United States

The problem is that even with the current heightened interest in Obama, teens still aren’t going to pay much attention to candidates for offices other than president. They don’t care about Cambridge and Boston city councillors. So, how do we grab their attention? What’s something in which they have a lot of interest and about which they have a lot of knowledge? Several years, ago one of my teaching assistants (“mentors” in CSA jargon), himself a Harvard undergraduate, made an excellent suggestion, which we’ve followed ever since: hold an election for three Supreme Musical Artists of the Past Fifty Years.

So that’s what we do. We collect nominations on the first day. Then, at various points throughout the course, we hold elections using the different methods listed above, always starting with the same nominees. Maybe the results will differ, depending on the method. Needless to say, the results among 15-year-olds bear no relation to the candidates for whom I would have voted. In fact, about a third of the nominees were individuals or groups that I hadn’t even heard of. Anyway, with no further ado, here were the winners from the two-round-runoff method, each listed with the number of votes in the second round (stay tune for the results of other methods later in the summer):

37	Tupac Shakur
32	Lil Wayne
31	Chris Brown

And the runners-up in the second round were...

23	Michael Jackson
15	The Beatles
15	Jonas Bros.

MBTA fares steady in real dollars for 100 years

2008-07-15T07:47:00.004-04:00

Take a close look at the yellow bars in this bar chart:

Much to my surprise, it turns out that subway fares in Boston have remained nearly unchanged for 110 years when adjusted for inflation, especially when you ignore the short-lived drop to ten cents in 1950. This chart comes from a fascinating document entitled “Report on the Proposed 2007 MBTA Fare Restructuring and Fare Increase,” published by the MBTA in July of 2006.

Why am I so unusually interested in this geeky document? Perhaps it’s because I’m a math teacher — or maybe it’s because I’m building a model railroad based loosely on the T, though I think there’s a lurking variable there that explains both phenomena. In any case, the general public should also become aware of it, especially with all the recent complaints against the MBTA. Many, perhaps even most, of those complaints are certainly justified, but isn’t it interesting that the fare hasn’t actually risen significantly in real dollars in over a century? Using my trusty TI–83 Plus calculator, I computed a linear regression for the data, with years since 1900 as the input values and the fares in 2005 dollars as the output values, excluding the anomalous dip in 1950. The slope indeed turned out to be indistinguishable from zero — actually 0.0013 to two sig figs. Even when I included the 1950 fare it was still only barely higher, being 0.0017. The correlation coefficient wasn’t good, but it’s still quite compelling that the best-fit line should be nearly flat.

No surprise: they support Obama.

2008-07-14T14:56:00.007-04:00

As I mentioned in my post of two days ago, the sophomore component of the summer course I teach at Crimson Summer Academy focuses on models of voting. Although the emphasis is primarily on applied mathematics, the 2008 course was destined to be more political than the previous summers’ versions. For the first time it was clear that voting would not be merely an academic exercise for these teens who won’t be able to vote for three more years. Ordinarily I try to avoid talking about politics with students, and in the typical math class it’s easy enough to avoid it. But in these circumstances there was no alternative but to take this as a teachable moment and embrace the students’ natural interest in the presidential race. Keep in mind that these are inner-city kids who attend public and parochial schools in Cambridge and Boston, with the largest contingent living in Dorchester and Roxbury.

So I started by polling the students about their political views. Here were the results:

0	John McCain
0	Ralph Nader
25	Barack Obama
4	None of the above
1	Prefer not to say

I guess we won’t invite McCain to speak to the class.

Interred with their Bones

2008-07-13T17:52:00.003-04:00

After many hours of listening — and I do mean many — I have finally finished the audiobook version of Interred with Their Bones, by Jennifer Lee Carrell. At times I wasn’t sure whether it was worth slogging through to the end, but I like to listen to something when taking a walk, and Interred with Their Bones held my attention sufficiently.

As you can tell, I am mostly unenthusiastic about this mystery novel. I am told that it was inspired by the DaVinci Code, but I guess I’ll never know, since I steadfastly refuse to read any more Dan Brown after suffering through Digital Fortress. They say that Carrell is a better writer than Brown, but that’s not hard, as I’m not the first to observe. In any case, Carrell combines implausible but exciting action with long academic passages about Shakespeare’s lost play Cardenio and the long-standing controversy about the authorship of Shakespeare’s plays. As something of an academic myself, I found these discussions reasonably interesting, though not very suitable to the audiobook format. The action scenes seemed more like a treatment for a subsequent movie. Shakespearean themes run throughout the novel, from the characters' professions as actors, directors, and professors through the Shakespearean locales and staged events intended to mimic Shakespearean scenes to the characters’s names (Rosalind, Kate, Henry, Athenaide). Well, I don’t think that Athenaide is actually a Shakespearean name, but it could just as well be.

This novel belongs to the genre in which it’s hard to tell the good guys from the bad guys. No spoilers here, but suffice it to say that there are several plot twists that are not too severely telegraphed. Some reviewers found Interred with Their Bones to be fast-paced. I did not. I’ll admit that it’s breathless, and maybe that qualifies. Also, there’s far too much wanton killing. Read it if you’re interested in Shakespearean issues and academics, but don’t bother if you’re looking for thrills and actions.

Cuteness counts

2008-07-12T13:12:00.003-04:00

My regular readers know that I teach Quantitative Reasoning (QR) at the Crimson Summer Academy (CSA) over the summer. (If you don’t how what CSA is, read my blog posts from May 7, 2007, and April 30, 2008.) The theme for all courses for the summer is The Student as Citizen, and the particular QR unit for rising sophomores is models of voting. More on that in a later post, since of course it’s especially interesting in this particular summer. Anyway, one girl’s succinct comment on Barack Obama yesterday was, “Obama’s cute.”

I didn’t know how to respond to this observation, but another girl in the class did: “Obama isn’t cute! Deval Patrick is cute!”

I decided to stay out of this conversation. Fifteen-year-old girls don’t see the world in quite the same way as I do.

Roche Bros. soft-shells better than Legal Seafood's!

2008-07-11T19:41:00.003-04:00

Which is a better place to buy soft-shell crabs, the Legal Seafoods fish market at Chestnut Hill or the Roche Bros. supermarket in West Roxbury? The obvious answer is Legal, of course. Everyone knows that fish markets are better than supermarkets, and Legal is well-known for selling impeccably fresh fish (not to mention fresh ads). But the Conventional Wisdom is apparently wrong. I’ve bought soft-shell crabs three times in the past month — once at Legal and twice at Roche Bros. — and the verdict is clear. The Roche Bros. product (at three dollars per crab) was tastier, fresher-tasting, and plumper than the Legal product (at six dollars per crab, though for slightly larger ones, I must admit).

On a slightly different matter, it's unfortunate that the Shaw’s and Stop & Shop markets in Dorchester can’t provide food and service of the quality provided by the West Roxbury Roche Bros., where the food is always good and the employees are both well-trained and friendly.

Peabody Square on Chronicle

2008-05-07T21:38:00.001-04:00

It was great to see my neighborhood featured on Channel 5’s Chronicle this evening! And no, it wasn’t because of crime, but because of diversity and the new transit-oriented development near Ashmont Station. The episode, called “Happenin’ Hoods,” included a segment on a “Boston neighborhood that combines the best of the old and the new”: Peabody Square, Dorchester. What came across was a neighborhood with lots of elegant old housing stock, an excellent restaurant, new condos and rental apartments, and — most importantly — a rich diversity in racial groups, ethnicity, sexual orientation, class, and income levels. In this part of Dorchester nobody blinks at an interracial gay couple, and that’s how we like it.

In the Woods

2008-05-06T06:09:00.002-04:00

It had to come to an end at some point. The experience of listening to the audiobook version of In the Woods, by Tana French, was a constant delight that enveloped me for 21 hours over a period of more than two weeks. Much of the credit has to go to narrator Steven Crossley, who brings the entire narrative to life, including an array of a dozen major characters who all sound distinct and true-to-life in Crossley’s reading. It’s a total pleasure to listen to him.

It’s also a total pleasure to be captivated by the gorgeously poetic language of Tana French, whom I don’t otherwise know as an author. The heightened intensity of her words couldn’t possibly continue for 21 hours, and of course it doesn’t, but quite a number of passages read more like poetry than prose. All of this occurs in the context of a novel that looks like a police procedural but isn’t really. It’s actually a psychological novel about introspection, the effect of early experiences, and interactions among well-developed characters. Some reviews have missed the point and have criticized French for not following all the conventions of the mystery genre. But it’s unfair to criticize her for not writing a different book! In the Woods doesn’t follow the mystery genre because it’s not a genre novel. Like a number of other examples of serious literature, it adopts the framework of a police procedural but has an entirely different program. I don’t want to reveal any of the details other than to say that the narrative takes place within a homicide squad of a modern Irish police department. Definitely read it — but don’t expect everything to be nicely tied up at the end as you would anticipate in a conventional mystery!

Salt of the earth

2008-05-05T06:36:00.001-04:00

Barbara and I went to Sel de la Terre to celebrate her birthday yesterday. As always, the food and service were excellent, though I found the entire experience a bit pricey: $200 in total, including wine (one of the least expensive bottles on the wine list!), tax, and tip. And then there was the parking, an astonishing $34 for anything over 80 minutes at the garage (which is shared by the Aquarium, an Emack & Bolio’s, and a Legal Seafoods restaurant). We hadn’t realized that valet parking would have been a bit cheaper, although the expected tip would eat up most of the difference. Maybe this won’t be an issue once Sel de la Terre moves to the new Mandarin Oriental Hotel. But anyway...back to the food...

For our first course, Barbara had giant white prawns, which came with spinach, creamy polenta, bacon, and greens. She reports that it was all delicious, as long as she could ignore the fact that the prawns came with their heads on. I had flatbread pizza with caramelized onions, spinach, lamb bacon (!), Comté cheese, fried capers, and créme fraiche. It sounds overly elaborate, but all the flavors melted seamlessly together to create an excellent dish.

Barbara then had steak frites with asparagus, cooked perfectly and very French. My main dish was described as follows on the menu:

Braised lamb shank with spring bean cassoulet, merguez, caramelized rhubarb and sweet onion compote.

I’m not sure how much merguez there was, but everything else was there in perfect balance — a great combination.

The service was wonderful. Perfect, you might say. The waitress was friendly without being intrusive, knowledgeable but never pretentious, and attentive without hovering.

