“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.
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.
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).
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.
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.
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).
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.
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).
With high school students after a focus group in Taichung.
Conclusion
This article describes but a few of the pedagogies used by Taiwanese math teachers as they practice their craft. We still have a long distance to go as a global math community until we reach the point where math teachers everywhere have implemented research-informed best practices that can drastically improve their students’ ability to learn. Perhaps the NCTM summarized best the shift taking place in the global landscape: “Students must rethink what it means to be a successful learner of mathematics, and teachers must rethink what it means to be an effective teacher of mathematics” (2014).
Learning about the culture of education as well as math instruction in Taiwan has been a transformative learning experience of a lifetime. While some of the culture that surrounds Taiwanese education is deeply ingrained within the history of this incredible country, there are many elements found in the pedagogy of Taiwanese math teachers that can be effectively incorporated into public schools throughout the United States. Now, it is up to all of us to implement these best practices and transform our education system once and for all.
After all, our students are counting on us.
Let us rise to the challenge.
Works Cited
Arcarvi, A. (2003). “The Role of Visual Representations in the Learning of Math” Educational Studies in Mathematics, 52, no. 3 pg. 215-241
Dewey, J. (1938). Experience and Education.NY, New York: Kappa Delta Pi.
Fuson, K., Kalchman, M., and Bransford, J. (2005). “Mathematical Understanding: an Introduction” in How Students Learn History, Mathematics and Science in the Classroom., edited by Donovan, S., & Bransford, J. Washington, D.C.: National Academies Press.
Green, E. (2015). Building a Better Teacher: How Teaching Works (and how to teach it to everyone).New York ; London: Norton et Company.
Hoyles, C., Morgan, C., & Woodhouse, G. (1999). Rethinking the Mathematics Curriculum. doi:10.4324/9780203234730
Hsieh, F.-J. (1997). 國中數學新課程精神與特色. [The essence and features of new mathematics curriculum in junior high school]. Science Education Monthly, 197, 45-55.
Hsieh, F.-J., Lin, P.-J., Chao, G., & Wang, T.-Y. (2009). Policy and Practice of Mathematics Teacher Education in Taiwan.
Hsiao S., & Po-Hsuan W. (2018). Mandatory Education for Five-year-olds is Popular. The Taipei Times. March 19, 2018 Print Edition: Volume 19, Number 27.
Huang, Y.-J. (2003). 臺灣地區新職業聲望與社經地位量表」之建構與評估:社會科學與教育社會學研究本土化. [The construction and assessment of the “new occupational prestige and social for Taiwan”: The indigenization of the social science and sociology of education research], Bulletin of Educational Research Vol.49(4). 1-31.
Liu, K. (2013). Critical reflection as a framework for transformative learning in teacher education. Educational Review, 67(2), 135-157. doi:10.1080/00131911.2013.839546
Ministry of Education (2017). Ministry of Education Objectives for 2018 (January-December) released 7/19/2017. Taipei, Taiwan: Ministry of Education.
Ministry of Education (2017). International Comparison of Educational Statistical Indicators. Taipei, Taiwan: Ministry of Education.
Morin, E. (1993). 複合思想導論[Complex Thought]（施植明，譯）。臺北市：時報文化。
Morin, E. (1999). The Seven Complex Lessons in Education for the Future. Helsinki, Finnish: UNESCO. Qualifications and Curriculum Development Agency. National Curriculum. Retrieved from http://curriculum.qcda.gov.uk/index.aspx
NCTM (2014). Principles to Actions: Ensuring Mathematical Success For All. Reston, VA: NCTM, National Council of Teachers of Mathematics.
Sahlberg, P. (2015). Finnish Lessons 2.0: What Can the World Learn from Educational Change in Finland? New York: Teachers College, Columbia University.
Sahlberg, P. (2018). FinnishED Leadership: Four big, inexpensive ideas to transform education. Thousand Oaks, CA: Corwin.
U.S. Congress, Office of Technology Assessment (1992). Testing in American Schools: Asking the Right Questions, OTA-SET-519. Washington, DC: U.S. Government Printing Office
Wagner, T., & Dintersmith, T. (2016). Most Likely to Succeed: Preparing Our Kids for the Innovation Era. New York, NY: Scribner.
