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

Arcarvi, A. (2003). “The Role of Visual Representations in the Learning of Math” Educational Studies in Mathematics, 52, no. 3 pg. 215-241

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

Friedman, T. (2012). Pass the Books. Hold the Oil. The NY Times Retrieved March 02, 2018, from http://www.nytimes.com/2012/03/11/opinion/sunday/friedman-pass-the-books-hold-the-oil.html

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

Ministry of Education (2017). Ministry of Education Objectives for 2018 (January-December)  released 7/19/2017. Taipei, Taiwan: Ministry of Education.

Ministry of Education (2017). International Comparison of Educational Statistical Indicators. Taipei, Taiwan: Ministry of Education.

Morin, E. (1993). 複合思想導論[Complex Thought](施植明,譯)。臺北市:時報文化。

Morin, E. (1999). The Seven Complex Lessons in Education for the Future. Helsinki, Finnish: UNESCO. Qualifications and Curriculum Development Agency. National Curriculum. Retrieved from http://curriculum.qcda.gov.uk/index.aspx

NCTM (2014). Principles to Actions: Ensuring Mathematical Success For All. Reston, VA: NCTM, National Council of Teachers of Mathematics.

Sahlberg, P. (2015). Finnish Lessons 2.0: What Can the World Learn from Educational Change in Finland? New York: Teachers College, Columbia University.

Sahlberg, P. (2018). FinnishED Leadership: Four big, inexpensive ideas to transform education. Thousand Oaks, CA: Corwin.

Seoul, A. R. (2011). Teacher, Leave Those Kids Alone. Retrieved March 03, 2018, from http://content.time.com/time/magazine/article/0,9171,2094427,00.html

Turton, M. (2012). The View From Taiwan. Retrieved March 04, 2018, from http://michaelturton.blogspot.com/2012/03/friedman-on-taiwan.html

U.S. Congress, Office of Technology Assessment (1992). Testing in American Schools: Asking the Right Questions, OTA-SET-519. Washington, DC: U.S. Government Printing Office

Wagner, T., & Dintersmith, T. (2016). Most Likely to Succeed: Preparing Our Kids for the Innovation Era. New York, NY: Scribner.

Williams, C. (2017). Teaching English in East Asia: A Teachers Guide to Chinese, Japanese, and Korean Learners. Singapore: Springer imprint is published by Springer Nature.

Zakaria, F. (2012). When Will We Learn. Retrieved March 07, 2018, from https://fareedzakaria.com/2011/11/28/when-will-we-learn/

Zhao, Y. (2014). Who’s Afraid of the Big Bad Dragon?: Why China has the Best (and Worst) Education System in the World. San Francisco, CA: Jossey-Bass.

The Shifting Landscape of Math Education in Taiwan

With a traditional culture that has generally emphasized standardized testing and the Confucian ‘sage on a stage’ model of instruction, there is a lot of controversy regarding Taiwanese education reform. In fact, “the fundamental purpose of education has long been debated in Taiwan. 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 education reform in Taiwan started during the late 1980’s, when a team led by Dr. Fou-Lai Lin “gradually began to investigate mathematics teaching through research and literature studies instead of only through their own experience. As a product of these occurrences, mathematics teacher education in Taiwan moved towards a new realm, combining practical experience with mathematics education research” (Hsieh et. al., 2009). In 1996, “in-service and pre-service math teachers throughout Taiwan began to deeply consider the way students think, shifting the view towards teaching from teacher-centered to student- oriented” (Hsieh et. al., 2009). The following year, the Ministry of Education implemented a new national curriculum for junior high school students. Many of these changes “centered on students; the links between mathematics and life; the cultivation of students’ creativity, thinking, as well as reasoning abilities; and on an active attitude towards learning mathematics and appreciating mathematics (Hsieh, 1997).” The intent of these reforms “means that in mathematics education the emphasis will shift to problem-solving and process-monitoring and away from memorizing and plugging into formulas. Problem solving through which one can learn the methods of acquiring knowledge is one aspect of mathematics education that has been more or less neglected in Taiwan, but is now gaining attention alongside the emphasis on mathematics education for lifelong learning” (Hoyles, Morgan, & Woodhouse, 1999).