Not surprisingly, we had no room for dessert and both of us even had leftovers to take home. I suppose it was worth the $200 for a once-a-year (or perhaps twice-a-year) experience.

Boston Trolley Meet

2008-05-03T18:16:00.001-04:00

Just got back from the Boston Trolley Meet (actually held in Somerville, not Boston). This event, sponsored by the Boston Chapter of the National Railway Historical Society, offered a combination of layouts, dealer tables, and field trips. The actual exhibit provided a good balance between “real” trolleys (mostly historical material on the prototype) and model trolleys (mostly layouts and rolling stock). Unfortunately the layouts focused almost entirely on the trolleys themselves, with very little in the way of scenery or structures, and the rolling stock was almost all very expensive, so I didn’t buy any. (I’m not in the market for a $300 trolley car.) It will still useful — and fun — to look through the various books, posters, maps, and DVDs, and to see how the various layouts presented working models of trolleys in tight spaces.

Technology in school

2008-05-01T15:24:00.002-04:00

No, this isn’t another one of those essays about the usefulness of technology in teaching math. This is a response to a fascinating post in Heather’s Comparative Childhood blog, in response to a newsletter from her daughter’s middle school. Here’s an excerpt from the newsletter:

Cell Phones, I-Pods, MP3 players, any other electronic devices are not permitted for student use at any point during the school day. If these items are seen or heard during school hours, they will be confiscated and a parent will have to pick up the device from your child’s house office.

This seems pretty reasonable, especially since the careful wording doesn’t prohibit possession of such devices, merely their use or visibility during the school day. And, of course, it is a middle school.

Heather’s post includes the following observations:

Is there ever a circumstance in which the presence and use of an iPod (or cell phone or MP3 player or digital camera or gameboy or fill-in-your-electronic-device-of-choice-here) is justifiable in a school setting? I guess I’m taking the perspective of the teacher on this one. There is nothing more annoying than someone’s cell phone going off during a lecture. And there is nothing more rampant in university settings than “creative” new ways to cheat during examinations. I can’t believe that the use of electronics for cheating begins at the college level.

My understanding on the ban of cell phones in public schools was that it was originally put in place to prevent drug deals going down on the school premises. But now cell phones could be used for anything from covertly cheating by sending text messages to voyeuristic photography in the ladies room to remotely setting off bombs. I won’t waste my space here, but we need only use of imagination to think of the ills of other electronics in the school settings. Nintendo DS’s create their own network within a local range.

These are eminently reasonable comments, but I need to take a different point of view, even though Heather is trying to take the perspective of the teacher. Of course she’s absolutely right that it is annoying and disruptive for a cell phone to ring during class, and she is also absolutely right that they need to be prohibited during tests, as they can be used for cheating (as Weston students know all too well). But there are also too many valuable uses of these electronic devices for them to be banned entirely in school — at least in high school, and I suspect in middle school as well. At Weston High School we ban cell phone use (or even visibility) in the classroom, but not in the cafeteria or outdoor areas; iPod use is left to the discretion of the teacher. Cell phones are a valuable way for students and parents to get in touch with each other, so students should be allowed to use them outside of the classrooom. And MP3 players may help many kids concentrate in noisy situations or just when taking a test; while I certainly don’t allow kids to shut out the world during a class discussion or lecture, I think it can be valuable to do so when trying to concentrate on individual work. I admit that there’s a small chance that a student may use an iPod for cheating, but that’s a lot harder than texting on a cell phone, which is currently the preferred method among high-school students and Boston firefighters. Of course a variant of the method used by the firefighters would be very difficult to prevent in school settings:

...a group of Boston firefighters took turns going into a men’s room at the Quincy middle school and sent answers via text message on their cellphones to colleagues in the testing room.

We can easily prevent this precise method of cheating in school by allowing only one student at a time to go to the bathroom and by banning cell phone use in the classroom during the test, but how do we prevent texting between a student who goes to the bathroom during the test and a classmate who has already taken the test and is currently in the cafeteria during a free period? Temporarily confiscating cell phones at the beginning of the test is the method preferred by some teachers. That works well...except for kids who have a second cell phone hidden away.

And while I’m looking at Heather’s blog, let me recommend several of her recent posts, especially the ones entitled “Wow” and “What would Jesus do, indeed”.

Where can Dorchester kids get into college?

2008-04-30T06:01:00.004-04:00

Where can Dorchester kids get into college? Anywhere!

Some of my Weston students believe that they are entitled to go to Harvard and BC and Bryn Mawr, but kids who go to public schools in Dorchester and Roxbury certainly aren't in their league. If your parents are rich and well-connected and have provided you with every educational opportunity that money can buy, you deserve to get into Harvard, don't you? But if your parents are low-income immigrants who have sent you to the school formerly known as Dorchester High School, you don't have a chance.

Or do you? Well, admittedly the deck is stacked against you; the odds are in favor of the Weston student. But let's look at some of the 29 high-school seniors who have been attending the Crimson Summer Academy for the last two summers, starting with some of the most competitive colleges:

Harvard admitted 3. That’s 10% of the class — can’t beat that at Weston.

Smith admitted an astounding 5 of the 15 girls!

BC admitted 3.

MIT admitted 1!

Brandeis admitted 1, Bryn Mawr 2, Johns Hopkins 1, Penn 1, Pitt 1, Syracuse 6, Union 2, Wellesley 1, Wesleyan 1; Barnard put 2 on their wait-list.

Some of the remaining six may also be highly competitive schools (I just don’t know about all of them): Denison admitted 1, Lehigh 3, Mass Art 1, Northeastern 8, Regis 3, and Wheaton 3.

OK, they’re not all from Dorchester and Roxbury, but they all attend public schools in Boston and Cambridge, and this college admissions record would be the envy of any public school and even most private schools too. Well done!

Money talks in Weston

2008-04-29T16:00:00.001-04:00

In Algebra II class today we happened to be talking about a certain prominent mathematician/physicist, and I remarked that he’s “the smartest living American, as he himself will be happy to tell you.”

“That can’t be true!” objected one student. “Bill Gates is the smartest living American!”

“What makes you think that?” I asked, being genuinely puzzled.

“Because he’s a billionaire,” replied one student. “He’s the richest man in the country,” said another. Several others chimed in with similar sentiments.

I told them that they had been living in Weston too long.

Death Comes for the Fat Man

2008-04-27T10:02:00.002-04:00

Highly recommended: Death Comes for the Fat Man, by Reginald Hill. This latest installment of the literate Dalziel-Pascoe series continues the high standards of its predecessors, though Dalziel plays almost no role in it. I won’t tell you what the title really means, because it would of course be a spoiler. Does Dalziel die, or is the title just a teaser?

Anyway, you should probably have read some of the earlier books in the series before tackling this police procedural, but that’s OK: if you’ve never read any Dalziel-Pascoe, go to the library and read some of the earlier ones! Then you’ll be ready for Death Comes for the Fat Man. But be sure to have a dictionary at your side as you read them, so you won’t be caught short by words like sempiternal. Every Reginald Hill novel is good for learning a few new vocabulary words. Of course they’re also good for plot and characterization, which are the real reasons to read them.

Amazing math applets

2008-04-25T15:26:00.003-04:00

Check out the Lawrenceville School’s amazing math applets! They provide links to class-demonstration applets that range from the unit circle and the sine function through transformations and vector addition all the way to slope fields and Riemann sums — not to mention the ever-popular Generic Applet, from which all the others can be built. Here’s a screen shot of the Sine and Cosine applet just to show one tiny example of what can be done:

Visiting Elmira

2008-04-23T20:16:00.002-04:00

Barbara and I just got back from spending a week in Elmira. Actually it was just five days, it only felt like a week. Mostly I played a bunch of computer Scrabble, took some walks in the surprisingly nice weather, and caught up on my reading. We also spent a very pleasant half day in Corning; I recommend the old part of town, recently renamed the Gaffer District. Oh, well, I guess I needed the vacation.

Daddy’s Girl

2008-04-21T07:00:00.003-04:00

On the whole I recommend Daddy’s Girl, by Lisa Scottoline. Formally it’s a mystery, but it’s mostly about families. Like many mysteries, it also carries a theme of law vs. justice, and Scottoline does an effective job of exploring this issue. Her protagonist’s relationships with her brother and her boyfriend are annoying, especially with the loud brother who talks in all caps — actually I listened to the audiobook version, so the caps were converted to shouting, as the author presumably intended, but I still kept wishing that Natalie would tell him to shut up. My other reservation was the implausible plot. But these deficiencies are outweighed by the convincing portrayal of the academic setting at Penn Law School and of Natalie’s large Italian family — perhaps similar to Scottoline’s? Who knows? Anyway, it’s certainly not the best mystery of the year, but it’s worth reading.

All-Dorchester seder

2008-04-19T07:17:00.002-04:00

Yes, it was one night early for Passover, but last night Barbara and I attended the 2008 All-Dorchester Seder, which is held every year at the First Parish Church. A seder at a church? Well, yes. In the first place, it’s a Unitarian Universalist church, so no one should be surprised that they would be hosting a seder. And in the second place, this endeavor is deliberately an interfaith community-building activity, so it’s best not to hold it in a Jewish facility even if one still existed in Dorchester. (For those who don’t know, most members of Dorchester’s once-vibrant Jewish community have long since fled to the suburbs, although there are still a few left here, and there’s a fair number of us who have moved into Dot in the past 25 years.)

Like many other worthwhile all-volunteer activities, the All-Dorchester Seder needs more publicity. I give the volunteers full credit for their hard work and accomplishments, but there really should have been more than 38 of us at this event. Religiously it was a good mix — about half of the people sitting near me being Jewish — but racially it was hardly representative of today’s Dorchester, since almost everyone there was white.

“Next year in Jerusalem!” Well, not exactly. As the Seder leader observed, this wish is to be interpreted symbolically, not literally. Very few of us intend to be in Jerusalem next year. But maybe next year there can be more attendees, with more racial diversity. I’ll remind everyone again in eleven months.

Justice Denied

2008-04-17T16:15:00.003-04:00

Just finished reading J.A. Jance’s Justice Denied, the 18th novel in the author’s J.P. Beaumont series of Seattle-based police procedurals. Though it’s not one of her best, Jance clearly hasn’t gotten tired and can still write a taut mystery with interesting characters. She explicitly deals with recurrent themes like “Can you trust this woman?” without making the reader feel that it’s merely a formula. Family relationships, especially those between parents and their adult children, add an extra touch, especially since the families involved vary in age, race, and social class. The author perfectly captures the internal monologue of a male protagonist who’s intellectually smart but can occasionally be socially clueless, not that I know anyone like that. Justice Denied is well-plotted but stronger on psychology than on action, so don’t read it if you’re looking for an action-packed mystery. But if you’re interested in story lines and characters, do read it, even if you aren’t familiar with any of the 17 previous novels in the series.

