Tyranny of 10


Philadelphia -- WHY DO Asian students do better in mathematics than American students, finishing first in international exams while Americans aren't even close? Over the years, the question has received many different answers, and now yet another has emerged.

Not long ago Albert Shanker, president of the American Federation of Teachers, cited an article in a London weekly, the Times Educational Supplement, which blamed the English language. The article suggested that the reason Asian students do better is that their languages more clearly reflect the structure of our common 10-based number system.

The words in Japanese and Chinese for 12, 25 and 67, for example, are analogous to 1-10-2, 2-10s-5 and 6-10s-7, respectively. The article also suggests that the regularity of this system is much easier for small children to grasp.

This sounds like the perennial yearning for kilograms, meters and liters, and the simultaneous disparaging of pounds, inches and gallons. There certainly is a logical two-fisted (10-fingered) defense of this fixation on 10, but I suggest that 10 already permeates our language to a greater degree than is warranted.

Granting that the role of 10 in our number system might be clearer if our number words were rationalized, I suspect that the impact would be marginal at best.

Students' difficulties in math seldom have much to do with number words but with higher-order conceptual matters.

Mathematical understanding depends about as much on computational and representational skills as novel-writing depends on a grasp of grammar and spelling. The skills are necessary, obtained soon enough and, of course, nowhere near sufficient.

In Martin Amis' book, "The Information," the narrator theorizes that the universe seems to prefer the kilometer to the mile since certain constants turn out to be powers of 10.

Ten is ubiquitous, appearing in everything from the Ten Commandments to David Letterman's top-10 lists.

And other numbers are routinely rounded to 10 or to multiples of 10 whether this conforms with reality or not. We're told, for example, that we use 10 percent of our brain power and that 10 percent of men are homosexuals.

We're also constantly reminded that decades define us. Is there anything more vapid? In the free-love, anti-war '60s, hippies felt so-and-so. The greed of the '80s led yuppies to do such and such. Sullen and unread Generation X-ers -- Roman numeral Ten-ers? -- never do anything. We should brace ourselves for the millennial fatuities to come in the year 1999.

There is another drawback to our obsession with 10. Those of us who have suffered through a milestone -- a kilometerstone? -- such as a 40th or 50th birthday, might prefer a number system based on, say, 12 or 16. In a 12-based system these numerical traumas could be postponed until the ages of 48 or 60 (4-12s or 5-12s, that is).

The solace this would provide would probably outweigh any advantage to students from a change in our system of number words.

John Allen Paulos, author of "Innumeracy" and "A Mathematician Reads the Newspaper," is professor of mathematics at Temple University. He wrote this for the New York Times.

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