Williams, C. (2017). Teaching English in East Asia: A Teachers Guide to Chinese, Japanese, and Korean Learners. Singapore: Springer imprint is published by Springer Nature.
Zhao, Y. (2014). Who’s Afraid of the Big Bad Dragon?: Why China has the Best (and Worst) Education System in the World. San Francisco, CA: Jossey-Bass.
With a traditional culture that has generally emphasized standardized testing and the Confucian ‘sage on a stage’ model of instruction, there is a lot of controversy regarding Taiwanese education reform. In fact, “the fundamental purpose of education has long been debated in Taiwan. This ongoing debate has led to a learning system that over-emphasizes academic performance and neglects other dimensions of learning. But recently, the Taiwanese government adopted the use of a constructivist approach to teaching mathematics. This new approach to teaching and learning focuses on the whole child” (Eisenhart, 2011).
Contemporary education reform in Taiwan started during the late 1980’s, when a team led by Dr. Fou-Lai Lin “gradually began to investigate mathematics teaching through research and literature studies instead of only through their own experience. As a product of these occurrences, mathematics teacher education in Taiwan moved towards a new realm, combining practical experience with mathematics education research” (Hsieh et. al., 2009). In 1996, “in-service and pre-service math teachers throughout Taiwan began to deeply consider the way students think, shifting the view towards teaching from teacher-centered to student- oriented” (Hsieh et. al., 2009). The following year, the Ministry of Education implemented a new national curriculum for junior high school students. Many of these changes “centered on students; the links between mathematics and life; the cultivation of students’ creativity, thinking, as well as reasoning abilities; and on an active attitude towards learning mathematics and appreciating mathematics (Hsieh, 1997).” The intent of these reforms “means that in mathematics education the emphasis will shift to problem-solving and process-monitoring and away from memorizing and plugging into formulas. Problem solving through which one can learn the methods of acquiring knowledge is one aspect of mathematics education that has been more or less neglected in Taiwan, but is now gaining attention alongside the emphasis on mathematics education for lifelong learning” (Hoyles, Morgan, & Woodhouse, 1999).
Liu Mong-chi presenting a session on how to design questions that test students’ core competence: “If the only metric we use to determine the effectiveness of our education system is PISA, we will not have an effective education system.”
In modern-day Taiwan, the Ministry of Education is currently piloting a new national curriculum that will be rolled out during the 2019-2020 school year. One of the Ministry’s noted goals is to “progressively implement the 12-Year Basic Education program, incorporating development of adaptive learning and completely non-exam-based secondary school admission” (Ministry of Education, 2017). Policy makers are are planning to adapt the Taiwanese curricula to encourage creative problem solving (Hoyles, Morgan, & Woodhouse, 1999). The Ministry has also put forward that “teachers are required to pay closer attention to the learning process and children’s conceptualization of content and ideas rather than focusing on simply attaining the correct answer” (Eisenhart, 2011). These proposed reforms look to address the pitfalls of current educational practice and intends to inspire students to collaborate through project-based learning and standard-based grading. During one interview, a teacher noted how these changes will take the future generation of Taiwanese students onto a positive new path that will prepare them for the adaptive challenges of our increasingly globalized world.
As the vision of Taiwan’s new 12-year basic education program is developed, its ideas of “spontaneity, interaction, and common good” are synthesized with reference to the educational ideas of John Dewey (1938), postmodernism, and complex thought (Morin, 1999; 1993). These instructional shifts encourage Taiwanese teachers to let students drive their learning and take ownership of their thinking with an aim to inspire rather than to control (Fan, 2016). After all, “if we continue to ignore the power of students’ own ideas and conceptions, we will only perpetuate the notion that mathematics and science (among other subjects in our school curricula) are irrelevant, uninteresting, and difficult to learn” (Sahlberg, 2018).