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Liu Mong-chi presenting a session on how to design questions that test students’ core competence: “If the only metric we use to determine the effectiveness of our education system is PISA, we will not have an effective education system.”

In modern-day Taiwan, the Ministry of Education is currently piloting a new national curriculum that will be rolled out during the 2019-2020 school year. One of the Ministry’s noted goals is to “progressively implement the 12-Year Basic Education program, incorporating development of adaptive learning and completely non-exam-based secondary school admission” (Ministry of Education, 2017). Policy makers are are planning to adapt the Taiwanese curricula to encourage creative problem solving (Hoyles, Morgan, & Woodhouse, 1999). The Ministry has also put forward that “teachers are required to pay closer attention to the learning process and children’s conceptualization of content and ideas rather than focusing on simply attaining the correct answer” (Eisenhart, 2011). These proposed reforms look to address the pitfalls of  current educational practice and intends to inspire students to collaborate through project-based learning and standard-based grading. During one interview, a teacher noted how these changes will take the future generation of Taiwanese students onto a positive new path that will prepare them for the adaptive challenges of our increasingly globalized world.

As the vision of Taiwan’s new 12-year basic education program is developed, its ideas of “spontaneity, interaction, and common good” are synthesized with reference to the educational ideas of John Dewey (1938), postmodernism, and complex thought (Morin, 1999; 1993). These instructional shifts encourage Taiwanese teachers to let students drive their learning and 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 changes are not unique to Taiwan, either: “China, the leading economic competitor of the United States, is decentralizing its curriculum, diversifying assessment, and encouraging local autonomy and innovation. Meanwhile… Singapore is promoting a creative environment characterized by ‘Teach Less, Learn More’” (Finnish Lessons 2.0). In other Asian countries, schools “are limiting direct instruction and mere recitation of facts and looking for more innovative pedagogies and encourage students to design and make things” (Wagner & Dintersmith, 2016). When observing classrooms throughout Taiwan, it is apparent that lesson structure plays an important role both during class and when a teacher is preparing for a lesson. 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 fully capitalize on harnessing student’s own ideas and conceptions, many schools in Taiwan (and throughout the world) are recognizing the importance of teaching students how to work collaboratively, create viable arguments, and critique the reasoning of others. Student voice is featured prominently within many Taiwanese math classes, often for students to share their strategy on how to solve a complex problem. Unlike in the U.S., most Taiwanese high school math classes only complete a few rigorous problems during each period, as opposed to drilling a few dozen scaffolded problems over the trajectory of a lesson. This means that students spend more time thinking deeply about a few hard problems, which enables them to reflect critically about their solution strategy. When students are solving these problems, the types of questions that Taiwanese teachers ask their students are noticeably different than the types of questions often 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).

To this end, some Taiwanese teachers are moving away from rigid algebraic algorithms to flexible divergent thinking. For an algebraic example that highlights this phenomenon, consider the simplification of the following expression, which was recently given to an 8th grade class at a junior high school in Taiwan. How would most American students go about simplifying such an expression?

Screen Shot 2018-04-28 at 2.43.47 PM

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. Look instead what one Taiwanese 8th grader wrote on the board:

Screen Shot 2018-04-28 at 2.44.15 PM

Before jumping immediately into the problem, the student reflects for a second and sees that by re-grouping the six, she can attain 42, which allows for a more straight forward simplification. The student then had to only multiply 3 times 14 to get the correct answer.

Screen Shot 2018-04-28 at 2.44.24 PM

Another example was seen during a 9thgrade geometry class. After deriving the ‘interior angle’ formula of a polygon, a student worked a problem down to the following expression:

Screen Shot 2018-04-28 at 2.44.32 PM

Again, most American students would start by distributing the 180 to the parenthesis, or by simplifying 360 times five equals 1800. Instead, consider what one Taiwanese 9th grader wrote:

Screen Shot 2018-04-28 at 2.44.39 PM

Because Taiwanese students were encouraged to think divergently about the algebra at hand instead of rigidly following an algorithm, the students could regroup certain terms to make the complex expression simpler. In many classroom observations, different students were solving algebra using a multitude of different strategies, allowing them to think more concretely about the algebra and open up the world of mathematics.

