<body><script type="text/javascript"> function setAttributeOnload(object, attribute, val) { if(window.addEventListener) { window.addEventListener('load', function(){ object[attribute] = val; }, false); } else { window.attachEvent('onload', function(){ object[attribute] = val; }); } } </script> <div id="navbar-iframe-container"></div> <script type="text/javascript" src="https://apis.google.com/js/plusone.js"></script> <script type="text/javascript"> gapi.load("gapi.iframes:gapi.iframes.style.bubble", function() { if (gapi.iframes && gapi.iframes.getContext) { gapi.iframes.getContext().openChild({ url: 'https://www.blogger.com/navbar.g?targetBlogID\x3d12969692\x26blogName\x3dLearning+Strategies\x26publishMode\x3dPUBLISH_MODE_BLOGSPOT\x26navbarType\x3dBLUE\x26layoutType\x3dCLASSIC\x26searchRoot\x3dhttps://larrydavidson.blogspot.com/search\x26blogLocale\x3den_US\x26v\x3d2\x26homepageUrl\x3dhttp://larrydavidson.blogspot.com/\x26vt\x3d-7810603580866381255', where: document.getElementById("navbar-iframe-container"), id: "navbar-iframe" }); } }); </script>

Saturday, December 31, 2005

Dadaism lives

As reported on NPR’s Weekend Edition Saturday this morning, we will be observing International Dadaism Month for a short month consisting of only 13 days: 4 February, 1 April, 28 March, 15 July, 2 August, 7 August, 16 August, 26 August, 18 September, 22 September, 1 October, 17 October, and 26 October. Hmm....


Friday, December 30, 2005

From David Allen

Two quotations (from David Allen’s newsletter):
A task left undone remains undone in two places — at the actual location of the task, and inside your head. Incomplete tasks in your head consume the energy of your attention as they gnaw at your conscience. They siphon off a little more of your personal power every time you delay. No need to be a perfectionist, that’s debilitating in an imperfect world, but it’s good to be a “completionist.” If you start it, finish it — or forget it.
[Brahma Kumaris]

If you worry about everything, then you don’t have to worry about anything.


Thursday, December 29, 2005

Worth a detour

Despite the general lack of excitement in Elmira, it does boast two great attractions: the Arnot Art Museum and the Chemung Valley History Museum.

Walking into the history museum, I was immediately taken aback by being offered the senior citizens’ admission fee.

“Really?” I asked, not thinking of myself as old.

“You’re over 55, aren’t you?” replied the considerably older man at the desk. I had to admit that I was. But how did he know?

Anyway, the museum has a well-done permanent exhibit on Mark Twain and the history of the Chemung Valley (southern tier of New York and northern tier of Pennsylvania). It also currently has three temporary exhibits, one on the Underground Railway (and the general history of black residents of the Elmira area), one on the history of Route 17 (which is currently being turned into I-86), and one on the history of patriotism in the Chemung Valley. This last one was surprisingly interesting, containing far more than the solutions to geometry problems represented by U.S. flags with various numbers of stars. In particular, it emphasized the roles of voting, citizen participation, and dissent. Above the whole exhibit was a quotation from General Wesley Clark: “Dissent is the highest form of patriotism.”

A refreshing view in these days of the religious right and the current administration in Washington.


Wednesday, December 28, 2005

Hotel or B&B?

When we go to Elmira (see yesterday’s post), Barbara and I usually stay at the Hilton Garden Inn in Horseheads. (Yes, you heard that right: Horseheads.) Like any of the low-end Hiltons, it is boring, predictable, and perfectly adequate. So for 2005 we decided on a more exciting option: a high-Victorian Bed & Breakfast in Elmira, the Painted Lady. Our beautiful suite at this warm and friendly B&B was only slightly more expensive than our room at the Hilton would have been, but it returned many times the subjective value.

There is, of course, always a trade-off when choosing good B&B’s over average hotels:
  • In a B&B — in the right B&B, at any rate — you get personalized service, great breakfasts, comfort, an atmosphere completely free of residual smoke, and a home-like feel.

  • In a hotel — in the right one, again — you get room-service, fresh towels and sheets every single day*, a 24-hour front desk [who cares?], a swimming pool, and a microwave oven in the room.
The B&B is clearly worth the trade-off, especially when it’s the Painted Lady, which provides elegant but comfortable surroundings, restaurant advice and reservations, a jacuzzi in each guest room, a billiards room and a lovely piano room on the first floor, and a real featherbed. Like the hotel, they also provide a fridge in each room, and Wi-Fi with free Internet access and a VCR/DVD player, so there’s no need to suffer technology withdrawal. These modern necessities come amidst the 12-foot ceilings and exuberant ornateness of the peak of the Victorian era, where “too much is never enough.”

