When former U.S. Secretary of Education William Bennett visited Taiwan last January, he voiced familiar praise for the island's math education system, stating that there was a lesson to be learned for the United States. Bennett cited figures from the 1992 International Assessment of Educational Progress (IAEP), which tested a total of 175,000 nine- and thirteen-year-old students in twenty countries on their knowledge of math and science. In the survey, developed by the U.S. Educational Testing Service, Taiwan's thirteen-year-olds ranked first in the world.
Bennett's words made headlines around the island and brought a new wave of pride in the much acknowledged math skills of local students. But not everyone is happy with the education system that produces these results. Many local educators say IAEP test scores reflect both strengths and weaknesses in math education, and they question whether the achievement is worth the sacrifice demanded of students.
Lin Fou-lai (林福來), a professor of mathematics at National Taiwan Normal University, says the main forces behind the high IAEP scores are students' efforts, parental pressure, and the local math curriculum. "In the United States, Switzerland, or Canada, the curricula vary among schools," he says. "But in Taiwan, all schools follow one standardized instructional program." While standardization ensures all students an equal education, it has a downside. "This intensifies competition among students," Lin says. All students know they will eventually face the high school entrance exam, where they will have to outscore three-fourths of their classmates to secure one of the limited openings.
Professor Huang Men-fon fears that teachers will not be able to adopt the new interactive teaching style scheduled to be introduced into all grade schools by 1996. "All teachers are trained in the traditional style."
Another difference is that local students spend more time at school and studying than their peers elsewhere. Each week, Taiwan students attend school six days for a total of thirty-two hours of actual class time, while U.S. students attend five days for a total of twenty-eight hours. The IAEP report also found that Taiwan's thirteen-year-olds spend more time doing homework. Among American eighth-graders tested, 15 percent reported spending more than four hours a week on math homework, 22 percent spent two to three hours, and 63 percent spent an hour or less. In Taiwan, 24 percent reported spending more than four hours on math homework each week, 29 percent spent two to three hours, and 47 percent spent an hour or less.
But these figures do not include the time local students spend in weekend and evening "cram schools" and at cram-school homework. More than half of all junior high school students attend these schools, usually for a minimum of three hours a week per subject. Thus a typical eighth-grader arrives at school by 7:30 AM for a pre-class reading or quiz session, gets out at 5:00 PM, after a mandatory after-school study or quiz session, grabs dinner at a local noodle stand, then attends cram school from 6:00 to 8:00. Many students don't get home until 9:00, when they must start the day's homework assignments.
Another difference, according to Lin Fou-lai, is that homework is more closely linked to academic success in Taiwan than it is in the United States. He explains that while many American students can achieve high marks without doing much homework, Taiwan students must spend a substantial amount of time on homework in order to make good grades. "This suggests that doing homework is often a way of punishing lazy students in the States, while in Taiwan, it is a necessary part of the educational system," Lin says. In fact, local teachers often give more homework to their best students in order to challenge them. A third difference is that Taiwan students take more math exams; the IAEP survey found that 87 percent take at least one math quiz per week, while only 68 percent of their U.S. counterparts do so.
Role reversal—In Wu Jui-hsiang's fourth grade math class, students get a chance to talk while the teacher listens. Wu switched to the new teaching method because, she says, "I want children to enjoy learning math."
Teachers are not the only ones pressing students to excel in math. Some parents begin sending their children to math cram schools at five years of age; a few kids begin at the age of three. Parental emphasis on the subject is not based on interest, but a practical consideration: math is one of the most important sections of the entrance exams. It is crucial to get ahead in math as early as possible because students who do well are separated into advanced classes in seventh grade, and any advantage in preparing for the highly competitive exams is welcomed. Last year, among Taipei students, about 25 percent passed the annual high school entrance exam. Those who fail to get into high school can either quit school, try again after a year in special entrance-exam classes, or try to test into a private senior high school, vocational school, or five-year junior college. But failing the public high-school entrance exam after years of preparation and pressure is often traumatic.
From a very young age, most children are pushed to put studying above any outside interests. Leisure time is limited, and they are discouraged or forbidden from playing outdoors or watching TV. When asked what drives her to study, Taipei fifth-grader Tai Yin-fang (戴吟芳) immediately replies, "My parents' encouragement." For most kids, leisure time is strictly monitored. "On TV, I am only allowed to watch the news," pouts Chang Ya-ching (張雅菁), a sixth-grader at Jen-ai Primary School. "But I like watching soap operas." Parents make an exception for the news because the entrance exams include current events.