Another exemplar aspect of Taiwanese math pedagogy is how teachers prominently feature multiple modalities in their pedagogy, as well. The National Council of Teachers of Mathematics has put forward that “effective mathematics teaching includes a strong focus on using varied mathematical representations” (NCTM, 2014). In fact, multiple studies have found that “when students learn to represent, discuss, and make connections among mathematical ideas in multiple forms, they demonstrate deeper mathematical understanding and enhanced problem-solving abilities” (Fuson, Kalchman, and Bransford, 2005). Taiwanese teachers in particular focus heavily on different visual representations of abstract mathematics, which help students “advance their understanding of mathematical concepts and procedures” (Arcavi, 2003).

Creating arguments and critiquing the reasoning of others, on the other hand, is a pedagogical shift that Taiwanese teachers are struggling to implement. In one classroom observation, a teacher in Kinmen repeatedly told students that, “we cannot work independently anymore; we need to work with others and learn to cooperate more.” Although this teacher had strong messaging, they struggled to give students concrete strategies to help facilitate meaningful groupwork.

During another school visit, several educators in Kaohsiung have asked how teachers in the United States facilitate rigorous discussions and Socratic seminars with their students. In Newark, the Office of Mathematics argues that “mathematical discourse should be well-planned, intentional, and embedded in whole-class and small-group settings.” Classroom discussion is one of the most important levers in student success: when educators “decrease the teacher talk and increase the student talk by providing them with learning intentions and success criteria, and a deeper understanding of how to have a discussion with the class” (DeWitt, 2017). In fact, “students who learn to articulate and justify their own mathematical ideas, reason through their own and others’ mathematical explanations, and provide a rationale for their answers develop a deep understanding that is critical to their future success in mathematics and related field” (Michaels, O’Connor, and Resnick, 2007). These shifts are most profound when teachers view themselves as a facilitator of knowledge instead of a giver of knowledge, a shift that will be enduring for many teachers (NCTM, 2014). In a country with a strong culture that has many roots in Confucianism, this instructional shift will inevitably take time to fully implement.

While these are just some of the pedagogies that Taiwanese math teachers use throughout their practice, we still have a far way to go as a global math community until every school has implemented research-informed best practices that will help students learn better. Perhaps NCTM summated this global shifting landscape most succinctly: in math classes in 2018, “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). Let us now resolve to work relentlessly to achieve this end and share the innate beauty of mathematics with everyone.

 

Works Cited

Arcarvi, A. (2003) “The Role of Visual Representations in the Learning of Math” Educational Studies in Mathematics, 52, no. 3 pg. 215-241

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

DeWitt, P. (2017). 3 ‘Simple’ Ideas Every Educator Should Work on in 2017. Retrieved from http://wps.greenwichcsd.org/superintendent/2017/01/06/3-simple-ideas-every-educator-should-work-on-in-2017/

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/

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.

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.

Michaels, S., O’Connor, C., & Resnick, L. (2007). Deliberative Discourse Idealized and Realized: Accountable Talk in the Classroom and in Civic Life. Studies in Philosophy and Education, 27(4), 283-297. doi:10.1007/s11217-007-9071-1

Ministry of Education (2017). Ministry of Education Objectives for 2018 (January-December)  released 7/19/2017. Taipei, Taiwan: Ministry of Education.

Morin, E. (1999). The Seven Complex Lessons in Education for the Future. Helsinki, Finnish: UNESCO. Qualifications and Curriculum Development Agency. (n.d.). National Curriculum. Retrieved from http://curriculum.qcda.gov.uk/index.aspx

Morin, E. (1993). 複合思想導論[Complex Thought](施植明,譯)。臺北市:時報文化。

NCTM (2014) Principles to Actions: Ensuring Mathematical Success For All. Reston, VA: NCTM, National Council of Teachers of Mathematics.

