At 08:33 PM 12/12/2004 -0500, you wrote:

But the best defense - the first to get beyond the utilitarian argument - came from a certain Miss Collins. She is my daughter's math teacher[....] "What we do isn't exactly what mathematicians do," she explained. "And I know more alums here become artists than become mathematicians. But kids don't study poetry just because they're going to grow up to be poets. It's about a habit of mind. Your mind doesn't think abstractly unless it's asked to - and it needs to be asked to from a relatively young age. The rigor and logic that goes into math is a good way for your brain to be trained."

Three cheers for Miss Collins! Her statement should be framed and hung on the walls of math class rooms everywhere, perhaps with the additional observation that there's another payoff. Given the right "habit of mind" a person who grows up to be neither a poet nor a mathematician may nevertheless take delight in reading a poem, or in understanding a logical mathematical argument.

Henry Baker wrote:

In today's specialized world, it isn't clear that the productivity of the economy is all that much better if 50% of the population got a little better in math. However, a case could be made that it is vital that the best 5% be very, very good at math. Ask everyone on an airplane going Mach .9 at 40,000 feet if they hoped that the designers of that airplane were very good at math!

But that's a straw man argument. Of course people who design airplanes ought to be good at math -- and they are! But in the worst case, the airplane-designer type will end up good at math despite their high school math curriculum, not because of it. --Michael -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.

It may be of interest that I designed the Singapore school math curriculum, including the cover of the booklet, somewhere in the late fifties. I also remember going to the Government printers, to make sure that the typesetting was properly taken care of. It is doubtless different now, but had a big influence for a long time. Must try to find my copy. Still well worth looking at. R. On Mon, 13 Dec 2004, Henry Baker wrote:

There is an article in this morning's (Mon 12/13/2004) Wall Street Journal about school systems importing the mathematics curriculum from Singapore. Apparently, it is pretty good at certain types of every-day algebraic problems.

Singapore math is also now a darling of the home-schooling crowd...

---

Every time I read articles like these, I always ask myself: "do I want to teach the best 5% better, or do I want to teach the best 50% better?" In today's specialized world, it isn't clear that the productivity of the economy is all that much better if 50% of the population got a little better in math. However, a case could be made that it is vital that the best 5% be very, very good at math. Ask everyone on an airplane going Mach .9 at 40,000 feet if they hoped that the designers of that airplane were very good at math!

At 01:49 PM 12/12/2004, Daniel Asimov wrote:

...

Here's the link: http://www.nytimes.com/2004/12/12/weekinreview/12mcne.html; it's valid through most of next Saturday, Dec. 18.

(Note: If they make you divulge your e-address and choose a userid, I can assure you from almost 10 years' experience that -- unless you opt in for receiving various e-mails from the Times -- you won't get any e-mail from them or anyone else as a result of registering.)

I'm curious what people's reactions are to this opinion piece.

--Dan Asimov

http://www.nytimes.com/2004/12/12/weekinreview/12mcne.html?oref=login&pagewa...

December 12, 2004

The Last Time You Used Algebra Was...

By DONALD G. McNEIL Jr.

IN the 1986 movie, "Peggy Sue Got Married," Kathleen Turner, an unhappily married wife and mother, magically returns to relive her senior year as the most popular girl at Buchanan High.

She leaves a math test blank, and when her teacher (described in the screenplay as "an officious little creep") demands an explanation, answers: "Mr. Snelgrove, I happen to know that in the future, I will never have the slightest use for algebra. And I speak from experience."

Audiences and critics loved the line, presumably because they too rejoiced in knowing that they had never, ever used the quadratic formula again. (Disclosure: I squeaked by in calculus while never really grasping it, and can no longer help my ninth-grade daughter solve equations with two variables. The toughest math I tackle now is calculating a tip in a moving taxi.)

Last week, the United States proved, yet again, that its mathematical literacy is abysmal. In a survey by the Organization for Economic Cooperation and Development, it ranked 28th out of 40 countries in mathematics, far below Finland and South Korea, and about on a par with Portugal.

