David C. Geary, a researcher with the psychology department at the University of Missouri at Columbia, recently conducted a comparative study of the arithmetic skills of American and Chinese children.
Working with Liu Fan, of the Office of Psychology at the Chinese Institute for Educational Science in Beijing, Mr. Geary compared the addition skills of 1st-grade students at a school in Hangzou, China, with those of their peers who attend a school in Columbia, Mo.
While emphasizing that the study sample of 52 children is small, Mr. Geary argues that this preliminary investigation indicates that Chinese students, in effect, used more sophisticated methods than their American peers to solve the problems, an advantage that he argues carries over into more complex mathematical tasks.
Mr. Geary discussed the findings of his research, which are scheduled to be published in the journal Psychological Science, and the possible implications for American mathematics educators, with Staff Writer Peter West.
Q. Do you have a background in education or educational theory?
A. No, my primary interest is in cognitive development.
I’m a developmental psychologist who’s interested in the development of math skills in kids. So I approached this (study] from a cognitive-science perspective, rather than an educational perspective.
I’ve been looking at the development of numerical skills, and individual differences in numerical skills, for five or six years.
Q. Could you describe what it is you set out to discover with this study?
A. It’s well known that Asian children outperform American children on I standardized math tests].
But [we wanted to know], what is it that they’re doing that gives them the edge?
And so, based on some of my previous research, and research of others in this area, I thought that there were three [possible explanations]. One is that it is possible that the Chinese children are using problem-solving strategies that are qualitatively distinct from American kids.
Another possibility is that Chinese and American kids are using the same types of strategies to solve, say, addition problems, but there’s a difference in the developmental maturity of the strategy mix.
And the third possibility is that Chinese and American kids are doing exactly the same things, but {that the] Chinese kids are quicker at executing the processes underlying those strategies.
The task we administered allowed us to score problem-solving strategies on a trial basis. It also allowed us to measure the speed with which they could execute very basic processes, like how quickly they could retrieve a fact from memory or how quickly they could use a counting process to solve a problem.
Q. And your findings were?
A. What we found was that the Chinese 1st graders and the American 1st-grade kids were using the same types of strategies to solve addition problems. They were either remembering the answer, counting to solve the problem, or decomposing [the problem into more simple problems].
The types of strategies we saw were the same, but the developmental maturity of the mix was different.
And so we saw much more direct retrieval, and a greater use of decomposition when they couldn’t remember the answer, in the Chinese kids than in the American kids.
The Chinese kids, in fact, showed a strategy mix that we typically don’t see until 4th or 5th grade in American kids.
A. In your paper, you note that counting was the primary strategy used by the American students. What is the significance of this?
A. It’s developmentally less sophisticated.
Q. What are the implications of this study for American educators, who often are encouraged to emphasize process over rote memorization?
A. It was very clear from our studies that the Chinese kids not only knew more, but they had a better conceptual understanding of arithmetic and numbers sets ... than American kids, who were being directly taught the concepts. You certainly don’t want to make any major changes based on the one study or a few studies.
But I really suspect, not only from this study, but from other research we’ve done, that with mathematics you really can’t skip the basics.
I think I understand the rationale in trying to get to the conceptual sorts of things. But I think to really understand mathematics at any level, you really need to practice.