Sahlberg, P. (2018). FinnishED Leadership: Four big, inexpensive ideas to transform education. Thousand Oaks, CA: Corwin.

Wagner, T., & Dintersmith, T. (2016). Most Likely to Succeed: Preparing Our Kids for the Innovation Era. New York, NY: Scribner.

Why Taiwan? (Part 2: A Cultural Perspective)

“There are these two young fish swimming along, and they happen to meet an older fish swimming the other way, who nods at them and says, ‘Morning, boys, how’s the water?’ And the two young fish swim on for a bit, and then eventually one of them looks over at the other and goes, ‘What the hell is water?’” -David Foster Wallace, This is Water

At the end of World War II, many world leaders realized that they needed to take steps to prevent another great war from ever happening again. One of these people, Senator J. William Fulbright, set an ambitious goal: he believed that if potential leaders could learn about one another’s cultures and build strong relationships with people abroad, they would be less likely to support future wars against those countries.

To achieve this end, Senator Fulbright introduced a bill in 1945 that called for the “use of surplus war property to fund the promotion of international good will through the exchange of students in the fields of education, culture, and science.” On August 1, 1946, President Harry S. Truman signed the bill into law, and officially created the Fulbright Program, the flagship international educational exchange program sponsored by the U.S. Government.

While I have long considered applying to the Fulbright Program, teaching a diverse population of students in an urban public school for the last several years has truly piqued my interest in learning about different cultures. Having previously had the opportunity to travel abroad, I have come to realize that my interest in visiting different countries centered on much more than tourism: I wanted to meet the people of other countries and come to genuinely understand their customs and way of life.

In the course of traveling, I have come to realize that you never really know where life will take you. I remember the friendliness of Patagonia’s indigenous people on my journey throughout South America and can recall the great conversations I had over dinner with locals while in Portugal two summers ago. When traveling through Havana last year, I listened to dozens of Cubans share their affection for the American people while at the same time respectfully disagreeing with U.S. government policy, particularly the failed embargo. I also have fond memories of my last night in Madrid, when six people from six different countries communicated using their newly acquired Spanish.

It is through these experiences that I have come to appreciate more fully the power of diversity. I also believe that traveling is one of the best ways to get to know the world, and perhaps more importantly, to get to know yourself. There is something about the serenity of traveling alone and the personal growth that comes about because of it that helps you look at life through a completely different lens.

Although I have been incredibly privileged my entire life, and have had multiple opportunities to travel throughout the America’s and Europe, I have never visited Asia before this trip. In applying for a Fulbright, I looked to study in a country whose customs are completely different from those with which I was familiar, a place that I ordinarily would not have thought to visit. I wanted to get to know the culture of a place to which few Americans have traveled to and come to appreciate the subtle nuances that make eastern culture so special.

As such, I was excited to see Taiwan, the Republic of China, on the list of Participating Territories for the 2017-2018 Fulbright ‘Distinguished Awards in Teaching’ Program. I was equally thrilled last April, when I received an e-mail letting me know that I will officially be spending 2018 abroad in Kaohsiung City, Taiwan. Once abroad, I will be hosted as a visiting scholar at National Kaohsiung Normal University in Kaohsiung City, the third largest city in Taiwan.

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Kaohsiung City at night

I am looking forward to conducting research and living in Taiwan, a country with a fascinating history. An island nation of 23.4 million people, its sovereignty has been hotly contested for over 500 years. After claiming Taiwan in 1895, the Japanese granted the land back to the Republic of China after being defeated in World War II. However, when Mao Zedong assumed power over the Chinese mainland in 1949 and renamed it the People’s Republic of China, the deposed government established a new seat of power in Taiwan. Currently, the mainland People’s Republic of China claims sovereignty over Taiwan, while Taiwan claims sovereignty over the entire mainland as the original Republic of China. Most international organizations, including the United States, do not recognize Taiwan as a sovereign state.

