An American Abroad

This past memorial day, on my flight from Kuala Lumpur back to Kaohsiung, I had the privilege of sitting next to an active-duty member of our U.S. military currently stationed in Okinawa, Japan. During our four-hour flight, we had an incredible conversation that covered just about every topic, including the role of America’s military in 2018, the current geo-political climate of the world, and yes, Mr. Trump. The marine I sat next to told humorous, informative, and enlightening stories about being stationed in Romania, training troops in Bulgaria, and moving to Japan. Towards the end of the flight, I asked him what his current responsibility in the military was, and he talked about how, in his perspective, the U.S. military’s greatest strength is in soft diplomacy. He talked about the need for our soldiers to gain trust in foreign lands by getting to know the locals, understand their culture, and grow to mutually understand one another. Although we were the same age and had taken radically different paths in life, we both somehow ended up on the same flight, headed to the same destination, with the same goal in mind: to advance the virtues of the United States through the use of soft power.

Decades ago, Joseph Nye originally coined this term – soft power – in his critically-acclaimed work Bound to Lead: The Changing Nature of American Power. He wrote that, “if a state can make its power seem legitimate in the eyes of others, it will encounter less resistance to its wishes. If its culture and ideology are attractive, others will more willingly follow… when one country gets other countries to want what it wants, [it] might be called soft power, in contrast with the hard or command power of ordering others to do what it wants.” More recently, Nye has suggested that the “best propaganda is not propaganda,” and that “credibility is the scarcest resource.” Former Secretary of Defense Robert Gates believed in this vision, and advocated that the Bush administration consider “a dramatic increase in spending on the civilian instruments of national security – diplomacy, strategic communications, foreign assistance, civic action, and economic reconstruction and development.”

Not a day passed by in these last eight months that I did not work hard to advance the soft power efforts of our country. As a cultural ambassador for the United States, I was invited to meet Taiwanese President Tsai Ing-wen, had an interview with Taiwan’s Minister of Foreign Affairs Joseph Wu, and gave a presentation to the U.S. Assistant Secretary of State Marie Royce. On a daily basis, I had the opportunity to interact with ordinary people that have never met an American before. I visited at least one high school (in Tainan) that told me that I was the first American to ever visit their school. On many occasions, I was asked representative questions about the United States, and while I always strived to be welcoming and open to dialogue, I always made it clear that I was sharing my opinion, as there is no such thing as a representative American perspective. In truth, I was trying my hardest to avoid the danger of telling a single story.

I also had the opportunity to visit the cold war outpost of Kinmen and even played basketball with students that are living in a former warzone – talk about true soft diplomacy! Kinmen (formerly known as Quemoy) was the site of the last battles of the Chinese civil war, and was later shelled heavily by the PRC’s Liberation Army throughout the 1950’s. The Taiwanese island is so close to the mainland that my cell phone network automatically switched to a mainland Chinese phone carrier! This trip also served as an important reminder of the urgency to study our history so that we may never repeat the mistakes of our past. For me, I still question how I somehow have made it through 13 years of public education (and an additional 8 years of university) without every hearing about the role Quemoy and Matsu played in the Taiwanese Strait Crisis.

Speaking of learning about our past, I also saw the atrocities of war first-hand when I visited Vietnam. Unlike many conflicts, including World War II, the Vietnam War ended in the 1970’s. This means there are millions of people still alive that remember the war like it was yesterday, and one cannot walk a single block in Ho Chi Minh without seeing someone that has been negatively impacted by Agent Orange. It was sad standing at the War Remnants Museum, next to captured American tanks and airplanes, and asking whether all these deaths, destruction, and birth defects were worth it. At the time, many Americans subscribed to the so-called “domino theory,” and believed that if one country were to become communist, all of Asia would quickly become communist. In hindsight, it is clear just how wrong many of those leaders were in our past. In some ways, America in 2018 in similar to America in 1968, because during the war, “the United States was widely unpopular around the world, as it is now… Yet despite unpopular government policies, our openness and self-criticism allowed the American idea to retain its appeal. A free press, independent courts, and a Congress willing to confront the executive branch can provide a similar measure of soft power today.”

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Standing at the War Remnants Museum in Ho Chi Minh City next to a U.S. Army helicopter captured during the Vietnam War.

It frustrates me to no end when people accuse me of being anti-military because I am anti-war. I have the deepest respect for our armed forces and will be forever grateful for their sacrifices. But we must question, why do we constantly get involved in meaningless conflicts that put our brave soldiers in harm’s way to begin with in the first place? My grandfather, who meant the world to me, served in the Korean War. While we only have a few photos of him during this time period, look at how happy he looks when he is with his fellow Koreans. I particularly love the photos of him standing with Korean children. To me, I have no doubt about it: my grandfather fundamentally believed in the idea of soft power, and worked hard to win over the hearts and minds of the Korean people.

