I am offically at the ‘T-minus one month’ mark, and I honestly cannot believe how fast this entire Fulbright experience has gone.
This past week, I had the chance to talk with Marie Royce (Assistant Secretary of State for Educational and Cultural Affairs) on the importance of soft diplomacy and how the United States needs to support the Fulbright Program now more than ever. I also had the opportunity to present my research at the Foundation for Scholarly Exchange a few weeks ago in Taipei. Below is a copy of what was printed on my poster that was created by the Fulbright Taiwan staff:
“Reflecting on hundreds of classroom observations throughout Taiwan, Paulsen will share his thoughts on the best practices of Taiwanese teaching techniques, education policy, and culture, and offer recommendations on how to implement these ideals in urban schools throughout the United States.
Andrew Paulsen is currently the Lead Math Teacher and an Instruction Coach at East Side High School, the largest comprehensive high school in Newark, New Jersey. Originally from Levittown, New York, Andrew received his B.A. from Marist College, his Master’s in educational leadership, management, & policy from Seton Hall University, and his Ed.M. in public school leadership from Columbia University’s Teachers College. He aspires to change the world, one student at a time.”
Here is a video of my final presentation:
After the presentation, I was presented a certificate from Dr. Vocke, the Director of Fulbright Taiwan.
I am officially back in Kaohsiung for my last four weeks in Taiwan. After departing from this incredible country on July 15th, I am looking forward to traveling through mainland China with my parents for a few weeks, and then coming back to the United States at the beginning of August. Here is to one more awesome month in beautiful Taiwan!
Last week, I had the absolute pleasure of visiting the city-state of Singapore, a country with a fascinating history: After being a British colony for over 100 years, the Imperial Japanese Army colonized the area in 1942 during World War II. After the emperor officially surrendered to the allied forces, Singapore was handed back over to British control, and was shortly part of the Federation of Malaya (modern-day Malaysia) before becoming an independent nation in 1965.
Japanese Commanders leaving City Hall after the signing of the Potsdam Declaration
The former site of the Singapore City Hall
In many ways, Singapore is an incredible success story, largely because their leaders put innovative policies in place that transformed their country from a so-called “third-world” country to a “first-world” country in only one generation. Singapore was able to achieve this ambitious vision by effectively and efficiently enacting a series of research-based reforms that helped Singapore develop into a true international city. The founding father and first prime minister of Singapore, Lee Kuan Yew, offered citizens of his fledging nation five core principles: democracy, justice, peace, prosperity and equality. In many ways, Singapore has lived up to these ideals, and has become a model urban utopia that celebrates cultural differences.
Today, Singapore’s education system is widely held up as one of the best in the world. During my visit to Singapore, I had the opportunity to visit three schools, attend two professional development sessions (a workshop for math teachers and a training on positive education), and speak at the annual reThinking Numeracy conference. Without trying to sound hyperbolic, the schools throughout Singapore were some of the best I have ever seen in my entire life. This video gives a fantastic overview of education in Singapore:
The Ministry of Education (MOE) has developed a school structure that is somewhat different than the United States. Across the country, public school students are broken into primary schools (grades 1-6), secondary schools (grades 7-10), and postsecondary schools (grades 11-12 at a junior college [humanities-based], polytechnic institute [STEM-based], or vocational college). During secondary school, students take a plethora of subjects, including math, science, geography, history, literature, design & technology, food & nutrition, art, music, physical education, English, and a class in their mother tongue language (Chinese, Malay, Tamil, etc.). The Ministry has “been moving in recent years towards an education system that is more flexible and diverse” in an attempt to give students a more “broad-based education to ensure their all-round or holistic development, in and out of the classroom.” Classes typically start at around 8am, and the last class ends at around 3pm, depending on the school. Once at the secondary level, students are broken down into three streams: Express, Normal Academic, and Normal Technical.
Unlike in the United States, teachers have multiple career pathways, too, including a teaching track (senior/mentor teacher, lead teacher, master teacher, principal master teacher, etc.) a leadership track (subject head, head of department, vice principal, principal, cluster superintendent, zonal superintendent, etc.), and a specialist track (curriculum writers, content specialists, etc.). In the United States, the only career “promotion” is through school leadership, a policy which often takes many of our most transformational teachers out of the classroom. It is also interesting to consider that all principals have a five to seven-year term, at which point they become a principal at another school or move up the school leadership career ladder.
