Taiwan Today

As Taiwan continues to excel in global rankings of students’ math proficiency, academics and educators debate the merits of the nation’s approach to teaching the subject.

In preparation for an upcoming science fair, Yin Shao-fan (尹少凡) and his teammate rehearse their math-themed project in front of classmates, outlining the method used to find the shortest path that touches every point on an interconnected series of cubes. The eighth-grader at Taipei Municipal Dunhua Junior High School offers a step-by-step explanation of how to obtain the optimal solution to this variation of the route inspection problem, also known as the Chinese postman problem, a well-known puzzle in graph theory.

A member of the school’s math and science program for gifted youngsters, Yin has repeatedly practiced the algorithm used to uncover the answer. Unlike students in conventional math classes, however, he has also completed exercises to confirm the veracity of the method itself. Though challenging, the latter process is intended to help the young scholar gain an appreciation of how mathematical models are created and tested—knowledge that will hold him in good stead should he ultimately decide to pursue a career in engineering, physics or any one of a host of other scientific disciplines.

Yin is among the nearly 6,400 Taiwan middle schoolers enrolled in math and science programs for gifted students. These courses take a markedly different approach than the standard curriculum, explained Huang Peng-chiung (黃彭泂), Yin’s teacher.

“Most students in elementary and junior high schools are forced to do lots of drills and memorize a lot of formulas. This may help them get good grades, but their interest in math rarely lasts,” said Huang, who taught the regular curriculum for five years before taking over the advanced program.

“In the advanced classes, we encourage the gifted students to craft their own solutions to problems using a logical, analytical approach, through either individual or collaborative assignments,” he added. “Much of this is extracurricular work. It’s also quite challenging, which makes it more fun for them when they find the answers.”

Making the Grade

High achievers like Yin have contributed to Taiwan’s excellent rankings in global studies of math proficiency, including the Program for International Student Assessment (PISA) conducted by the Organization for Economic Cooperation and Development (OECD). In the 2015 PISA results, released in December last year, Taiwan ranked fourth in both the math and science categories. The triennial survey of 72 countries and economies evaluates the knowledge and skills of 15-year-olds.

In the science component of the 2015 survey, Taiwan scored 532 in comparison to the OECD average of 493, moving up nine places from the previous edition to trail only Singapore, Japan and Estonia. The nation maintained fourth place in the math category, finishing behind Singapore, Hong Kong and Macau. Its score of 542 points was significantly higher than the average of 490.

According to Wang Cherng-shian (王承先‬), deputy director-general of the K-12 Education Administration under the Ministry of Education (MOE), the excellent PISA results in math are a testament to Taiwan’s educators. “Our math teachers are well versed in problem-solving, analysis and reasoning, and possess excellent presentation skills,” he said, adding that efforts to adopt situational math courses using examples from everyday life may also have contributed to the nation’s performance.

Despite the overall rosy assessment of Taiwan’s scholastic environment, the PISA math scores also highlight a troubling disparity in students’ abilities, a trend academics sometimes refer to as the “twin-peak phenomenon,” according to the education official. In the previous PISA results from 2012, the discrepancy between the Taiwan students in the top and bottom 10th percentiles reached 301, which professor Hung Pi-hsia (洪碧霞), national project manager for Taiwan PISA 2012, said equates to a seven-year gap in math competencies. 

An initial assessment of the 2015 results indicates that the gap may have contracted slightly. However, this seems to be due to a drop in the number of high achievers rather than a decrease in the proportion of low performers, according to Hung.

Seeking Fresh Insight

To address this imbalance, the MOE in 2014 launched a project aimed at improving teaching methods in math and helping low and mid-level achievers gain an appreciation for the subject. Under this program, elementary and junior high schools can request to host regular math workshops for teachers presented by education scholars. During the current academic year, 85 elementary schools and 17 junior high schools have applied to hold such workshops, which are typically arranged three to four times each semester.

At a recent event, Lee Yuan-shun (李源順‬), a math education professor at the University of Taipei, listened as several teachers at Taipei Municipal Yong-Chun Primary School discussed their concerns about the current curriculum. According to the educators, many students find the lessons hard to comprehend and get bored by the quantity of arithmetic exercises that they are expected to complete.

These concerns are not new to Lee, who noted surveys conducted in August 2015 showed that nearly 30 percent of the respondents, aged between 13 and 65, identified math as their least favorite subject in school. He said that math lessons in many countries in East and Southeast Asia, including Taiwan, emphasize drills and memorization over comprehension and explanation, an approach that impacts students’ ability to analyze, extrapolate and integrate knowledge.

Nevertheless, this methodical, repetitive approach is not without its benefits. For instance, the practice of encouraging students as young as second-graders to memorize multiplication tables can train children to quickly complete complex calculations without the assistance of a computing device.

That is why, to a certain extent, Lee endorses the U.K.’s recent move to adopt the “Shanghai method” of teaching math in half of the nation’s schools—part of a government drive to stop youngsters falling behind their Asian counterparts. Shanghai was the best performer in the math category of the 2012 PISA, while Britain placed a distant 26th. “If students have fully grasped the why and the how, repetitive drills can help enhance their math competencies,” Lee said.

The professor warned, however, that the approach used in Shanghai, Taiwan and elsewhere in Asia, with its distorted focus on repetition, drills and paper-and-pen learning, can suppress creative thinking and problem-solving, limiting students’ ability to relate what they learn to real-world situations. He believes that Taiwan should develop a teaching method that combines memorization with analytical and creative skills.

Lee’s concern about an undue emphasis on repetition is shared by Jean Hou (侯貞伊), who teaches the math class for gifted students at New Taipei Municipal Linkou Elementary School. Hou said that even though she places a focus on creativity, students still have a hard time integrating different math disciplines.

For example, she noted that while her students have studied angles, most of them cannot apply this knowledge to drawing polygons with a compass. Even those in the gifted class prefer repetitive drills to challenging new problems, she added.

Creative Endeavor

Yau Shing-tung (丘成桐), the William Caspar Graustein professor of mathematics at Harvard University, has fundamental doubts about the benefits of the Asian approach and questions the U.K.’s decision to adopt the Shanghai method.

Yau, a Hong Kong native and naturalized American, said that it makes little sense for the U.K. to look up to Shanghai since Hong Kong, a former British colony, has produced greater numbers of outstanding mathematicians than the mainland Chinese city. He urged educators to analyze the impacts of teaching methods over a period of a least a decade as he believes the drills-oriented Shanghai approach may dampen students’ interest in the subject by the time they enter middle school.

In general, students in Asia lag far behind their counterparts in the West when it comes to imagination and creativity, the most important elements in mathematical competency, Yau said. “As far as research, the best students still come from Europe and America—the very best ones. They are much more creative.”

Many of the world’s leading tech enterprises are increasingly hiring based on competency and creativity rather than exam performance, said the professor, a winner of the prestigious Fields Medal—widely considered the equivalent of a Nobel Prize in mathematics.

Yau’s words of advice, to some extent, align with the concerns raised by educators in Taiwan. While international league tables like PISA are dominated by Asian nations, many teachers believe it is time for countries in the region to look beyond such global rankings and place a greater emphasis on creativity and comprehension in math education. 

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Joyce Huang is a contributing writer based in Taipei.

Copyright © 2017 by Joyce Huang