Professor Chu Chien-chen—"In order to make high marks on their math exams, students spend a great deal of time calculating and repeating exercises without thinking." The downside is that many students never fully grasp mathematical theories.
Even reading is monitored by many parents. Chan Chi-ying (詹季英), a teacher at a math cram school in Taipei, says although many of her students are forbidden by their parents from reading anything but textbooks, she has set up a reading area filled with comic books, story books, and encyclopedias. "Leisure reading also plays a part in helping children develop their imagination and personality," she says. "Parents are too impatient to wait for long-term achievement in their children."
Some teachers and counselors worry that the narrow focus on preparing for the entrance exam creates an unhealthy level of stress and encourages students to link their self-image too closely to academic success. The school system creates additional strain by separating the best students from their classmates, says Susan Lin (林壽美), a counselor at Cheng-te Junior High. Soon after they begin junior high, students are tested into special math, English, and science classes. This division increases the pressure on top performers, leaves average students with a sense of failure, and creates resentment between the two groups.
"Those who perform well might, at some point, falter because they cannot bear the pressure of innumerable exams, and because they worry that they will not achieve the standards set by their teachers," Lin says. She says the pressure can sometimes drive good students to seek an escape, such as feigning illness in order to stay home. Poor achievers have a different strategy. "Those who are not performing well academically may quit trying to learn because they have little chance of passing the entrance exam," Lin says. Making matters worse, some teachers give up on low-achieving students and allow them to do whatever they like during class time as long as they are quiet. In the worst cases, these students vent their frustration by dropping out of school or turning to crime.
Educators also point out that the intense academic competition can skew educational priorities. Professor Lin Fou-lai says the current educational policy "does not aim to educate all citizens, but to promote a contest of elimination."
Family affair—The hectic study schedule affects Mom and Dad as well. One mother says, "The life of a junior high school student in Taiwan is really tough. Even we parents suffer."
Many parents realize the pressure is not healthy. Shen Yiu-yu (沈幼玉), a mother of two boys aged ten and thirteen, puts it simply: "If my children could study under a different educational system from the current one, I'm sure they would be much happier. The life of a junior high school student in Taiwan is really tough. Even we parents suffer." Both sons attend school six days a week, then go to cram school, the oldest for four days a week, the youngest for two. The family cannot plan weekend outings because of the eldest son's study schedule. And cram schools and private tutors are expensive. A month's worth of eight half-hour elementary-level math lessons costs at least US$37 at a cram school while eight ninety-minute junior high or high-school classes run about US$74. Private tutors are far more expensive. In a society with an annual per capita GNP of about US$11,000, the cost of sending a couple of kids to cram school adds up quickly.
In addition to the negative effects on students, the educational system may actually limit children's ability to learn, educators say. "In order o make high marks on their math exams, students spend a great deal of time calculating and repeating exercises without thinking," says Chu Chien-chen (朱建正), a professor of mathematics at National Taiwan University. Chu finds that students are often adept at memorization but lack the ability for independent thinking. "They cannot solve problems they have not done before," he says. Under this system, the study of math is relegated to the level of arithmetic, and can be reduced to the rote execution of problem-solving formulas. Among local IAEP test takers, 54 percent said they consider math to be "mainly memorization."
Such attitudes are built early in life with classes at a cram school. One of the most popular teaching methods for kids under ten, the Kumon method, was introduced from Japan in the mid-1960s. In it, students build math skills through repetition exercises that gradually gain in complexity. Eventually, pupils are expected to solve mathematical problems automatically. Although the Kumon approach has recently been criticized for stressing memorization too heavily, many parents swear by it. For older students, cram courses closely follow the memorization-heavy standardized junior high and high school math curriculum.
Such methods, teachers say, can snuff out a student's interest in math and can squelch general enthusiasm for learning. The IAEP survey found that Taiwan kids, despite scoring highest on the math test, were ranked sixteenth out of the twenty countries surveyed in level of interest in math. Another finding: the higher the grade level, the lower the math interest.
With these problems in mind, the government and private educational foundations in Taiwan are working to improve the mathematics curriculum. In 1992, the Ministry of Education introduced an experimental interactive teaching method for math classes, which was designed by a group of math teachers and other educators. The program was launched in thirty-one elementary schools around the island during the 1992-93 school year and will be expanded to all elementary schools by the 1996-97 school year. The group, which now includes some thirty educators who meet once a week, has also revised the first- and second-grade math textbooks and has introduced these new texts into the thirty-one schools. They plan eventually to revise all elementary-level math textbooks.
