Learning Strategies

So let’s suppose that the Boston Globe (4/24) is reporting on a crime story, based on a press release from the office of Suffolk County DA Dan Conley. And let’s suppose that the crime took place in the Beacon Hill neighborhood of Boston. Would you expect that the article would begin like this?

A Dorchester man was sentenced yesterday to more than seven years in jail for selling crack cocaine from a Beacon Hill apartment.

Well, Chris Stanley observed that the DA Office’s 4/20 press release began like this, so we know where the Globe got it from:

A Suffolk Superior Court jury yesterday convicted a Dorchester man of selling crack cocaine out of a Charles Street apartment in the shadow of Beacon Hill last year, Suffolk County District Attorney Daniel F. Conley announced.

Apparently the Globe, which is located in Dorchester, and the DA’s Office, which includes both Beacon Hill and Dorchester in its jurisdiction, both feel compelled to identify a crime with Dorchester just because that’s where this criminal comes from, even though this particular crime took place in tony Beacon Hill. Yes, crime is admittedly more of a problem here than there, but why make it seem worse than it is?

Labels: Dorchester

As I reported in my post of April 19, Weston High School’s spring musical this year is My Favorite Year. Yesterday’s opening-night performance was thoroughly enjoyable, with some surprising casting and some unusually strong performances. Joav Birjiniuk, Laura Caso, Todd Elfman, Quinton Kappel, and Natalie Birren were all memorable in their portrayals of an interesting array of show-business types. I find it particularly intriguing when an obviously Jewish actor manages to be convincing in portraying an obviously Gentile character and then an obviously non-Jewish actress is equally convincing playing a Jewish mother.

Labels: movies, Weston

When classes ended at 2:50 this afternoon, one of my students asked me if I would like to learn how to play Mao. I said that I didn’t know anything about it, but I was indeed available after school. “What’s the game about?” I foolishly asked.

“I can’t tell you that,” Alli replied.

That sounded ominous, but I agreed. So Alli rounded up several of her friends — another junior girl, two junior boys, and a senior girl — along with a couple of other math teachers and myself. All of the students already knew this game. None of the adults knew it.

“What are the rules?” asked my colleague Sharon.

“We can’t tell you,” they all replied. “Part of the game is to figure out what the rules of the game are.”

This was quite annoying, at least for someone like me. I like to know what the rules are. At least we could tell that it involved a regular deck of cards. The dealer reluctantly gave up one piece of information: in order to win, you have to get rid of all your cards.

So the game commenced. We were each dealt some cards and proceeded to discard them in turn — except that penalties were exacted for all kinds of mysterious offenses, such as “touching cards during a point of order” or “failure to have a nice day.” As a math teacher, I’m accustomed to looking for patterns, but these were hard to discern, to say the least. It turns out that my colleague Dan figured out almost all the rules very quickly, and that was because he is an experienced card player. Apparently Mao is based on Uno, which I’ve never heard of. Since Dan knew various discard games, including Uno, he had some idea of what sort of rules might exist, and that made all the difference.

Fortunately I had no time to look up the game online, or I would have discovered what it’s all about. That would have spoiled all the fun. When I have the time, I’m going to read the entire article about it.

There’s probably a moral here about the kind of patterns we expect kids to see when they’re learning math. If you don’t have some idea of the space in which the patterns exist, you’ll find it very hard to discern them.

Labels: teaching and learning, Weston

As part of the aforementioned fundraising for the Mayor of Dorchester campaign and Dorchester Day activities, the Ashmont Adams Neighborhood Association and the St. Mark’s Area Main Streeet volunteres will be sponsoring a Cinco de Mayo celebration on (of course) Saturday, May 5. As Barbara points out, under the circumstances it should really be called Cinco de Mayor, shouldn’t it?

Labels: Dorchester, food

I just finished reading Body Double, by Tess Gerritsen. I have mixed reactions. On the whole, I suppose, I would say that I recommend it with reservations. It definitely kept my attention, and I didn’t want to quit in the middle; although it’s definitely a thriller rather than a mystery, there was plenty of suspense, and several questions were resolved in surprising ways. Several characters were reasonably three-dimensional, including the two major ones. So what makes me less than fully enthusiastic? I suppose it’s because too much of the book seemed obvious, from the twins separated at birth to the medical examiner out of Patricia Cornwell. Still worth reading, but...

