“Every so often someone asks me: ‘What’s your favorite country, other than your own?’
I’ve always had the same answer: Taiwan. ‘Taiwan? Why Taiwan?’ people ask.
Very simple: Because Taiwan is a barren rock in a typhoon-laden sea with no natural resources to live off of—it even has to import sand and gravel from China for construction—yet it has the fourth-largest financial reserves in the world. Because rather than digging in the ground and mining whatever comes up, Taiwan has mined its 23 million people, their talent, energy and intelligence—men and women. I always tell my friends in Taiwan: You’re the luckiest people in the world. How did you get so lucky? You have no oil, no iron ore, no forests, no diamonds, no gold, just a few small deposits of coal and natural gas—and because of that you developed the habits and culture of honing your people’s skills, which turns out to be the most valuable and only truly renewable resource in the world today… Sure, it’s great to have oil, gas and diamonds; they can buy jobs. But they’ll weaken your society in the long run unless they’re used to build schools and a culture of lifelong learning.”
-Thomas Friedman, The New York Times, March 11th, 2012
When Portuguese sailors first sailed past Taiwan during the 16th century, they nicknamed the island Formosa after its natural beauty. In most countries throughout the world, these natural landmarks are prominently featured on currency, alongside images of memorable leaders and famous monuments that celebrate key moments in the course of their history. In contrast, Taiwan’s legal tender promotes a notably different message: the importance of education. On the back of the Taiwanese NT$1,000 banknote, for example, we find a group of children gathered around a globe. This phenomenon is not surprising, as Taiwanese citizens believe strongly in the innate power of public education (Hsiao & Po-Hsuan, 2018). This rich culture and deep respect for learning dates back centuries to a period when most of Asia was under imperial rule and civil service exams were omnipotent:
“The first examinations were attributed to the Sui emperors (589-618 A.D.) in China. With its flexible writing system and extensive body of recorded knowledge, China was in a position much earlier than the West to develop written examinations. The examinations were built around candidates’ ability to memorize, comprehend, and interpret classical texts. Aspirants prepared for the examinations on their own in private schools run by scholars or through private tutorials. Some took examinations as early as age 15, while others continued their studies into their thirties. After passing a regional examination, successful applicants traveled to the capital city to take a 3-day examination, with answers evaluated by a special examining board appointed by the Emperor. Each time the examination was offered, a fixed number of aspirants were accepted into the imperial bureaucracy”
U.S. Congress, 1992
This imperial system of examination (known in Mandarin as 科舉 or kējǔ) was originally considered to be an equitable way for all students to have an opportunity to rise beyond their current caste. Kējǔ also helped those in power identify and recruit into government service individuals who were capable and virtuous rather than to fall back on members of the hereditary noble class (Zhao, 2014). Seen by many to be fair, objective, and open, kējǔ set the stage for the development of a meritocracy for years to come (Zhao, 2014).
Centuries later, Sun Yat-sen, the founding father of the Republic of China, continued to praise kējǔ as the bedrock of the world’s best education system. Dr. Yong Zhao reminds us of an oft-told tale of Sun’s about the drawbacks of a society without standardized tests. Sun related the story of an election in the west between a doctor and a rickshaw driver. Although the doctor had received more formal education than the driver, he lost the popular vote. This outcome, Sun would insist, was the consequence of popular election without examination (Zhao, 2014).
After overthrowing the Qing dynasty and bringing an end to Imperial China, Sun Yat-sen set up a new government in Beijing known as the Republic of China. The founding document of the R.O.C. included an entire branch of government focused on examination; this five-power constitution continues in modern day Taiwan.
The Taiwanese system of education
While standardized testing is deeply ingrained in Taiwanese culture, the country’s education system is unique for a multitude of other reasons. First of all, Taiwanese teachers are classified as white-collar professionals; they value the quality of their work and take pride in what they do (Huang, 2003). The reputation of teachers is second to none; teaching jobs are held in high esteem and the pride of place given to education in traditional Chinese culture enhances the social status of teachers (Hsieh et. al., 2009; Fenton, 2016).
