From the lettering on the book bags carried by little kids on Saturday afternoons, you can see the latest trends in the "supplemental school" market in Taiwan. For example, Mandarin Daily News Writing School, Hess English School, and Yamaha Piano Class have all been in the market for years and are top-ranked concerns. Recently, children with "Kumon mathematics" stenciled on the bags have been multiplying rapidly, so to speak.

What's the deal with Kumon math? Kumon is from the Japanese, and its characters are pronounced "kung-wen" by Chinese. So some people just hear the words "kung-wen mathematics" (whose Chinese characters imply the word "achievement"), and assume it actually means "document mathematics" (which is also pronounced "kung-wen"). From that they guess that it's probably a mathematics memorization drill class.

While not exact, that's not far from the truth.

In fact, the original name in Japanese was literally "document mathematics," following the characters in the name of the teacher who came up with the method in 1958. Thus in Japan and other countries, the name is indeed written in characters meaning "document mathematics." Only in Taiwan, where the Youth Talent Development Association of Republic of China (which brought the method to Taiwan) was worried about the connection many people would make with the rather boring drill-like implications of "document," were the Chinese characters altered to have the same pronunciation, but a meaning of "achievement."

Teacher Kumon graduated from the Department of Mathematics at Osaka University. Based on his 33 years of math teaching experience, he combined all the various types of math one would take from primary school through university, and divided them into 405 stages according to the degree of difficulty and how they connected to each other. He produced systematized teaching materials to permit students to achieve easy familiarity through repeated practice.

This method, which goes against all the tenets of modern educational theory, nevertheless swept Japan. Eleven years ago it came to Taiwan, and has now crossed the ocean to the US.

Looking carefully at the Kumon mathematics book, in fact there's nothing special about it. It's just one set of calculations after another, allowing students to continually review. For example, in the lesson on subtracting one-digit numbers from two-digit numbers, the first level is only subtracting one digit numbers from two digit numbers beginning with one (ten to nineteen). There are 100 problems. The students must be able to do all 100 correctly in ten minutes; only then can they go to the next level--subtracting one-digit numbers from 20 through 29. If there is an error or too much time is taken, they must do these over repeatedly until the standard is achieved.

How can such a monotonous, mechanized study method keep the interest of kids? According to Kumon's way of thinking, small children in fact really like repetition. A lot of parents have the experience of having told "Cinderella" to the kids ten times, only to have them be still fascinated the next time. Or how about driving back and forth in the living room with toy cars--although nothing changes, they never get tired of it. . . . He took hold of this special feature of small children, and designed teaching materials to enable kids to achieve the goals of accuracy and speed through repetition.

Moreover, because it is monotonous, kids feel it is simple. If the child can't advance in level, it's usually not because of wrong answers but because the answers aren't quick enough, so they will still feel they have accomplished something--they can have the proud feeling getting full score and of feeling that "nobody taught me, I did it myself."

Therefore, Kumon believed the earlier a child begins studying, the better. Teaching materials begin with lessons on holding a pencil and drawing a line. One can advance step by step right up through university level. But if you wait until fifth or sixth grade to start, because the habit of repetition has not been developed since a young age and kids of this age already have no patience with monotonous things, it is impossible to use this method of study.

Hu Nai-wen, a third grader, is one of the 70,000 kids in Taiwan who have studied Kumon math. Now every night she spends ten or twenty minutes doing 100 calculations, while Mrs. Hu is responsible for timing and grading. When the twice weekly "cram school" time comes, Hu Nai-wen takes her little bag to teacher's house to be tested. The teacher has little involvement in teaching per se. The main task is to determine whether or not the child can go up a level based on accuracy and speed.

"I often get 100!" says little Nai-wen with a feeling of accomplishment.

According to Tsai Hsueh-ni Chairman of the Board of Directors of the YTDA, Chairman of the CCPDA, currently there are 800 Kumon classrooms in Taiwan. Of course the most concentrated area is Taipei, but all cities and counties, including Penghu, have theirs.

Following the rapid spread of Kumon mathematics, it was inevitable that this method of teaching by practicing calculations would attract the attention of various sectors, with detractors and supporters coming in droves.

Wu Wu-tien, director of the Graduate Institute of Special Education and the Special Education Center at National Taiwan Normal University, believes that from the point of view of child education, Kumon math allows children to start at a level they can deal with regardless of ability, and to advance at a pace that need not be the same as others, nor need be compared with others. This can lower the child's apprehension in studying math. It can be especially encouraging for introverted or slower students.