Although a founding member, Taiwan is currently the most populous state and largest economy that is not a member of the United Nations. Taiwan’s government represented the entirety of China until 1971, when the People’s Republic of China assumed China’s seat. Geographically, Taiwan is a few hundred miles to the east of Hong Kong, and is roughly twice the size of New Jersey (and with 23 million people, has almost triple NJ’s population).

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New Jersey overlaid on top of Taiwan for comparison

I also look forward to experiencing Taiwan’s universal healthcare system first-hand after having read so much about it over the course of the last several years. Other interesting facts about Taiwan: the country competes in international competitions as Chinese Taipei, was the first democratic country in Asia, and was nicknamed Ilha Formosa (Beautiful Island) by Portuguese explorers passing by the island en route to Macau as early as the 16th century.

As we move forward in a world that is increasingly changing and globally connected, the essential role each of us must play in fostering cross-cultural exchange becomes more apparent. For how else will we achieve a better tomorrow? If we can learn to listen attentively to one another, appreciate the wealth to be found in diverse cultures, and develop a stronger sense of the many different lenses through which one can view life—what Senator Fulbright referred to as “mutual understanding”—we might just start to care for one another in unprecedented ways. My only hope is that I can help contribute to Fulbright’s vision of creating a world with a little more knowledge and a little less conflict.

Perhaps David Foster Wallace said it best: “It is about simple awareness — awareness of what is so real and essential, so hidden in plain sight all around us, that we have to keep reminding ourselves, over and over: This is water, this is water.” Maybe in Taiwan, I will actually be able to see the water once and for all.

 

This post is the second in a two-part series that attempts to answer the question, “Why Taiwan?” The first essay, focused on an educational perspective, can be found here.

Why Taiwan? (Part 1: An Educational Perspective)

I was born to be a teacher. For as far back as I can remember, I have always loved school and valued education as one of life’s most valued treasures. While I have always had a passion for education, teaching has lit a fire in me; I truly feel alive when leading instruction in front of a classroom. Though I love what I do, I take my role as an educator seriously, as I fundamentally believe that we are teaching the future leaders of our world. As it has been said, we are currently preparing students for jobs that do not yet exist, using technologies that have not yet been invented, to solve a wide variety of complex problems.

During the 21st century, our international community will need to respond to these critical global issues, including food security, public health (and the so-called “death gap”), and world peace. To solve these obstacles, we will need a new generation of creative leaders: people who appreciate diversity, can think ethically, strategically, and divergently, and refuse to be satisfied with the status quo.

To create these transformational leaders, we arguably need an education revolution in this country. The achievement data is clear: a significant opportunity gap exists between middle- and upper-class students and those living in poverty. As our schools slowly become re-segregated, many of our most vulnerable communities are being left behind (Frankenberg, Lee, and Orfield 2003; Orfield, Kucsera, and Siegel-Hawley 2012). Although we have made some progress over the years, I must ask: how can we live in the richest country in the world and continue to allow the opportunity gap to be so wide?

Over the past six years, I have had the absolute privilege of serving the students and families of the Newark Public Schools. During this time, I have learned so much about the unique challenges facing urban communities and the incredible resolve of Newarkers fighting for a better tomorrow. Between the city’s inspirational residents, delectable cuisine, and exceptional transportation options, Newark has genuinely become one of my favorite places in the world. As it has been said, Newark, like ancient Rome, is “a living reminder of a glorious past, a predictor of a possible future, and a lesson in the persistence of the individual and of the human spirit.”

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Newark, affectionately known as the “Brick City,” at dusk.

While I have a deep admiration for the “Brick City” and the people that live there, I have also witnessed first-hand the educational inequality that has plagued our country for decades. I have previously written about the unacceptable transportation issues within our district bureaucracy, but busing logistics is just the tip of the iceberg. Last week, the Baltimore City Public Schools made national headlines when the press learned that some of their schools had broken heating systems and children needed to wear their jackets to  class. Year after year, I have watched students fight an uphill battle within a system that, arguably, was not designed with their success in mind. If I have learned nothing else over the course of the last six years, it is that we have a long way to go until every young person has the opportunity to attend a great public school.