These progressive changes are not unique to Taiwan, either: “China, the leading economic competitor of the United States, is decentralizing its curriculum, diversifying assessment, and encouraging local autonomy and innovation. Meanwhile… Singapore is promoting a creative environment characterized by ‘Teach Less, Learn More’” (Finnish Lessons 2.0). In other Asian countries, schools “are limiting direct instruction and mere recitation of facts and looking for more innovative pedagogies and encourage students to design and make things” (Wagner & Dintersmith, 2016). When observing classrooms throughout Taiwan, it is apparent that lesson structure plays an important role both during class and when a teacher is preparing for a lesson. This idea was featured prominently in Elizabeth Green’s critically-acclaimed book Building a Better Teacher:
“One striking example was the way teachers structured their lessons. American teachers rarely talked about lesson structure – the way class proceeds from a beginning to a middle to an end – and yet, watching each individual teacher at work, Stigler felt as though they’d all read the same recipe. ‘A cultural script,’ he called it… Some American teachers called their pattern ‘I, We, You.’ The Japanese teachers, meanwhile, turned ‘I, We, You’ inside out. You might call their version ‘You, Y’all, We.’ They began not with an introduction, but a single problem that students spent ten or twenty minutes working through. Next, the teacher brought them back to the whole group, asking students to present their different ideas for how to solve the problem on the chalkboard. Give the answer and the reason for the answer. Finally, a teacher led a discussion, guiding students to a shared conclusion – What did you learn from today’s problem, or what new questions do you have, if any?” (Green, 2015)
To fully capitalize on harnessing student’s own ideas and conceptions, many schools in Taiwan (and throughout the world) are recognizing the importance of teaching students how to work collaboratively, create viable arguments, and critique the reasoning of others. Student voice is featured prominently within many Taiwanese math classes, often for students to share their strategy on how to solve a complex problem. Unlike in the U.S., most Taiwanese high school math classes only complete a few rigorous problems during each period, as opposed to drilling a few dozen scaffolded problems over the trajectory of a lesson. This means that students spend more time thinking deeply about a few hard problems, which enables them to reflect critically about their solution strategy. When students are solving these problems, the types of questions that Taiwanese teachers ask their students are noticeably different than the types of questions often posed by American teachers:
“In comparisons of mathematics teaching in the United States and in high-achieving countries, U.S. mathematics instructions has been characterized as rarely asking students to think and reason with or about mathematical ideas. [American] teachers sometimes perceive student frustration of lack of immediate success as indicators that they have somehow failed their students. As a result, [American math teachers] jump in to ‘rescue’ students by breaking down the task and guiding students step by step through the difficulties. Although well intentioned, such ‘rescuing’ undermines the efforts of students, lowers the cognitive demand of the task, and deprives students of opportunities to engage fully in making sense of mathematics” (NCTM, 2014).
To this end, some Taiwanese teachers are moving away from rigid algebraic algorithms to flexible divergent thinking. For an algebraic example that highlights this phenomenon, consider the simplification of the following expression, which was recently given to an 8th grade class at a junior high school in Taiwan. How would most American students go about simplifying such an expression?
Most American children would follow “PEMDAS” (the rigid algorithm commonly used for order of operations), and start by multiplying 6 times 14 times 21, and then dividing by 42 OR simplifying the 21 and the 42 to ½ first. Look instead what one Taiwanese 8th grader wrote on the board:
Before jumping immediately into the problem, the student reflects for a second and sees that by re-grouping the six, she can attain 42, which allows for a more straight forward simplification. The student then had to only multiply 3 times 14 to get the correct answer.
Another example was seen during a 9thgrade geometry class. After deriving the ‘interior angle’ formula of a polygon, a student worked a problem down to the following expression:
Again, most American students would start by distributing the 180 to the parenthesis, or by simplifying 360 times five equals 1800. Instead, consider what one Taiwanese 9th grader wrote:
Because Taiwanese students were encouraged to think divergently about the algebra at hand instead of rigidly following an algorithm, the students could regroup certain terms to make the complex expression simpler. In many classroom observations, different students were solving algebra using a multitude of different strategies, allowing them to think more concretely about the algebra and open up the world of mathematics.
Another exemplar aspect of Taiwanese math pedagogy is how teachers prominently feature multiple modalities in their pedagogy, as well. The National Council of Teachers of Mathematics has put forward that “effective mathematics teaching includes a strong focus on using varied mathematical representations” (NCTM, 2014). In fact, multiple studies have found that “when students learn to represent, discuss, and make connections among mathematical ideas in multiple forms, they demonstrate deeper mathematical understanding and enhanced problem-solving abilities” (Fuson, Kalchman, and Bransford, 2005). Taiwanese teachers in particular focus heavily on different visual representations of abstract mathematics, which help students “advance their understanding of mathematical concepts and procedures” (Arcavi, 2003).
