Tampines Primary School Visit

Today we visited Tampines Primary School in the Tampines area of Singapore near the airport in the southeast part of the island. It took about 40 minutes to get there by train. The building is completely new and beautiful. In Singapore, you will be hard-pressed to find a school built before 1990 because the government believes in leveling old buildings and constructing new ones every 20 years. As a result, many of the school buildings we visited were built recently, and the technology and variety of services offered at each school blew me away. For example, all Primary schools have a dentist’s office (we visited the one at Tampines and saw two students about to see the dentist),

Anyone have a cavity?

and we toured the new gym at Tampines and saw three separate gym classes of 30 students each with plenty of space to stretch and play a game involving dribbling basketballs and passing them to lit points on a $30,000 electronic game board.

Physical fitness is a big part of the general curriculum in Singapore

Although I'm not sure if this wall scoring maching was the best investment..

I’m not sure if that game board was the best investment, but the school also has state-of-the-art technology in each classroom.

We were greeted by the gracious principal and given gift bags and served a delicious breakfast of a chicken curry over naan-like flat pancakes. She told us that when schools are rebuilt from the ground up, the students and staff at the school relocate to a building for a little more than a year while their old building is razed and rebuilt. I was amazed to hear that construction on the new Tampines complex (Tampines Primary is located adjacent to Tampines Secondary, but they each have separate spaces, including separate gyms) took only 15 months to complete. Everything in Singapore seems to be done as efficiently as possible (but we were told that the building crew worked 24-7 on the project — something that would not happen in Boston), and building schools is no exception.

We visited many classes today at Tampines, and just like at all of the other classrooms we visited this week, whenever we entered a class, all of the students stood up to greet the principal and guests. Very cute and courteous. Since we visited Primary school (grades 1-6) classrooms today, we saw many teachers instructing using the model method that is a cornerstone of the Singapore math approach and a way to deconstruct word problems.

Model method to mapping word problems

More visualizing word problems

More word problem mapping

As part of the method, for example, if the question said that Paul had 10 dollars and John had six dollars more, a Singaporean student would start to problem solve visually by drawing a small square to represent Paul’s money and then a slightly larger rectangle to represent John’s money. At the point where the two shapes were congruent would be a dotted line on the rectangle, representing where Paul and John’s money was equal, and then a student would write a six to the right of this dotted line showing how much more money John had than Paul. This is obviously the most basic of examples of word problem modeling, but we also saw teacher’s model this method with more difficult problems involving algebra on Smartboards (some teacher’s ease of use and mastery of the Smartboard is something I had never witnessed before, and this is what happens when technology is readily available in every classroom).

In Singapore, since there is uniform technology, a uniform vertically-aligned curriculum, and uniform problem solving strategies, both teachers and students know what to expect and what is expected of them. In most of the classes at Tampines students had individual white boards and small erasers, which some classes have at my school (including mine) have, and the students were writing the answers to short answer questions on them and the teachers were getting instant feedback on their lessons.

Students provide instant feedback to instructor teaching telling the passage of time

One thing I was curious about since some of the classes we visited had nearly 40 students was what happens to the quite students in the back who are physically present for lessons but who may be struggling with the content.

Average class size during school visits was about 32

I learned that teachers use after-school time to work with these students, which is what happens at my school as well. One lesson we observed today involved a second grade class talking about how many hours pass between two times and also what time it will be after a certain amount of time lapses. I liked how the teacher broke the simplistic problems down into their most basic form and solved each part in multiple ways using multiple representations. Teachers in Singapore do a fantastic job of clearly and explicitly teaching each step needed to solve a problem and showing alternate ways to solve the problem. Because they are explicitly teaching problem solving strategies to students at such a young age, students have much less difficulty in later years when presented with more challenging problems because they have established strategies to break them down and solve them.

The problem solving critical thinking skill is taught at a young age and continually retaught

All schools have explicit habits of mind that are taught and practiced

Also, I am not sure that teachers in Boston are teaching how to read a clock effectively enough, because every year I have students who cannot tell time (not knowing the difference between 1:25 and 5:05, for example) reliably when I use clocks to talk about angle measures.

Tampines is the first community school in Singapore, which means that on the weekends, the hallways are blocked off so people cannot enter classrooms, but people from the community can use the facilities at Tampines. Boston has schools like this as well where local residents can use the gym or swimming pool of a school.

I was extremely impressed by the library at Tampines.

Young students quietly reading in library

It had a mock peach tree, a train carrying books, and it had reading materials for students who speak all of the major languages of Singapore (English is the official language, but most people do not speak English at home). What struck me about the library was the group of model students (or at least I thought they were) browsing the shelves for books, helping the librarian check out their books, and then sitting quietly at tables reading. I was floored by this. These were probably third grade students.

The principal told us that teachers went to Malacca, a resort beach area in Malaysia for a recent professional development retreat –wow.

Perhaps the class I was most impressed with was the fourth grade class in which the teacher modeled how to use the mounted Smartboard to model solving word problems using model drawing.