Labels: books

I wrote earlier about the Dorchester Chili Cookoff, a fundraiser for the Mayor of Dorchester/Dorchester Day Parade. It turned out to be a good experience, but with some flaws. Ten or eleven neighborhoods contributed entries, and IMHO the winner was Ashmont Hill. It was the only vegetarian entry (!) and the only spicy one (!!), so it didn’t actually win. Apparently my opinion was definitely a minority one.

But, speaking of minorities, that wasn’t the real flaw. First of all, each group dished out three or four ounces of chili! Obviously it was impossible to taste every entry, so my considered judgment is based on a sample of four. Not fair, I suppose. Second, continuing the theme of yesterday’s post, I was deeply disappointed in the lack of diversity among the participants. Considering that Dorchester is about 50% black and Hispanic, why is it that everyone there — on both sides of the tables — was white (except for a tiny Asian representation)? Admittedly the event was held in Florian Hall, a bastion of white Dorchester, but still.... Were there no neighborhood groups in Codman Square or west of Washington Street that were interested in participating? Were there no African-Americans who wanted to join in the festivities and help pick a winner? Did they feel unwelcome? Is chili just a white, yuppie phenomenon? I don’t get it.

Labels: Dorchester, food

At the Saturday Course in Milton — frequently mentioned in this blog — we teach students from many different cities and towns, including Milton itself and Boston. So we were wondering why we don’t have a more diverse student body, since the majority of Boston public-school students are non-white.

The discussion took a brief diversion as we realized that our significant Asian minority doesn’t “count” — apparently only blacks and Hispanics count toward diversity. But that’s a story for another time.

Though our student body does have more than a handful of blacks and Hispanics, it’s still unrealistically few. “But we’re only a mile from Dorchester!” exclaimed one participant in the discussion. That is true. And since Dorchester is about 50% black and Hispanic, why do so few take advantage of the wonderful educational opportunity that the Saturday Course offers?

Let’s look at a few figures. About 17% of our total enrollment comes from Boston, including 7% of the total from Dorchester and 10% from other Boston neighborhoods. That’s fairly respectable, though we invite many more — and plenty of those 17% are white or Asian. What causes this problem? Is it a vicious circle, where a lot of non-white families don’t want to enroll because there are so few non-white kids? Or is it a transportation problem? Is attending an enrichment program on Saturdays too much of a middle-class white-and-Asian thing to do? What’s the cause of the under-representation of blacks and Hispanics in programs like this?

Labels: Dorchester, life, teaching and learning

I finally watched My Favorite Year, in anticipation of Weston High School’s production of the musical version of this classic 1982 film. A slightly disguised roman à clef about Mel Brooks, Sid Caesar, and Errol Flynn, this movie manages to be both funny and touching. You can rent it from Netflix, as I did. It’s worth watching!

Labels: movies, Weston

“What does this mean?” a local realtor asked Barbara, pointing to a “Craig Galvin for Mayor of Dorchester” sign. “Dorchester is part of the city of Boston; it doesn’t have its own mayor!”

So Barbara patiently explained that although there is no official position of Mayor of Dorchester, this has long been an honorary post, the campaign for which serves as a fundraising device for the annual Dorchester Day parade. She refrained from observing that any local realtor should know more about the culture of the community in which he’s selling homes. She also refrained from pointing out the irony that Galvin is also a local realtor, so maybe the clueless one should know more about him as well. Dorchester Reporter editor Bill Forry writes about the history of the Mayor of Dorchester position:

The contest, which started back in 1998 when retired labor boss Pat Walsh seized the first-ever title by raising a still-unmatched sum of $23,000, has had its ups and downs. In some cases, the eventual winner has run unopposed, generating little, if any, interest, and even less money for parade organizers, who count on the contest to help them cover the estimated $50,000 pricetag of the annual jaunt up the avenue.