Multiple Representations
Multiple Representations
Multiple Representations
Multiple Representations
Creating arguments and critiquing the reasoning of others, on the other hand, is a pedagogical shift that Taiwanese teachers are struggling to implement. In one classroom observation, a teacher in Kinmen repeatedly told students that, “we cannot work independently anymore; we need to work with others and learn to cooperate more.” Although this teacher had strong messaging, they struggled to give students concrete strategies to help facilitate meaningful groupwork.
During another school visit, several educators in Kaohsiung have asked how teachers in the United States facilitate rigorous discussions and Socratic seminars with their students. In Newark, the Office of Mathematics argues that “mathematical discourse should be well-planned, intentional, and embedded in whole-class and small-group settings.” Classroom discussion is one of the most important levers in student success: when educators “decrease the teacher talk and increase the student talk by providing them with learning intentions and success criteria, and a deeper understanding of how to have a discussion with the class” (DeWitt, 2017). In fact, “students who learn to articulate and justify their own mathematical ideas, reason through their own and others’ mathematical explanations, and provide a rationale for their answers develop a deep understanding that is critical to their future success in mathematics and related field” (Michaels, O’Connor, and Resnick, 2007). These shifts are most profound when teachers view themselves as a facilitator of knowledge instead of a giver of knowledge, a shift that will be enduring for many teachers (NCTM, 2014). In a country with a strong culture that has many roots in Confucianism, this instructional shift will inevitably take time to fully implement.
While these are just some of the pedagogies that Taiwanese math teachers use throughout their practice, we still have a far way to go as a global math community until every school has implemented research-informed best practices that will help students learn better. Perhaps NCTM summated this global shifting landscape most succinctly: in math classes in 2018, “students must rethink what it means to be a successful learner of mathematics, and teachers must rethink what it means to be an effective teacher of mathematics” (2014). Let us now resolve to work relentlessly to achieve this end and share the innate beauty of mathematics with everyone.
Works Cited
Arcarvi, A. (2003) “The Role of Visual Representations in the Learning of Math” Educational Studies in Mathematics, 52, no. 3 pg. 215-241
Dewey, J. (1938). Experience and Education.NY, New York: Kappa Delta Pi.
Fuson, K., Kalchman, M., and Bransford, J. (2005) “Mathematical Understanding: an Introduction” in How Students Learn History, Mathematics and Science in the Classroom., edited by Donovan, S., & Bransford, J. Washington, D.C.: National Academies Press.
Green, E. (2015). Building a Better Teacher: How Teaching Works (and how to teach it to everyone).New York ; London: Norton et Company.
Hoyles, C., Morgan, C., & Woodhouse, G. (1999). Rethinking the Mathematics Curriculum. doi:10.4324/9780203234730
Hsieh, F.-J. (1997). 國中數學新課程精神與特色. [The essence and features of new mathematics curriculum in junior high school]. Science Education Monthly, 197, 45-55.
Hsieh, F.-J., Lin, P.-J., Chao, G., & Wang, T.-Y. (2009). Policy and Practice of Mathematics Teacher Education in Taiwan.
Michaels, S., O’Connor, C., & Resnick, L. (2007). Deliberative Discourse Idealized and Realized: Accountable Talk in the Classroom and in Civic Life. Studies in Philosophy and Education, 27(4), 283-297. doi:10.1007/s11217-007-9071-1
Ministry of Education (2017). Ministry of Education Objectives for 2018 (January-December) released 7/19/2017. Taipei, Taiwan: Ministry of Education.
Morin, E. (1999). The Seven Complex Lessons in Education for the Future. Helsinki, Finnish: UNESCO. Qualifications and Curriculum Development Agency. (n.d.). National Curriculum. Retrieved from http://curriculum.qcda.gov.uk/index.aspx
Morin, E. (1993). 複合思想導論[Complex Thought]（施植明，譯）。臺北市：時報文化。
NCTM (2014) Principles to Actions: Ensuring Mathematical Success For All. Reston, VA: NCTM, National Council of Teachers of Mathematics.
