A number of readers took me to task for a recent column in which I said that the English language might be partly responsible for the poor math performance of U.S. and British students.
The column, "Eleven, Twelve, Thirteen" (July 9, 1995), was based on the differences between Chinese and Japanese number words and number words in English. As Ian Thompson, author of an article in the Times Educational Supplement (May 26, 1995) points out, these words are somewhat irregular in English--particularly in numbers between ten and twenty. Thompson theorizes that this irregularity handicaps children in learning the important concept of place value. The English language, Thompson notes, does not give English-speaking children any clue that eleven means 10 plus 1 or that twelve means 10 plus 2, and numbers in the teens reverse the underlying tens and ones pattern. (We say fourteen, fifteen and sixteen but twenty-six and thirty-six.) Children learning their numbers in Chinese or Japanese have a system in which the number words perfectly mirror the numbers: After ten, comes ten one (11), ten two (12), ten three (13). And there are other places where English number words are likely to be confusing to children just beginning to learn math, whereas they are entirely transparent in Chinese and Japanese.
This looked like a reasonable hypothesis--and a comfortable one, too. It would be agreeable to think that the English language is responsible, in part at least, for the embarrassing discrepancies between the math performance of U.S. and Asian students. Unfortunately, the hypothesis works only if you ignore most of the facts. Leonard Gillman, a retired professor of mathematics at The University of Texas at Austin, lays out some of them in his letter:
French, German, and Dutch share most of the same faults and feature several of their own, so those kids should be doing as badly in math as the Americans. Are they?
The German for 11 and 12 is elf and zwolf (from which the English was presumably derived); the French also use special words, albeit more recognizable: onze, douze, continuing with treize, quatorze, quinze, seize, before reaching the sensible dix-sept. ...
The number 20 in French is vingt; what on earth is that? For 30 through 60 they say trente, quarante, cinquante, soixante, which are recognizable if you agree that te (with a silent "e") reminds you of dix (10). But then out of the blue, they introduce a new system: 70-79 are (in English) sixty-ten through sixty-nineteen. At this point they go bonkers. For eighty, they say four twenties and then carry through the preceding idea, with 90-99 being four twenties ten through four twenties nineteen.
The German 20- 90 are like English, with zig corresponding to our ty and presumably suggesting zehn (10). But the numbers ending in 1-9 are in a class by themselves: one and twenty through nine and ninety. Thus in German, except for the multiples of ten, not a single name for a two-digit
number matches the place values.
Nicoll Cooper of Cambridge, Mass., makes similar observations about German and French number words. He also questions the applicability of Thompson's "number theory" to Italians and Indians. Italian, he says is "logical (though with place values reversed) from 11 through 15, then fully logical from 16 on. So Italians ought to be better than Germans in test results and everybody better than the poor French. Do test results bear this out?" Mr. Cooper also wonders about numbers in Hindi since, as he points out, "Indians are often frighteningly good at mathematics and revel in numbers as in the Ganges."
Jeffrey Deboo of Berkeley, California, writes that Japanese number words, far from being regular, are more irregular than English ones because they vary according to what is being counted:
The basic numbers one, two, three are ichi, ni, san. When counting human beings, these numbers become hitori, futari, sannin; when counting animals, ippiki, nihiki, sanbiki; when counting small objects, hitotsu, futatsu, mittsu, etc., with about a dozen categories in all. ... l think this is at least as confusing as saying eleven instead of ten one.
Is there a message here? Sure. When you are looking at a big problem, it can be tempting to grab for an explanation that gets you off the hook. But Jeffrey Deboo has a better suggestion for how we should use our energies: Why not look at the education systems in Asian nations--and in other countries where math education is successful--and see how we can adapt what they are doing? That will be lots tougher than speculating about the influence of the English language on the way our students learn, but it's much more likely to get us where we need to go.