Often there are two candidates for Mayor of Dorchester, who compete to see who can raise more money. But not this year. As Forry observes, an unopposed candidate generates little interest and less money. So, in a new twist as an additional fundraiser in this one-candidate race, the first annual Dorchester Chili Cookoff will be held at Florian Hall this Sunday, April 22, at 5:30 PM. Be there!

Labels: Dorchester, food

After a few weeks in the Minuteman Library Network queue, Jerome Groopman’s recently published book, How Doctors Think, finally became available, so I promptly checked it out and checked it out. It lives up to its publicity, though the brief reviews and interviews are (unsurprisingly) in some ways misleading. Yes, Dr. Groopman does tell us about doctors usually make snap judgments and how they make mistakes in their thinking. That much is true...and valuable. But focusing on this idea greatly oversimplifies a more complex book. The title suggests a lot more than snap judgments and mistakes. It doesn’t say “How Doctors Think Incorrectly,” but — more simply and more comprehensively — “How Doctors Think.” And that’s what we learn.

Of course it’s more sensational to focus on medical mistakes. The doctor who reaches a judgment in ten seconds rather than ten minutes can be alarming — and even ten minutes seems far too short. What especially interests me as a math teacher is that the two most common mistakes that Groopman discusses are the same as my math students’ two most common mistakes: they want a really quick answer rather than think about a problem in depth, and they want an algorithm they can follow rather than think about each problem individually. Surely it’s no coincidence that doctors and math students fall into the same trap. Groopman tells plenty of true anecdotes about medical errors of both of these types. Like any good story-teller, he writes about concrete examples, involving himself wherever possible, rather than using impersonal, “scientific,” third-person examples. These anecdotes are successful in bringing Groopman’s ideas to life without overwhelming the reader with too many examples.

Doctors are understandably reluctant to criticize each other. Groopman cites plenty of instances of poor judgment, though never by name, and plenty more instances of excellent judgment and devoted care, naming names in those cases. As an oncologist, Groopman is particularly moving in his long exposition of cancer cases in friends, acquaintances, and strangers, where we learn of the many alternatives that physicians have to consider and how they think about those alternatives.

We all need medical care, and we all want to trust our doctors. But we need to be our own best advocates. In some ways this highly readable book will scare you, but in other ways it will give you a glimpse into the mind of the doctor and will help you advocate for yourself.

Labels: books

Rudbeckia Hirta reports that her college students don’t know how to work with percents. I would like to say I’m surprised. I would like to say that all Weston High School students know how to work with percents.

I would like to say that.

But I would be lying. I know perfectly well that there are plenty of Weston High Schools who don’t know how to do certain problems involving percents — at least the ones like “7 is 6% of what number?” But surely they can do some of the problems that some of Hirta’s college students can’t do:

We did a problem where they were told the price of the item ($20), the sales tax rate (8%), and the percent discount (25%). The question asked whether getting a discount of 25% and then not having to pay the 8% tax could be thought of as a 33% savings from the usual, non-discounted, with-tax price. (This problem was based on an advertisement that I got in the mail claiming just that.) One student couldn’t figure out why the $20 item was $21.60 after tax. No one could decide whether or not paying $15 for the item would be a 33% discount from the $21.60 normal (with-tax) price.

We did another problem in which we were calculating what percent of the positive tests from a medical test were patients who actually had the condition. We found that of the 604 patients who tested positive that only 10 of them had the condition (the remaining 594 were false positives). I calculated the rate as 10/604 and stated that it was about 1.7%. One of my students raised her hand and asked why 10/604 is about 1.7%.

In another problem, we were trying to calculate 60% of 495,000. A lot of students in my class didn't know how to do it.

All right, maybe I’m just too optimistic. But I really do believe that almost all Weston High School students could calculate 60% of 495,000 — especially with the use of calculators, which these college students also had. In fact, I’m pretty confident that almost all Weston Middle School students could do these problems as well.

Hirta also points out that her “students prefer to study the computational tasks that they're used to but can not do (and would fail if we spent significant time on) but despise working with the abstract concepts that they are smart enough to do a reasonable job of understanding.” That doesn’t surprise me either, but that’s an issue for another day.