The school facilities I visited were genuinely immaculate. Quite frankly, I have never seen a school in the entire world that could rival the facilities of the schools I visited in Singapore. All of the schools I visited were modern, open, and conducive to learning. One of the public schools I visited was in the process of converting their physical library to a more digital one to better “prepare for the future.” While their new library will still have books, the new space is designed to foster group work and collaboration. Similar to the process in Taiwan, the students stay in one homeroom all day and move classes for specific special classes, such as art. The homeroom teacher is also responsible for teaching the national character and citizenship education (civics) curriculum.
Visiting different classrooms was also very special. In every math class that I went to, I observed engaged students that were doing all the heavy lifting and working collaboratively to solve the task at hand. When walking around during one lesson, I noticed one group was particularly struggling with the assignment. I went over to their group and asked them what they thought of math class. Without hesitation, one boy said, “math class is ok, I guess, but I struggle. But that is ok, because I am just going to work harder to get better!” It was clear that public school teachers here have worked hard to implement a true growth mindset in their students.
In Singapore, the students and teachers eat lunch together, which is a great way to build community throughout the school. Teachers also eat the same lunch as the students do (which was absolutely delicious, for the record). After our meal, I had the chance to talk with a couple of teachers and students about their experiences in Singaporean schools. For the first time in my life, everyone at this public school had a positive view of the education system. One teacher was particularly inspiring and talked about how we are shifting towards phenomenon-based learning throughout the world. He said: “I think we are shifting that globally… in the United States, the students are talking less and the teachers are talking more. It is so refreshing, because we actually get to hear what the students are thinking. [By letting students work collaboratively], they also have the opportunity to learn from one another.”
In the afternoon, I had the opportunity to talk with the Math Department Head at the public school I visited. When asked about his vision for an ideal math class, he said that a lesson needs to be motivating, and start off with a strong hook. He continued on, saying that “students must be willing to make mistakes; the more mistakes they make, the better, because that means we have more to learn. Math is not about drill and kill, it is about learning for life. [Math] needs to have meaning. Math is about conversations. We need to speak, and agree or disagree, and to listen and learn from one another.” So inspiring!!
There were also a couple of specific math pedagogies that I learned during my trip to Singapore. When going over a test, the students do all of the heavy lifting, and are often given copes of answers by their peers that are not quite correct, yet. The students then go through a protocol (called UCAP) where the students need to find the mistake, and then identify whether the mistake is an understanding (blank, halfway, etc.), conceptual (wrong method/formula), arithmetic/algebra (procedural mistake), or a protocol (Units, significant figures, presentation, etc.) error. The students then need to correct the wrong answers in groups.
In Singapore, some schools use an interesting stoplight system so that teachers know how students are perceiving the lesson in real time. Each student has a red, yellow, and green card on their desk, resembling a traffic light. All of the students start the lesson with the green card showing and flip their card to yellow or red as the lesson progresses so that every student can discretely communicate with the teacher their level of understanding (Green = understands everything; Yellow = a little confused; Red = completely lost with today’s lesson). There are also protocols (RRRAW) for critiquing the reasoning of others, which includes revising (student A said…), repeating: (saying it in your own words), reasoning (why do they said that?), adding on (students add their own opinions), and wait time (every time you ask a question, you need to wait at least 3-7 seconds). While there are many other things that can be learned from observing schools throughout Singapore, these are just a sampling of the high-impact strategies that educators can implement in their classes tomorrow to increase their teaching toolbox.
I was also graciously invited to attend a professional development session designed for Singaporean teachers. The session was on modeling real life problem situations mathematically. We started the session off by describing the need for research-infused pedagogies and set learning intentions and success criteria for mathematical modeling learning experiences. The facilitator talked about why modeling tasks were so important, as our students are living in a world where disruptive technologies are transforming our global economy. Perhaps most humbling was how open the Singaporean teachers were to new ideas and to bettering their craft. At one point, the facilitator asked how many in the room think they could run a vertical marathon, and proudly proclaimed: “for those that raised your hand, you can.” In Singapore, they truly practice what they preach.
I was also legitimately blown away by the focus on civics and positive education. At every secondary school in Singapore, there is a dedicated career and education counselor that is tasked with helping students prepare for the next step in their learning journey. One Singaporean teacher told me that “all students have the opportunity to be great, but they shouldn’t compare themselves to one another. The most important thing is improving against your previous score. There is always room for improvement!” Inspired by the innate sense of a growth mindset, I attended a positive education training that was very informative. Simply put, the facilitator started the session by declaring that if we are serious about wanting our students to flourish, wemust put wellbeing at the heart of education. She defined flourishing as the combination of doing good and feeling good, and offered the following framework to transform our schools:
I fundamentally believe in this vision of positive education and need to do more reflecting and thinking about how we can systematically implement these best practices back home in the states (more information about positive education will be shared in a future blog post on democratizing our classrooms). The next day, I attended the reThinking Numeracy Conference, which was headlined by Melissa Daniels and Steve Leinwand. Melissa Daniels is currently the principal of one of the High Tech High schools, a charter network in San Diego, California that has gained national attention lately for their innovative work in putting PBL at the heart of their school model. She started by asking a provocative question: When was the last time you really learned something? After reflecting individually for a few minutes, a few people shared their thoughts, and she noted how no one said anything about sitting in a lecture. She went through the learning environment educators need to setup to create meaningful learning experiences for every child.