Sahlberg, P. (2018). FinnishED Leadership: Four big, inexpensive ideas to transform education. Thousand Oaks, CA: Corwin.
Wagner, T., & Dintersmith, T. (2016). Most Likely to Succeed: Preparing Our Kids for the Innovation Era. New York, NY: Scribner.
2014 was the year of traveling and the year of weddings, and it was definitely a year to remember. As I mentioned in last year’s year in review, I rung in 2014 sixty-feet underwater in the middle of the Atlantic Ocean on an amazing dive trip with two of my teacher friends, Nick and Karina. It was my first live-aboard, and it was an absolutely incredible experience that I will always cherish; I already cannot wait to go diving again! Later in the month, Matt, Victoria and I flew down to Louisville for our good friend Steve Townsend’s wedding. Although we were there for only a few days, we tried to make the most out of the experience, and checked out the Louisville Slugger Factory, ate some delicious Hot Brown’s at the eminent Brown Hotel, and had an Inside-the Gates tour of Churchill Downs, too.
At Steve’s wedding in Louisville
Spring went by so fast. Our basketball team won the state tournament, Teach For America-New Jersey celebrated their 20thanniversary, and we celebrated MIPO’s 35th anniversary in the city, too. In March, I was once again privileged to chaperone another overnight college visit trip to Connecticut and Rhode Island, which was humbling and empowering as usual.
Eric showing me around Turner Sports
April was one of the best months of the spring, as I was able to get to two new cities: New Orleans and Atlanta. In short, both cities lived up to the hype. In New Orleans, we went for the annual NCTM conference, which was just as informative as the conference in Denver. I would highly recommend checking out my full write-up about New Orleans here. After landing in Newark, I had less than 12 hours before I was on another plane bound for Atlanta. It was my first time to visit “Hotlanta,” and I was excited to see my good friend Eric Vander Voort, who I hadn’t seen for a while, and is currently working at Turner Sports. In the five days that I was there, we killed the city, going to just about every famous restaurant and museum the city had to offer. Oh, and did I mention that we ran into Shaq at the Turner Sports building, too? Talk about once in a lifetime!
In May, some of my best friends in the world graduated from Marist, and in June, between chaperoning more trips, speaking at Honor Society Dinners and gearing up for the World Cup, I moved out of Newark to Rahway, which is about fifteen minutes south of the city. Speaking of soccer, this was the first year I actually followed the World Cup, and it really got me into soccer.
At the College Summit at Yale University
In July, I was invited to be in Dan Torres’ wedding, which was incredible! It was held in upstate New York, and it was great re-connecting with so many people I hadn’t seen in over a year. I was also fortunate to have the opportunity to chaperone a weeklong overnight College Summit visit to Yale, and met some great rising seniors that all had unique stories about their pursuit of their future. The following week, I was able to visit my longtime friend Johnny Delgado in St. Louis, and return to the baseball mecca that is Busch Stadium. In addition to visiting Johnny, it was my second time to the city, although it was my first time seeing the new stadium.
On the field at Busch Stadium
In August, I was so blessed to be able to visit Spain for a month. I went to study Spanish, live with a host family, and experience as much of the culture of España as I possibly could. In the three weeks I was there, I was able to get to four major cities, including Madrid, Toledo, Valencia and Barcelona. I had the best paella I’ve ever had in my life, experienced my first professional soccer game, y aprendí un poco más español. Quite frankly, it was one of the best trips that I have ever taken in my life. I never had the opportunity to study abroad while I was in college, so I felt that this was my chance to study abroad and take in a new culture while learning a new language along the way.
Before I knew it, the summer was over, and a new school year was around the corner. This year, I was appointed to be a lead teacher in the math department, something I was extremely excited about. My classes were awesome, and it is honestly hard to believe how fast the first four months have gone.
At Austin’s last high school soccer game
Just when the leaves were changing colors, we took a busload of students down to Rutgers for the day to check out the New Brunswick campus, and I also saw my first Red Bull soccer game, too. In October, I saw the U.S. men’s national team play Ecuador in Connecticut with Rob and Jeff, which was really cool (even if I did get to the game a little late…). One of the funniest aspects of the trip was that many of my students are Ecuadorian, so it was a lot of fun leading up to the game. At the end, the teams tied 2-2. After getting back, I was able to cheer on our boy’s soccer team and watched them win the Newark City Championship, and go to Austin’s last high school soccer game, too.