Labels: math, teaching and learning, Weston

As I reported yesterday, part of Weston High School’s Earth Day observances was a screening of An Inconvenient Truth. This event was attended by everyone — students and teachers alike. (Almost everyone, actually. A few kids skipped out, and some stayed home.) By and large I was quite impressed with the students’ attentiveness; the usual teenage cynicism and restlessness didn’t keep them from watching quietly, even when Al Gore was being especially geeky. Not that there’s anything wrong with being geeky. The audience’s attention flagged only after the film was over, when they had to sit through a brief slide show that presented statistics from a survey of ways in which students do or don’t protect the environment.

Anyhow, I found An Inconvenient Truth an extremely compelling documentary, both as a film and as a piece of educational propaganda. Duarte Design’s visual representations of statistics were especially well done, being crisp, vivid, and devoid of chart clutter. Edward Tufte was probably pleased — relatively speaking, since Tufte makes compelling arguments against PowerPoint that carry over in part to Keynote, which is what Gore uses. But, for the techies among my readers, here are some observations about Keynote from designer Ted Boda:

Al Gore’s presentation was in fact using Apple’s Keynote presentation software (the same software Steve Jobs presents from) and did so for a number of reasons. As a designer for the presentation Keynote was the first choice to help create such an engaging presentation.

Apple’s Keynote anti-aliases its fonts and graphics, scales vector objects and supports QuickTime videos easily and without any plug-ins. Duarte used a combination of Keynote’s graphics and graph tools, Illustrator, Photoshop, AfterEffects (for more complex animations) and dropped in numerous videos from different sources to complete his presentation. Some of the videos dropped were up to 1920x1080 (HD), they played and scaled extremely well and was something our team could not even begin to think about doing in PowerPoint.

Thousands of people have commented on the effectiveness and importance of Gore’s message about climate change and the environment, so I want to focus on the presentation of statistics. As a math teacher, I am always interested in multiple representations of mathematical objections — equations, functions, statistics, or whatever — and I am always interested in excellent teaching. Gore has some lessons to teach us here. I can do no better than to quote Garr Reynolds:

Three things stand out about Al Gore’s presentation:

(1) He looks relaxed, like he’s in his realm. It’s a serious issue, and he is serious, yet he’s a pleasure to watch and listen to. Where was this guy in 2000 indeed.

(2) The technology is transparent to the audience, as it should be. He’s got to be the only 50-something politician (former politician?) who can actually use slideware without stinking up the place.

(3) His slide images are photographic imagery of high quality. The design of the visuals are powerful yet complementary and subordinate to Gore and his message (though in many ways, the visuals are the message in this instance; certainly the visuals are crucial to his case).

Labels: life, math, movies, teaching and learning, Weston

We observed Earth Day today at Weston High School (since the real Earth Day will come right after April vacation). Classes were shortened to 55 minutes to allow time for a screening of An Inconvenient Truth, and we had guest speakers available throughout the day. Results of a student survey of environmentally aware behavior were presented, and everyone was encouraged to cut down on our use of resources through recycling, reuse, carpooling, and the like. I distributed some flyers on wind power from Mass Energy and the New England Wind Fund. Science teachers and members of Students for Environmental Action prominently wore their “I’m a tree hugger” tee shirts.

Student responses were generally positive, though of course there were some who considered it all a left-wing plot and there were others who are too much in love with their SUVs to believe that they could be harmful. Actually, I shouldn’t say “others,” as these were probably not disjoint groups.

Labels: life, teaching and learning, Weston

Continuing my inadvertent theme of reading books with a strong sense of place, I just finished The City of Falling Angels, by John Berendt of Midnight in the Garden or Good and Evil fame. In this case it’s not a coincidence, as it was recommended by an Italian teacher with whom I was discussing Blood from a Stone. Like that book, The City of Falling Angels is about Venice; unlike that book, it is non-fiction. As Berendt points out in an interview that constitutes the afterword, Venice shares many characteristics with Savannah, even though they’re actually totally different: both are unique, bound by their history, and inward-looking.

