Why the Chinese Teach Math Better
From Common Knowledge, Volume 12, Number 1 & 2, 1999.
© 1999 Core Knowledge Foundation. Not to be copied or reproduced without permission from the Core Knowledge Foundation, 801 E. High Street, Charlottesville, VA 22902.
The work of Harold Stevenson and coworkers and the Third International Math and Science Study results both show that Asian children learn mathematics better than ours do. What accounts for this?
To try to understand some of the differences, Liping Ma asked 72 Chinese teachers some of the same questions which had been asked of U.S. elementary school teachers in a study done at Michigan State under the direction of Deborah Ball. The results are summarized in her important new book: “Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States,” Lawrence Erlbaum Associates.
One of the four questions asked was to divide 1 3/4 by 1/2, explain how you did the calculation and make up a good story problem or model for 1 3/4 divided by 1/2. The Michigan State study had shown that many U.S. elementary school teachers have problems with fractions, some in doing and explaining calculations, and more with making up word problems. All of the 72 Chinese teachers were able to do the calculation and explain how it was done, and 65 made up appropriate word problems. After stating a word problem, one of the Chinese teachers said that she preferred not to use dividing by 1/2 to illustrate the meaning of division of fractions because one can easily see the answer without really doing the division. She then proposed asking how long a jump rope is if 4/5th of it is 1 3/4 meters.
Another of the Chinese teachers gave three different problems, all dealing with sugar. If you have 1 3/4 kg of sugar and want to wrap it into packs of 1/2 kg each, how many packs can you wrap? Next, you have 1 3/4 kg of white sugar and 1/2 kg of brown sugar, how many times more is the weight of white sugar than that of brown sugar? Finally, you have 1 3/4 kg of sugar on the table and that is half of what you have at home. How much sugar do you have at home? This teacher would put all three problems on the board and have the students compare the different meanings they represent. Then the students would be asked to make up their own story problems to represent different models of division by fractions. Most of the examples given by the U.S. teachers dealt with round food, like pizza, or money, while the Chinese examples were from many different areas. This is just one of many areas where the Chinese teachers have a deeper understanding of elementary mathematics than most of our teachers do.
Part of the reason for this is the better school mathematics program they had. To check that her impression from growing up in Shanghai and teaching there was correct, Ma asked the same questions of students in ninth grade, the last year of regular schooling before prospective elementary school teachers take a two or three year program to prepare them to teach. forty percent of these students made up a correct word problem, compared with less than 5 percent of the U.S. teachers interviewed. All of the ninth grade Chinese students did the calculation correctly and could explain how they did it, while about 50 percent of the U.S. teachers could do this.
The education of Chinese teachers continues after they start to teach. In addition to a detailed national curriculum with sufficient aid to help new teachers, teachers in China study their textbooks very carefully, figure out different ways to work the problems and to explain the material to students. While in school, prospective teachers do not specialize. However, when they start to teach they usually specialize in one or two subjects. Except for the teachers in a rural school, the Chinese teachers taught mathematics and at most one other subject. There is also a tendency to change grade levels, and so develop a deeper understanding of other levels of mathematics. A number of the teachers Ma interviewed had developed what she called PUFM, or Profound Understanding of Fundamental Mathematics.
The Mathematical Sciences Education Board has a report suggesting that not only do teachers need a broader base of knowledge, but that the depth needed depends on the level of mathematics taught, with high school teachers needing a deeper knowledge of mathematics than elementary school teachers. Ma’s work strongly suggests that is false.
Elementary school teachers need as deep an understanding of the mathematics they teach as high school teachers need of what they teach. Both need a deep knowledge of the mathematics which comes in later grades, at least three or four, for this knowledge should influence how topics are taught. Everyone concerned with mathematics education should read this book.
RICHARD ASKEY is a professor of mathematics at the University of Wisconsin, Madison.
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Last updated: Thu, May 22 2008