Second, most Taiwanese educators believe in the concept of a growth mindset. Simply put: if teachers believe that their students can do better, they will; if teachers give up on their students easily, then their students will give up, too (Dweck, 2016).
Third, Taiwanese pre-service teachers are exceptionally well-qualified academically; most have excelled in school. Consequently, university education departments are quite selective, and only the best available candidates are accepted. This situation stands in marked contrast to that of the United States, where the lure of Wall Street and Silicon Valley often attracts the best and the brightest (Kristof, 2011; Zakaria, 2012). In fact, the results of a 2010 study suggest that the majority of U.S. education majors come from the bottom third of their graduating class (Kihn, Miller, & Auguste, 2010).
After a number of school visits throughout Taiwan, it is evident that although most teachers are present at school for more than 10 hours a day, they rarely lead instruction for more than three or four hours daily. Data from the Taiwanese Ministry of Education (2017) confirms that the average teacher leads instruction for 560-720 hours per year. In contrast, the majority of high school teachers in the United States spend almost double that amount of time leading instruction over the course of a school year (Ministry of Education, 2017). Consequently, Taiwanese teachers have significantly more time available each week to prepare lessons, mark classwork, and reflect on how best to improve children’s learning (Gove, 2012). They are also able to meet with colleagues in professional learning communities to plan classes and grade their students’ work collaboratively. Most importantly, they have an opportunity to reflect upon their pedagogy. This extensive reflection time enables teachers to become action researchers, develop and evaluate new teaching methods, and keep tabs on one another’s performance (Gove, 2012; Liu, 2013).
Note, too, that the Taiwanese education system includes more than government-run schools; it also encompasses a consortium of cram schools. However, it is virtually impossible to find stories in the mainstream media today about East Asian education that boldly confront the existence of this parallel educational system (Turton, 2012). These cram schools (known in Mandarin as 補習班 or bǔxíbān) are akin to large tutoring centers that lecture students about mathematics, Chinese, and English.
The practice of late-night tutoring is particularly controversial in this part of the world. Although many schools in Taiwan are remarkably equitable, these night classes are one way in which parents with means use their resources to give an unfair advantage to their children, but often at an extraordinary financial and emotional cost (Williams, 2017). These bǔxíbāns are so pervasive in East Asia that neighboring South Korea passed a law in 2011 that enacted a strict 10:00 PM curfew to lessen the stress load on students (Seoul, 2011).
Education reform
Today, considerable controversy surrounds the concept of education reform throughout the world. In Taiwan, the fundamental purpose of public education has long been debated. This ongoing debate has led to a learning system that “over-emphasizes academic performance and neglects other dimensions of learning. But recently, the Taiwanese government adopted the use of a constructivist approach to teaching mathematics. This new approach to teaching and learning focuses on the whole child” (Eisenhart, 2011).
Contemporary educational reform in Taiwan began to unfold in the late 1980s when a team led by Dr. Fou-Lai Lin decided to investigate the teaching of mathematics; this group reviewed the literature and relied on research methodology rather than solely on their anecdotal experience. As a result, mathematics teacher education in Taiwan entered a new phase, one that combined practical experience with empirical research (Hsieh et. al., 2009).
In 1996, mathematics teachers throughout the country began to focus on the way in which students thought, thus shifting away from a teacher-centered approach and towards a student-oriented method of learning (Hsieh et. al., 2009). The following year, the Ministry of Education implemented a new national curriculum for junior high school students. Many of the changes involved in this initiative focused on the cultivation of students’ creativity, thinking, and reasoning abilities, as well as the links that exist between mathematics and life. The message was clear: an attitude toward active learning and the appreciation of mathematics was being put into place (Hsieh, 1997).
These reforms shifted the emphasis in mathematics education away from simply memorizing and plugging into formulas and towards developing problem-solving skills and process-monitoring. Historically, problem solving had been largely neglected throughout Taiwanese schools; today, however, it is gaining attention alongside an emphasis on mathematics education for lifelong learning (Hoyles, Morgan, & Woodhouse, 1999).