Berendt recently spent several years living in Venice, and this leisurely book is the result. Don’t read it if you want fast-paced action! Although it’s written in the form of a novel — with a story line, three-dimensional characters, conflict, and resolution — it’s definitely not a novel. And it’s not a comprehensive view of Venice and Venetians; some reviewers justifiably complained about Berendt’s focus on upper-class Venetian society, but read the book for that particular perspective, that slice of life in Venice. It’s not only not a novel, it also isn’t a sociological treatise. What it does is bring Venice to life, along with many of its fascinating characters. (Unlike what he did in Midnight, Berendt has created no composite characters and no fictionalized events: this is totally non-fiction.) The principal narrative arc is the famous arson fire in the Fenice opera house, which frames the story line but in no sense dominates it. Yes, you do find out who (probably) set the fire, but that’s not the point: you have to enjoy hearing in depth about the many people Berendt meets or learns about in Venice, thinking about them as forming the big idea of the book, not as asides. There is a lot of focus on the ex-pat community — not surprisingly, since Berendt was temporarily one of them. Peggy Guggenheim and Ezra Pound may not spring to mind as true Venetians, but they’re an important part of the story. Read it before you go.

Labels: books, travel

What is model railroading? Sure, it’s a hobby, but all sorts of disparate activities are admitted into the big hobby tent; some are sports, some are arts, some are crafts. All of them are leisure activities that one does for fun rather than for profit. So cooking, for example, is a hobby for some, a job for others, a profession for a few. Model railroading, as I said, is a hobby — very, very few make a living from it! — and it encompasses a remarkable number of crafts and technologies.

Some model railroaders are really toy train enthusiasts; they “play with trains” as adults, having enough of a layout to be able to enjoy operating their not-particularly-realistic trains without worrying about scale realism or scenery. At the other extreme are the true railroad modelers, who can be fanatical about scale accuracy, faithfulness to the prototype, and detailed scenery and structures. There’s a whole huge range in between. But almost everybody finds himself (or occasionally herself) spending time on a wide variety of crafts, some of which may be more enjoyable than others, and all of which can turn out to have the side benefit of being educational and absorbing. There’s construction of benchwork, buildings, roads, terrain, and scenery; there’s the sometimes complex task of wiring an entire layout; there’s the artistry involved in creating backdrops and scenic details, as well as the routine painting of almost everything; there’s laying and ballasting track; there’s controlling the trains, with or without the aid of a computer. And there’s a large side of the hobby that I have very little to do with: realistic operation of a railroad, completing with timetables, picking up cargo, switching, and delivering the cargo. Quite an amazing variety of crafts for one hobby!

“Model railroading today is a great exercise in systems integration,” says joe.daddyo in the Layout Construction Yahoo newsgroup.

Labels: model railroads

In my post of February 23, I quoted from an NPR interview with Susan Eaton and said, “I’ll have to read the book.” Not surprisingly, I wasn’t the first in the queue for a library copy of The Children in Room E4, but I’ve finally had the chance to read it. You should do so too.

It’s also not surprising that the radio interview didn’t do the book justice: paradoxically, it’s both broader and more specific than I had expected. A great deal of the book is devoted to the long history of school desegregation in the north, especially in Hartford. As an effective journalist, Eaton brings this history alive by telling the stories of a variety of participants. This is where the breadth comes in. On the other hand, the main arc of the narrative is really what the book’s title promises: it’s about the children in Room E4 — students of color in inner-city Hartford. Under the amazing instruction of their dedicated teacher, they studied and studied and prepared and prepared for Connecticut’s standardized test, on which they did astonishingly well. The achievement gap disappeared.

For one school.

For a year.

For a price.

The price was the abandonment of science, of social studies, of art, of music, even of recess. Somehow the middle-class, predominantly white, suburban school was still able to achieve, without abandoning those important endeavors. I suppose one could argue that it’s impossible to succeed later on without basic skills in the three R’s, so it was worth giving up everything else in pursuit of the standardized test. But the results didn’t last and weren’t replicated, despite all the great promise of the No Child Too Far Ahead Act. Oops, I mean No Child Left Behind, of course. Anyway, read the book!

