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Education Reporter

Math Battles Add Up: East Meets West  
As U.S., Far East Try Each Other's Methods
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How best to teach math to schoolchildren is still hotly debated after waves of reform efforts in both American and Asian schools.

Over the last 15 years, public school districts across the U.S. embraced "constructivist math" (also known as "whole math," "new new math," "fuzzy math" or "modern math"), so named because students are supposed to construct their own knowledge instead of learning through drills and memorization of math facts. The constructivist approach has been endorsed by the National Council of Teachers of Mathematics and the National Science Foundation but harshly criticized by college professors of mathematics and science, some 200 of whom signed a letter of protest to the Clinton Administration Education Department. (For a recent example of criticism by an MIT Ph.D. in engineering, see Focus.)

The poor showing of U.S. math test scores in international comparisons has prompted parents and some school districts to consider alternatives. In 1999 the U.S. ranked only 19th among industrialized countries on student math scores. (See Education Reporter, Apr. 2004.) Some of these alternatives draw on pedagogical methods used in Japan or Singapore, countries with a history of producing better student math skills on average. Singapore ranked first in 1999.

Kumon stresses drills 
One such alternative program is Kumon, an intense, structured approach that originated in Japan. Kumon is offered in private instruction to elementary grade levels outside the school day and involves daily homework drills, for a cost of about $100 per month. Kumon claims to serve more than 100,000 children in the U.S. and more than 3.3 million worldwide, with about 90% in Asia.

Kumon does not try to be fun and its materials are not visually exciting. However, it gives students the drills and mental arithmetic skills that American public schools have been less willing to provide in recent years.

Public school districts are increasingly experimenting with math curricula from Singapore or Japan. Singapore, a nation of 4.5 million people, climbed from the middle of the international rankings to the top in just four years after implementing a new teaching system. It relies on diagrams, models and increasingly complex word problems. The student is taught to find different ways to solve problems instead of simply applying formulas. At times the students solve problems without pencil or paper. There is less repetition than in a traditional math curriculum. However, in Singapore this approach starts with a strong emphasis on computation in early grades before other topics are introduced, which does not necessarily happen in the U.S.

The North Middlesex school district became the first district in Massachusetts to sign on to the Singapore curriculum with encouragement from the state education department.

'Integrated math' 
Georgia's proposed new math standards are based on a Japanese approach which starts with a strong base of arithmetic skills in grade school. In high school, it blends algebra, geometry, trigonometry and statistics together instead of having them taught in separate courses. This so-called "integrated math," which gives students more options for solving a problem, is also being tried in New York.

It is not clear, however, that any particular middle or high school Asian math curriculum represents an improvement over traditional American methods. Far Eastern countries have been revising their approaches for some time and newer methods receive their share of criticism on their home turf. Japan's education reforms in the last two decades led to Japan dropping from first place to fifth place between 1981 and 1999 on an international standardized math test given to junior high school students.

Backlash in Japan 
The Japanese government undertook to reform its famously regimented schools in order to encourage students to think outside the box like American entrepreneurs. However, the reforms — which involved cutting down on drills and rote memorization and unleashing the students' creativity — have led to a backlash against "loose education" standards.

The Wall Street Journal recently reported on Japan's most popular elementary school teacher, who is leading a back-to-basics movement. Hideo Kageyama says that drills serve as mental calisthenics that strengthen the brain and build self-confidence, and he is apparently getting better results on test scores and placement in elite universities. (11-3-04)

Back in the U.S., math curricula are hammered out at the state or district level, and "fuzzy math" continues to provoke controversy. The Rockland, ME school board canceled the Math Connections high school program the night before the start of school on September 2 after board member Audrey Buffington called the planned pilot program "a disaster waiting to happen."

The program was chosen earlier even though only eight schools in the state had used it and four had decided to drop it. Moreover, board member Peter Smith said he spoke to the dean of math at the University of Maine who said Math Connections was not a good program and does not prepare students for college math. (Courier-Gazette, 9-9-04)

Calculators are a problem 
Increasing reliance by U.S. math educators on calculators for arithmetic (at the expense of drills) has undoubtedly weakened students' mental computational skills. Nine-year-olds who use calculators cannot compute on their own, and letting students use calculators on tests of computation skills makes the tests worthless, concluded an analysis of National Assessment of Educational Progress scores by Tom Loveless of the Brown Center on Education Policy earlier this year.

A larger problem in math education in the U.S. is the widespread lack of content knowledge among teachers. For example, almost two out of three Philadelphia middle school math teachers failed an exam last spring to gauge their mastery of the subject. (Education Week, 11-3-04)

Research on math teaching 
University of Michigan education researcher Deborah Loewenberg Ball has concluded after 20 years of study that having "mathematical knowledge for teaching" has an impact on students' learning. Such knowledge is not the same as general math ability or proficiency or general teaching ability; it has to do with being able to explain student mistakes, determining whether alternative problem-solving approaches by students are valid, and coming up with word problems on the spot that illustrate key concepts.

Teachers' scores on math-knowledge assessments matter more than how much time they spend teaching math, whether they are certified, or whether they have taken extensive mathematics or math teaching courses, Ball reports. (Education Week, 10-13-04)

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