The good proprietors of the Painted Lady (who are originally from Massachusetts, by the way) claim to provide
refined elegance, luxurious surroundings and pampered relaxation.
And they really do! I highly recommend their B&B.

*The B&B norm is purportedly every two or three days — though our towels were changed and our bed made every day except for Christmas Day itself.


Tuesday, December 27, 2005

Sunny Elmira

Here I am, enjoying my vacation in the tropical paradise of Elmira, New York. No, wait! I must be thinking of someplace else. Elmira isn’t a tropical paradise — it’s a cosmopolitan urban center with hundreds of exciting cultural opportunities to choose from.

Well...no...it isn’t that either. It’s merely where I have to go to visit the in-laws.

But perhaps you’ll detect a certain theme to some of the people I ran into during this visit:
  • The scruffy-looking man hurrying past me as I’m unloading the car, pausing only to ask, “I just found a VCR; do you know anyone who would like to buy one?”

  • The guy in front of Barbara and me in the cashier’s line at the drugstore who tells us (over and over again) how he couldn’t find an electric menorah anywhere else.

  • The helpful customer in the super market who looks at the Bounty paper towels in our cart and proceeds to tell us why we should buy Viva instead, going into great detail about their coefficients of absorbency and the exact differences in unit prices between different types of Viva.

  • The library patron who gets my attention as I’m about to enter the public library and proceeds to say, “Did you know that somebody died from a hangnail on this very spot earlier today? He was standing there bleeding to death, and I tried to call 911 but couldn’t get through.”

  • Another library patron who proceeds to ask me questions until I say that I’ve only been there for ten minutes, whereupon she apologizes and said that she assumed I was a librarian.

  • A third library patron who walks up to me to tell me that he had found a wallet-sized calendar and asks me whether it’s mine.
OK, enough of that. Stay tuned for posts on our B&B and the Chemung Valley History Museum (the two truly interesting things about our visit).

Labels: ,

Thursday, December 22, 2005

The goal of all creative activity (including math?)

From Mark Bernstein:
...the goal of a Web site must ultimately be, quite simply, to make people think. Even simple sales sites aspire not simply to gain an order, but rather to gain a customer — and to change the customer so they’ll become an even better customer. The Bauhaus Manifesto claimed that
Das Endziel aller bildnerischen Tätigkeit ist der Bau!
The ultimate aim of all creative activity is the building!


Wednesday, December 21, 2005

Does Santa work for Bush?


Monday, December 19, 2005

Wikipedia's virtues

There has been a flurry of attacks on one of the most useful sites on the Internet: the Wikipedia. It’s the source that I recommend most often for math and computer science. But students tell me that it’s disparaged by their other teachers, who consider it unreliable at best and scurrilous at worst. A recent USA Today article has exacerbated these opinions. My first reaction was to smile at the idea that USA Today was calling some other source unreliable. Then I read the somewhat sensationalistic article, after which I discovered that it was talking about a single unfortunate case in which one guy from Nashville had posted a fake biography as a misguided joke on a co-worker.

The truth — as the highly reliable journal Nature and the highly respected paper The Guardian point out — is that
The Wikipedia is one of the wonders of the internet... for most of the time it worked remarkably well, reflecting the essential goodness of human nature in a supposedly cynical world and fulfiling a latent desire for people all over the world to cooperate with each other without payment. The wikipedia is now a standard source of reference for millions of people.
Back in the spring and summer, I decided to test out the accuracy of the Wikipedia. So I checked more than 200 entries on a variety of topics from mathematics, computer science, and linguistics — hundreds of entries, containing thousands of facts. Of course I didn’t know everything discussed in these entries, but I purposely picked topics on which I had a reasonable amount of expertise. Out of these thousands of facts, I found exactly two — count them, two — that I knew to be incorrect. This is an astonishing rate of accuracy. I’m sure I missed some errors, but still...

Would the New York Times be that accurate? I doubt it. It publishes several corrections a day, and it’s famous for a series of deliberately fraudulent articles. We trust the New York Times, the paper of record, but we’re apparently not supposed to trust Wikipedia because it’s written by ordinary people?

