How come Asian students do so much better in math than American students? It's not just that they score at the top of international exams designed to compare math achievement--while our students are somewhere at or close to the bottom. Every measure we have shows
that Chinese, Japanese and Taiwanese students achieve at a higher level than American students, beginning in first grade.
There isn't any shortage of theories about this, and many are plausible, at least in part--Asian students work harder; they spend more class hours learning math; the teaching materials and methods their teachers use are superior to most of ours. Now, Ian Thompson, a lecturer at the University of Newcastle upon Tyne in England, offers a new and intriguing explanation of the achievement gap. In a recent article in the Times Educational Supplement (May 26, 1995), Thompson points out that students in England, too--and indeed all English-speaking students--do poorly in math in comparison with Asian students. The problem, he says, is in the English language--specifically, the irregularity of our number words.
What do English number words have to do with math achievement? Thompson believes that they can hinder young students' understanding of place value, a basic concept that these youngsters come up against as soon as they start learning two-digit numbers: "This subtle and powerful concept involves the use of just 10 different symbols, and yet, by ascribing a different value to a numeral dependent on its position in relation to other numerals, it allows the writing of numbers of any size." Thus, we understand the difference between 46 and 64, even though the individual numbers are the same, because of the concept of place value. Failure to understand it, Thompson says, "will almost inevitably lead to later difficulties with mental or written computations."
According to Thompson, the number words in Chinese and Japanese are logical and regular. Counting from one to ten proceeds as it does in English. But after ten, comes ten one (11), ten two (12), ten three (13), and so forth. Ten nine (19) is followed by two ten (20), two ten one (21), two ten two (22); and two ten nine (29) is followed by three ten (30), all the way up to nine ten nine (99) and beyond. Place value is just as clear in the words as it is in the numbers themselves.
The Finish system is not entirely logical or regular, and it contains words that, as Thompson says, "are likely to conceal the basic tens and ones pattern of the system." The irregularities are especially striking between eleven and twenty--just where they are likely to create the most confusion for young students who may just have mastered the numbers from one to ten and are not yet secure about the basic pattern.
The words 'eleven' and 'twelve' give no hint of the fact that they mean ten and one and ten and two. Numbers in the teens are confusing because "they contain words which reverse the underlying tens and ones pattern: we say fourteen and sixteen but twenty-six, thirty-six and ninety-six." And children who are just learning to count and compute using two-digit numbers are likely to be further confused by the fact that place value is observed when we express the teen numbers as numerals: Fourteen and fifteen, for example, are written as place value dictates (14 and 15), rather than as they sound (41 and 51 ).
Thompson points to several other irregularities in the numbers between one and one hundred, like the pronunciation of 20, 30 and 50. It is not 'two-ty,' 'three-ty' and 'five-ty,' as in the other decade words, but twenty, thirty and fifty. And he stresses the extreme regularity of comparable words in Asian languages. From one to one hundred, Japanese uses the word for ten in 90 of the numbers, "thereby helping to reinforce the basic underlying regularity of the number word system." In English, we use three different words to mean ten. The word ten is used only once. The suffix 'teen' signifies ten in the numbers from 13 to 19, and then 'ty' abruptly takes its place. Again, the relationship between 'teen,' 'ty' and 'ten' will not be immediately clear to young students who are just beginning their study of math.
These irregularities undoubtedly look small to adults. We take eleven, twelve and thirteen for granted, and most of us have forgotten any problems we had in learning how to count and compute. But small things can cause enormous problems for first graders who are struggling to learn the basics of math, and Thompson points to a cause at the very beginning of schooling that could very well lay the groundwork for later problems.
Has Thompson presented us with the whole answer to the troubling question of why Asian students achieve at higher levels in math than American students? No, and he doesn't pretend to. Undoubtedly many factors, both cultural and educational, contribute. But his suggestion is worth attention and study. If it turns out to be sound, we should seriously consider introducing number words that consistently reflect place value into American schools.