Steve Leinwand was also very informative. As a senior education researcher, consultant, and lead writer of NCTM’s landmark publication Principles to Action, I knew I had a unique opportunity to learn from one of the true experts in the field. Steve offered ways to make math accessible to all students, including asking alternate applications, giving the correct answer and asking why it is correct, encouraging student discourse, utilizing more multiple representations, adding relevant context to the material at hand, embedding more literacy skills throughout a lesson, and constantly asking students to ‘convince me.’ Perhaps math teachers should be more like English teachers and adapt what the text bestows by turning exercises into more opportunities for learning. He also suggested that “instead of bombarding students with the whole word problem, the entire graph or figure or table, use the power of PowerPoint to gradually release or reveal the problem, graph, figure, etc. using questions to probe understanding of prior and new content.”
It truly was an incredible week of learning in Singapore. Some teachers do not believe Singapore’s education system has a replicable model, because of how small the country is geographically. I respectfully disagree with this argument and feel that we have a lot to learn from both Singapore and Malaysia (in addition to everything we can learn from Taiwan, too). I encourage all Americans, if they have the opportunity, to visit Singapore (and travel internationally as much as possible). English is widely spoken throughout the country, and it is incredible how the government has been able to fully embrace the innate power to be found in diversity. The Vision of Singapore’s Minstry of Education is ‘Thinking Schools, Learning Nation,’ and in many ways, their public schools truly are molding the future of their incredible nation. Wouldn’t it be incredible if every country had the same bold vision for public education?
“Education is the fundamental method of social progress and reform.” -John Dewey, School Journal vol. 54 (January 1897), pg. 78
Last month, I had the opportunity to speak at the FLIP x Education conference held annually in Kaohsiung. At the conference, I had the privilege of meeting Mr. Chen [陳光鴻], who is leading the “shifting landscape of math education in Taiwan.” It is so inspiring to listen to him talk about the future of math education, and I have often described him as the Dan Meyer of Taiwan.
Early in our conversation, Mr. Chen asked me what I thought PBL stood for, which I answered as most teachers from the United States would: problem-based learning. I first learned about this progressive approach to education when I was enrolled in graduate school and one of my professors lead a memorable seminar on the debate between constructivism (proposed by education philosopher John Dewey and advanced by icons such as Piaget and Montessori), and neo-traditionalism (lead by E.D. Hirsch). Hirsch gew up during the Jim Crow era in the segregated south, where “racism was automatic and rampant.” To help fight the opportunity gap, he advocated for a traditional school model where all students learn the same “core knowledge.” Dewey advocated for a more progressive school model that favored a collaborative approach where students learn dynamically through hands-on projects and from their peers.
Although we had a great debate in my graduate school class, what does the research suggest? The long-suppressed eight-year study famously noted that students “educated in progressive schools show more leadership, think more clearly, take a keener interest in books, music, and arts, and get slighty better grades in college than those of traditional schools.” Dr. Jo Boaler has a plethora of contemporary research that suggests the power of a progressive model of education is truly limitless and could help move our entire nation forward.
Back in Kaohsiung, Mr. Chen challenged me, and told me that we do not need problem-based learning; rather, we need Phenomenon Based Learning. At first, I thought this might be a translation error or perhaps a cultural misunderstanding. Mr. Chen told me that we need to strive for phenomenon-based learning, which he defined as a cross-curricular problem-based learning approach that gives students democratic ownership over their learning. He excitingly proclaimed, “there should be no kings or queens teaching a classroom!” He then laid out a vision of what school could be in Taiwan. Almost a hundred of years after John Dewey visited the Republic of China, he would be proud of educators like Mr. Chen that are looking to lead an education revolution.