Or perhaps we trust the Encyclopedia Britannica. The Nature article referred to above (from the AP by way of MSNBC) found exactly the same number of serious errors in 42 articles on Wikipedia and a corresponding 42 articles in the Britannica. We need to take Wikipedia’s articles with several pinches of salt, but that’s true for all sources. We teach our students to be skeptical, not credulous, regardless of the source.

I do agree that citing the Wikipedia can be irksome to teachers, since the cited webpage may be different next year or even next week. But that's a problem for all Internet-based sources, not just Wikipedia.

Finally, I have a conjecture about the possibility that Wikipedia might be much more reliable in certain disciplines than in others. People are not going to take the time to write and post an intricate article about the Mandelbrot Set or ergative languages unless they know what they’re doing. But I suppose a random person with an axe to grind or even just a strong opinion might well post inaccurate information about political or social topics, either intentionally or unintentionally. So maybe that’s why Wikipedia seems so reliable in math, linguistics, and computer science, whereas it might not be so reliable in English and social studies. In any case, I urge you to check out the entries for some topics in which you have some expertise of your own. I can’t judge the accuracy of humanities articles, but I have a suspicion that even they are more accurate than most people think. Let me know your experiences, especially in comparison to other sources.

Labels: ,

Saturday, December 17, 2005

The night before solstice

’Twas the last day for this session’s Saturday Course. The “On Stage” class performed James Finn Garner’s very amusing “’Twas the Night before Solstice,” which begins as follows:
Twas the night before solstice and all through the co-op
Not a creature was messing the calm status quo up

The children were nestled all snug in their beds,
Dreaming of lentils and warm whole-grain breads.

We’d welcome the winter that day after school
By dancing and drumming and burning the Yule,

A more meaningful gesture to honor the planet
Than buying more trinkets for Mom or Aunt Janet,

Or choosing a tree just to murder and stump it
And dress it all up like a seasonal stumpet.

My lifemate and I, having turned down the heat,
Slipped under the covers for a well-deserved sleep,

When from out on the lawn there came such a roar
I fell from my futon and rolled to the floor.

I crawled to the window and pulled back the latch,
And muttered, “Aw, where is that Neighborhood Watch?”

I saw there below through the murk of the night
A sleigh and eight reindeer of nonstandard height....


Thursday, December 15, 2005

Highlighting considered harmful?

As our students were reading silently (see yesterday’s post), teachers were strongly encouraged to model the process by silently reading the same book along with the students. We were meeting in homerooms — eleven or twelve students per teacher — so this was straightforward and visible. I was using a yellow highlighter as I read (“active reading”).

A colleague, on seeing this, claimed that research shows that highlighting is harmful. Supposedly underlining is better. I was surprised to hear this, and I’ve been unable to find any research that supports this claim, or that in fact makes any distinction between highlighting and underlining. Can any readers point me to such evidence?


Wednesday, December 14, 2005

Silent reading: The first day

As I described in my post of November 3, Weston High School is currently engaged in a school-wide interdisciplinary project: reading Tracy Kidder’s Mountains Beyond Mountains and integrating it into every course in every subject. The integrating will happen in January, and Kidder is coming to speak to the whole school at the beginning of February. We began the project yesterday with a 15-minute intro in the auditorium followed by a 30-minute silent reading period.

Apparently silent reading is no longer done in school, or maybe it just isn’t done in high schools, or maybe most kids don’t read anymore. Too many students said that they couldn’t possibly read silently for half an hour, and too many said that they couldn’t possibly read a 300-page book by January.

This might, of course, be statistically misleading. After all, it’s the complainers who are most vocal and most likely to say something — in this and every other context. Let’s see what happens next week, when we have three 39-minute silent reading periods.

Labels: ,

Tuesday, December 13, 2005

A linguistic exercise

My favorite linguistics blogger, the Tensor, reports an interesting exercise that was held in one of his classes:
...the professor had us do a little exercise: sit down with a piece of paper and name as many [living] languages as you can.  She mentioned that someone has done a survey of linguistics graduate students and found that they can name something like 70-80 languages off the top of their heads... I was sure I could do better, but given that class time was limited, she couldn't just let us keep writing until we ran out.  So, later that day, I sat down and wrote down as many as I could come up with.  It's surprisingly hard—in particular, I didn't want to write down anything unless I was sure it was a language and not a language family or ethnonym, and that narrowed it down quite a bit... In the end, I was able to come up with 138, including several errors...
So how could I resist such a challenge? In addition to the possibilities that the Tensor mentions — incorrectly listing language families and ethnonyms — there’s also the possibility of incorrectly listing a dialect and calling it a language. For instance, is Galician a language, or is it just a dialect of Portuguese? We know that Flemish is just a dialect of Dutch, but we’re not sure about Galician. Anyway, I was disappointed to fall short of the Tensor’s 138: despite being a former linguist, I could only come up with 106, one of which was not listed as an official language in Ethnologue’s authoritative list of all 6912 living languages: Athabascan must be a language family, not a language. Galician does count, since it is listed as a separate language, not as a dialect of Portuguese. I got a few names slightly wrong, but I’m still including them in my count. (Note that there are 7299 names for these 6912 languages.) Anyway, I’m not so impressed with myself, coming up with less than 2% of the world’s languages.


