The well-documented gaps between Asian children and U.S. children in mathematics achievement may reflect the Asian children’s superior understanding of numbers, which in turn may be related to differences in language, according to a new study.
In a study that confirmed earlier findings, Irene T. Miura and her colleagues asked 1st graders from France, Japan, Korea, Sweden, and the United States to use blocks to represent two-digit numbers. While the Western children tended to construct representations based on units, such as stringing together 42 unit blocks, the Asian children tended to use standard base-10 representation, such as indicating four 10’s blocks and two unit blocks. In addition, the Asian children were much better able than the Americans to demonstrate an understanding of place value.
Writing in the March 1993 edition of the Journal of Educational Psychology, Ms. Miura and her colleagues suggest that these differences may reflect the fact that, unlike in Western countries, Asian children learn standard base-10 notation when they learn the names of numbers. The word for “12'’ in Japanese is “10-two,’' for example.
Ms. Miura, a researcher from the San Jose State University college of education, spoke about her study with Associate Editor Robert Rothman.
Q. This is not your first study of this kind. How did this research come about?
A. There is a lot of literature on differences in math, particularly between Asian kids and the U.S. If you look at international comparisons, the Japanese, the Taiwanese, now the Koreans are doing so much better in math than American kids are. But that [difference] doesn’t extend beyond math, to reading scores, social studies, anything else. It may be the longer school day, homework, parents--I do think those account for some of the variations. But that doesn’t account for enough of it. ...
If you look at the data here, Asian-language speakers are doing very well in math in this country--only the first-generation ones. ... Those data suggest that there’s got to be something in English [that relates to the differences in math achievement]. ...
We took base-10 blocks, and showed them to U.S. 1st graders. What we found was, if you ask a child to show you “42,’' an English-speaking child shows you 42 units. A bilingual Japanese child shows you four 10’s and two [units]. That was attacked by people who said, “These are bilingual kids.’' So we took it to Japan and to China, and found the same thing. And Korea. The patterns were the same.
Q. What do you think accounts for the differences among children from the different countries?
A. It’s the number system. As you are learning to count to 10 in Japanese, you can generate the rest of the numbers, up to 100. In the U.S., and the same thing in Sweden and France, once you get to 10, [you reach an impasse]. The word “11'’ doesn’t have the components of 10 and one in it. You have no idea 11 is 10 and one more. Twelve also. Thirteen is “thir’'--which is like three--and 10, but it’s backwards. ... You have to teach a child 13 is 10 and three more.
Twenty is another word. A Japanese child would say “two-10.’'
Look at American textbooks in 1st, 2nd, 3rd grades. You’ll see a drawing of 335. It has three 100’s, three 10’s, and five 1’s. For an Asian child, 335 is spoken “three-100, three-10, five.’' They understand. Nobody has to teach you how the system works. You learn the system as you learn numbers. In America, you have to teach them.
Q. Is this difference a serious handicap for American children, or can they make it up with schooling?
A. You can make it up with schooling. But look at the National Assessment of Educational Progress results. They are not very good. Two-thirds of 3rd graders appear to master place value of 10’s, and fewer than half, beyond 10’s. Only half of the kids in 3rd grade can work with place-value ideas beyond 10. ...
[And] 25 percent of 7th graders still don’t get place value. In Asia, 1st graders in the first half of the year have got it.
Q. And place value is an essential basic skill in math?
A. Understanding place value is fundamental to math. It’s a basic understanding for what you are doing when you are adding, subtracting, multiplying, and dividing. It makes a big difference in computation, and computation is a lot of math. ...
There are also other language characteristics that may help Asian kids in math--in problem-solving. ... [In addition,] when we say “one-third,’' we have to teach that there is a whole, it is divided into parts, and this is one of those. In Japanese, you say, “Of three parts, one.’' That’s how one-third is spoken.
It makes teaching a little different when language supports the concepts you’re trying to teach.
