Understanding how various aspects of mathematics education work together is necessary if reform efforts are to succeed, Ms. Newton argues. She compares U.S. and Chinese mathematics education to provide perspectives that might further such understanding.
IN TRADITIONAL Chinese medicine, a key maxim is "Zhi Bing Yao Zhi Gen," which literally means, "To cure a disease (you) must cure the underlying cause." I am reminded of this principle whenever I reflect on K-12 math education reform in the U.S. President Bush's 2006 State of the Union Address prompted yet another wave of debate on what actions the government should take in order to improve math and science education so that the U.S. can sustain its economic competitiveness internationally. What has not been brought to the forefront, however, is that cultural beliefs about mathematics and how it should be taught will profoundly influence how reform efforts, such as new curricula or teaching methods, will work themselves out in practice.
As someone who was educated in mainland China and has subsequently studied math teaching and learning in the U.S., I have been struck by the many differences in the beliefs surrounding math instruction between the two countries. I hope my reflections on what I have seen can help highlight some key issues identified in the mathematics reform literature and provide a lens for examining how mathematics instruction functions in the U.S. and China.
CULTURAL BELIEFS AND ATTITUDES
When it comes to attitudes about who can learn math, it is common in the U.S. to give more weight to ability than to effort. (1) It is widely acceptable for anyone in the U.S. to say, "I just can't do math." Since ability is widely believed to be fixed and uncontrollable, attributing success or failure to high or low ability has an important impact on motivation. Presumably, inasmuch as ability is seen as fixed and not subject to individual control, ascribing failure to low ability leads students to give up. Effort, on the other hand, is clearly within an individual's control, and so ascribing success in learning mathematics to effort leads students to sustain their hope and increase their persistence.
Unlike the U.S., some societies put greater emphasis on effort than on ability. (2) That is certainly the case with China, as I can attest. Though English was the only school subject that I was passionate about when growing up, I was nonetheless pushed by my engineer father into being a math and science major in high school. He often said, "If you aren't good at math, physics, and chemistry, how can you make a living? What are you going to do?" My father's attitude toward the importance of math and science was typical of the value placed on such subjects by Chinese society in general. In my high school, only about 15% of the students were on the liberal arts and humanities track, while the rest of us pursued math and science. Persistent effort was highly regarded and encouraged. Our teachers liked to emphasize that, if you do not think you can grasp a concept as fast as others, then you must work harder or start earlier (e.g., preview the textbook before the class when a new concept will be taught).
People's beliefs about what mathematics is also seem to differ. In Western thinking, mathematics is often described as the most "certain" branch of human knowledge. In mathematics, people in the West will say, it is easy to distinguish "right" from "wrong." (3) Such a heavy emphasis on truth and correctness in mathematics contrasts sharply with how mathematics is treated in some high-achieving Asian countries. For instance, the Third International Mathematics and Science Study (TIMSS) revealed that Japanese math teachers emphasize developing conceptual understanding rather than simply obtaining correct answers. (4) The Singapore math curriculum at both the elementary and secondary levels clearly specifies that the essence of school mathematics is problem solving. …