Monday, December 12, 2005

Too funny

A parody of one of those pharmaceutical-company ads for a prescription medicine.

A Japanese documentary on how to eat sushi.


Sunday, December 11, 2005


From Diane Greco’s fascinating December 8 post in her blog:
The assumption that children of the same age constitute a true peer group only holds true for children of average development. The term peer does not, in essence, mean people of the same age, but rather refers to individuals who can interact at an equal level around issues of common interest.


Saturday, December 10, 2005

Mercury Rising

Just finished watching Mercury Rising. Cryptology and the NSA. An autistic boy. Bruce Willis. Alec Baldwin. Generally good acting. What more could one want?

Well, characterization and depth, to name two. More cryptology. More NSA. Less conspiracy theory.

Generally a disappointment. Oh, well.


Friday, December 09, 2005

No snow day

Weston, of course, had to have school today. Having a snow day would have been too wimpy. You can’t be Lake Wobegon if you call off school. We didn’t even get dismissed at mid-day, although the forecast correctly predicted a horrible and unsafe drive home (a half day counts as one of the 180 required days under state law). School was not dismissed until 2:50.

The parking lot, of course, was a zoo, with hundreds of cars and lots of buses trying to get in and out. Cars were skidding every which way and getting stranded across the roadway. So I decided to wait until 4:00 to leave. Helpful colleagues and custodians shoveled out cars from approximately eleven inches of snow.

I arrived in JP (to pick up Barbara) at 7:30.

That was a total of three and a half hours, for what’s normally a 45-minute drive. More to the point, I saw many, many stranded cars and several accidents. Why wasn’t school canceled for the day, as it was in most of the surrounding communities? We’re always told that it’s a matter of safety — well, driving home wasn’t safe.

Since 7:30 was too late to head for home and cook dinner, Barbara and I had to go out locally to eat. (I also needed the break!) Had a great meal at JP Seafood, and finally arrived home at 9:15. After this exhausting day — I had left home at 6:15 AM, which was 15 hours earlier — we figured we would now have to shovel our sidewalk. This is a legal requirement after the snow stops. Much to our surprise and pleasure, we discovered that our next-door neighbor had cleared the entire sidewalk with his snow blower!

Unasked-for acts of kindness are always the best.

But why did we have school?


Thursday, December 08, 2005

Critical friends

At yesterday’s faculty meeting, a group of teachers modeled the process of participating in a Critical Friends Group (CFG) in the context of Looking at Student Work (LASW). If you can get through the jargon, the combination of CFG and LASW provides a valuable pair of related techniques: educators help each other out in a collegial, even collaborative spirit, by examining what one teacher (the “presenter”) is trying to accomplish and by looking at the work of students in the presenter’s class. Note that “critical” in this context means that the friends are essential or important, not that they criticize.

In this particular exercise, the presenter was a fellow math teacher who was sharing student work on a game theory problem. The participants were teachers from all five of the major academic departments: math, science, English, history, and foreign language. Even though the math problem under consideration was interdisciplinary and involved reading and analyzing an article from USA Today, it was still difficult for non-math people to understand.

The process is highly structured — partly to reduce the likelihood of personal comments and the defensiveness that would surely result from such comments, and partly to ensure that talking is balanced by sufficient listening. It looked convincing to me. I would like to be a participant in such a group, but I wonder how it’s possible to understand one another’s discipline and values in order to make the process more meaningful.


Wednesday, December 07, 2005

PopCo revisited

In the past two weeks I haven’t had as much time to read as I would like. I’m woefully behind on the Globe, and it’s only today that I’ve finally finished reading PopCo. In my post of 11/23, I gave my initial impressions of this novel by Scarlett Thomas. Now I can say more. (It’s always best to read an entire book before reviewing it.)

I highly recommend PopCo, at least to readers of a technical bent. It probably helps to be a nerd or a geek. How often do you come across a novel that contains a table of the first 1000 primes, after all?