The Taiwanese Ministry of Education is currently piloting a new high school mathematics curriculum which will be rolled out nationwide during the 2019-2020 school year. One of the Ministry’s noted goals is the progressive implementation of a 12-Year Basic Education program, incorporating the development of adaptive learning along with a completely non-exam-based secondary school admission process (Ministry of Education, 2017). Policy makers plan to adapt the Taiwanese curricula so as to encourage problem solving that is creative (Hoyles, Morgan, & Woodhouse, 1999). The Ministry has also made it clear that teachers must pay closer attention to the process of learning as well as to the way in which children conceptualize content and ideas rather than simply focus on arriving at the correct answer (Eisenhart, 2011).
These proposed education reforms seek to address the pitfalls found in current educational practice and to foster collaboration among students through project-based learning and standard-based grading. One teacher noted that these reforms will set future generations of Taiwanese students in a positive new direction and prepare them to face the adaptive challenges found in our increasingly globalized world.
Next steps
As the guiding vision of Taiwan’s new 12-year basic education program is further developed, the principles of spontaneity and interaction, as well the common good that it promotes, will be integrated with the educational philosophy of John Dewey (1938), postmodernism, and complex thought (Morin, 1999; 1993). These structural shifts will encourage Taiwanese teachers to let students drive their own learning and to take ownership of their thinking with an aim to inspire rather than to control (Fan, 2016). After all, “if we continue to ignore the power of students’ own ideas and conceptions, we will only perpetuate the notion that mathematics and science (among other subjects in our school curricula) are irrelevant, uninteresting, and difficult to learn” (Sahlberg, 2018).
These progressive innovations are not unique to Taiwanese education. The People’s Republic of China, the United States’ leading economic competitor, is in the process of decentralizing its curriculum, diversifying its methods of assessment, and encouraging local autonomy and innovation. Singapore is also promoting a student-centered learning environment characterized by the principle of ‘Teach Less, Learn More’ (Sahlberg, 2015).
In other countries throughout Asia, leaders are ensuring that schools limit direct instruction and the mere recitation of facts and instead look for more innovative pedagogies that encourage students to design and produce authentic products (Wagner & Dintersmith, 2016). After observing many classrooms throughout Taiwan, it became evident that lesson structure also plays an important role both during class and while a teacher prepares for a class. This idea was featured prominently in Elizabeth Green’s critically-acclaimed book Building a Better Teacher:
“One striking example was the way teachers structured their lessons. American teachers rarely talked about lesson structure – the way class proceeds from a beginning to a middle to an end – and yet, watching each individual teacher at work, Stigler felt as though they’d all read the same recipe. ‘A cultural script,’ he called it… Some American teachers called their pattern ‘I, We, You.’ The Japanese teachers, meanwhile, turned ‘I, We, You’ inside out. You might call their version ‘You, Y’all, We.’ They began not with an introduction, but a single problem that students spent ten or twenty minutes working through. Next, the teacher brought them back to the whole group, asking students to present their different ideas for how to solve the problem on the chalkboard. Give the answer and the reason for the answer. Finally, a teacher led a discussion, guiding students to a shared conclusion – What did you learn from today’s problem, or what new questions do you have, if any?”
Green, 2015
To capitalize more fully on the ideas and conceptual understanding of all students, many schools in Taiwan (and indeed throughout the world) are recognizing the importance of teaching students how to work collaboratively, to create viable arguments, and to critique the reasoning of others. In many Taiwanese classes, students are encouraged to share their personal strategy on how to solve a complex mathematics problem. This is markedly different than the majority of schools throughout the United States, where students are often drilled in a few dozen scaffolded problems over the course of a lesson. In most Taiwanese high schools, students during a single math class might complete a few rigorous problems during each period, allowing students to be able to spend more time thinking deeply about a few hard problems and to reflect critically on their solution strategy.