We continued to talk about how teachers can transform high school classrooms, and how we can let students take true ownership over their learning. Mr. Chen asked me to describe my vision of an exemplar math classroom, and I talked about my experience implementing Agile Mind – a research-based platform that, in my perspective, is the best phenomenon-based learning curriculum currently available in the United States. As an organization that is dedicated to empowering students throughout the country, I have seen first-hand the impact that a progressive instruction model has had on my classroom in Newark, NJ. This is what my classroom looked like before Agile Mind:
This was taken in the beginning of my second year of teaching. Although the classroom management is pretty tight for a second-year teacher, the entire class is completely dominated by the teacher (me). Sure, we may have sung “Happy Birthday” to build some culture in the beginning, but I completely monopolize the rest of the class. By doing so, I inadvertently rob my students of any opportunity to meaningfully engage with the lesson. This video resembles a glorified version of show-and-tell, where the magic of mathematics has been reduced to forcing students to copy down what I write on the board. Also, consider how I had extremely-low expectations of my students, as I was teaching an elementary math standard in a high school algebra class.
During this point in my teaching career, I falsely believed that teachers were keepers of knowledge that had to exert control over their classes to ensure compliance. I was not happy with how my classes were going, and although my students generally respected me as a teacher, many still hated math class. I started attending every professional development session I could find, and I realized that something was fundamentally wrong with the way my class was structured. After reading dozens of books, attending conferences, and struggling through many internal biases, I realized that if I wanted to offer a transformational learning experience, I needed to change my teaching style and implement a progressive instruction model that would democratize the learning environment. Take a moment to consider what my classroom looked like a few years after Newark adopted Agile Mind and I implemented a more democratic classroom:
Notice who is leading the mathematics during this lesson. In this video, students are doing almost all of the heavy lifting, and my role has been reassigned from a lecturer to a facilitator of knowledge. One can gather the strong sense of community that has been developed, and it is clear that students have taken genuine ownership of their learning. The ideals of restorative practices have replaced a zero-tolerance approach to behavior management. The lesson structure of “I Do, We Do, You Do” has been replaced with “You-Do, Y’all Do, We Do.” Students believe in the core sentiments of academic youth development, and that mistakes are expected, respected, and inspected. While I am proud of the growth that I have made as an educator, I still have a lot to learn; this is one of the main reasons that I am currently in Asia researching education and pedagogy.
To be fair, it is not just the curriculum that has changed, but also the entire power structure of the classroom. Some teachers and school leaders wrongly believe that ‘power’ in schools is a fixed commodity. Rather, I vehemently believe now more than ever that empowering students and giving them ownership of their learning and academic trajectories can genuinely transform any classroom in any school throughout our country (a future post will consider specific ideas on how teachers can democratize their classrooms).
One of the struggles I have throughout Taiwan (and in the United States, to be honest) is that although some teachers are open to the idea of collaborative learning and PBL, they worry that their students will not do well on end-of-year assessments and college entrance exams. On the contrary, I honestly believe that a progressive style of learning will help achieve both ends. The proof is in the pudding: On the 2016 PARCC administration, I was so proud of my students for attaining the highest high school passing rate in the entire Newark Public Schools. In 2017, my students had a higher passing rate on the rigorous Algebra II PARCC test than the New Jersey state average. Although the 2018 results are not in yet, I am confident that my students will do equally well this year. To me, it is evidence to suggest that true phenomenon-based learning is essential if we are serious about helping students develop the intellect, character, and skills needed to solve the adaptive challenges of the 21st century.
I was also fortunate to see Mr. Chen lead a professional development session in Taichung, where he is slowly equipping an army of teachers with the mindset, skills, and rigor needed to go out and set the world on fire. Thank you, Mr. Chen, (謝謝,陳光鴻!) for your leadership, your dedication, and your awe-inspiring vision. To me, it is incredible that halfway around the world, we are working towards the same goal of transforming our schools. As I tell my fellow teachers often, keep fighting the good fight!
And thank you to all those back home in the states that have pushed me to become a better educator, including all of my incredible students over the years, Nick Romagnolo, Michael De Antonio, Jr., Honoré Hodgson, Abby Neumeyer, Michelle Lin, and Leeann Kerst. Let us continue to fail forward and resolve to work relentlessly until every child has the opportunity to attain a truly excellent education.
Note: This article was submitted to the Fulbright Taiwan Annual Research Journal.
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.
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 than government-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).
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.
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).
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.
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“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 fromChinafor 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 nooil, no iron ore, no forests, no diamonds, no gold, just a few small deposits ofcoaland 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.”
As often put forward, Taiwan outperforms many countries on international benchmarks, including the infamous PISA. For the last two months, I have been conducting dozens of interviews with teachers and observed many lessons at a wide variety of schools throughout Taiwan. As one professor told me, most people in Taiwan, including parents, believe that education is universally important, which is often determined by grades, which are made up almost entirely of test scores. While the nature of standardized testing is deeply engrained within Taiwanese culture, there are many other aspects that make the Taiwanese education system so unique.