Don’t families in Weston talk about politics at home?

2008-04-16T17:18:00.005-04:00

Overheard this morning at Weston High School...part of a conversation between two sophomores:

“What can you tell me about John McCain?”

“Who’s he?”

”Oh, he’s some dude who’s running for President.”

Double Vision

2008-04-14T18:28:00.002-04:00

I have just finished reading Double Vision, by Randall Ingermanson. This science fiction thriller has a great concept, but the execution is disappointing. On the plus side, the novel speaks effectively to those of us who have worked in the computer industry, especially if we have any interest in computer science and physics. Knowing something about RSA and factoring certainly helps, but it isn’t necessary. Knowing something about quantum computing might also help — but since I know almost nothing about that field, how could I be sure? Anyway, the idea behind the book is fascinating, and the fact that the protagonist is a computer programmer with Asperger’s makes it fit into my accidental recent theme of Asperger’s Syndrome. However, there’s also the minus side: implausible characterization, poor writing (à la Dan Brown), unbelievable plot, and excessive Christianity. Worse yet, there’s a subsubplot concerning Jews for Jesus, and if anyone can explain to me how that organization is distinct from Christians, please let me know.

Dorchester and Weston

2008-04-13T17:59:00.005-04:00

According to an article in this morning’s Boston Globe, the average annual income in Dorchester 02124 (where I live) is $34,556. The average annual income in Weston 02493 (where I teach) is $531,374. That’s a ratio of slightly more than 15 to 1. No comment.

Pirates in Weston

2008-04-12T09:26:00.000-04:00

Last night the Weston High School Theatre Company put on a charming performance of Gilbert and Sullivan’s The Pirates of Penzance. The acting and singing were strong; the scenery, set, and costumes terrific; the pit orchestra first-rate. Derek Kief’s portrayal of Frederic was suitably over-the-top, showing a gift for comedy that I hadn’t known was in him. In the other male lead roles — it’s always a tough task to fill these male leads in high-school productions — Quinton Kappel’s Pirate King and Ben Heath’s Police Sergeant were amusingly effective. Both did a fine job; but, of the two roles that stole the show, the male one was clearly Alex Engler’s outstanding performance as Major General Stanley. Strong acting and singing from females is usually not quite so difficult to find in high schools, so it was no big surprise that Erika Grob’s Ruth was convincingly multi-faceted, nor that the bevy of General Stanley’s daughters formed a delightful chorus. The other role that stole the show, the female one, was (appropriately enough) Natalie Birren’s Mabel, fulfilling the operatic expectations of this exceptional coloratura role. And the choruses of pirates and policemen provided amusing comedic touches in their well-coordinated ensemble work. Presumably because of the gender imbalance of available cast, many girls had to double up as pirates and policemen, and there was only a limited attempt to make them up to look like men.

This morning I had to consult two of the most treasured volumes in my home library: Isaac Asimov’s Annotated Gilbert and Sullivan and Martyn Green’s Treasury of Gilbert and Sullivan (an appropriate name for a treasured volume). Both works are highly recommended. Concerning the “orphan/often” puns, Asimov comments that “even the most devoted pun lover might feel a little uneasy at this sequence, and parts of it are sometimes cut in actual performances.” But fortunately nothing was cut from this sequence in the Weston performance.

Alex Engler brought down the house in his flawless, very rapid rendition of the famous Major General’s patter song. A second patter song was added, presumably because this format is such a favorite with audiences: the song from Ruddigore, “My eyes are fully open to my awful situation,” was inserted, slightly changed with substitutions such as Frederic for Roderic. Asimov comments on this song:

This is the fastest of the patter songs... Gilbert was an absolute fiend on having his words heard through and above the music (which must have bothered Sullivan who felt his music was being sacrificed to Gilbert’s words), so it must have cost the librettist a deal to indicate that in this song, at least, hearing the words was all but impossible.

Asimov is referring to the couplet, “This particularly rapid, unintelligible patter/ Isn’t generally heard, and if it is it doesn’t matter!”

And speaking of the Major General’s song, we math teachers always enjoy the various allusions to mathematics in it:

I’m very well acquainted, too, with matters mathematical
I understand equations, both the simple and quadratical
About binomial theorem I am teeming with a lot o’ news [pause to think]
With many cheerful facts about the square of the hypotenuse.

I’m very good at integral and differential calculus
...
In conics I can floor peculiarities parabolous...

A few other random observations:

I am not sure why Ruth wasn’t made up to look older and less attractive, as Gilbert makes a point of contrasting her with the General’s daughters.

Speaking of daughters, I’m not sure why they got changed into General Stanley’s wards.

Asimov observes that Frederic’s 21st “birthday” wouldn’t actually come until 1944 rather than 1940 as Gilbert claims, since 1900 hadn’t been (wouldn’t be) a leap year! (This is true, despite the fact that the New York Times apparently printed an editorial on February 29, 1940, entitled “Frederic’s out of his indentures.”)

As is traditional in G&S, a number of small changes were made to enhance the performance, such as looking up into the sky and “estimating” the time as 11:38 (11:30 in the original) — again something especially amusing to math teachers.

Anyway, congratulations to Director John Minigan and all of his fine cast and crew!

An evening in Jamaica Plain

2008-04-10T06:16:00.003-04:00

Barbara and I spent a few hours yesterday evening in Jamaica Plain. First we walked to the Axiom Gallery, which is hosting an intriguing Math and Art exhibit through April 27 right next to the Green Street T station (confusingly on the Orange Line, not the Green Line). Most of the art is worth seeing for its own sake, but the special appeal for me was the large number of connections with some of the topics that my precalculus class has been studying this year. The sculptures of Bathsheba Grossman are particularly striking. For example:

The works of Kevin van Aelst were also vividly related to what we’ve been studying, as his Dragon Curve, Sierpinski Arrowhead (made of Triscuits!), and Cantor Set made out of a fractal egg all show:

I was also intrigued by the works of Keith Peters, which could readily be modeled in NetLogo or StarLogo, even though he apparently used neither, and also by the works of J. Michael James, whose fractal condor was especially beautiful as it swooped around on a large screen.

All in all, definitely a worthwhile experience. I just wish the exhibit had been more extensive, so that I could have justified recommending it to my Weston students. Barbara and I spent 45 minutes there, but I think most of my students would feel done with it after 20 — hardly worth the trip from Weston. But it would be worth the trip from Dorchester, even if we hadn’t already been in JP (where Barbara works).

Anyway, after visiting the gallery, we walked to Cafe D, where we had a pleasant and delicious dinner. Crispy calamari followed by a fish taco and salad for Barbara; arancini followed by duck confit with a cassoulet of braised white beans, portabella mushrooms, and pancetta for me. With wine, tax, and tip, it all came to just under a hundred dollars, which seems to be par for the course these days. It might or might not be worth the trip from Dorchester (on the edge, in my judgment), but, as I said, we were there anyway.

Gun, with Occasional Music

2008-04-09T06:11:00.002-04:00

Take one part Raymond Chandler and two parts Philip K. Dick. Or maybe it’s two parts Dashiell Hammett and one part Aldous Huxley. Let’s try all four. Then add three parts of George Orwell. Mix them all together, and you get Gun, with Occasional Music, by Jonathan Lethem, a noir science fiction thriller that successfully carries off this odd hybrid. I listened to the audiobook version, and I’m not sure whether it would have taken more time or less time to figure out what was going on if I had read it in print. Anyway, this odd tale of California in the very near future portrays a world of humanoid (“evolved”) animals, near-universal legal drug use, and a totalitarian government, all with a definite gloss of science fiction rather than fantasy. The noirish atmosphere is palpable and unsubtle. Characters are fairly interesting, the plot is intriguing, but basically the setting is all. Do read it (or listen to it), even if you don’t think it’s your cup of tea.

N is a Number

2008-04-08T05:56:00.003-04:00

I mentioned two days ago that I was going to watch N is a Number: A Portrait of Paul Erdős, a documentary that had been enthusiastically recommended to me by my former student, Kelly Mathislife. She writes that N is a Number is the “best movie ever” — although she does admit to a slight bias since Erdős is her hero.

So now I’ve watched it, with help from Netflix, which coincidentally delivered the DVD on Erdős’s birthday! This really was a genuine coincidence, since I had put it in my queue a couple of months ago with no idea when it would rise to #1. Anyway, Kelly knows that I certainly intend no disrespect toward her when I point out that of course she was exaggerating; N is a Number isn’t quite the “best movie ever.” It isn’t even even the best documentary ever. But it’s definitely a well-made, captivating documentary that should be watched by every math teacher, math student, and mathematician. It becomes totally clear that Erdős meets Paul Graham’s criteria that I discussed two days ago: absolute honesty and caring obsessively about his work.

Erdős, who died 12 years ago at age 83, was one of the greatest mathematicians of the 20th Century and certainly the most prolific; he is best known for his peripatetic life style, having had no fixed abode and collaborating extensively with hundreds of other mathematicians wherever he traveled. The movie is successful at vividly letting the viewer know the kind of person Erdős was, portraying him in person and through the eyes of his collaborators. Fortunately the filmmakers were willing to use subtitles extensively, since the accents of various Hungarian mathematicians (and others) could get in the way of ready understanding, even though almost everyone in the documentary was speaking English. As a math teacher, I thought there was a bit too much of an emphasis on anecdotes, but that’s a small cavil; I use anecdotes myself in similar ways, and I recognize that it’s the best way for the film to appeal to a general audience, who wouldn’t want to watch or listen to lots of mathematics.

I want to quote a couple of snippets out of N is a Number. One comes from Ron Graham — another Graham! but no relation to the aforementioned Paul Graham, as far as I know — who has a major role in the movie:

When mathematics appears in print, it’s theorem, proof, theorem, proof, but when we’re doing math it’s a completely different thing. It’s three or four people sitting around with cups of coffee, a pad of paper, throwing ideas back and forth, making a lot of conjectures, most of which turn out to be completely false.

That’s what should happen from time to time in our math classes, but it almost never does, even at Weston, except in last year’s Friday-afternoon optional after-school math get-togethers.

