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 U.S. children do.
What accounts for this?
To try to understand some of the differences, Liping Ma asked 72 Chinese teachers and a sample of ninth-grade Chinese students four of the same questions that had been asked of U.S. elementary school teachers in a study done at Michigan State University under the direction of Deborah Ball. The questions involved doing fractional division calculations and coming up with good story problems to illustrate each question.
The results are summarized in Ma’s important new book: Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States (Lawrence Erlbaum Associates, paperback $19.95). Everyone concerned with mathematics education should read this book.
What Ma found was that the Chinese teachers have a deeper understanding of elementary mathematics than most of our U.S. teachers.
Having grown up and taught in Shanghai, Ma suspected that part of the reason for this was the better mathematics program the Chinese teachers had while they themselves were in school. This is why she asked the same questions of Chinese 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.
Ball’s study showed that only half of the U.S. teachers could do the calculation correctly and explain how they did it. Ma found that all of the ninth grade Chinese students could do both correctly. Less than 5 percent of the U.S. teachers interviewed could make up a correct word problem, compared to 40 percent of the Chinese students.
Surprisingly, prospective Chinese teachers do not specialize while in school. However, when they start to teach they usually specialize in one or two subjects. Except for teachers in rural schools, the Chinese teachers studied by Ma taught mathematics and at most one other subject.
But 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, figuring out different ways to work the problems and to explain the material to students. They also tend to teach at multiple grade levels, and so develop a deeper understanding of other levels of mathematics. A number of the teachers Ma interviewed had developed what Ma called PUFM, or Profound Understanding of Fundamental Mathematics.
Ma’s work strongly suggests that 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 that comes in later grades, at least three or four, because this knowledge should influence how topics are taught. This view runs counter to that of a report from the Mathematical Sciences Education Board, which suggests that elementary school teachers do not need as deep a knowledge of mathematics as do high school teachers.
Richard Askey is a professor of mathematics at the University of Wisconsin-Madison. This review is condensed from one that first appeared in a recent issue of Common Knowledge, the newsletter of the Core Knowledge Foundation.