Based on the philosophy that knowledge is constructed through an individual's own mental efforts, a theory drawn from Constructivist educators such as Jean Piaget, the new method is a significant break from the traditional Chinese teaching style in which a teacher gives students problem-solving formulas to memorize. Although memorization and repetition exercises are still a part of the learning process, much of class time is spent in discussion rather than in honing skills for speed and accuracy.
Under the new system, students are not asked to answer problems, but to find and explain possible methods of problem-solving. After introducing a story problem, a teacher will ask students how to find the answer rather than simply asking for the answer. Students try and choose from among the possible methods they have learned, or invent a new way to solve the problem.
Perhaps most importantly, the teacher-pupil relationship is transformed from one involving a superior and inferiors to one of equals. Instead of speaking from the head of the classroom, teachers sit with the students to facilitate a discussion. Once students begin debating a problem, the teacher interferes only to keep the class on track, to engage all students, and to clear up misunderstandings.
Math teacher Wu Jui-hsiang (鄔瑞香) from Tung-yuan Primary School in Taipei taught in the traditional style for more than twenty years before trying the new method. Asked why she switched, Wu says, "I want children to enjoy learning math." She traces her enthusiasm back to a visit from a former student six years ago. The young woman had become a junior high English teacher. When Wu asked why she had not chosen to teach math, the woman replied that she never really understood her math classes; she got high grades by memorizing formulas and solutions. Shocked by this frank confession, Wu began promoting educational reform.
Now entering her third year using the interactive style, Wu monitors her students' progress by recording her classes and reviewing the videotapes after school. She also asks each youngster to keep a math diary to record the concepts discussed in class. Pupils are encouraged to develop their own language, using a combination of words and pictures, to describe math concepts. This helps them absorb and analyze what they have covered.
How does the new method compare with the old? Wu says her students grasp math concepts quickly and seem to have more fun in class. She says students develop important non-mathematical skills as well, including critical thinking, self-confidence, and a respect for the viewpoints of others.
Outside the public schools, several private institutions are also promoting educational reform. Since 1987, the Mandarin Daily News has hosted a "Math Classroom" series of classes designed to boost interest in math among fourth- and fifth-grade students. Each year, a total of ninety kids attend one of three sessions. For US$130, they join a two-hour class once a week for three months. The goal is to present math problems in a fun atmosphere that encourages independent thinking. In one popular program, the classroom is turned into a stage where youngsters act out real-life roles that require math skills, such as cashiers, street vendors, accountants, and engineers. The programs are designed by academics from local elementary schools, high schools, and universities. "The program's primary goal is to help kids get over math phobia and to build curiosity and interest in the subject," says supervisor Lee Pik-lan (李碧蘭). The classroom has become so popular that parents queue up the night before registration day. Some even rent rooms in nearby hotels and take turns waiting in line all night.
The China Youth Foundation also began hosting public riddle-solving activities last year and has attracted about a thousand students and parents to each of its seven events. The activities, usually held in a public park, encourage parents and children to work together to solve math problems based on concrete examples, such as measuring the depth of a nearby pond. The goal is to prove to both children and parents that solving math questions can be fun and that math is relevant to real life. The organizers encourage children to try their own methods to solve the problems, and stress that correct answers are secondary to encouraging kids to think creatively.
Despite these successful ventures, selling more conservative parents and teachers on the new teaching methods is proving difficult. "All teachers have been trained in the traditional style," says Huang Men-fon (黃敏晃), a professor at National Taiwan University who is helping to revise the math curriculum. Those who support the interactive style fear that, while new textbooks and teaching manuals will be issued throughout the elementary school system by 1996, many teachers will not fully adopt the new program.
Parental attitudes can be even more difficult to change. For a parent well aware of the importance of passing the high school entrance exam, it is difficult to accept the idea that the learning process is more important than academic success.
But more and more parents are becoming frustrated at the negative side effects of the math education system. Many of them remember enduring math classes themselves. "When I was in junior and senior high school, the subject that scared me the most was math," says Shen Yiu-yu. "I can still remember how I struggled to memorize formulas and dreaded taking the exams. I hate to watch my own children going through the same struggle. I hope the math education system will really be reformed so this nightmare will stop haunting me and my children."