To re-think education in the United States, we need to look critically at a number of issues both within and outside our current system. While we still have a great deal to learn from ideas, research, and innovation carried out from universities, think-tanks, and scholars in the states, there are also many creative developments underway in schools throughout the world. Over the course of the past decade, Finland’s unique educational philosophy has become a worldwide sensation. Although Finland has plenty of progressive schools, efforts to replicate their instruction model has had its fair share of challenges, and students living in Asia perform better in higher-level mathematics, especially in Taiwan, Japan, Singapore, and South Korea. U.S educators and policy makers alike have only recently begun looking towards the far east in search of best practices beyond the primary school level. Though several white papers, policy positions, and research projects have tried to expand this effort to high school mathematics instruction, little success has been realized.

Taiwan leads the world in mathematical performance among all students in their country. The results of the Programme for International Student Assessment, colloquially known as the PISA, are clear: for the most recent year in which data is available, Taiwan was ranked as the 4th best country in the world for mathematical performance. The United States finished 36th.  The OECD (who organize the PISA) also uses a so-called “snapshot of equity in education” to determine how equitable the education system is in any given country. In this category, the U.S. currently ranks 25th, while Taiwan ranks 4th. It is worth noting that the Republic of China’s success in education stretches beyond the area of mathematics, as Taiwan currently ranks 8th internationally in reading comprehension and 13th in science, too.

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Using another standardized metric, the Trends in International Mathematics and Science Study (TIMSS), eighth graders in Taiwan ranked 2nd internationally in science and 3rd in mathematics. Taiwanese students also achieved outstanding results in the International Mathematics and Science Olympiad. The Ministry of Education also has a plethora of current initiatives that are aimed at increasing creativity through art and music programs. If you put any faith in these standardized metrics (which, to be fair, are inherently controversial), it is clear that Taiwan is doing something special when it comes to educating its youth.

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During my time abroad, I will have the opportunity to observe hundreds of educators teaching at dozens of schools, learn more about their pedagogical approach, and work to apply as much of it as possible to my work with under-resourced students back home. Although a few ideas in this area have emerged from Japan and Singapore, the approach taken in Taiwan has received little public exposure despite the tremendous success on international benchmarks. This Fulbright project looks to change this paradigm once and for all.

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Stock photo of Taipei, the capital city of Taiwan.

As we look forward towards an ever-changing global economy, we as educators need to do a better collective job preparing our students for the complex world in which they will live and work. Commenting on the results of the 2015 PISA, the report’s authors noted that, “while changing how teachers teach is challenging, school leaders and governments should try to find ways to make teaching more effective.” Perhaps I am hopelessly optimistic, but I do believe success is possible.

I have worked hard the last six years to ensure that all of the students whom I taught received a great education, but I must confess that I have learned far more from my students over the years than I have ever taught them. While I am truly excited for the year of personal and professional growth that lies ahead, I also want to ensure that my time abroad actually makes a difference for our most vulnerable students. I hope that my studies in Taiwan can be part of the revolution that is committed to giving all students the chance to attain a truly excellent education.

 

This post is the first in a two-part series that attempts to answer the question, “Why Taiwan?” The second essay, focused on a “cultural perspective,” will be posted next week.

 

Fulbright Orientation

“I am at a particular point on my journey. I have no clue if anything I think is right, but it’s the truest answers I have found thus far” –Tom Rademacher, It Won’t Be Easy

Fulbright swag!

I started to write this post on the Amtrak down to Washington, D.C. As I sat on the train, I could not help but be contemplative about the next major step in my life while simultaneously being reflective of the incredible journey thus far. This Fulbright orientation has been over a year in the making – I applied almost a year ago today, and found out that I was accepted into the program in April. As I read through the list of Fulbright grantee’s from around the world and their inquiry project proposals, I became increasingly excited to meet some of the best educators our world has to offer.

