Learning Strategies

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

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.

Labels: linguistics, teaching and learning, Weston

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:

1. Go to www.blogger.com.


2. Follow the 3 easy steps displayed on that page.

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

Labels: teaching and learning, technology

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?

Labels: math, teaching and learning, Weston

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.

Labels: teaching and learning, Weston

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.

Labels: teaching and learning, Weston

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.

Labels: teaching and learning, Weston

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.

Labels: books, movies

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.

Labels: books, movies, teaching and learning

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.

Labels: books, teaching and learning, technology

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!

Labels: books

I guess Kalmbach didn’t have 100 fingers:

Labels: math, model railroads

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.

Labels: life, model railroads

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.

Labels: model railroads

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...

Labels: math, teaching and learning, Weston

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...)

Labels: math, teaching and learning

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.

Labels: Dorchester, food

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.

Labels: math, Weston

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!

Labels: books, teaching and learning

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!

Labels: books

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.

Labels: math, teaching and learning, technology, Weston

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.

Labels: teaching and learning, Weston

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).

Labels: life, teaching and learning, Weston

(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.

Labels: life, teaching and learning, Weston

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....

Labels: Dorchester, life, teaching and learning, Weston

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.

Labels: life, teaching and learning