Learning Strategies

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

Labels: books, Dorchester, food, life, linguistics, math, model railroads, movies, teaching and learning, technology, travel, Weston

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.

Labels: movies, Weston

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.

Labels: teaching and learning, Weston

“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.

Labels: math, teaching and learning, Weston

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.

Labels: teaching and learning, technology, Weston

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.

Labels: life, math, teaching and learning, Weston

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.

Labels: math, teaching and learning, Weston

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:

1. What can spreadsheets add to high-school math?
2. When and in what order should we teach various spreadsheet techniques?
3. 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.

Labels: math, teaching and learning, Weston

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.

Labels: teaching and learning, technology, Weston

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.

Labels: linguistics, Weston

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.

Labels: Dorchester, life, linguistics, teaching and learning, Weston

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”.

Labels: teaching and learning, technology, Weston

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.

Labels: Weston

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.”

Labels: life, Weston

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.

Labels: Dorchester, Weston

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!

Labels: Weston

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.

Labels: Dorchester, food, math, teaching and learning, travel, Weston

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!

Labels: math, movies, teaching and learning, Weston

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.

Labels: teaching and learning, Weston

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.

Labels: life, teaching and learning, Weston