In July the International Math Olym-piad, with its 400-some whiz-kid competitors from 85 countries, is opening amid great fanfare in Taipei. Rather than being content to dwell on the excellent records of past ROC teams, the general public might be better asking themselves if the mathematical abilities of Taiwan's students are really as outstanding as statistics would suggest.

When students who hate math in Taiwan and have failing grades in the subject go abroad to study, they commonly find themselves at the head of their math classes.

Yin Ping, the author of Going to New Zealand, emigrated because she was dissatisfied with Taiwan's educational environment. Her daughter Patricia often failed math in Taiwan, but after two months at a junior high school in New Zealand, her math teacher decided to move her up two grades.

In her new class she performed very well and could learn in half an hour math skills that the New Zealand students needed a week to understand. "The teacher was elated and practically bowed to her in gratitude," Yin writes in Going to New Zealand. "Now it appears that Patricia has what it takes to become a mathematician, and I think her teacher hopes she will become one."

Chen Shu-ling, who went to Britain for one year because of her husband's work, tells a similar tale. Her daughter went there in the seventh grade and quickly jumped to the best section.

Finding math happiness

There is a Chinese saying that "the orange tree bears no fruit if planted on the other side of the Zhun River." In the case of Taiwan's math education, the situation seems to be reversed, with transplants that were barren in Taiwan yielding prized fruit across the water. The parents of these children have various thoughts on the subject.

Yin Ping holds that her child couldn't study math well here because "math class in Taiwan moves too fast and exceeds the comprehension abilities of kids who are by no means stupid." Yin Ping's daughter Patricia adds, "Taiwan's math teachers are too full of themselves. If you don't understand and ask questions, the teachers say you're stupid. In New Zealand the teachers do their best to make you feel that math is fun. And if your performance improves slightly, they say 'Excellent!'"

Chen Shu-ling, the author of My Little Girl Studies in Britain believes that her daughter, who had always been ashamed of her performance in math class in Taiwan, was able to gain new confidence in Britain because British math classes are matched to students' abilities.

Chen points out that in British state-supported junior high schools, pupils who are particularly good at math are put in a self-study class. There the teacher gives each student a math progress chart with various categories at the top, such as "calculations," "estimates," "symbols," and "measures." The students study by themselves and "the teacher corrects the students' exercises and answers their questions," says Chen. This method sounds simple, but it allows the students to master each topic before moving onto the next, and, more importantly, the children are very happy.

The parents of these students who have studied abroad are very positive about the education their children received there and pull no punches in their criticisms of Taiwan's "overly demanding" math education. Yet it would be too simplistic to jump from here to making a blanket condemnation of how math is taught in Taiwan.

Hung Wan-sheng, a math professor at National Taiwan Normal University, argues that the reason that students from Taiwan do so well in math abroad is not unconnected to the good foundations acquired from intensive drilling in Taiwan. Were the children simply poor math students in Taiwan, or did they confront psychological obstacles that arose from poor teaching?

Teaching students to take tests?

Exactly how good are Taiwan students' mathematical abilities? On this question, academics have come to varying conclusions. The 38th International Math Olympiad is being held in Taiwan in July. The Ministry of Education, which is one of the event's sponsors, explains that Taiwan's selection to host the Olympiad is an affirmation of its recent performances at the event and of math education in Taiwan. Since the ROC began competing in the Math Olympics in 1992, it has obtained 21 silver medals, 10 bronze medals and a gold medal for a a perfect score in 1993.

An assessment of math and physics education in 20 countries made in 1992 included lists of outstanding students. The ten best math students in the 12-15 age group were all from such East Asian nations as Japan, Korea, Hong Kong and Taiwan. Taiwan's top performer ranked third overall.

Some believe that the results of such competitions as the International Math Olympiad are unreliable. "Asian students start taking exams when they are very young and grow up with them," says Hung Wan-sheng. "On pencil and paper tests with time limits, Asian students do perform superbly." He believes that it's even more true that Asian students put a lot of emphasis on test results and always do their best to prepare for them. The fact is that the vast majority of Asian participants at the International Math Olympics prep themselves by laboriously going over questions on the old exams.

Whether "an ability to take tests" is one form of mathematical genius has been debated for many years. Hung Wan-sheng points out that the "maths tripos" for students at Oxford and Cambridge was perhaps the hardest test of mathematical ability in the 19th century, but of all those who placed among the highest scorers on it, only one, James Maxwell, went on to become a great mathematician.

Taiwan has only been participating in the International Math Olympiad for six years, and it's too early to know how many of its medal winners will go on to become leading lights in the field of math, but Hung notes that "mainland China, which started competing before Taiwan, has discovered that among its participants in the Math Olympiad those who haven't won medals have ended up doing better in the field than those who have won medals, so it has begun putting less stress on such competitions."

From happiness to deep study

"Math competitions are one channel for giving secondary-school students who excel in math a chance to measure themselves against other top students from around the world," Hung says, "but they're not of much use for judging the quality of Taiwan's math education."

In fact, differences between Western and ROC attitudes toward math education have been discussed by academics at least since the 1980s when Harold Stevenson began conducting comparative research. In a 1991 study, Stevenson concluded that American and Taiwanese children had similar levels of cognitive development but found that Taiwan's students far outperformed their American counterparts in math. He explained the difference by noting that Taiwanese students spent more class time on math and also more time doing math homework, and that the direct approach teachers took to explaining mathematical concepts and going over the process of making calculations in large classes was a "more efficient" way of teaching the subject.

But Tseng Shuang-fan, the director of education at Yiming Elementary School in Taichung County, used the methodology of another American researcher, Zalman Usiskin, to argue that Taiwan's students were good at performing calculations but poor at thinking about how to solve problems.

Two years ago the BBC produced a news segment about math education in Taiwan which described large class size and stress on intensive drilling as major reasons Taiwan students excel in math.

These perspectives have astonished math teachers here, because they praise exactly the aspects of Taiwan's math education that parents have been criticizing in recent years as the source of math anxiety.

When Western and Asian scholars compare the methods, attitudes and effects of math education systems, they are of course also concerned about "level of achievement." In particular Taiwan parents wonder about the effect that alleviating their children's math anxiety will have on their math skills. And those Western experts who have come to Taiwan to uncover the secrets of our success have also noted that the intensive drilling in Taiwan math classes may just hone ability to perform calculations but not engender true mathematical understanding. Perhaps Asian and Western math educators ought to think long and hard about how to strike a proper balance between happiness and in-depth study, and about whether students of math can have both.

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Chen Shu-ling's daughter studied for a year in Britain. It did wonders for her confidence in math class (needless to say it also helped her English), and it motivated her mother to write a book about her experiences studying abroad. (courtesy of Chen Shu-ling)

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At the 1997 International Math Olympiad in Argentina, Taiwan's competitors posed with the Russian team. The outstanding performances of Taiwan students at the Olympiad has attracted the attention of many foreign scholars, who have come to observe the methods of math education in the ROC. (courtesy NTNU Math Education Center)