The other snippet comes from Erdős himself:

We’re trying to read the pages of The Book. We don’t create mathematics, we’re just trying to read the pages of The Book.

How Platonist can you get? This is clearly the right attitude toward the mathematical endeavor!

Heroes

2008-04-06T09:28:00.002-04:00

As I was reading Paul Graham’s essay, “Some Heroes,” it struck me that I’ve never liked being asked who my heroes are. In his second and fourth paragraphs, Graham reflects on the question itself:

I’m not claiming this is a list of the n most admirable people. Who could make such a list, even if they wanted to?

...

When I thought about what it meant to call someone a hero, it meant I’d decide what to do by asking what they’d do in the same situation. That’s a stricter standard than admiration.

I had never thought of that criterion before, but perhaps it would unstick me. Then I thought of the statement from one of my former students that Paul Erdős is her hero. [Brief aside: it’s tough to get the correct diacritic over that o. The natural tendency is to try for an unlaut — Erdös — especially since umlauts are relatively easy in HTML. But in Hungarian the diacritic looks like a double acute accent rather than an umlaut, producing a character with Unicode ID 0151. Thus you want “&#” followed by “x0151;” in HTML. End of aside.] So I wondered whether Erdős would fit the description in Graham’s next paragraph:

After I made the list, I looked to see if there was a pattern, and there was, a very clear one. Everyone on the list had two qualities: they cared almost excessively about their work, and they were absolutely honest. By honest I don’t mean trustworthy so much as that they never pander: they never say or do something because that’s what the audience wants. They are all fundamentally subversive for this reason, though they conceal it to varying degrees.

More on Erdős after I watch the movie about him. But note that Graham’s characterization is not a definition of “hero”; it’s simply a comment on two of their properties. Graham’s twelve heroes are Jack Lambert, Kenneth Clark, Larry Mihalko, Leonardo da Vinci, Robert Morris, P.G. Wodehouse, Alexander Calder, Jane Austen, John McCarthy, the Spitfire, Steve Jobs, and Isaac Newton. Could I make a similar list (though surely not duplicating any of Graham’s)?

I don’t think so.

But it did make me think about the issue. Which people have influenced me to such an extent that I would consider them to be my heroes? Would I really “decide what to do by asking what they’d do in the same situation”? Would my list consist of people who “cared almost excessively about their work” and “were absolutely honest”?

I suppose Isaac Asimov, Socrates, Charles Darwin, and Bertrand Russell would come to mind first. And maybe Johann Sebastian Bach. And probably Martin Gardner and Noam Chomsky. And it’s a cliché to put one’s mother and father on such a list, but it’s a cliché for a reason, so I will do that as well. And shouldn’t Shakespeare and Ibsen be on the list? And perhaps James Joyce? Well, that’s twelve, but I’m not convinced. This bears more thought...

21

2008-04-05T14:25:00.005-04:00

Two and a half years ago I wrote a brief negative review of Bringing Down the House: The Inside Story of Six M.I.T. Students Who Took Vegas for Millions, by Ben Mezrich. I suggested that the account seemed to be fictional (even though it claims to be non-fiction) and that it “alternates between melodrama and tedium.”

Now they’ve gone and made a movie of it, 21. The plot outline on IMDb asserts that the movie is a “fact-based story,” But Drake Bennett’s article about it in the Boston Globe has this comment on the original book:

Bringing Down the House is not a work of “nonfiction” in any meaningful sense of the word. Instead of describing events as they happened, Mezrich appears to have worked more as a collage artist, drawing some facts from interviews, inventing certain others, and then recombining these into novel scenes that didn’t happen and characters who never lived. The result is a crowd-pleasing story, eagerly marketed by his publishers as true — but which several of the students who participated say is embellished beyond recognition.

I haven’t seen the movie yet, but the Globe article certainly makes me skeptical. Read the article, not the book.

Math is hard, let’s go shopping, says Barbie (and others)

2008-04-04T19:04:00.006-04:00

Remember the big kerfuffle in 1992 when Mattel released a Teen Talk Barbie that said “Math is hard, let’s go shopping”? (Actually, if you look it up, you’ll find some references that quote it that way, and others that quote it as “Math class is tough. Want to go shopping? Okay, meet me at the mall.”) The reason for the kerfuffle was of course the not-so-subtle subtext suggesting that teenage girls can’t do math — because it’s too hard for them — so they should go shopping instead.

So, yesterday I stopped at the Trader Joe’s in Cambridge on the way home, and I happened to get a chatty cashier. She asked me what I do for a living, and I told her I’m a high-school math teacher. Needless to say, I expected to hear the familiar reply: “I never was any good at math.” Sure enough, that’s pretty much what she said. (Actually, it was a bit more complicated. She told me that she did well in geometry but never understood algebra. Except for geometry she did poorly in both high-school and college math because she could never deal with formulas. But now she’s an artist... well, you don’t want to know the whole story, but the key line is that she finally realized that math and art are actually a lot more alike than she had ever guessed, since “math and art are both about patterns and relationships.” Yes!)

And then this afternoon I got a phone call from my dental hygienist who told me that we needed to change my appointment because she has to take four weeks off to study for retaking her dental school admission exams, since she failed the math portion. “I never was any good at math.” Sigh. As Jerry P. King put it, “There will come a time when mathematical ignorance, like public smoking, will become socially unacceptable.” But for now for some reason it’s acceptable to admit inability to do math but not inability to read.

P.S.: Speaking of Trader Joe’s, there are 16 Trader Joe’s in Masssachusetts, so why isn’t there one in Dorchester? The demographics are right. Pass the word to the Trader Joe’s management!

The Big Nap

2008-04-03T20:08:00.002-04:00

On February 26, I wrote a mildly positive review of Nursery Crimes, by Ayelet Waldman. Because another novel in this series, The Big Nap, appeared to be more interesting, I decided (without great enthusiasm) to give it a read. I am pleased to report that this effort is distinctly more successful than Nursery Crimes, even though it has the same protagonist and the same basic formula: the Harvard-educated lawyer is still a stay-at-home mom, not the most promising premise for a story, even if she does turn out to be a (very) amateur detective as well, aided by her former prosecutorial experience.

Anyway, the most interesting aspect of The Big Nap is the interactions between the mainstream-Jewish protagonist and members of the Orthodox Jewish community in Los Angeles, especially the Hasidic subculture. As happens when reading many good works of fiction, I learned a lot from this novel (though I believe that the Verbover branch of Hasidism is an invention of Waldman and/or her husband, Michael Chabon, since I can find no references to it outside of their respective novels). While The Big Nap is still a light novel, it definitely has more heft than its predecessor and I found it worth reading. Maybe it would have meant still more to me if I had ever had the experience of being a mother, but (un)fortunately I haven’t. Nevertheless, I still recommend it to fellow non-mothers if you want an easy-to-read detective novel with a multicultural Jewish theme.

By the way, the significance of the title’s apparent allusion to Raymond Chandler’s The Big Sleep (or perhaps it’s to the movies made from the Chandler novel) escapes me. Maybe it would help if I read the book or saw the film...

Career Day

2008-04-02T21:06:00.006-04:00

Today was a very successful Career Day at Weston High School. I highly recommend the concept to other high schools — if you have a dedicated, highly organized team of people to take care of all the logistics. People who have served on the Local Arrangements committee for conferences and conventions will know what I’m talking about, but others might not realize how daunting it all is.

We started with a plenary session in which Alec Sulkin delivered the keynote address and Odds Bodkin provided entertainment. Actually, and fittingly, the keynote address was definitely entertaining as well as being educational, and the entertainment also had an educational component. Sulkin is a writer and supervising producer for Family Guy, so it came as no surprise that his talk was both engaging and amusing. Bodkin is a musical story-teller who is great at what he does, but unfortunately what he does isn’t a great match for a teenage audience. Sulkin’s talk, not surprisingly, is just right for a teenage audience — at least in their eyes. Adults may disagree.

Anyway, after the plenary, we split up into a couple of hundred breakout sessions. (As I say, the organization of this event was a staggering achievement.) Each student was assigned to four out of five sessions (to allow time for lunch); they made selections ahead of time, and they got their choices except if a session was full and the student had neglected to select alternates. If you read the descriptions of the speakers, you will see the huge variety offered. Here are excerpts, with one description randomly chosen from each of the five umbrella areas:

The Arts: When she was 25, Hilary Price was the youngest woman ever to have a syndicated daily comic strip. Her strip, Rhymes With Orange, appears in 150 newspapers internationally, and locally in The Boston Globe. Rhymes With Orange won Best Cartoon Panel last year from The National Cartoonists’ Society.
Business: This speaker is currently in marketing/sales of high tech multiplexers, routers, WAN, LAN and IP Telephony. But, it’s the way he got there that matters. He has been a substitute high school teacher, worked for a private detective, in a textile mill in Maine, in a furniture store and a phone company and owned a bar. This speaker will give you perspective that there are many opportunities for you, not just one path to success.
Crafts: What is it like to work on innovative product development for iTunes, iPods or the present Macintosh product line? What does it take to be part of a company that encourages employees to spin off other companies and lead with innovation? This speaker, an account manager in the higher education channel, will discuss the variety of jobs at Apple Computer including sales, marketing, product development and technical support in the field. Discussion on Campus Rep jobs that are also available when you attend college so you can get an early look at life working at Apple will also be presented.
Science: Jill Downing is a cardiologist who practices at Boston Medical Center in Boston's South End. She is interested in preventive cardiology which involves working with patients to identify and modify heart disease risk factors. Currently she spends her time with clinical research at BMC. Her career in health care began as a registered nurse working in such diverse settings as Honduras, the Dominican Republic, and Boston. Her experience highlights some of the challenges faced by the aspiring medical professional in terms of balancing career and family demands.
Social Services: Alan Solomont has been a community organizer and an entrepreneur. He is a veteran of six presidential campaigns and teaches a college course on the American presidency. He is a philanthropist and trained to be a registered nurse. He is proof that a career need not follow a straight line, and that there are many ways to make a difference.

OK, so you may disagree with what goes under the Crafts category. And we note that some speakers chose to include their name within their brief bios, and others didn’t, but all the names are on the website. It was definitely a fine day. Of course it helps to have the kinds of connections found in a community like Weston.

Which is more important, sports or academics? And what about the arts?

2008-03-31T14:19:00.001-04:00

Every school will tell you that academics are more important than sports. After all, it is a school. Even the most sports-minded principal will ban an athlete from playing football if his grades are too low, but no one would ban a student from class because his athletic performance was poor.