In fact, I was the first person in my family to visit the Korean peninsula since he was honorably discharged almost 70 years ago. Standing in the de-militarized zone and briefly walking into North Korea was an experience that brought many personal feelings to bare. I can only hope that he would be proud of me.

Nothing, however, was as powerful as visiting Hiroshima.

At 8:15am on August 6th, 1945, a U.S. army B-29 bomber dropped an atomic bomb on the Japanese city of Hiroshima, and our world was changed forever. It was surreal being one of the few Americans to ever walk around the atomic bomb dome and the Peace Memorial Museum, and I was at a particular loss for words when I was standing directly underneath the hypocenter of the bomb. When visiting the memorial, it was interesting that the memorial did not solely blame the United States, but rather both countries, for putting their egos in front of the lives of innocent citizens. For me, the hardest part of the day was visiting an elementary school that survived the initial impact, where a majority of the young students were killed instantly.

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“I heard what others have said about Hiroshima. Now I have seen for myself, and I am utterly devastated.” -Desmond Tutu

While visiting Hiroshima was without question one of the most difficult places that I have ever been to, there were many difficult conversations I had throughout my time in Asia. When I met with Assistant Secretary of State Marie Royce, I told her how difficult it was being asked questions about the current administration or our country’s absurd obsession with guns everywhere I went (I encourage all of my fellow Americans to read an op-ed I wrote that boldly declares that our problem with gun violence is #NotNormal). Truth be told, I was asked questions about school shootings and Trump on a daily basis during my time abroad, which were unequivocally the hardest to answer as a representative of our country. It is not necessarily because of Trump’s policies, as I am all for a political disagreement – dissent and diversity of thought and culture is what truly makes America great. Truth be told, it has been embarrassing to be an American abroad during the so-called era of Trump. Simply put, our president does not represent our country well, and respect for America around the world is in an objective freefall (well, except for in two countries: Russia and Israel). As I told our Assistant Secretary last month, it has been hard serving as a cultural ambassador for the United States during this tumultuous time period under an administration that does not believe in soft power.

Why has it been so hard answering question about Trump? Maybe it is because he praises dictators while he is incredibly hostile with our closest allies. He openly mocks disabled people, and makes lewd remarks of women. His Secretary of Education knows nothing about schools while his EPA Director has repeatedly abused his authority. After complaining for years about how much golf President Obama has played, he has played more golf than any other president. Trump and his administration lie about everything, including paying off people that he had had affairs with and meetings during his campaign. He is a proponent of separating vulnerable families at the border and wants to widen the death penalty for drug dealers. He calls African nations “sh*t-hole countries”   and calls immigrants of color, “animals.” And to put the figurative sprinkles on top, he neither believes in the power of soft diplomacy nor the mission of the Fulbright Program.

On the contrary, I have seen the innate power of soft diplomacy first hand. I have gotten to know so many amazing people, in a part of the world that is greatly misunderstood by the west. I have come to have a deep appreciation for Taiwanese hospitality, and the importance of standing up for what is right.

At the end of the day, the “greatest threat to the American idea is what we may do to it ourselves. Terrorism is like jujitsu: The small players win if they make the large player use his strength against himself. If we respond to terrorism by becoming less open—economically, socially, and politically—we lose. As George Kennan warned in 1946, at the start of the Cold War, the greatest danger that can befall us is that we shall allow ourselves to become like those with whom we are coping.”

Here is my charge to my fellow Americans: We can do better. Scratch that, we must do better. I encourage you all to get your information and news from objective news sources, such as BBC and NPR, and stop watching outlets such as MSNBC, CNN, or FOX. If you have the opportunity, travel abroad as much as possible, and strive to really get to know the people of foreign countries and their culture and way of life. Try to listen to others more, especially people that do not look like you or may have different worldviews. Push your thinking by watching documentaries and reading books and attending local lectures and talks. Perhaps most importantly, reflect critically on your belief system, and constantly ask yourself why you believe what you believe. If there is anything that I have learned in my first 27 years of life, it is that people are people everywhere. At the end of the day, everyone I have ever met wants their family to be healthy, their kids to be successful, and to be treated fairly and justly. Is that too much to ask?

When President Obama visited Hiroshima, he reminded us that, “we have long known the agony of war. Let us now find the courage, together, to spread peace and pursue a [better] world.” Perhaps I am an eternal optimist (and pacifist), but I fundamentally believe that we can make this world a better place if we try. I mean, why not aim to create good instead of evil? Why not look to make peace instead of war? Why not try to spread love and compassion instead of hate and arrogance?