But math instructors have a markedly different view. They even believe that overly mechanized repetition can be counterproductive, and ruin the child's ability to think.

"Math education should be combined with life, to let children understand that every manipulation of figures has its own significance, and to stimulate the child's thinking ability," argues Chu Chien-cheng, associate professor of mathematics at National Taiwan University.

Problems which use common life situations like "Mother wants to hang a curtain that's 150 cm wide, with ten hooks at the top. How much space should there be between each hook?" are nowhere to be found in Kumon mathematics.

"Believing that math is just manipulating a bunch of symbols with no meaning is the biggest crisis in math education," says Chu with concern.

Nevertheless, according to a study by Wu on behalf of the US Educational Testing Service, the results of research on the math part of the Scholastic Aptitude Test (SAT) for students who have taken Kumon math in Taiwan show that after the ordinary student goes through the program, a fifth grader would be at the same level as an American high school junior.

What's even more interesting is that the math SAT places emphasis on reasoning and abstract thinking, which is not exactly similar to Kumon, which stresses familiarity with calculation. The assigning of topics is also different. Before this test, the YTDA was worried that there would be a negative impact on grades, but the outcome was quite the opposite.

"This doesn't by any means show that memorization of calculations can assist in reasoning. A more reasonable explanation is that children who have received training in Kumon mathematics don't have anything against math, and after developing confidence in studying will have more interest in learning when they meet reasoning problems, and will take the initiative to think," explains Wu Wu-tien in more detail.

Whether this explanation is reasonable is open to debate, but from the way the grammar school math curriculum is set out, "heavy on the reasoning, light on the calculation" is already the inevitable trend in math education.

Fan Min-hsiu, a sixth grade teacher at the Kuting elementary school, points out, "Beginning last year, the complicated repeating calculations have already been cut out of fifth and sixth grade texts, with kids now allowed to use electronic calculators. Even if there are calculations, they don't go past the hundreds place."

Given the arguments among scholars and specialists, the secrets of Kumon have been revealed layer by layer. But this hasn't hurt business, and classrooms are still packed.

The reason? The attitude of most parents is not actually so strict. Most have just heard friends say that, "Studying Kumon is pretty good," so they take their children to attend.

Although Kumon math holds meetings to announce the names of those learning beyond their grade level, "it's like studying piano, not everyone can become a maestro," says Mrs. Yu, whose son has still not learned to handle the course after two years. A Mrs. Wang states the "modest hope" of most parents: it's enough if the children can acquire a good base here, and thereafter not be afraid of math as their parents.

As for pre-schoolers, parental motives are even simpler. "Going with their elder brother and sister to kill some time sure beats sitting at home with nothing to do and just turning into an idiot watching TV," says Mrs. Liu.

Because Kumon stresses speed and concentration, some parents hope to rely on it to correct bad habits in the kids, like restlessness, inability to concentrate, slow responsiveness, impatience, and so on.

In this respect, Kumon math is not so omnipotent as many parents hope, and can even have a negative impact. "My son is very fidgety. Doing these repetitious math problems goes against his personality, and he feels very stressed," says Mrs. Liu. In order to prevent a gradual increase in mother-son confrontation each time it was time to do homework, and to avoid leading to even greater frustration for the child, she decided to beat a retreat.

For most parents to seriously evaluate whether or not the child should continue in the Kumon program, most wait until after fifth grade. For one thing all-day classes begin in fifth grade, and children don't have that much spare time. Also, starting in fifth grade math problems shift from stressing calculation to stressing thinking, so that the Kumon method of rehearsed calculating is strained.

Although Professor Wu's research suggests that Kumon students have superior reasoning ability to ordinary students, this theory doesn't convince parents who can see what's going on in front of them. That students after fifth grade shift their attention to other interests means that Kumon math is concentrated in the age cohort of children below fifth grade.

Perhaps it is as teacher Fan Min-hsiu says: "It doesn't hurt to learn anything. The question is whether its worth the time and money to make the child go and learn. If you don't do this, is there something even better to choose? This is the issue of opportunity costs."

Children have to face competition from others from an early age. The significance of "math" in this competition includes ratings and confidence.

"Let's see whose painting is more beautiful." Art class is one of the many skills classes in the country.

The younger children are, the more interest they have in learning by repetition.

The Kumon math ladder is built at one's own speed. The teacher merely has to give some directions when necessary.

Primary school math education tends towards, "heavy on the reasoning, easy on the calculations."

The Kumon math instructors are housewives with college education plus some additional training.