The orientation itself was genuinely one of the most inspirational weeks of my life. I was able to network with teachers from Morocco, principals from India, and counselors from New Zealand. It was surreal having the opportunity to discuss educational policy with teachers from Finland, talk about math pedagogy with educators from Singapore, and learn about the unique challenges of education in Botswana first-hand. And it turns out that I am officially the youngest member of this year’s cohort, too…

Sitting with educators from Singapore & Taiwan during the opening reception

During the orientation, we learned about intercultural discovery, communicating across cultures, and the extensive logistics of the program. Senator J. William Fulbright, who sponsored the landmark legislation that later became known as the Fulbright Program in 1946, had this vision that if we knew people from other countries, we would be less likely to go to war with those countries. In 2017, we are constantly confronted with serious and legitimate challenges in the modern world. I am of the belief that no one country can solve these issues alone; people from around the world must come together to solve increasingly complex problems such as climate change, global poverty, or even violent extremism.

Listening to Anthony Koliha, Director of Global Education at the U.S. Department of State

I am beyond excited about spending 2018 abroad in Kaohsiung, Taiwan. As I alluded to in an earlier post, once I arrive in Taiwan, I will be researching eastern pedagogical approaches at National Kaohsiung Normal University, and consider how to implement best practices in sustainable and culturally responsible ways. During the orientation, I was able to spend a lot of time with Michelle Nien-Ching Chuang, a Fulbright Teacher from Taiwan that is studying the American education system at Indiana University this fall. She taught me all of the ins- and outs- of the Taiwanese education system, the delicate challenges facing students in Taiwan, and how to pronounce Kaohsiung correctly (it is pronounced “gow – shuung” and is written in Mandarin as 高雄).

Skyping with Michelle and Jessica

Although I have had the opportunity to travel abroad many times in my life, I have never spent more than a month overseas. It will be hard saying goodbye to many people, but I am definitely looking forward to the extended time away from everyone that I know and away from western culture, too. I also wonder if I will experience culture shock, and, if so, to what extent. The Fulbright commission did a really great job explaining the various stages of culture shock that most people go through when they are abroad, including the “honeymoon” stage, initial culture shock, adjustment, adaptation, and re-entry shock.This week-long orientation was unequivocally the marquee event of my summer, which has truly been special. This has also been the first summer in which I have not had any graduate studies to worry about, meaning that I have had a significant amount of down time to recharge and reflect about life. I have been fortunate to have the time to read a plethora of books and spend a lot of time out on the golf course, too. I have also spent a considerable amount of time working as a teacher coach and educational consultant, which has been an incredible learning experience. I have spent a majority of my time this summer leading professional development and coaching teachers in the Philadelphia Schools, the Newark Public Schools, and the NYC Department of Education. In NYC, I was excited to help support the mayor’s “Excellence for All” Initiative, specifically in the DOE’s Algebra for All program throughout the city. My experience varied daily, as did the teacher quality from school to school. It is one thing to talk about educational policy on the 30,000 feet level, and another altogether to actually see the achievement gap being closed or expanded depending on which school I was at.

Some of the best educators our world has to offer. It truly was a pleasure working with them!

Just last week, I was honored to be featured on the closing panel of the annual conference of CMSM in Scottsdale, Arizona, which explored the future of religious life in this country. The panel, moderated by my friend and mentor Marist Brother Seán Sammon, explored what the leaders of religious congregations across the country need to better connect with the next generation. I lead a provocative discussion about the need for an inclusive church that truly looks out for the most vulnerable and those on the margins on society. I look towards the leadership of people like Cardinal Joe Tobin, who strives to build bridges, not walls.

 

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During the closing session at CMSM with Brother Seán, Ryan, and Duffy.

Anyone that remotely knows me understands just how much I love teaching, which I personally consider a vocation that means infinitely more to me than just a job. For me, there is no greater feeling than standing in front of a classroom of our future leaders, or helping a student learn something they previously thought they never could. I love serving the students and families of Newark, NJ, and know that I will miss them immensely when I travel abroad in less than five months. Many people have asked me what will I do when I return, but I am not sure yet. The State of New Jersey issued my principal certification a few weeks ago, but I honestly do not know where I will find myself when I return stateside at the end of next summer. As it could be said, I am at a particular point on my journey. I have no clue if anything I think is right, but it’s the truest answers I have found thus far.