But take a look at the pages where schools are mentioned in the newspaper. It’s almost all because of sports. (OK, there’s also crime, but let’s not go there.) Even in Massachusetts it’s really a joke to expect the same kind of coverage for the math team as the paper gives to the football team (or, in the case of Weston, as it gives to the swimming and golf teams). Yes, yes, I know that participating in an athletic team can build all sorts of virtues, from persistence and cooperation to sportsmanship and planning, but it’s still not what the mission of a school is all about.

And then we get to the arts. Weston has first-rate theater and music programs, an excellent Art Department, a very successful dance team, but what kind of coverage do they get? I was reminded of this issue in a post by Adam Gaffin in this morning’s Universal Hub:

Writing on the Herald site, Tai Irwin contrasts the Globe’s coverage of the Massachusetts High School Drama Guild Finals — which it sponsored — with its Sunday coverage of high-school athletes. The final tally:

Athletes: 16 pages of coverage.
Drama kids: Zero.

The excerpt from Tai Irwin is telling:

... The message is very clear: although Westford, Nauset, and Weston received awards, and many students were singled out for theatrical excellence, once again it’s sports that matter most, even to the exclusion of intellectual and artistic activities. What a great thing to tell our kids, over and over again. Never mind the brain pursuits — the science fairs and business/educational coops, and never mind the arts, dance, music, drama. The thing that is going to solve all our problems and nurture all our values best is sports. ...

I couldn’t say it any better myself. So I won’t try.

Crazy Chinese words?

2008-03-30T19:30:00.003-04:00

Don McLeroy, chairman of the Texas State Board of Education, certainly understands cultural sensitivity with his global perspective:

“What good does it do to put a Chinese story in an English book?” he said. “You learn all these Chinese words, OK. That’s not going to help you master... English. So you really don’t want Chinese books with a bunch of crazy Chinese words in them. Why should you take a child’s time trying to learn a word that they’ll never ever use again?”

He added that some words — such as chow mein — might be useful.

Oh, well, it’s Texas. Weston is much too enlightened for such attitudes. We take our global perspectives seriously, as you can see from the list of current projects, which include Giant Chinese Dragons & Lions, Uganda Professional Development Project, Columbian Exchange, Rhythm Kids: An African Drumming Experience, and Bringing the Art Experience of Ecuador into the Classroom.

How to create a blog

2008-03-29T15:48:00.001-04:00

In one of those typical synchronicities, two of my students have just asked me how they can create their own blogs — a Weston sophomore yesterday, and a Saturday Course fifth-grader today. The Weston student suggested that I should post the answer in my blog, so here it is, short and sweet:

Go to www.blogger.com.

Follow the 3 easy steps displayed on that page.

That was easy^®, as they say at Staples.

What's the matter with math today?

2008-03-28T18:09:00.005-04:00

What’s the matter with math education today? No, it’s not that kids don’t know the basics, despite what some people say. And it’s not that teachers are teaching “fuzzy math,” despite what some people say. Paul Lockhart has the correct analysis:

If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done — I simply wouldn’t have the imagination to come up with crushing ideas that constitute contemporary mathematics education.

This sentence comes from “A Mathematician’s Lament,” an essay by Paul Lockhart, a professional mathematician. The link to this essay was found in Keith Devlin’s regular column in MAA Online, a publication of the Mathematical Association of America. (Devlin is best known for his radio columns, Saturday mornings on NPR’s Weekend Edition, and is less well-known as the author of The Numbers behind Numb3rs, which will be the topic of another post in this blog. But I don’t want to discuss Devlin here; I want to discuss Lockhart.)

Every math student, every parent of a math student, every curriculum developer, and especially every math teacher should read Lockhart’s essay. It’s not that it’s perfect, for of course it has many flaws, but its point of view is so provocatively on target that it will provide essential fodder for critical discussions. It zeroes right in what’s important in mathematics and on the misplaced emphasis of the way it’s taught in school (or skool, as my friend Brian would write):

I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of mathematics in our mathematics classes.

If your art teacher were to tell you that painting is all about filling in numbered regions, you would know that something was wrong. The culture informs you — there are museums and galleries, as well as the art in your own home. Painting is well understood by society as a medium of human expression... But if your math teacher gives you the impression, either expressly or by default, that mathematics is about formulas and definitions and memorizing algorithms, who will set you straight?

I could keep quoting thought-provoking excerpts, but I’m not going to do so; just read Lockhart’s essay yourself!

But wait! I can’t resist quoting his “completely honest” course description for the typical Algebra II course as taught in American high schools:

The subject of this course is the unmotivated and inappropriate use of coordinate geometry. Conic sections are introduced in a coordinate framework so as to avoid the aesthetic simplicity of cones and their sections. Students will learn to rewrite quadratic forms in a variety of standard formats for no reason whatsoever. Exponential and logarithmic functions are also introduced in Algebra II, despite not being algebraic objects, simply because they have to be stuck in somewhere, apparently. The name of the course is chosen to reinforce the ladder mythology.

Fortunately things aren’t quite this bad at Weston. But it’s still painfully close to the truth. Solutions, anyone?

“You’ll enjoy the same success and happiness...”

2008-03-26T06:25:00.003-04:00

Novelist Elinor Lipman wrote an excellent essay in the Boston Globe the day before yesterday, entitled “If I ruled the admissions universe.” I would like all high school juniors to read it. I just wish I could agree with it.

The thrust of the essay was an attempt to reduce college admissions anxiety by pointing out that your future is not determined by where you go to college. You are just as likely to be successful and happy if you go to your local state college as you will be if you go to Yale. That bit may be true, although it’s very hard to tease out the statistics, since of course we’re not talking about equivalent populations. Let’s look at some excerpts:

...My mission today is to celebrate the safety over the reach, to say to high school seniors, “You who are waiting anxiously for that fat envelope, please know that you’ll enjoy the same success and happiness whether you end up at Bates, Bowdoin, or Ball State.”

When I was 20 an older friend predicted, “Ten years from now, no one will care where you went to school. In fact, no one will ask.” Ridiculous, I thought. She turned out to be right. Where you live between the ages of 18 and 22 won't define who you are. One day soon, the proud new college decal on your family car’s rear window will start looking a little uncool.

...

In 1987, a friend’s son wrote to admissions officers explaining that he had fallen in love and was therefore distracted, so could they please excuse the C in physics? They did. He went to Yale. If he hadn’t? I daresay he would be the same hero he is today, getting the wrongly convicted out of prisons through the Innocence Project.

...

If I ruled this new admissions universe, I would study the applications and sniff out the resume padders whose parents could afford the semester in the rain forests. I’d want good smart kids, including the ones who didn’t shine as brightly as the alleged stars at this moment in their high school lives... Maybe I would go with the lottery, or maybe just take the first 1,000 who applied. Studies would have shown that you are all excellent, and in the end, I couldn’t go wrong.

So how would this essay go over in a town like Weston? I suppose I should simply ask some of my high-achieving juniors to read it, and we’ll see what they say. As a graduate of Lowell High School and Simmons College, the undeniably successful Lipman must know what she’s talking about, but my prediction is that her essay won’t be persuasive. She makes some fine points, but...I’m not convinced. I wish I could agree with it.

MCASitis

2008-03-25T07:56:00.003-04:00

Today was the first day of disruptive MCAS testing. One of my sections of college-prep Algebra II was wiped out, the other was barely affected. There will be a repeat performance on Thursday. Somehow this is supposed to improve education, even though it takes away from learning time and increases student anxiety.

Speaking of which, take a look at pediatrician Dr. Gwenn’s article on MCASitis (thanks to Adam Gaffin’s Universal Hub for the link). Here is an excerpt:

Yesterday I saw a young girl in my office who had very bad tummy aches... Chatting with this young, pleasant child and her mom I learned she’s in third grade in a town near mine and facing the dreaded MCAS testing today — our State’s standardized testing that starts in third grade and goes all the way through tenth. Out of the blue she said, “I’m scared of the MCAS — my teachers told me that the graders are tough and we have to watch how we answer the written answer.”

Now I had my answer. This young girl had what I have come to call “MCASitis”...a form of performance anxiety brought on every Spring here in Massachusetts. You likely have a similar form in your State.

Test taking anxiety is truly real, even for young kids. And, with anxiety can come physical symptoms such as stomach aches.

But of course it’s supposed to ensure that no child is left behind.

Wellness Day

2008-03-24T20:20:00.002-04:00

Today was Wellness Day at Weston High School — a day off for the students, and a day of professional development workshops for the teachers.

“Professional development”: what thoughts does that phrase conjure up? FWIW, let’s see what Wikipedia has to say:

Professional development often refers to verbal and tactile skills required for maintaining a specific career path or to general skills offered through continuing education, including the more general skills area of personal development. It can be seen as training to keep current with changing technology and practices in a profession or in the concept of lifelong learning.

Actually, that’s not bad, except for the bizarre reference to “verbal and tactile skills” in the first clause. The Commonwealth of Massachusetts appropriately requires all teachers to participate in professional development every year, and the town of Weston offers us a wide variety of opportunities, ranging from required curriculum-based seminars to optional workshops in the summer. Once a year we have Wellness Day.

So, what is it that makes me uncomfortable about this? I do recognize that all employers have a legitimate interest in keeping their employees healthy and productive. And I do recognize that a Wellness Day can be useful, fun, and intellectually stimulating. And I do recognize that it could also be an opportunity for community-building. Yet somehow it doesn’t add up for me. At least it doesn’t add up to professional development. Not to my eyes, at any rate.

And what, you ask, did I do today? We had some required activities, plus one session where there was a one-out-of-four choice, and two sesions where there was a one-out-of-many choice. During the day I participated in a “dumb game,” I listened to a very worthwhile presentation on bullying from a representative of the Middlesex County District Attorney’s office [!], I had lunch with my colleagues (a lovely make-your-own-fajitas meal organized and paid for by the PTO and prepared by the Administrative Council), I attended a session that showed a couple of movies about first aid, and I went on a long walk. I could have gone on the walk on my own, not on school time, but at least this way I got to have an extended one-on-one conversation with the drama teacher/theater director. I enjoyed that a lot, since I rarely get more than five minutes with him.

In fact, I enjoyed the whole day. But I’m still not convinced that it’s professional development.

Which comes first, the movie or the book?