The site of the book is a business retreat attended by “creatives” from a British toy company. Flashbacks provide additional characterization and background. For the first half of the book I was under the impression that the protagonist/narrator was a mathematician with a specialty in cryptology, but that turned out not to be true. Nevertheless, she’s both deeply interested and deeply knowledgeable about the subject. (I’ll avoid spoilers here, by the way.) Here are a few out-of-context mathematical/cryptological references that might lead the reader to believe that Alice Butler was a mathematician — and might turn off a reader who has the wrong attitude about math:
...a fifty-fifty chance of being correct, then — the same chance you’d have, incidentally, of finding two people with the same birthday in a room of twenty-three people...

The Monty Hall Problem, popularised by maths columnist Marilyn vos Savant, is... [followed by an entire page discussing the Monty Hall Problem]

It looked quite Vigenere-ish to me.

It wasn’t a Caesar shift cipher, that’s for sure: you can tell one of those just by looking at it.

...there would, as my grandfather once pointed out to me, be 403,291,461,126,605,635,584,000,000 potential keys to find, this being the factorial value of twenty-six (rather cutely written down by mathematicians as 26! and proving that they also have a thing for exclamation marks, just like the toy industry).

Alberti was a fifteenth-century architect, and is known as the true grandfather of contemporary Western cryptology. His code-wheel formed the basis for all forms of polyalphabetic ciphers that came later, including Enigma.

“So, the criterion for this exercise is that you’re in a group of about four people, with no one you already know,” Warren says. THere are twenty-six of us in this room. How many different ways are there of dividing us into sets of four or five?

...I have asked her about the Riemann Hypothesis because this is obviously the thing she is most interested in and perhaps she will like me more I understand the thing she is most interested in.

My grandmother...had an Erdos number of two.

It was when I was learning about Goedel’s Incompleteness Theorem, and trying out his number code. Every calculation I did came out with a number so big that it wouldn’t fit on my calculator.
There are also two very large and significant non-mathematical themes to PopCo. One is political and social, having to do with corporate culture, corporate responsibility, and so forth. This theme starts out as a broad and amusing satire of workshops and the like, but it ends up being surprisingly serious. The other non-mathematical theme has to do with the psychology of teenagers and pre-teens, both individually and in a societal context. Although it takes place in England, and although the characters certainly weren’t typical teens, the portrayal definitely rings true.

Thomas writes with a compelling and highly individualistic voice. She puts a bit too much sex, drugs, and rock-n-roll into this novel, and she has some annoying habits like referring to women as girls, but it’s still very much worth reading. Near the end, it turns out to be recursive in a manner that will appeal to any mathematically minded reader. But that’s not the main point. Or is it?

Labels: ,

Sunday, December 04, 2005

"Units" and "unit tests"?

The other day we were talking about “summative assessments.”. In math a summative assessment usually translates to a unit test. But what about those of us who don’t give unit tests?

About seven years ago, the Weston Math Department reformed its curriculum in several ways, the most significant of which was that we divided each year-long course into four major units. The idea was that teachers would encourage depth rather than breadth, that students would focus on deeper learning rather than learn hundreds of things at a shallow level. On the whole this has worked well, although the particular choice of units may need to be tweaked after so many years.

And what does this have to do with unit tests? When units are longer — only four per year — there’s a long wait for a so-called unit test. But that’s not my primary objection. After all, more quizzes (“formative assessments” in the current jargon) can always be given. Here’s why I don’t give unit tests:
  1. Unit tests encourage compartmentalization. If a test is on the “exponents and logs” unit, it sends a message that exponents and logs won’t be needed later on. Tests should always be cumulative.

  2. Unit tests can’t be scheduled far in advance, since there’s no way to predict exactly when a unit will end. Students deserve to know well in advance when their tests will be held. I can tell them tomorrow that their next test will be on January 6, which I couldn’t do if the test has to come at the end of a unit.

  3. Unit tests discourage continuity. A test should be a snapshot of where we are at the moment, connecting previous and subsequent learning. (Perhaps this point should be combined with #1.)

  4. Unit tests encourage teachers to “teach to the test.” But if I don’t know what will be on the next test, I won’t have it in my mind as I teach.
Perhaps the whole idea of units is a bad idea. I love the idea of concentrating on fewer topics and doing them in greater depth, but we can do that without explicit units. Mathematical topics should be part of a web of interconnected ideas that flow smoothly (or sometimes roughly) from one week to the next.

Labels: ,


This page is powered by Blogger. Isn't yours? Made with Macintosh