When Taiwanese students are solving problems in class, the types of questions that their teachers ask them are also often noticeably different than those posed by American teachers:
“In comparisons of mathematics teaching in the United States and in high-achieving countries, U.S. mathematics instructions have been characterized as rarely asking students to think and reason with or about mathematical ideas. [American] teachers sometimes perceive student frustration of lack of immediate success as indicators that they have somehow failed their students. As a result, [American math teachers] jump in to ‘rescue’ students by breaking down the task and guiding students step by step through the difficulties. Although well intentioned, such ‘rescuing’ undermines the efforts of students, lowers the cognitive demand of the task, and deprives students of opportunities to engage fully in making sense of mathematics”
National Council of Teachers of Mathematics (NCTM), 2014
In contrast, some Taiwanese teachers are moving away from rigid algorithms toward more flexible and divergent thinking. The following algebraic example highlights this trend. Consider, for a moment, the simplification of the following expression, recently given to an eighth grade class at a junior high school in Taiwan.
x*6*14*2142
Most American children would follow “PEMDAS,” the rigid algorithm commonly used for order of operations, and start by multiplying 6 times 14 times 21, and then dividing by 42 OR simplifying the 21 and the 42 to ½ first (Green, 2014). Now, take a look at what one Taiwanese eighth grader wrote on the board:
x*6*14*2142=x*2*3*14*2142=x*3*14*21*242= x*3*14*4242
Before jumping immediately into the problem, the student reflected for a short period and realized that by re-grouping the six, she could attain 42, which allowed for a more straightforward simplification. Then the student had to only multiply 3 times 14 to get the correct simplification.
x*3*14*4242=x*3*14=42x
Another example was seen during a ninth grade geometry class. After deriving the ‘interior angle’ formula of a polygon, a student worked a problem down to the following expression:
n-2* 180=360*5
Most American students would start by distributing the 180 to the parenthesis, or by simplifying 360 times five equals 1800. In contrast, consider what one Taiwanese ninth grader wrote:
n-2*180/180=360/180*5
n-2=2*5
n-2=10
n=12
Because Taiwanese students are encouraged to think divergently about algebra instead of rigidly following an algorithm, they were able to regroup certain terms and make the complex expression simpler. In many classroom observations, students were solving algebra problems using a multitude of different strategies, allowing them to think more concretely about algebra, thus increasing both their accuracy and efficiency in solving complex problems.
Another striking aspect of Taiwanese mathematics pedagogy is the ability of teachers to include multiple modalities in their instruction. The National Council of Teachers of Mathematics has insisted that “effective mathematics teaching includes a strong focus on using varied mathematical representations” (NCTM, 2014). The results of multiple studies have demonstrated that students display greater mathematical understanding and enhanced problem-solving ability when they learn to represent, discuss, and make connections among mathematical ideas in multiple forms (Fuson, Kalchman, & Bransford, 2005). Taiwanese teachers, in particular, focus their attention on providing different visual representations of abstract mathematical concepts, thus helping students to advance their understanding of them. (Arcavi, 2003).
Conclusion
This article describes but a few ideas from eastern pedagogy and policy that school districts and individual teachers throughout the United States should consider adopting. We still have a long distance to go as a global mathematics community until we reach the point where math teachers everywhere have implemented research-informed best practices that can drastically improve their students’ ability to learn. Perhaps the National Council of Teachers of Mathematics summarized best the shift taking place in the global landscape: “students must rethink what it means to be a successful learner of mathematics, and teachers must rethink what it means to be an effective teacher of mathematics” (NCTM, 2014).
Learning about the culture of education as well as math instruction in Taiwan has been a transformative learning experience of a lifetime. While some of the culture that surrounds Taiwanese education is deeply ingrained within the history of Formosa, there are many elements found in the pedagogy of Taiwanese math teachers that can be effectively incorporated into public schools throughout the United States. Now, it is up to all of us to implement these ideas and transform our schools once and for all.
Our students are counting on us; let us rise to the challenge.
Managing Editor: Carolyn Ho
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