2008-03-23T05:56:00.001-04:00

In yesterday’s post, I recommended watching the movie of Mozart and the Whale before reading the book. And then I got to thinking about whether this was the natural order: after all, in most cases a movie is written after the book on which it is baed, so why shouldn’t it also be watched afterwards?

In standard mathematical fashion, let’s see whether we can abstract from the concrete example of one movie/book pairing to the more general case. What happens with other such pairs? Sometimes the order doesn’t matter. And often I read a book as soon as it comes out and then have to wait for the movie, so the order is imposed artificially. What are the consequences of reading the book first? On the plus side, you have the freedom to visualize characters and scenes as you wish, and you can learn the necessary background that might be omitted from the movie. On the minus side, the movie is usually a disappointment, precisely because it can’t possibly capture everything in the book. Furthermore, my own view is that surprises and plot twists in a movie are more effective when one hasn’t read the book first. There are surely exceptions, but on the whole I come down on the side of always reading a book after seeing the movie wherever possible.

Mozart and the Whale: The book

2008-03-22T07:54:00.002-04:00

On February 20 I reviewed Mozart and the Whale: An Asperger’s Love Story. After seeing and enjoying this fascinating movie, I decided to read the autobiography on which it was based. (Can I still call it an autobiography when it was “written” by two people, both Jerry Newport and Mary Newport? Not to mention Johnny Dodd, a writer for People who served as ghostwriter and who is duly credited?) I highly recommend reading this book — after you see the movie. Not surprisingly, the movie had to leave out lots and lots of material, and occasionally had to take artistic license, but it doesn’t actually contradict anything in the book, either in fact or in tone. The major difference is...well, I don’t want to reveal any spoilers, so let’s just say that the Newports’ relationship and Mary’s psyche turn out to be much more complicated than portrayed in the film. Again, no surprises there.

The only real problem with the book is that the first-person point of view changes without warning from section to section. Presumably Dodd interviewed the Newports extensively and fashioned the narrative out of their information with an attempt to capture their separate voices. But apparently he isn’t skilled enough to succeed at this endeavor, since it’s often impossible to tell who’s speaking except from external clues (like mentioning the spouse). Of course this makes me wonder whether he is actually capturing the voice of either Newport; probably what’s coming across is Dodd’s voice.

Goodbye, Arthur C. Clarke.

2008-03-20T06:26:00.003-04:00

Another of the great ones is gone. Scientist, science fiction writer, and visionary Arthur C. Clarke died the day before yesterday at age 90. He is best known for the novel 2001: A Space Odyssey, on which the eternally rewatchable movie of the same name was based (though they were written simultaneously!). But he made so many more contributions than that. The Wikipedia article on him provides a fairly decent summary, including links to various obituaries. I particularly recommend the article about him by fellow writer David Brin, in the Daily Kos of all places. The NPR story on yesterday’s Morning Edition was an effective four-minute vignette.

I particularly remember Clarke’s observation that “any sufficiently advanced technology is indistinguishable from magic,” as well as his agreement with the late, lamented Isaac Asimov that each would refer to himself as “the world’s second best science fiction writer.” As Asimov wrote in his autobiography:

Arthur Charles Clarke was born toward the end of 1917 in Great Britain. He is another science fiction writer who has been thoroughly educated in science and he did extremely well in physics and mathematics.

He and I are now widely known as the Big Two of science fiction. Until early 1988, as I’ve said, people spoke of the Big Three, but then Arthur fashioned a little human figurine of wax and with a long pin.

At least, he has told me this. Perhaps he’s trying to warn me. I have made it quite plain to him, however, that if he were to find himself the Big One, he would be very lonely. At the thought of that, he was affected to the point of tears, so I think I’m safe.

I’m very fond of Arthur, and have been for forty years. We came to an agreement many years ago in a taxi which, at the time, was moving south on Park Avenue, so it is called the Treaty of Park Avenue. By it, I have agreed to maintain, on questioning, that Arthur is the best science fiction writer in the world, though I am also allowed to say, if questioned assiduously, that I am breathing down his neck as we run. In return, Arthur has agreed to insist, forever, that I am the best science writer in the world. He must say it, whether he believes it or not.

I don’t know if he gets credited for my stuff, but I am frequently blamed for his. People have a tendency to confuse us because we both write cerebral stories in which scientific ideas are more important than action.

Both Clarke and Asimov were science-based writers of science fiction; neither was a prose stylist, but both of them stuck to a transparent style that let the content of their writing shine through with great clarity.

Eye of the Beholder

2008-03-19T05:25:00.001-04:00

I recently listened to the audiobook of Eye of the Beholder, by David Ellis. This work is a hybrid of two genres: the thriller and the police procedural. It’s definitely a page-turner — well, I can’t use that metaphor for the audiobook version, so let’s just say that it kept holding my attention and made me want to continue. But I’m not convinced that the hybrid genre has led to hybrid vigor. Perhaps that’s because of a continually jarring switch back-and-forth between a first-person POV and a third-person POV. The writing is clearly inspired by John Grisham and Jeffery Deaver, with an admixture of Ed McBain, but there are a lot of original aspects as well. In particular, the good guys aren’t completely good and some of the bad guys aren’t completely bad (except for one). In Deaver style, there are several plot twists whereby people aren’t who they seem to be. The major downside is that several scenes are extremely violent, enough so to turn off some readers completely. For those who can stand the violence, I recommend this study of lawyers, cops, criminals, and academe — quite a combination!

Countless

2008-03-18T06:21:00.004-04:00

I guess Kalmbach didn’t have 100 fingers:

Don’t procrastinate!Goodbye, George, I hardly knew you.

2008-03-17T19:50:00.005-04:00

Actually, I never knew you, sad to say. For 15 years now I have been intending to meet George Sanborn and talk with him about the MBTA (since my model railroad layout is based loosely on the MBTA of 1969). But I kept putting it off, and now it’s too late. Adam Gaffin’s remembrance, titled “Remembering Boston's train man,” links to Dirty Water and to Commute-a-holic. Read the comments to Gaffin’s post, and the various links in the original post and within the comments. As SwirlyGrrl says in her title to her otherwise blank post, “He will ride forever ’neath the streets of Boston.” Why did I keep thinking that I could always talk with him next year?

P.S.: I have just been told about the Globe’s article on George Sanborn. Read that too.

South Shore Model Railway Club

2008-03-16T17:22:00.002-04:00

This morning I went to the Spring Open House of the South Shore Model Railroad Club in Hingham, MA. Despite the excessive number of young children present, it was an excellent layout, with a reasonable but small quantity of vendors as well. The layout was well worth seeing, especially the structures and scenery. I especially liked the urban scenes, including a semi-covered track entering a city. The nearby harbor was less than completely effective, but water is especially difficult to model convincingly. I’m certainly not going to try to become a member, as their requirements include attending 18 meetings within a period of nine months! So I suppose it fits into the category of “a nice place to visit, but I wouldn’t want to live there.” I do, however, plan to return for a longer visit for their next open house in the fall.

Fractions

2008-03-15T19:56:00.003-04:00

That’s fractions, not fractals. (There is, actually, a significant and non-coincidental connection between the words, but that would be something of a digression.) I’m noticing two recent and diametrically opposed views on fractions — views that I want to discuss here.

First came a report in USA Today on January 23, entitled “Fractions should be scrapped” It quotes Dennis DeTurck, an “an award-winning professor of mathematics at the University of Pennsylvania”:

“Fractions have had their day, being useful for by-hand calculation,” DeTurck said as part of a 60-second lecture series. “But in this digital age, they’re as obsolete as Roman numerals are.”

DeTurck points out that the arguments against him “always boil down to: ‘What would we do in cooking and carpentry?’”

The article goes on to say that “DeTurck does not want to abolish the teaching of fractions and long division altogether. He believes fractions are important for high-level mathematics and scientific research. But it could be that the study of fractions should be delayed until it can be understood, perhaps after a student learns calculus, he said. Long division has its uses, too, but maybe it doesn’t need to be taught as intensely.”

In response, “Penn State mathematician [George] Andrews says he believes DeTurck’s ideas will ‘unfortunately’ gain traction because of the misguided belief that math education can somehow be made easy: ‘Math is hard. The idea that somehow we’re going to make math just fun is just a dream.’” It’s too bad the article is so thin, but that’s USA Today for you.

Then there’s an article in the Boston Globe two days ago. It’s far too long to quote here, but I can provide some excerpts:

Schools could improve students’ sluggish math scores by hammering home the basics, such as addition and multiplication, and increasing the focus on fractions and some geometry, a presidential panel recommended Thursday.

“Difficulty with fractions (including decimals and percents) is pervasive and is a major obstacle to further progress in mathematics, including algebra,” the panel, appointed by President Bush two years ago, said in a report.

So, what’s the truth? I have to admit that the phrase “panel appointed by President Bush” immediately makes me suspicious. And the conflating of fractions with decimals and percents makes me more so. But let’s continue:

Because success in algebra has been linked to higher graduation rates and college enrollment, the panel focused on improving areas that are the foundations of algebra. Average U.S. math scores on a variety of tests drop around middle school, when algebra coursework typically begins...

“Students don’t know how to translate fractions into decimals or into percentages and they can’t locate fractions on a number line,” said panelist Tom Loveless, a senior fellow and education expert at the Brookings Institution, a Washington-based think tank.

OK, I have to admit, that bothers me too. But let’s move on:

In general, U.S. math curricula ought to be streamlined, according to the report.

“There is I think a tendency in American curricula to cover too many things too shallowly,” Larry Faulkner, the panel’s chair and the former president of the University of Texas, said.

The report takes a diplomatic stance when it comes to taking a position on the best methods to teach math to kids.

In recent years, there has been a dispute over whether children should learn a sequence of basic skills in math, including multiplication tables and some memorization, or should understand the theory behind math problems and come up with solutions on their own.
The report says both quick and effortless recall of facts and conceptual understanding of math are beneficial.

In addition, the back-to-basics camp has tended to favor “teacher-directed” instruction, in which teachers do all the explaining, while the opposing side has backed “student-centered instruction,” in which students have the main responsibility for learning math — often through working with peers.

The panel found students can benefit from both styles.

Well, yes! It’s hard to know why this has to be an either/or situation. Of course we need to do both:

“You need some element of discovery to allow kids to secure concepts in their minds, and you need to be able to have a reasonably efficient approach to be able to cover the material,” Faulkner said.

