Asia's Success in Math Stems Not From Culture, But From Teaching
To the Editor:
I was intrigued to read your article "U.S. Schools Importing Singaporean Texts" (Sept. 27, 2000). I teach at the Paterson, N.J., school mentioned in the article as using the Singapore textbooks to supplement the math program in grades 1-8. My 8th grade classroom was the focus of an earlier article, "A Teaching Style That Adds Up" (Feb. 23, 2000), on our use of Asian methods to teach mathematics.
We became interested in Japanese- style lessons in 1997, after viewing the Third International Mathematics and Science Study videotapes. We began to experiment by using these techniques: beginning each lesson with a recap of the previous lesson; presenting a challenging problem; allowing students time to solve the problems individually, and then cooperatively; allowing the students to present solutions; engaging them in discussion and debate of the solutions and errors; teaching the salient mathematical points; posing similar, more complex, or practice problems; repeating the procedure; and, finally, summarizing the main points of the lesson. This way to teach math is typical in Japan, and has proven to be effective with our students.
When we looked at the curricular aspects of TIMSS, it was evident to us that, as the TIMSS researcher William Schmidt has said, curricula and textbooks in the United States are "a mile wide and an inch deep." Many mathematics texts and programs we studied, including those endorsed by the National Science Foundation as "exemplary," were found lacking. So we obtained translations of Japanese and Russian mathematics texts, as well as textbooks from Hungary, Korea, and other high-scoring TIMSS nations.
The curricula of these high-scoring nations, we found, were remarkably similar: They were very focused, with a limited number of topics taught in depth, for mastery, not merely "covered" at each grade level.
None of the U.S. math programs we examined, including those recommended by the NSF, could compare to the texts from these high-scoring TIMSS countries. The only solution, we decided, was to write our own curricula and lessons for grades 7 and 8. Teachers at our school worked cooperatively in the summer to develop lessons that were both engaging and centered around a limited number of important topics.
Despite our efforts to narrow the topics, our curriculum inevitably became a hodgepodge of the diverse topics typically tested in this country, owing to both the state standards and the prevailing "testing" culture. The problem, we found, is that, unfortunately, none of the topics our students are expected to understand and perform well on tests is addressed with enough depth for students to truly comprehend.
We also confronted problems from the culture of teaching and teachers' understanding of mathematical concepts. We began a process the Japanese call "lesson study" under the guidance of Makoto Yoshida and Clea Fernandez of Teachers College, Columbia University, with the assistance of teachers from a Japanese school in Greenwich, Conn., as well as other academic experts.
A common Japanese form of professional development, lesson study allowed us to plan and develop well-thought-out lessons that were taught, observed, revised, and taught again at a "lesson-study open house." We learned a lot from this experience, both in pedagogy and content knowledge. And we realized again that the lack of a focused curriculum like the one that Japanese teachers use made lesson study difficult.
Though we were aware that Singapore had ranked No. 1 among the 39 countries taking the TIMSS assessments, we did not know that its textbooks are written in English. A couple of years ago, we were given Xerox copies of some pages from the Singaporean texts and workbooks, and we decided to order the books from Family Things, the West Linn, Ore., distributor mentioned in your article..
After examining these materials, our teachers became enthusiastic, especially when they they were able to see some of the lessons from the teachers' guides modeled in classrooms. Though they are different from ours, the teachers' guides have some excellent lessons, activities, and games that, when used thoughtfully in conjunction with the texts and workbooks, are effective in developing deep understanding of fundamental mathematics. We also were impressed by the fact that noted mathematicians as well as educators had recommended the books.
We do not believe that these textbooks from Singapore are a panacea for the ills of American education. But we do believe they are a step in the right direction.
With all due respect to the former National Council of Teachers of Mathematics president, Gail Burrill, quoted in your article, the common warning about Asian programs' success being due to their delivery in a "different" and "homogeneous" culture doesn't hold water. Although there are cultural considerations in play, the secret of Asia's mathematical success is not in the culture, but in the methods, materials, and content knowledge of the teachers. The Singaporean books are sound mathematically and represent the standards espoused by the NCTM better than most U.S. textbooks.
In these texts and teachers' guides from Singapore, students are truly "making sense of things, exploring and investigating patterns, and building skills and conceptual understanding," as Ms. Burrill proposes. It should also be noted that, unlike the suggestion in your article, the Singaporean books are not like Saxon Math.
Of course, Singapore does not have a corner on the market for good textbooks. Similar ones from Japan, Korea, Russia, Taiwan, China, Hungary, and other high-achieving countries are more advanced and mathematically sound than typical U.S. texts. As your article pointed out, however, teacher professional development will be essential if American teachers are to use such books effectively.
Here is an example of a problem from Singapore's 6th grade textbook that students are taught to solve with visual representation, a method introduced at the 2nd grade level:
"David and Betty each had an equal amount of money at first. After David spent $18 and Betty spent $42, Betty's money was ²/³ of David's money. How much money did each of them have at first?"
Have your readers solve this and then tell me whether or not, as Ms. Burrill maintains, "A lot of the conceptual understanding that we would think is important is not evident from looking at this material."
Public School No. 2
Vol. 20, Issue 6, Page 42Published in Print: October 11, 2000, as Letters