During November, a bunch of friends and co-workers went down to Jamaica for my friend Nuno’s wedding. It was my first destination wedding, and it was awesome! In between the wedding festivities, I was able to squeeze in a trip to the famous Dunn River Falls and embark on a scuba diving excursion, too. The wedding itself was picturesque, as shown below. Two weeks later, I had another wedding, and Ryan and DJ got married, too!
Congrats to “Nuna”
In December, I had one of the most memorable days of my teaching career to date when I took almost 50 high schools students to visit my beloved alma mater, Marist. In between working with seniors on countless college and scholarship applications, I was able to go to a soccer scholarship dinner and finally try some authentic Norwegian food, too. For New Year’s, I went up to Connecticut, and had such an amazing time.
Another late night working on college applications
As I said, 2014 was the year of weddings and trips, and it really was quite a memorable year. It seems as though every year goes by faster, but I guess that is to be expected, especially as we get older; maybe that is why we need to make every second count!
One of the most memorable days of my teaching career
New Orleans. The Big Easy. N’awlins. NOLA. Whatever you would like to call it, New Orleans is high on the bucket for just about every American I know. When I found out that the NCTM conference was going to be held in New Orleans this year, a co-worker friend and I immediately knew that we needed to attend, and go down south to experience all of what New Orleans has to offer.
This flag flew above the USS Bayfield, and survived both the D-Day invasion in Normandy and a few months later during Iwo Jima.
On our first day in New Orleans, we went to the National World War II Museum, which was unbelievable. Throughout the four building exhibit, they had so much memorabilia from the Second World War, and it was exhilarating to say the least. After going through the World War II Museum, we had lunch at Cochon (which I would highly recommend!) and then headed back to the hotel to get ready for the conference. Afterwards, we took a quick trip down Bourbon Street, had some delectable Hand Grenades, and had a splendid dinner at The Court of Two Sisters.
Had to get some authentic Louisiana food when in NOLA!
On our second and third day, we had the conference for the greater part of the day, which was extremely informational and interesting. I was also able to meet two of my “math-educator” idols, Dan Meyer and JoBoaler. For dinner on Thursday, we went to Arnaud’s, a famous French restaurant located in the heart of the French Quarter. To top off a delicious dinner, they had a small jazz band come to our table and play “when the saints come marching home.” Talk about having a genuine New Orleans experience!
The Jazz Band playing “When the Saints come Marching Home”
Saturday was the last day of the conference, and, after attending the Pelicans game the night before, we were all really excited to check out the French Quarter Festival. To say we ‘killed’ the festival would be an understatement. We ate fried alligator, crawfish bread, beignets, and pork chop lollipops, just to name a few. In between all of the amazing food, we listened to some great jazz music, including a samba band from Brazil!
During our last full day, we got up early to have some world-famous beignets at Café Du Monde. Afterwards, we went to mass at the St.Louis Cathedral, which was beautiful. Interestingly, the cathedral has a flag for every country New Orleans has ever been apart of. We also had the opportunity to take a city tour, which included stops at City Park and a cemetery. Now, one may be wondering, why would you want to go see a cemetery when in New Orleans? You see, in New Orleans, everyone is “buried” in a mausoleum-esque above ground vault. It was really interesting to see how much different cemeteries are than the ones I am accustomed to up north. That evening, we had a chance to check out the world-famous “Commander’s Palace” Restaurant, which is where Emeril started his career. If you were looking to go to a place with authentic southern hospitality and food, I would definitely check this place out! Perhaps most notably, Commander’s subscribes to the ‘open kitchen’ philosophy, meaning that guests are allowed to freely roam throughout the kitchen at their own leisure.
At the end of the trip, it was clear that New Orleans lived up to the hype, and I already cannot wait to get back. Between all of the food, music, conferences and great people we met, it will most definitely be a trip I will never forget. As the French like to say, “Laissez les bons temps rouler.”