Labels: books, teaching and learning

Consider what we teach in high-school geometry:

• There’s a lot of content from various two-dimensional topics, such as congruence, similarity, angles, polygons, and area. Much of this rehashes what was already done in middle school, though (we hope) in greater depth.


• In some schools there’s some right-triangle trigonometry.


• Usually there’s a lot of time devoted to proof. In honors classes this becomes the principal focus of the course. Some students love proof; it gives them a real sense of power. Many students hate it and can’t make sense of it.


• There’s a bit of content from the third dimension, such as volume. It’s a pity that there’s so little, since we live (apparently) in three dimensions, as Tom Banchoff has eloquently pointed out.


• And what about non-Euclidean geometry? What is the real shape of space, anyway? For some reason this topic is treated as appropriate for honors classes but too abstract for everyone else.

There has to be some way to sell proof to more students. It doesn’t have to be done in geometry class — it could be tackled somewhere else — but experience has shown that geometry is where it’s most effectively learned, probably because one can draw pictures and because there’s a long tradition of postulates and theorems. Proof is important, since it teaches students to justify an argument and not merely take their teacher’s word for it. But that’s not the subject of this post. Here I want to consider the shape of space. Is it Euclidean? If not, why do we pretend that it is?

And...why is this topic considered so abstract? Probably it’s because seeing isn’t believing. The principal advantage of geometry — that one can draw and examine figures — seems to go away. And yet MacArthur-award winner Jeff Weeks has produced exciting and concrete mathematics materials that can be explored by kids as young as ten. Shouldn’t we be including this sort of content in regular high-school geometry? Let’s spend less time on rehashing middle-school material and more time challenging our students to think about the universe in new ways!

Labels: math, teaching and learning

Had lunch on Saturday at the newly opened Mifune in Arlington Center — despite the fact that a review on Yelp claims that they didn’t open until Monday. Here’s what the reviewer says, dated today, with a few irrelevancies omitted:

Mifune...is open! My GF and I swung past there last night and discovered they had literally opened that day. The new decor is lovely, nice burnished wood accents, a classy-looking sushi bar, etc...

It was clear that this was opening night and everyone seemed just a little... well, not entirely relaxed. That said, the service was attentive and pleasant.

The menu is extensive, with both Chinese and Japanese foods well-represented, not to mention a few curveballs like a Jamaican Salad (?). We shared some sushi followed by the House Special Pan-fried Noodles. The sushi was above-average, and they had some interesting rolls like tuna/asparagus. I liked that they went a little easy on the rice on the inside-out rolls, and the spicy tuna was very zingy. We both liked the noodles a fair bit — they were crispy on the edges and well-cooked in the middle, with a good mix of meats and veggies.

All in all a solid addition to the neighborhood, but I didn’t think it was hugely special. I will definitely be back for take-out lunches and to sample more of the menu.

...They weren’t taking credit cards yet so my GF had to run to CVS and buy us some toothpaste with cash-back :). I’m sure this will be resolved very soon, after all it was opening night...

Oddly enough, I ate there two days earlier, and they definitely took my credit card. Oh, well.

I have nothing to disagree with in the content of the review. We had an unusual and delicious appetizer, Tiger’s Eyes, which consisted of grilled squid stuffed with smoked salmon and asparagus, and ordinary but competent miso soup. My bento box contained the aforementioned sushi, the usual vegetables, and beef teriyaki. I agree that nothing was “hugely special,” but it was all excellent, so we too will definitely be back.

Labels: food

Barbara and I spent an enjoyable afternoon yesterday at the annual Ice Chips show in Boston (not Cambridge, even though the arena is on the extended Harvard campus). The “special guest star” was Sasha Cohen, but we went primarily to see my student Emily Naphtal, the 2007 Mexican National Senior Ladies Silver Medalist. (Mexican? Weston? Don’t ask. It’s a long story.) It was an afternoon of first-rate figure skating, with skaters ranging from tiny kids to senior citizens, but mostly teens and young adults. Go see it next year!

Labels: life, Weston