Implementing Eastern Pedagogical Approaches to Teaching Mathematics in Urban High Schools

Note: This article was submitted to the Fulbright Taiwan Annual Research Journal. 

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Leading a presentation about Taiwanese education in Taipei

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 $1,000 bill, for example, we find a group of children gathered around a globe. This phenomenon is not surprising, as Taiwanese citizens vehemently believe in the innate power of public education (Hsiao & Po-Hsuan, 2018). This rich culture and deep respect for learning dates back centuries to the time of Confucius, 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 eventually gave birth to the idea of meritocracy, a core value in many eastern countries (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. Young 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 truck 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, China’s last imperial dynasty, 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.

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Leading a math class in Kaohsiung

The Taiwanese system of education

While standardized testing is deeply engrained 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 a teacher believes that their students can do better, they will; if a teacher gives up on their students easily, then their students will give up, too.

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 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, P., Miller, A., & Auguste, B., 2010).

After a number of school observations throughout Taiwan, it has also been noted that, though the typical teacher in that country is present at school for more than 10 hours each day, he or she rarely instructs for more than three to four hours. 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 act as 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 educational system includes more thangovernment-run schools; it also encompasses a gigantic range of cram schools. However, it is virtually impossible to find stories in the mainstream media about east Asian education today that boldly confronts 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).

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Talking about Newark at a vocational school in Tainan

Education reform

Today, considerable controversy exists with regards to 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 focuseson the whole child” (Eisenhart, 2011).

Contemporary educational reform in Taiwan commenced during the late 1980s when a team led by Dr. Fou-Lai Lin decided to investigate the teaching of mathematics; they reviewed the literature and relied on research methodology rather than solely their own experience. As a result, mathematics teacher education 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 centered on students and the cultivation of their creativity, thinking, and reasoning abilities, as well as the links that existed 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. Problem solving, through which one learns methods for acquiring knowledge, had historically been largely neglected in Taiwan. Now, 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 math 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 a12-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 focusing 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. 

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Leading a Public Speaking class in Kaohsiung

Next steps

As the guiding vision of Taiwan’s new 12-year basic education program is further developed, the principles of “spontaneity, interaction, [and] the common good” that it promotes will be integrated increasingly with the educational ideas of John Dewey’s (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. 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 around 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). During many classroom observations throughout Taiwan, it is apparent 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 a number of Taiwanese math classes, students are encouraged to share their personal strategy on how to solve a complex problem. This is markedly different than some schools in the U.S, 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 has 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” (NCTM, 2014).

In contrast, some Taiwanese teachers are moving away from rigid algorithms toward more flexible and divergent thinking. 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 math 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, and 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). 

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With high school students after a focus group in Taichung.

Conclusion

This article describes but a few of the pedagogies used by Taiwanese math teachers as they practice their craft. We still have a long distance to go as a global math 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 NCTM 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” (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 this incredible country, 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 best practices and transform our education system once and for all.

After all, our students are counting on us.

Let us rise to the challenge.

 

Works Cited

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Dewey, J. (1938). Experience and Education.NY, New York: Kappa Delta Pi.

Eisenhart, C. (2011). Why do Taiwanese Children Excel at Math?. The Phi Delta Kappan. Retrieved from http://www.academia.edu/987689/Why_do_Taiwanese_Children_Excel_at_Math

Fan, H. C. (2016). Education in Taiwan: The Vision and Goals of the 12-Year Curriculum.Retrieved from https://www.brookings.edu/opinions/education-in-taiwan-the-vision-and-goals-of-the-12-year-curriculum/

Fenton, S. (2015). President Obama praises South Korea for paying teachers as much as doctors. The Independent. Retrieved March 08, 2018, from http://www.independent.co.uk/news/world/asia/president-obama-praises-south-korea-for-paying-teachers-as-much-as-doctors-10398802.html

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Fuson, K., Kalchman, M., and Bransford, J. (2005). “Mathematical Understanding: an Introduction” in How Students Learn History, Mathematics and Science in the Classroom., edited by Donovan, S., & Bransford, J. Washington, D.C.: National Academies Press.