Now (especially now) is the time for an effort like never before to achieve peace.

Let us all take hands.

This post is dedicated to Anthony Bourdain, someone that knew how to travel and celebrate life better than anyone. He worked relentlessly to show us that we should not be afraid of strangers in our global community, and that people are people everywhere. Thank you for inspiring so many people (including myself) to take this world by storm, Mr. Bourdain. 

Taiwan truly is the heart of Asia.

A bit of madness is key
to give us new colors to see.
Who knows where it will lead us?
And that’s why they need us!
So, bring on the rebels,
the ripples from pebbles;
the painters, and poets, and plays.
And here’s to the fools who dream…
crazy as they may seem.
Here’s to the hearts that break…
here’s to the mess we make.

It was a hectic couple of days leading up to my departure for this incredible journey. After a snow day, an emotional last day at East Side, and a truly surprising going-away party (thank you mom, dad, and Kim!), I was off to Asia to embark on the opportunity of a lifetime. I was super excited about visiting Japan and moving to Taiwan, but I also became sad about leaving home (for really the first time in my life).

As I sat on the plane, I reflected on leaving everything and everyone that I knew behind. I started to realize exactly what I had gotten myself into, as I was about to move to a country where I did not speak the language, personally knew nobody, and could not even read a menu. After enjoying the in-flight service and reading for a while, I decided to watch a movie, and happened upon La La Land, a movie that claimed the Oscar for Best Picture last year (well, for two minutes, at least). I felt that the beginning of the movie went slowly, and the only reason I did not turn it off was that I was stuck in an aluminum tube for the next twelve hours. I quickly fell in love with La La Land, as it intimately shows the often-untold sacrifices that people need to go through to chase their dreams. And that was before the audition scene:

In a weird way, it was almost like Emma Stone was speaking to me. Other than perhaps Stand By Me, rarely has a Hollywood Blockbuster ever had such a profound impact. I genuinely do believe that traveling is essential “to give us new colors to see,” as Ms. Stone so eloquently sings in this scene. Perhaps most importantly, she reminds us the importance of always striving to approach new situations with an open mind, as “who knows where it will lead us?” Watching La La Land reassured me that everything was going to be alright, and I was ready to take on this world by storm!

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At the Fo Guang Shan (佛光山) Buddhist Monastery in Kaohsiung.

After landing at Narita airport right outside Tokyo, I was excited to visit Japan and see Asia for the first time. On my first morning, I got up at 3am to get in line for the Michellin-starred SushiDai restaurant, which was hands-down the best sushi I have ever had in my entire life. After visiting four major cities (Tokyo, Kyoto, Nara, and Hiroshima) and falling in love with Japanese culture and their way of life, I was off to my Fulbright destination: Kaohsiung City, Taiwan.

My first month in Taiwan was really busy, as I had a lot of logistical things to take care of, including securing my apartment, completing all of my immigration paperwork, and adjusting to my new life for the next six months. After meeting my advisor, new colleagues at Kaohsiung Girls High School, and grabbing lunch with some former Fulbrighters, I was off to Taipei to speak at the Fulbright mid-year conference. After touring around the capital of Taiwan for a week, I was so honored to be invited to celebrate Chinese New Year with Michele’s family. During the holiday, all of the schools throughout Taiwan shutdown, and many of my friends took advantage of the extended break to travel internationally. February was definitely the hardest month to get through. Although I had the amazing opportunity to attend the Olympics and watch our women’s hockey team beat Canada to earn a gold medal, there were a lot of tough transitions to get through along the way.

You see, living abroad for an extended amount of time is an incredible experience, but it is not always rainbows and unicorns as Instagram would make us believe. As they told us during our Fulbright orientation, culture shock is a real thing, and there are times when it can be very lonely traveling by yourself (although I always try to make the best of every opportunity). The time change was difficult working through, too, as I almost always had to FaceTime with my friends and family in the morning before they went to sleep. Traveling to Asia also emulated what it must be like to be illiterate, as few signs (outside of airports and subway stations) are in English. On more than one occasion, I ordered something random from a restaurant with no English menu (which was almost always delicious, for the record, but is still an anxiety-causing experience). I may have learned 一點中文 , 我不台外說中文 , but I can still only read about 40 or 50 Chinese characters.