It is hard to believe that it has been a full year since I wrote last year’s ‘year in review.’ 2013 has gone by so incredibly fast, and since there have been so many great moments along the way, I sure hope I did not forget any here!
With the ESHS Student Council at the 2013 Inauguration
In January, I started off the year by attending the 2013 Presidential Inauguration with the East Side High School student council. It was so surreal to be standing on the national mall, listening to our president get sworn in and give his inaugural address. It was also great having higher level political conversations with some of our all-stars from East Side. Obama gave such a great speech, and I will never forgot when our students cheered like crazy when Obama mentioned immigration reform. Besides Obama, Kelly Clarkson perhaps unintentionally stole the show with her fantastic rendition of “My Country, Tis of Thee.” Attending the Inauguration was an experience I will undoubtedly never forget.
In February, I officially started my masters program at Seton Hall University, which I was extremely excited about. The masters will be a M.A. in Educational Leadership, Management and Policy, with a concentration in educational administration. I also had the privilege of meeting Bobby Marks, a Marist alum who is currently the assistant GM for the Brooklyn Nets, before watching a game at the brand-new Barclays Center with Meaghan and Brian.
In March, I had many TFA-related activities, and was able to visit Marist one weekend as well. After Easter, I geared up for April, which was one of the busiest and most fun months of the year. In April, it felt like just about every weekend I was in a different city. Between Boston, Denver, Newark and Poughkeepsie, I sure had a fantastic journey going across the country for everything from NCTM conferences to high school college visits. I would strongly recommend reading my full post on my adventures in April here. Playing some kickball to end the year
May was a graduate-filled month, as my first set of graduate classes were coming to a close and my next semester was already beginning. June went really fast as well, especially since we spent so many of the last days of school playing kickball with students and attending our high school’s graduation. I also experienced my first Portuguese Festival which was, well, one of the most interesting nights of the year. During the second weekend in June, my cousin Danny and his beautiful wife Elisabetta got married on Long Island! The wedding was so much fun, and one of the best I have ever been to.
The Wedding Party!!!
A week after school was over, I went on a family vacation to St. Maarten. It was, quite frankly, one of the nicest islands I have ever been on. Between amazing food, breathtaking views and an unbelievably relaxing atmosphere, it was the best way to wind down after a busy year. Perhaps most notably, I decided to get my open water scuba diver certification, and I went diving four times, including two deep dives to a coral and an old wreck. It was one of the coolest activities I have ever done.
With my family in St. Maarten
When I got home from the Caribbean, I worked summer school for a few weeks. In between teaching summer school, I had the opportunity to visit many places, including Princeton (as one of my good friends Kassie was staying there for the summer) and the floor of the New York State Exchange. I also squeezed in a boat tour of NYC sponsored by the Marist Alumni Association and a quick trip to Philadelphia and Boston before the summer was over. (I finally was able to get to the Sam Adam’s brewery, as well, which was something I really wanted to do for a while.)
With Kassie at Princeton University
And just like that, August was winding down, which meant school was just around the corner. After a few weeks of cleaning up my room and setting up my class, I went up and visited my beloved alma mater for one last time during Labor Day weekend. The end of the summer means the annual Brazilian festival comes to Newark, which of course means lots of great food, drinks and music to be had by all!
At the annual Brazilian Day Festival in Newark
September and October flew by, as we had so many different things going on. Between so much controversy in the Newark Public Schools and new laws being passed seemingly daily, it was hard to not get overwhelmed in all of the commotion brought upon by education. There was even more controversy in November, when the district and the union fought over teachers going to the annual NJEA conference held in Atlantic City. Unfortunately, no matter whose side you were on, the only people that lost at the end of the day were our students. We need to stop putting adults in front of education in our schools, and continue to work hard to a day when all of our students have the opportunity to attain an excellent education.
Also in November, the East Side Student Council visited two colleges in Pennsylvania, including the University of Scranton (where my sister currently attends) and Penn State. As you most likely have come to expect by now, it was another great trip that always helps to reset my perspective on life. I wrote a longer debrief of the trip on a previous post, which can be found here.
