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Wednesday, December 31, 2008


I just discovered a cool poster-creating applet called Wordle. In their own words:
Wordle is a toy for generating “word clouds” from text that you provide. The clouds give greater prominence to words that appear more frequently in the source text. You can tweak your clouds with different fonts, layouts, and color schemes. The images you create with Wordle are yours to use however you like. You can print them out, or save them to the Wordle gallery to share with your friends.
You can create an image from text that you type in, or from a URL of a blog with an RSS feed. In the latter case, the applet uses all the text it finds at that URL, excluding some common English words (or whatever other language you might choose).

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

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Tuesday, December 30, 2008

How many college recommendations?

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.

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Monday, December 29, 2008

In praise of Micci

A completely unsolicited testimonial:

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

The furnace works perfectly now.

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


Sunday, December 28, 2008

Dorchester Community Gardens

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

Now, as for the definition of “inner city”: Wikipedia says that it’s “the central area of a major city or metropolis,” going on to explain as follows:
the term is often applied to the poorer parts of the city centre and is sometimes used as a euphemism with the connotation of being an area, perhaps a ghetto or slum, where residents are less educated and more impoverished and where there is more crime.
Answers.com defines it like this:
The usually older, central part of a city, especially when characterized by crowded neighborhoods in which low-income, often minority groups predominate.
Whichever definition you prefer, Dorchester is certainly in part inner-city. I do tell people that I live in the inner city, but we also have community gardens and other green space.


Saturday, December 27, 2008

Fred the Footrest

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

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

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

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

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


Friday, December 26, 2008

Chinese food in Elmira

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

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

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Wednesday, December 24, 2008

What do I need to do to get an A?

“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.

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Tuesday, December 23, 2008

More about the Ashmont Grill and Tavolo

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

From September 8
9/8/2008 Ashmont Grill Wine Club

From October 27
10/27/2008 Ashmont Grill Wine Club

From November 3
10/27/2008 Ashmont Grill Wine Club

From December 22
10/27/2008 Ashmont Grill Wine Club

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

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

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

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

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

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

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Monday, December 22, 2008

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

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

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

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

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Sunday, December 21, 2008

David Handler's Berger & Mitry series

David Handler, best known for this Stewart Hoag series and other novels, has also written six books (so far) in his Berger and Mitry series:
  • The Cold Blue Blood (2001)
  • The Hot Pink Farmhouse (2002)
  • The Bright Silver Star (2003)
  • The Burnt Orange Sunrise (2004)
  • The Sweet Golden Parachute (2006)
  • The Sour Cherry Surprise (2008)
If you’re exceptionally observant, you’ll notice a certain pattern to those titles.

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

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


Saturday, December 20, 2008

Kindle for textbooks?

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.

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Friday, December 19, 2008


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

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

I will do likewise.

Well, maybe just four more.

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

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

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Thursday, December 18, 2008

Where are my model railroad pix?

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

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


Wednesday, December 17, 2008

Strip Search

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

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

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

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


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

But don’t think that Bernhardt extends genre stereotypes to gender stereotypes. No, we also have Esther Goldstein, a female mathematician who not only teaches math but also has apparently solved the Riemann Hypothesis (misspelled “Reimann” throughout the book). For reasons that apparently stem in some undefined way from an unhappy childhood, she is also reviving the ancient Pythagorean religion, the Brethren of Purity. Unfortunately she also turns out to be a psychotic mass murderer. But then again she is a math teacher, so you can’t expect her to be normal, can you? “Math has been riddled with positively brilliant madmen,” as she explains at one point.
  • The sympathetic characters, such as police lab technician Amelia, say things like, “I gave up on math after my second semester of algebra.”
  • Susan, even though she presumably has at least a master’s degree in psychology, says, “I hadn’t taken a math class since junior high school.”
  • The puzzle expert says, “I’m a word boy. Left brain. Math freaks are a whole different breed. And this doesn’t look like a real puzzle anyway. How can you solve an equation if you don’t have any of the numbers?
Bernhardt’s mathematical errors include confusing variables with unknowns and referring to expressions as equations. For example, on page 161, we have this excerpt:
It was another equation:
(p-1)!+1, all over p
Bernhardt’s account of the Pythagoreans’ attitude toward the irrationality of the square root of 2 is also muddled. For instance, Esther, the professional mathematician who’s an expert on the Pythagoreans, says, “The square root of two was a problem with no solution.”

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

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Tuesday, December 16, 2008

Misreading Larry Summers

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.

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Monday, December 15, 2008

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

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.

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Saturday, December 13, 2008

Obama and the Achievement Gap

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

Until now.

That’s change we can believe in.


Friday, December 12, 2008

iPhone games

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

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

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

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

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Thursday, December 04, 2008

Turn your iPhone into an ocarina.

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

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

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

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Tuesday, December 02, 2008

Teaching spreadsheets in high school math classes

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.

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Monday, December 01, 2008

"Everyone else does it."

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.

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