So it’s not clear just what the controversy is, nor what it says about fractions. Science teachers tend to emphasize decimals more than fractions, and students who are calculator-dependent are certainly more comfortable with fractions. Sometimes I fear that I take an elitist position, something like this: “Students in honors math classes need to understand fractions.” That’s surely true, but it’s not at all clear whether students in non-honors math classes need to do that. Maybe some of us are still living in the 19th Century. Maybe most people don’t need fractions. More later...

Happy Pi Day!

2008-03-14T20:40:00.001-04:00

Pi Day at Weston was uneventful, except that one of my students brought in a virtual pie. Actually it was a chocolate cake, but at least it was round. And she had intended to write some of the digits of pi on it. At least we got to watch the music video of the first half of Mathematical Pi, and two of my classes got to listen to the audio version of the whole song.

For further perspective, I note two reports from colleagues on the Web:

The pseudonymous Minneapolis math teacher, Three Sigma to the Left, reports a certain class distinction:

Since I’ve been here at this school I’ve always had at least one class with kids who cared about something to do with academics whether it was education for its own sake or education because they know they have to. And these kids know π Day. They know that it is their math teacher’s favorite day of the year.

Year after year here I’ve had kids want to have a party to celebrate. Have pie. Sing stupid songs. Someone always has π memorized to some ridiculous number of digits. I always tell the students that I can’t have a party because the administration won’t allow them (not true) but “if you throw a surprise party, I guess that really wouldn’t be against the rules.” Then I leave the room for a few minutes while the kids figure out who is bringing what and I don’t have to do a thing.

Now I have the lower kids. Not one has even mentioned π day. I find that astounding since they must have done something in middle school. You would think that they must know anyone in another class who is having a party.

I’m troubled by this concept of “the lower kids,” but we know what he means. At Weston High School (where, let us remember, all the children are above average, even though it’s a regular public high school) we have honors-level classes and college-prep classes, but we don’t have honors-level kids and college-prep kids. A student can be in an honors math class but a college-prep chemistry or vice versa. Nevertheless, I see somewhat similar reactions, where there’s enthusiasm for Pi Day in honors classes but not so much in college-prep classes. However, the distinction is blurred, apparently in contrast to Minneapolis: many students in one of my college-prep classes were enthusiastic for Pi Day and even insisted on having the virtual pie at precisely 1:59, which they immediately amended to 1:59:26. So there, I say!

The second report is from my friend and colleague Tamisha Thompson, whose blog is so appropriately titled “3.1415926535897932384626433832795028841971...”:

This is the first Pi day that I did NOT have a pi memorization contest, in all my (9) years of teaching. I really miss having the kids randomly storming up to me and shouting digits of pi all day. The classes I visited today were all doing different sorts of pi day activities: one class was measuring circular objects and dividing circumferences by radii (heh — I just wanted to say radii), another class was estimating the radius of a basketball, a third class was calculating pi from a hula hoop, then using the circumference to estimate the revolutions per minute while someone used the hula hoop (although I have to imagine that the calculations were a little off, since you probably have to take into account said hula-hooper’s waist measurement and the actual distance the hula hoop travels), and a fourth class was using the Internet to find answers to some pi challenges such as “Which Greek mathematician is given credit for creating Pi?”

You can tell that that’s middle school, not high school. (And I have a philosophical problem with the question of “creating pi” rather than “discovering pi,” but that’s another story...)

JP Seafood

2008-03-13T05:52:00.001-04:00

Last night Barbara and I ate at JP Seafood, one of our favorite restaurants for times when she works late in Jamaica Plain. (You’ll note that I’ve included the Dorchester label for this post, even though Jamaica Plain is not exactly Dorchester. But it’s a close enough jaunt so that Dot people should consider it.) My theory is that the name of this restaurant is a clever pun, since JP not only stands for Jamaica Plain but is also the country code for Japan in URLs. The lack of periods after the J and the P supports my theory, though the website has neglected to provide any evidence that I’m right.

Anyway, you’re wondering what this restaurant is like, and why Barbara and I keep returning to it. You’ve probably figured out from my theory that the place must serve Japanese seafood, and that is indeed its focus. There’s also some Korean food (as is typical in many Japanese restaurants) and some non-seafood-based Japanese food. And, oddly enough, there’s fish-and-chips as well. The sushi is great, as is the ok-dol bibimbop, so I usually tend to order a sushi appetizer followed by beef ok-dol bibimbop. Side salads of beansprouts and seaweed are both terrific. But last night I went for a delicious special of sauteed striped bass (actually “stripped bass” on the menu), which came with miso soup, spinach salad, beansprout salad, mushrooms, and rice. I also had to steal one of the yummy don shumai that Barbara had ordered, as well as a piece of her scallion pancake with squid and surimi.

Service is always excellent, and prices are amazingly reasonable. Even if you don’t happen to live or work in JP, it’s worth going to JP Seafood — especially if you’re tired of the six good restaurants in Dorchester.

Preparing for Pi Day

2008-03-12T06:21:00.000-04:00

To get ready for Pi Day, which of course comes the day after tomorrow, you should get yourself a Pi Plate, watch the music video of the first half of Mathematical Pi, and listen to the audio version of the entire song.

As Dog is My Witness

2008-03-10T16:11:00.002-04:00

I seem to be inadvertently continuing my Asperger’s theme here. As Dog is My Witness, by Jeffrey Cohen, is a mystery that features a couple of boys with Asperger’s; one is the innocent suspect, the other the informal detective. You may recall that I reviewed another book by Cohen on December 19. The two books are almost entirely different in everything except for a minor theme about scriptwriting and a major role for the locale, since both so clearly take place in New Jersey with a lot of Jewish characters. An aside:

Why is New Jersey called the Garden State?

Because there’s a Rosenbloom around every corner.

(Say it aloud to get the full effect.)

Anyway, the author is the parent of a boy with Asperger’s, so it’s no wonder that he can write about the subject with authority and confidence. More surprising is that he writes with a great sense of humor. The humor extends not only to Asperger’s — which Cohen carries out with aplomb and not a trace of making fun — but also to family relations. I particularly liked a subplot about the mother of a minor character (no, not a minor in that sense; he’s an adult), as well as a long subplot about the protagonist’s obnoxious inlaws. By all means read this book!

The Second Mouse

2008-03-08T07:31:00.001-05:00

The Second Mouse is a wonderful addition to Archer Mayor’s series of Vermont mysteries, which are always a pleasure to read because Mayor is so skilled at drawing verbal pictures of both the characters and the locales. As a reader, you always know where you are — usually a part of Vermont that’s not visited by tourists. The sense of place is overwhelmingly accurate. Characters develop convincingly from book to book. The good guys aren’t flawless, and the bad guys aren’t entirely bad. I’m not going to write anything more about The Second Mouse, the 17th in the series, except to say that you should definitely read it. And it wouldn’t hurt to read all 17 in sequence!

Maple

2008-03-06T06:24:00.001-05:00

Yesterday afternoon we had a half-day workshop on Maple, a computer algebra system. At least that’s how we think of it, but here’s the description on their website:

Maple is the leading all purpose mathematics software tool. Maple provides an advanced, high performance mathematical computation engine with fully integrated numerics & symbolics, all accessible from a WYSIWYG technical document environment. Live math is expressed in its natural 2D typeset notation, linked to state-of-the-art graphics and animations with full document editing and presentation control.

Users can perform everything from instant “in document” calculations to highly complex mixed symbolic and numeric programming involving millions of terms, at any precision desired. Maple’s intelligent technical document environment addresses the full spectrum of needs and requirements from high school students to advanced commercial research.

The question, of course, is how we can use this software productively in the context of high-school math courses. We looked at several possibilities yesterday, ranging from expansion of powers of trinomials to 3-D graphing. For instance, suppose we want to calculate the fifth power of a trinomial. If we simply type the appropriate expression, it gets echoed back:

But if we ask Maple to expand it, it does so:

And then suppose we want to solve or plot a system of three equations in three unknowns. Maple will do both:

This is just a beginning. We don’t know yet how we’ll use it, but it surely promises some major expansions of what we can do in high-school math.

Teaching boys and girls separately — and differently?

2008-03-05T06:32:00.001-05:00

There’s a fascinating pair of intertwined articles this week, one in the New York Times Magazine and one in Language Log. The Times article is the cover piece for the issue: “Teaching Boys and Girls Separately,” by Elizabeth Weil; the post in Language Log, “Scrupulously Avoiding Sigma,” is by my erstwhile classmate Mark Liberman. The reason I say that the articles are intertwined is that each one seems to quote the other. (Actually, I think Weil must be referring to an earlier post by Liberman.) Anyway, the discussions hinge on the question of whether scientific data and public policy actually support the notion of having separate classrooms for girls and boys in public schools from kindergarten through high school. Weil is sympathetic to the idea; Liberman is not.

Before commenting on the science, I want to give some personal and admittedly anecdotal views on the topic. I myself attending single-sex private schools from grades 3 through 12, first at Newark Academy and then at Phillips Academy, Andover. [Note that it’s not Phillips Andover Academy! This all-too-common error probably arose out of a confusion between Phillips Academy, commonly known as Andover, and Phillips Exeter Academy, commonly known as Exeter. But I digress.] While I received an adequate academic education at Newark Academy and an excellent one at Phillips, the social atmospheres at both were poisonous, overly competitive, and destructive. They certainly didn’t prepare me for the so-called real world. My AP Latin teacher told us that Andover would go coed over his dead body; that didn’t literally happen, but in fact he retired as soon as the decision to admit girls was announced. “I don’t know how to teach girls,” he claimed. This has never made much sense to me.

But back to the articles. Weil focuses on one Leonard Sax, who advocates full-time for single-sex classrooms based on several dubious claims:

Leonard Sax represents the essential-difference view, arguing that boys and girls should be educated separately for reasons of biology: for example, Sax asserts that boys don’t hear as well as girls, which means that an instructor needs to speak louder in order for the boys in the room to hear her; and that boys’ visual systems are better at seeing action, while girls are better at seeing the nuance of color and texture.

David Chadwell, one of Sax’s disciples and the coordinator of Single- Gender Initiatives at the South Carolina Department of Education, explained to me the ways that teachers should teach to gender differences. For boys, he said: “You need to get them up and moving. That’s based on the nervous system, that’s based on eyes, that’s based upon volume and the use of volume with the boys.” Chadwell, like Sax, says that differences in eyesight, hearing and the nervous system all should influence how you instruct boys. “You need to engage boys’ energy, use it, rather than trying to say, No, no, no. So instead of having boys raise their hands, you’re going to have boys literally stand up. You’re going to do physical representation of number lines. Relay races. Ball tosses during discussion.” For the girls, Chadwell prescribes a focus on ’the connections girls have (a) with the content, (b) with each other and (c) with the teacher. If you try to stop girls from talking to one another, that’s not successful. So you do a lot of meeting in circles, where every girl can share something from her own life that relates to the content in class.”