Gove, M. (2012). Classroom Crush. The EconomistRetrieved March 07, 2018, from https://www.economist.com/node/21547854

Green, E. (2014). Why Do Americans Stink at Math? The NY Times. Retrieved February 14, 2018, from https://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html

Green, E. (2015). Building a Better Teacher: How Teaching Works (and how to teach it to everyone).New York ; London: Norton et Company.

Hoyles, C., Morgan, C., & Woodhouse, G. (1999). Rethinking the Mathematics Curriculum. doi:10.4324/9780203234730

Hsieh, F.-J. (1997). 國中數學新課程精神與特色. [The essence and features of new mathematics curriculum in junior high school]. Science Education Monthly, 197, 45-55.

Hsieh, F.-J., Lin, P.-J., Chao, G., & Wang, T.-Y. (2009).
Policy and Practice of Mathematics Teacher Education in Taiwan.

Hsiao S., & Po-Hsuan W. (2018). Mandatory Education for Five-year-olds is Popular. The Taipei Times. March 19, 2018 Print Edition: Volume 19, Number 27.

Huang, Y.-J. (2003). 臺灣地區新職業聲望與社經地位量表」之建構與評估:社會科學與教育社會學研究本土化. [The construction and assessment of the “new occupational prestige and social for Taiwan”: The indigenization of the social science and sociology of education research], Bulletin of Educational Research Vol.49(4). 1-31.

Kihn, P., Miller, A., & Auguste, B. (2010). Closing the Teaching Talent Gap. McKinsey & Company. Retrieved March 06, 2018, from https://www.mckinsey.com/industries/social-sector/our-insights/closing-the-teaching-talent-gap

Kristof, N. (2011). Pay Teachers More. The NY Times Retrieved March 07, 2018, from http://www.nytimes.com/2011/03/13/opinion/13kristof.html?_r=0

Liu, K. (2013). Critical reflection as a framework for transformative learning in teacher education. Educational Review, 67(2), 135-157. doi:10.1080/00131911.2013.839546

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Can We At Least Get The Transportation Right?

The landmark court case of the 20th century, Brown v. Board of Education of Topeka [347 U.S. 483 (1954)], famously ruled that the “separate but equal” clause (originally established in Plessy v. Ferguson [163 US 537 (1896)]) was void. In the unanimous 9-0 decision, Chief Justice Earl Warren authored the opinion of the court, including the notable phrase, “separate educational facilities are inherently unequal,” making school segregation unconstitutional under the 14th amendment of the United States Constitution.

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Whereas most are aware that the Supreme Court took the case on appeal from the United States District Court for the State of Kansas, some are surprised to hear that the Brown case was actually a compilation of segregation cases throughout the south, including Briggs v. Elliott (filed in South Carolina), Davis v. County School Board of Prince Edward County (filed in Virginia), Gebhart v. Belton (filed in Delaware), and Bolling v. Sharpe (filed in Washington D.C.). One case in particular, Davis v. County School Board of Prince Edward County [103 F. Supp. 337 (1952)], was unique in that it was the only case born through grassroot student activism. This case was also of particular note, as it dealt with the issue of school facilities, curriculum, and busing, and argued that students from a segregated black school were not getting the same opportunities as those from the white school in the neighborhood.

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The cover of the New York Times the day after the Brown ruling

In the Brown ruling, the U.S. Supreme Court reversed the District Court’s ruling in Davis, and found, “the Negro school inferior in physical plant, curricula, and transportation, and ordered the defendants forthwith to provide substantially equal curricula and transportation and to ‘proceed with all reasonable diligence and dispatch to remove’ the inequality in physical plant.” Footnote 10 in the Brown ruling further explained that these systemic inequalities “results in the Negro children, as a class, receiving educational opportunities which are substantially inferior to those available to white children otherwise similarly situated.”