With Danny watching the Packers/Giants at Metlife Stadium
To end the year, I celebrated with some of my teachers friends (Nick and Karina) on board the Turks & Caicos Aggressor II. It was my first live-aboard, and I would definitely recommend it to anyone that is interested in Scuba Diving; It was honestly one of the best weeks of my life. And hey, what better way to start the New Year than be scuba diving fifty feet underwater?
Hanging out with the Delgado’s during Christmas Time
Well folks, that just about does it for 2013. Who knows what 2014 will have in store for us, but if the past is any indication for the future, I think I’m in for a really great year.
This past April was one hell of a month. After surviving my first official graduate school residency at Seton Hall during the first weekend, I was looking forward to going to Boston with the East Side High School Student Council on the 11th and 12th. This was my third overnight trip with the group, and, having had incredibly moving experiences the first two times around, I was extremely excited about this one.
With the East Side High School Student Council at Harvard University
In two days, we were able to visit four schools: Harvard, Boston College, Northeastern and Boston University. As was the case with previous trips, it was such an empowering weekend. Although I had a lot of great dialogue with the students during our two day venture throughout Boston, three specific conversations stick out: The first was at BC, when we were eating lunch. I was sitting across from a senior who recently moved to the United States from Ecuador seven months ago. We talked about the concept of poverty being relative, and how he plans to navigate going to college over the course of the next couple of years. Afterwards, on the “T” from BC to the North End, I had another great conversation with a sophomore that I often describe as having “unlimited potential.” We talked about college and what it takes to be successful, and ended with discussing possible college visits for the summer. This kid is only a sophomore and he has already seen more than two-dozen major universities! He is also very intellectually and emotionally mature; to be honest, he reminds me a lot of myself when I was in high school. I think he is going to be very successful one day.
A fantastic presentation about the admissions process to the ESHS Student Council at Boston College
The following morning, on the way home, I had such a powerful conversation with a group of students about changing the image of East Side and Newark in general. They were explaining some of the ideas they had to make their school a better place through different events and activities. For me, this resonated well with what Arne Duncan said recently: “Students are today’s leaders. Your voice and recommendations to re-imagine our school experience is vital.” I think we as a society discount the opinion of students far too often, and if we really want to make our education system the cream of the crop again, we must empower students and give them some autonomy to make a difference. Regardless, I genuinely enjoy chaperoning these trips so much, although I sometimes do feel a bit bad; I often feel that I learn way more from these amazing kids than I could ever teach them in a million years.
At the 2013 NCTM National Conference in Denver
The following week, my friend (who happens to be my boss) and I went to Denver, Colorado for the 2013 NCTM (National Council of Teachers of Mathematics) National Conference. What another great trip! We did so much in the five days we were there, as we ate at many fantastic restaurants (including Sam’s No. 3, Osteria Marco and Vesta Dipping Grill), saw a great deal of sites (including the DaVinci Museum, the state capital of Colorado and the 16thstreet mall) and had plenty of exotic food (including rattlesnake and raw kangaroo!). The conference itself was inspirational and moving, and gave me many great resources and ideas to implement in my classroom. It was great to network with teachers from all different types of schools all across the country. Some highlights of the conference include a Harvard Professor lecturing about the concept of fixed vs. growth mindsets, and Dan Meyer’s (author of the well-known “Math Class Needs a Makeover” TED talk) presentation on perplexity. We also planned it out so that we could attend two sporting events before we left, as we got to see the Avs play at the Pepsi Center and the Rockies play at Coors Field. I would be remiss if I did not mention that we got to see the Lawlor family-which was undoubtedly one of the highlights of the trip.
With Mike and the Lawlor family at Coors Field
As April drew to a close, I visited my beloved Marist in Poughkeepsie for one last weekend before the end of the academic year. As with high school, I am sure that the longer I am out of college, the less it will feel like home. But as of right now, I sure do miss Marist College. After catching up with a bunch of friends, we went to Darby’s, had some Irish Nacho’s and wings, and had a load of great laughs along the way. As I said goodbye to all of my friends, I reminded them to enjoy “their last three weeks at the best place in the world.” I think that sums up my feelings about my alma mater pretty well. And that was the end of a crazy month that I will remember for a long time. I now officially have less than eight weeks before my first year of teaching is under my belt. It has been a great run, but I am still wondering: Where has the time gone?
Andrew Paulsen 