There’s clearly a certain amount of truth there. But the leaps of reasoning are staggering. Sure, boys and girls behave differently on the average. For instance, at the Saturday Course, classes are usually more orderly, productive, and civilized when they are heavily female. But I only say “usually”: there is a huge number of exceptions. I have taught all-male classes that were wonderful and coed classes that were not. (The all-male classes have always been computer courses, which get very few signups from girls. I notice that courses in art, drama, and writing get very few signups from boys. Sigh.)

Liberman’s response focuses mainly on the (mis)use of statistics by advocates of single-sex classrooms. For example:

The rhetoric of science journalism — and sometimes the rhetoric of science — all too easily engages a sort of pop-Platonism that seems to be deeply connected to the way that we think about natural kinds. As a result, small (but statistically reliable) differences in group distributions are seen as essential properties of the groups themselves, and therefore of all the individuals that make them up. Or at least, all the normal or typical individuals. Intellectual and social mischief often ensues.

I’m willing to believe that average test scores might improve if students were segregated by gender, but I’m not willing to believe that that would be true for any specific individual, not that successful citizens would emerge from widespread adoption of this idea.

An Obama/Seeger serendipity

2008-03-04T05:57:00.002-05:00

Wow! I don’t often call a PBS show inspiring, but last night I watched the truly inspiring American Masters episode, Pete Seeger: The Power of Song, which had aired on my birthday and TiVo had kindly saved for me. I wonder how well this would resonate with today’s young people, most of whom haven’t even heard of Pete Seeger; and even those who have can’t possibly have the experience that comes from the civil rights movement and the anti-Vietnam-war movement. I suppose it could be like my reactions to the McCarthy-era segments of the show. To me those are merely history, albeit recent history that clearly affected my childhood in various ways.

Anyway, this episode was exceptionally well-written, filled with music as of course one would expect, but also filled with fascinating interviews with Seeger’s children and grandchildren and fellow musicians like Joan Baez, Arlo Guthrie, Bruce Springsteen, Ronnie Gilbert, Mary Travers, and Bob Dylan. There was even a cameo appearance by Bill Clinton. Seeger’s long experience with thinking globally and acting locally in the environmental movement was suitably and movingly stressed. Most significant was the implied relationship between the war in Vietnam and the war in Iraq. The seamless mixture of politics and song was just so appropriate to Pete Seeger’s life and work. But I wonder why they didn’t wait for his 90th birthday, which will come next year; that would be a suitable milestone.

Finally, the inspiration that comes from Pete Seeger and from his amazing abilities to connect with audiences, involving and uniting them, resonated in another way with me. Although there are dozens of obvious and not-so-obvious differences between him and Barack Obama, I realized that they evoke similar inspiration in their listeners. That gave me an extra appreciation for Obama, which was probably strengthened by an incident in my precalculus class yesterday afternoon. As we were waiting for one group to complete some complex preparations for presenting their fractal project, I wandered by a gaggle of half a dozen juniors who were talking politics. “Do you support Clinton or Obama?” one of them asked me.

“How do you know I don’t support McCain?” was, of course, my response.

“Because there are no Republicans on the faculty.”

I pointed out that I know of at least two Republicans on the faculty, as well as many who keep quiet about politics, and then explained why I don’t like to talk politics with students except with those whose views are already well-developed and are unlikely to be influenced by me. I really don’t want to be in the position of molding kids’ politics. They all assured me that they weren’t going to be influenced by me, so I countered by asking, “So who do you think I support?”

“Obama,” replied one student, “because Clinton is just too polarizing.”

I had to admit that he was correct and had even nailed my principal reason for supporting Obama. I said that I thought Clinton would be a good president and I would certainly vote for her over McCain, but I don’t think she would be a good nominee since there are so many people who have an irrational hatred of her (not to mention those who won’t vote for a woman, like a certain other member of this class).

Fractals are fractious

2008-03-03T08:12:00.003-05:00

(Thanks to Barbara for the title of this post.) Let me begin by setting the stage. On Friday I wrote about this year’s Fractal Fair. Groups of students (generally three in each group, occasionally two; generally juniors, but there were a couple of sophomores and a senior) researched a specific topic to do with fractals; created a product that might include posters, models, PowerPoint presentations, or whatever; exhibited the product at the Fractal Fair; and prepared to present it to their classmates this week. Everyone was supposed to be enthusiastic and upbeat as a result of the teamwork and the opportunity to show off their mathematical creativity. That was the theory, at any rate.

On Wednesday, during final in-class preparation, one of my groups suffered an all-too-public meltdown when two girls had a major conflict about who was doing what for their project. That was awkward and uncomfortable for all concerned, but it eventually got worked out by Friday. And then came the Fractal Fair, when a different pair of girls (not my students even) had a similarly all-too-public meltdown in the Library. Even the issues were similar: non-communication, different perceptions of what the product would be, different values concerning esthetics and content, etc. Drama, of course, is nothing new with this age group, but these reactions seemed a little excessive for a math project, though they were clearly genuine reactions. Why should fractals be so fractious?

Working together is difficult. It involves important skills like consensus and compromise. It involves continual communication. It involves trust. As I suggested last week in my post about Curriculum B, these goals are far more important than whether one can calculate fractal dimension or the rotation number of a bulb in the Mandelbrot Set. Part of me wants to just drop the issue and move on, but part of me wants to develop an important lesson out of the whole issue. Obviously I can’t reveal any more details here, in a public forum, but unfortunately I probably can’t even do so in class.

Listen to the kids? Or listen to the adults?

2008-03-02T06:30:00.001-05:00

In Universal Hub this morning, Adam Gaffin quotes Cara Lisa Powers on the subject of the Boston Globe’s coverage of a protest at the John D. O’Bryant High School of Mathematics and Science. The Globe ignored the kids. In this week’s Weston Town Crier, a letter is published protesting an article about students at Weston High School. The Town Crier placed too much weight on what the kids said. Since I live in Dorchester and teach in Weston, I had to compare and contrast. (Yes, the O’Bryant is actually in Roxbury, not Dorchester, but it’s pretty close and it’s an exam school that serves plenty of Dorchester kids.)

In her letter to the Globe reporter, Powers includes the following observation:

By only quoting the spokesperson from the Boston Public Schools, and not giving any voice to the youth, you are reinforcing the dominant perception that adults’ opinions are more valid than those of young people.

Indeed, the Globe article by Megan Woolhouse never presented the students’ point of view on the subject of being locked down for two periods because some students were “taking seven to eight minutes to get to class, instead of the typical four minutes.”

I can’t find an online copy of the letter written by a committee of six parents to the Weston Town Crier (published on page 8 of the 2/28/2008 print version), but here is an excerpt:

The presence of two Weston seniors was a welcome addition to the engaged discussions of all those in attendance.

Unfortunately, Mr. Leiner chose to give the two students’ opinions about alcohol and drug use the weight of fact rather than opinion. He did this without taking the time to validate these views with either the actual survey results available or the health and education professionals present at the meeting. His choices did offer the reader catchy, attention-getting quotes while putting these minors at potential risk for misunderstandings within the community and with their peers.

Indeed, the Town Crier article by Gabriel Leiner did give the students’ views “the weight of fact rather than opinion,” but it didn’t completely ignore the cited survey or the views of adult professionals. Check the link to read the article for yourself. Also note a sentence in a comment by an anonymous alum: “In every high school there are students who drink and those who study, but in weston there is a different class of student, those who study and drink.” Hmmm....

"Boys and girls,..." What's wrong with that?

2008-03-01T15:13:00.004-05:00

One of my colleagues objects when a teacher addresses a group of students as “Boys and girls,...” No, it’s not that she would prefer it if we said “Girls and boys,...”; that’s not the issue, though of course one should try to be at least equitable when using the phrase. In fact, one could argue that it would be best to say “Girls and boys,...” all the time, simply as a corrective measure. But that misses the point: my colleague doesn’t want us to say either version.

At first I was unconvinced. It’s not that I ever use the phrase. I don’t, even with fourth-graders. But to me it sounded harmless and inclusive.

All it took for me to see the light was for this colleague to propose addressing a class as “Blacks and whites,...” or “Jews and gentiles,...” I got the point.

The Sixth Annual Fractal Fair

2008-02-29T15:54:00.002-05:00

You’re familiar with the fact that high-school students often display their creativity in the fields of art, music, and theatre, and everyone has heard of science fairs, but similar opportunities in mathematics are all too rare. Today we held the Sixth Annual Fractal Fair at Weston High School. Here was the description I had written for the morning announcements:

Come see the creative projects of 60 students at the sixth annual Fractal Fair on Friday, February 29! It will be held in the High School Library (including the Library Computer Lab) from 9:15 to 1:15, which is most of Blocks B, D, and H. Learn about models of 3-D fractals, the creation of special effects in movies, fractals in science, fractal music (with original compositions!), the fractal structure of plants, fractal movies, the fractal dimension of coastlines, the creation of forests, a card game with fractal images, and other applications of fractals in mathematics, science, and art.

The students’ projects definitely met expectations, in terms of both creativity and mathematics. Almost all of the participants had had to learn material that was new to them, in order to extend what they learned in class, and all of them had to organize and present their knowledge in a manner that would make sense to adults and students who knew nothing about fractals. This year, for whatever reason, there was very little about the Mandelbrot Set; most of the projects investigated fascinating connections with chemistry, biology, physics, geology, music, and art. Very impressive work!

The only downside was that we didn’t get a large enough audience. About eight parents attended, and maybe a dozen teachers or administrators, and (I would estimate) approximately 50 students in addition to the 60 participants, but we should have had more. There were several dozen students working in the library during the event, including some who had exhibited last year, some who have just been studying fractals in non-participating math classes, and some who will be studying fractals last year — but I was quite unsuccessful at persuading more than a handful to look at the posters and computer presentations. They were all too intently studying! I suppose that says something about Weston, but couldn’t they have taken 15 minutes out of their studying to see what their fellow students have accomplished?

On a related matter, I will also have to write a follow-up post about issues arising among competitive students when creating products in groups of two and three. But I first have to figure out what I can say in a public forum.