Teachers here are considered white-collar professionals that value the quality of their work and take pride in what they do as a profession. In Taiwan, teachers have a tremendous reputation, and a “high prestige to teaching jobs and a significant regard to education in the traditional Chinese culture place lofty social status to teachers” (Hsieh et. al., 2009). Most educators strongly believe in the concept of a growth mindset: If teachers believe that kids can do better, they will; if teachers give up, then their students will give up, too. Taiwanese pre-service teachers are of high quality, and most have done well in school. As a result, education departments at local universities are very selective, and only take the best candidates available. This is markedly different that in the United States, where the lure of Wall Street and Silicon Valley often recruit our best and brightest (Kristof, 2011; Zakaria, 2012). In fact, a recent analysis suggests that the majority of education majors in the United States come from the bottom third of their graduating class (Kihn, Miller, & Auguste, 2010).
Perhaps one of the most surprising aspects of the Taiwanese education system is how trusting teachers are of their students. At seemingly every level of schooling, students have a 10 to 20-minute break between every class and are allowed to do pretty much whatever they want to during this time (most students go outside and have an impromptu recess). Students are also allowed to use their phones, ask for extra help from their teacher, or even go to the cafeteria if they are hungry. What is most surprising is that there is little adult supervision during this recess – students are allowed to go wherever they want within the school grounds. When the break is over, a soft chime rings, and all of the students go to class. Even in the younger grades, students as young as seven years old are expected to go to their class by themselves (the teachers neither lead them nor make them line up as is common practice throughout the United States). Perhaps this trust is facilitated by an extensive early childhood education program: it is currently reported that over 96% of Taiwanese five-year-olds are enrolled in pre-school; on top of these extremely high participation rates, an astonishing 81.7% of the population “agree that the government should prioritize the implementation of compulsory education for five-year-olds” (Hsiao & Po-Hsuan, 2018).
In many of my school observations, I have noticed that although the typical teacher is physically at their school for over 10 hours daily, they rarely teach more than three or four hours a day; the average Taiwanese teacher leads instruction for 560-720 hours per year (Ministry of Education, 2017). To put this figure into perspective, the average high school teacher in the United States spends almost double the amount of time leading instruction over the course of a school year (Ministry of Education, 2017). As such, in Taiwan, “teachers have much more time to prepare lessons, mark classwork, and reflect on how best to improve children’s learning” (Gove, 2012). During this time, Taiwanese teachers often meet with their colleagues in professional learning communities, plan lessons and grade student work collaboratively, and perhaps most importantly, reflect upon their pedagogy. This extensive reflection time “liberates teachers to act as researchers who continually develop and evaluate new teaching methods, and who keep tabs on one another’s performance” (Gove, 2012).
While the idea of teachers performing action-research is not new, it is yet another example of a best practice that is rarely followed through upon in the west. In most public schools throughout the United States, reflection often becomes one more bureaucratic piece of paperwork that teachers need to complete, as opposed to becoming a natural and organic part of a teacher’s daily routine. Perhaps this is partly due to eastern culture: in the days of Confucius, many Academy’s had designated pools that teachers would walk around after their class had concluded to help them literally look at themselves and reflect back on their teaching. Contemporary scholars argue that teachers “should not only pay attention to the cognitive processes [how they reflect], but also the content of their thinking (what they reflect on), the goals of their thinking (why they reflect), and how their thinking influences their teaching practice in the classroom (what transformative learning they experience)” (Liu, 2013).
It is important to note that the Taiwanese education system is not “merely the government-run school system, but encompasses a gigantic range of cram schools. It is virtually impossible to find writing on Taiwan (and Asian) education in the mainstream media that sturdily confronts the existence of a parallel but gray educational system” (Turton, 2012). These cram schools, often called bǔxíbāns in Taiwan, are akin to large tutoring centers that lecture students about mathematics, Chinese, and English. These bǔxíbāns are pervasive in east Asia; in fact, neighboring country South Korea passed a law in 2011 enacting a strict 10:00pm curfew to lessen the stress load on students (Seoul, 2011). This 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 that parents with means use their resources to give an unfair advantage to their children, often at an incredible financial and emotional cost (Williams, 2017).
Learning about the educational culture of Taiwan has truly been an incredible learning experience. While some of the culture surrounding education is deeply ingrained within the history of the country, there are also many aspects of the operation of Taiwanese public schools that can easily be incorporated into our public schools back home. It is now up to us to implement these best practices and transform our education system once and for all.
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.
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.
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.
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.
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.
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.
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?