Once March rolled around, I had a bunch of school visits lined up and ready to go. I have learned so much about Taiwanese culture and have grown to love many aspects of this special country. I will definitely miss all of the incredible hospitality, amazing food, and ‘futuristic’ transportation options. I spent every Monday learning from the incredible educators at Kaohsiung Girls High School and enjoyed our weekly “Subway” meetings. I have come to really look forward to every Monday, as we had the chance to talk about education, politics, and yes, even gun violence (a future blog post will consider my thoughts about being abroad during this tumultuous time period in American history). On a serious note, I really cannot thank Hsin-Wei Chen [陳欣薇], Yi-Fan Chen [陳怡帆], Yi-Hsiang Chang Chien [張簡逸翔], Jia-Wei Sun [孫嘉偉], Hsun-Hsun Chung [鍾恂恂], and Hsien-Tsung Lin [林憲聰] enough for everything they have helped me with. 謝謝!

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With this awesome crew during a “Subway Meeting” after an observation at KGHS

During the Spring, I had the chance to speak at a plethora of conferences and visit a few other countries, as well. The longer I was in Taiwan, the larger my network grew, and I was soon invited to visit schools in every major city. I really appreciate Mr. Chen [陳光鴻], who is leading the effort to implement Phenomenon-Based Learning throughout Taiwan. I held focus groups in Taichung, taught math lessons in Kaohsiung, and visited vocational schools in Tainan. I watched students riding unicycles in Kinmen, and met Taiwanese President Tsai ing-wen in Taipei. Over time, I slowly acclimated to Taiwanese culture (and yes, I had plenty of amazing Taiwanese food at all of the famous night markets throughout the country).


Taiwan is special for countless reasons, but my favorite part can be summarized in three words: mindfulness of others. Although most social norms around personal space can be quite different in Taiwan, people often act with others in mind instead of only thinking about themselves. Take something simple, like letting people pass on an elevator: in the U.S., there are signs everywhere that tell people to stand to the right and let people pass to the left, but people still do not listen. In Taiwan, it seems as though everyone automatically does the right thing to make life easier for everyone else, and it is like that for everything. You can take a nap on a crowded MRT, because people are quiet. Once on the subway, people never sit in the designated priorty seat to make it easier for others that really need the seat (see photo below). The culture of respect creates an unbelievably safe atmosphere that leads to modern day miracles. On countless occassions, I have left my phone, wallet, and Macbook out at a busy Starbucks  and no one ever stole it. I have seen people leave their key in the ignition of their scooter, because they have such a deep trust that no one will steal it. When you cultivate a society that is mindful of others, life is better for everyone (even the dogs are rarely leashed, and are always well-trained). We have a lot to learn in the United States, where we value individualism over just about everything else, almost to a fault.

As I wrap up my time here in the Republic of China, I am often asked what I am going to tell my friends and family about Taiwan when I get back to the states. The first thing that I am going to talk about is the amazing Taiwanese hospitality. In the almost 30 countries that I have been privileged to visit, the people of Taiwan are some of the nicest and most welcoming people that I have ever met in my entire life. On a daily basis in Kaohsiung, people will come up to me and say ‘hello,’ and try to help me out in anyway that they can. Sure, the Taroko Gorge was one of the most beautiful parts of nature that I have ever seen, but the true beauty of Taiwan is its people.

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The Taroko Gorge (太魯閣) is gorgeous, but the true beauty of Taiwan is its people.

Second, albeit controversially, is that I believe now more than ever that Taiwan is unequivocally a sovereign state that deserves the recognition and protection of an independent nation unconditionally. If there is any policy that I agree with the current administration on, it is their support of the Republic of China. Taiwan is a beacon of hope that shares the democratic values of the United States, and we need to ensure that our countries have an enduring friendship that will stand up to geopolitical rivals. Perhaps Director Moy, the de facto United States ambassador to Taiwan, said it best during our end-of-year Fulbright banquet:

In a weird way, my Fulbright experience is like a movie playing before my eyes. On some days, it feels like I have been living in Asia for years. On other days, I feel like it was just yesterday that I was sitting on a plane waiting to take on the world. As they say, maybe “a bit of madness is key, to give us new colors to see. Who knows where it will lead us? And that’s why they need us! So, bring on the rebels, the ripples from pebbles; the painters, and poets, and plays. And here’s to the fools who dream… crazy as they may seem. Here’s to the hearts that break… here’s to the mess we make.”

謝謝 , 台灣![Xièxiè, Táiwān!]

很高興認識你們 , 我學到了很多東西。[Hěn gāoxìng rènshí nǐmen, wǒ xué dàole hěnduō dōngxī.]

我會想你的![Wǒ huì xiǎng nǐ de!]

台灣將永遠在我心中。[Táiwān jiāng yǒngyuǎn zài wǒ xīnzhōng.]