Today, I feel keenly aware of these specific words in Warren’s opinion of the court: “substantially equal transportation.” More than 60 years after the Brown decision, I ask: what constitutes “substantially equal transportation” in 2017? While our schools today may not be legally segregated (although modern scholars and trends may disagree), our schools are undoubtedly segregated by socio-economic status. In the spirit of Warren’s opinion, I argue that many of the amazing students that attend the Title I school that I teach at in Newark, objectively receive transportation that is substantially unequal to that of their peers in Millburn or Livingston.

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Our Student Council visiting Dartmouth College this past Spring

As a chaperone on Student Council trips, I have been afforded the incredible opportunity to attend many college visits over the years. Of the dozens of field trips that I have helped lead, I can count on one hand how often our bus has been punctual. Time after time after time, I find myself calling a random bus company, asking why our bus is late, and what time the bus will arrive at our school. After getting on the bus (often hours after the scheduled pick-up time), I then have to call the college we are scheduled to visit, and apologize profusely that our group is going to be two or three hours late for our appointment, which typically means less time on campus for our students (many of whom are aspiring first-generation college graduates). Even once the buses do arrive, they are often outdated, not clean, and smaller than modern buses, with unknown safety records. On one trip in 2013, the bus company “mistakenly” sent only two of the three buses back to the Museum of Natural History in New York City, forcing a group of teachers to take the subway back to Newark in order to make it possible for all our students to cram onto the other two buses.

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Our Robotics team hard at work

Our Robotics Students have also had their fair share of issues with transportation problems. One of the more infamous stories include an overnight robotics trip in 2015. During the second day of the field trip, the team was waiting for the bus at the hotel, when they found out that the engine could not start. Since the competition had strict rules and regulations, the teachers on the trip had to pay for an “Uber” out of pocket for some of the members, while the rest of the team had to wait for an airport van to cram 8 people in it. After getting the bus working again, the driver claimed he was not aware that the trip was a multi-day event, and returned to Newark during the competition without notifying any of the teachers. This meant that our entire robotics team was stranded in another city hours away from Newark with no viable transportation options. After several demanding phone calls and hours after all of the other teams went home, another bus finally showed up. The next day, on the way back to Newark, the bus could not go faster than 15 miles per hour, and ended up breaking down in the middle of the highway. The bus started smoking, and students were forced to evacuate and stand on the shoulder of a busy highway; the chaperones on the trip immediately called the police and filed a report. A few hours later, a “rescue” bus showed up, and got the students home hours after their scheduled arrival.

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Our Student Council, led by Ms. Naparano and Mrs. Wiseman, visiting TCNJ this past Monday.

As it has been said, those who do not learn from history are doomed to repeat it. This story played out yet again on our college visit to TCNJ two days ago. Our contract (see below) was approved for the bus to pick us up at 7:45am, but after twenty-three (23!!) phone calls and being disrespected and lied to over and over again, the bus finally showed up in front of our high school at 9:13am. On top of everything else, the driver had no directions to our destination. What was at one point a simple mistake that was disconcerting and frustrating, became yet another example of the perpetuation of inequality facing our most vulnerable students.

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These are just three stories regarding busing issues of literally hundreds that I could have shared that directly impact the students of the Newark Public Schools every single week. As someone who personally rode the bus to middle school daily, I can only remember one ‘freak incident’ that we had. For three full years, I took the public-school bus back and forth from school, almost always without a hitch. Truth be told, it would be forgivable if a school vehicle occasionally got a flat tire or caught in traffic. What my students contend with is not a couple of ‘freak incidents,’ but rather a broken system that clearly does not value the students of the Newark Public Schools and does not allow them access to the quality of transportation that students in more affluent areas take for granted. From my figurative seat on the bus, I am made acutely aware of the inferiority in transportation every time we have a field trip. I have tried everything at my disposal, including calling bus companies, sending e-mails, filing grievances, and even attending school board meetings; nothing seems to ever change. Perhaps it is time we finally “proceed with all reasonable diligence and dispatch to remove all inequality in transportation,” as Earl Warren put forward more than sixty years ago. In 2017, there remains a plethora of adaptive challenges and deep-seated systemic racism and inequalities that persist in our public-school system that are going to require significant resources and innovative leadership to overcome. But seriously, can we at least get the transportation right?