The survey tested simple, "everyday" skills like estimating the size of Antarctica or footsteps in the sand. Nonetheless, as in past comparisons, American 15-year-olds did rather better than students in Mexico, Indonesia and South Africa, and substantially worse than those in rich countries, especially Asian ones.

These annual humiliations produce two consistent reactions.

One set of experts grouses that the surveys are unfair: average American students are compared to distant elites; Americans play sports and hold jobs; foreign countries impose national standards while America believes in local school boards.

Another set gloomily predicts that math malaise will ultimately gut the economy, frequently citing an estimate that American businesses waste $30 billion a year on remedial training. (In 1990, the elder President Bush announced an expensive plan to have American students lead the world in math by the year 2000.)

But there is also the Peggy Sue school of thought, which asks: So what?

In all but the most arcane specialties (like teaching math), the need for math has atrophied. Electronic scales can price 4.15 pounds of chicken at $3.79 a pound faster than any butcher. Artillerymen in Iraq don't use slide rules as their counterparts on Iwo Jima did. Cars announce how many miles each gallon gets. Some restaurant bills calculate suggested tips of 15, 18 or 20 percent. Architects and accountants now have spreadsheets for everything from wind stress to foreign tax shelters. The new math is plug-and-play.

True, those calculators and spreadsheets and credit card machines need to be programmed. But, in between bouts of visa restrictions, American universities successfully import thousands of math whizzes each year because jobs await them, and the tiny percentage of American-born students who do Ph.D. work equal the world's best.

In math, as in chess, countries that produce the most grandmasters per capita - like Hungary and Iceland - not only don't rule the world, they don't even rule chess. Sheer power counts, as it did in chess for the Soviets. America may lose math literacy surveys, but it dominates number-crunching in every sphere from corporate profits to supercomputers to Nobel prizes.

So is it necessary that the average high-schooler spend years nailed to the axes of x and y?

Maybe not, said Robert L. Park, former director of the American Physical Society, an independent group of physicists, who teaches at the University of Maryland.

"As a teacher, I'd like to think it's going to have a huge payoff," he said. "But I'd like to know the answer."

He once calculated that a third of the Americans who won Nobel prizes were born abroad, and said that an open-door policy benefited both sides: American universities get well-trained, driven students, and they in turn flourish in the more creative atmosphere here.

Bob Moses, who developed the Algebra Project in Cambridge, Mass., focuses on the other end of the spectrum: poor blacks and Hispanics who are the first in their families to aspire to college. "No one is going to pay you because you can do division," he said, but added that without a grasp of the concepts his students would be "serfs in the new information age," stuck in dead-end jobs as surely as illiterate Europeans were forced to the bottom of the job heap by the Industrial Revolution.

Most experts point out that careers in science or computers require mathematics, even when it is not a real job skill but a filter for the lazy or stupid, as passing freshman physics is for pre-med students. (Disclosure: me, for example.) Physics requires calculus, calculus requires algebra and trigonometry, and so on. One must start early.

In the age of Googling and spell-checking, noted Diane Ravitch, the education historian, the "so what?" question could be asked about learning virtually any subject.

"But a democratic society demands an educated populace," she said. "Why spend hundreds of billions on public education if we're going to sling it over our shoulder?"

But the best defense - the first to get beyond the utilitarian argument - came from a certain Miss Collins. She is my daughter's math teacher at a school where there are no boys to distract or intimidate calculating young women.

"If you ask the girls," she said, "they'll say it's another hoop they have to jump through to get into a good college."

She feels otherwise.

"What we do isn't exactly what mathematicians do," she explained. "And I know more alums here become artists than become mathematicians. But kids don't study poetry just because they're going to grow up to be poets. It's about a habit of mind. Your mind doesn't think abstractly unless it's asked to - and it needs to be asked to from a relatively young age. The rigor and logic that goes into math is a good way for your brain to be trained."

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