The bǔxíbān (補習班) experience: My night at a Taiwanese Cram School

As previously mentioned, the Taiwanese educational system 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, which literally translates to ‘supplementary learning class’) are akin to large tutoring centers that lecture students about mathematics, science, Chinese, and English.

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A typical bǔxíbān in Kaohsiung, Taiwan

After hearing about cram schools in dozens of interviews conducted throughout Taiwan, I was visit a bǔxíbān and actually see what one is like for myself. Thanks to some of my colleagues at Kaohsiung Girls High School, I was able to visit one of the most famous cram school teachers, Teacher Lin, at 志光公職補習班 (Zhiguang Public Cram School). When I first walked into the cram school, I was surprised at how elaborate the facilities are. I really enjoyed how this school celebrated academic success and had a “Hall of Fame: of all the university acceptances form previous students. This learning center had several floors and different rooms for different needs: The main classroom (four different rooms for different subjects), a study room with a “teaching assistant” (but is a full-time licensed teacher), a computer room, and a “relax” room where kids can get water or tea. The classroom I visited was about twice size of a typical American classroom and had over 100 seats, but somehow does not feel crowded.

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One of the most interesting aspects of the cram school structure is that all lessons are recorded for kids that are absent or were confused with a particular topic and wanted “extra help.” The school has a library of videos that teach students any topic imaginable and is akin to an old-school version of Khan Academy (with their current teacher). The students can watch the videos of the lesson anytime they want and can rewind or slow down the video at their own discretion at any time.

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During the class, I was interested in how engaged the students were in the lesson. Teacher Lin has created his own resource (books) for each math topic, and each problem has a similar problem with a given answer for more practice. The use of multiple representations is rampant and is very strategic about using different colors to highlight how different parts of the pictorial representation relate to the procedural applications. Another interesting tidbit is that the teacher uses different parts of the board for different parts of the lesson. The far-left part of the board is kept up and used as a defacto anchor chart Teacher encourages different methods to solve the same problem and uses jokes and brain-breaks to divvy up the lesson. Perhaps most importantly, kids can still be kids – eat, drink, get up and take a break or use the restroom, etc.


After class ended, I had a chance to have an impromptu focus group with the students in the class, which was an interesting learning moment, too. Class got out at 9:30pm, and even I was tired – but I was not attending school all day! I asked the students what a typical day looked like for them, and they shared that their public schools get out at 5, cram school starts at 6 and gets out at 9:30, with a 20-minute break at 7:50. Students get home at 10, take a shower, relax, and start HW/studying at around 11. Students spend 1-2 hours and then go to bed around midnight. I also asked if any of the students hang out with their friends or play video games, to which they replied: “Yea! On the weekends mostly. And sometimes during school (haha)!”

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I also asked the students their perspective about the Taiwanese education system, and they shared that, “we wish there was more collaboration… I don’t like sitting and listening to a teacher for three hours. I went to school in Denmark for a year, and it was very different.”

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Post-bǔxíbān dinner at Smokey Joes!

While the practice of late-night tutoring remains controversial, I was really impressed with some of the aspects that I saw during my bǔxíbān visit. It should be noted, too, that although many public 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). While visiting a cram school was a tremendous experience and I gained a lot of interesting ideas about pedagogy, I am deeply conflicted about pushing our students too hard. I am all for high expectations, but to a point. After all, shouldn’t kids be kids?


Works Cited

Turton, M. (2012). The View From Taiwan. Retrieved March 04, 2018, from

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.

Fulbright Research Presentation

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:

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The poster that was made for my final presentation

“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.

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Receiving my Fulbright certificate

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!

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My Fulbright Taiwan Certificate of Achievement. I loved that they printed my Chinese name (柏安尚) on it, too!

Singapore: Thinking Schools, Learning Nation

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.

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.

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Sunsets in Singapore are beautiful, too!

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!!

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With Samuel, an incredible school leader in Singapore

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.

The Singaporean currency also prominently features education

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:

Pos Ed Model2

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.

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Speaking at the reThinking Learning Conference

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.”

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Steve Leinwand speaking at reThinking Learning

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?

Phenomenon-Based Learning

 “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.

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This bust of John Dewey graciously welcomes all visitors to Columbia University’s Teachers College.

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.

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Talking with 陳光鴻 about Phenomenon Based Learning at the FLIP x Education Conference in Kaohsiung

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).

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Co-teaching Mr. Chen’s math class in Taichung

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.

Implementing Eastern Pedagogical Approaches to Teaching Mathematics in Urban High Schools

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

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 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).

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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.


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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