4th grade teacher models problem solving using smartboard

The teacher visually models the problem solving steps

She was so skilled with the Smartboard, modeling the important step of reading the question carefully and highlighting the key information (she ended up highlighting nearly every word in different colors, reducing each word’s importance in my mind, but the fact that she explicitly modeled highlighting in such a visual way was powerful). The teacher asked good questions of the students to keep them leading the lesson such as, “OK, so what do we need to do first,” and “Visually, we must understand what is happening here.” The teacher showed the students a peer rubric they would be using to rate each other’s work, and she was clear that to earn a perfect score in any category, the work must be flawless. Another random observation of this class was that even though every student  had a mini white board and eraser, only about five students in the class were taking notes during the teacher’s model lesson, and they were all female, and they were all taking notes in notebooks. I also noticed that every student had a pouch of supplies including not just pens and pencils and erasers and a scientific calculator but also colored pencils, a little scissors and a glue stick. Each and every student came to school every day with this fundamental need met when they walked through the main gate of the school. Unfortunately, my students have struggled with supplies over the years and any good suggestions on what to do about this would be greatly appreciated.

After the school visit, I went book hunting with Perla and Patsy and we bought a bunch of Singapore math books and practice problem books. I am excited to see the methods I have witnessed all week explained in greater detail in these books. I am also looking forward to using some of the rich examples and practice problems in my lessons.

I have had an unbelievable time here in Singapore over the past two weeks. I learned how to fold geometric shapes at the Origami conference and heard numerous teachers tell wonderful success stories involving using origami as a medium to teach and explore mathematics. I have made many contacts and some new friends, and I look forward to staying in touch with many people from the conference. I would like to thank the Fund for Teachers program for making it possible for me to be here, and I would also like to thank Patsy Wang-Iverson, the mathematics guru who set up and led the school tours this week. I have seen the Singapore approach to teaching math using models and explicit step-by-step problem solving up close and personal, and I have been blown away by the country’s interest and support of its educational system. I have seen more technology in schools the past few days than I have seen in Boston Public Schools in the past few years, and I hope this changes. Each school had 3 or 4 air conditioned computer labs of 40 computers, and every classroom had a visualizer, mounted projector and Smartboard. The Singaporean education system wowed me for many reasons: it believes in recruiting  the best candidates to the profession, training them well, implementing a uniform, vertically-aligned curriculum, and providing them with the technology and the professional development they need to thrive. As the educational system in the United States becomes more cloudy by the day with the advent of more unproven charter schools and less money for public schools, the divide between the two education systems appears to be widening, and this is unfortunate. I remain positive about the potential of the public school system in the United States, but it is clear to me that we need to rethink our priorities and be more proactive and calculating in our policy decisions before the system cracks completely.

Well, it is late and I have a flight tomorrow to meet Jenn in Thailand for three-and-a-half weeks of travel. I am excited. When I return to the states I am going to review all of my notes and read my new books and use the two weeks to prepare for the coming school year. I will try to update this blog from Thailand and Cambodia, but the posts will be less frequent and most likely shorter. I will also post pictures as soon as I can.

Thank you for reading about my experiences in Singapore over the past two weeks, and feel free to contact me with questions or comments.

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Catholic High School

Today Patsy, Perla and I woke up before dawn and braved a downpour at 6:30 a.m. to take a short cab ride over to Catholic High School (http://www.catholichigh.moe.edu.sg/), a primary (1st – 6th grade) and secondary (7th – 10th grade) all-boys school in Singapore.

Despite its name, the school is non-denominational (though there are crosses everyone, and the school was founded 75 years ago by a Christian man), and there is a high concentration of students of Chinese descent as it is a bilingual English-Chinese school. We met with Ms. Ling Yuan, who may be the nicest person I have ever met (she apologized that it was drizzling and rain drops were landing in my tea when she walked us from the school all the way to the train station after our visit).

Perla, Patsy, Me, and Ms. Yuan

The parent center at Catholic High School. Parents are encouraged to volunteer and spend time at the school.

She is a science chair at Catholic High School, where about 1,100 boys attend each school, which is connected by a series of unbelievably gorgeous walkways, bonsai gardens, rock waterfalls, and coy fish streams. I am not making this up.

Schools in Singapore are calm and inviting

A bonsai garden at school -- nice!

All schools assemble outside every morning and sing the national anthem. Unfortunately, we missed Catholic's opening ceremony because of rain.

Catholic High School’s Primary School caters to students of all ability levels, whereas its Secondary School is on the express stream (the fastest track to university). Because of this, and perhaps the fact that studying Chinese is compulsory, only about 50% of Catholic’s Primary students stay for Secondary School. We shared a tour with a group of teachers and school administrators from the Philippines. We visited both math and science classrooms.

I was impressed with my first impressions of Catholic High School. Ms. Yuan, and the school’s principal, Mr. Lee, are both impressive figures, and they spoke of the grand list of Catholic High graduates in prominent places. As we walked around the sprawling campus (most of the Primary and Secondary schools we have visited have a green space surrounded by levels of classrooms, all with their doors open..) I could not help but notice all of the signs of encouragement, educational displays and learning experience. Someone could literally walk around the school for a day and win most trivia matches.. At my school, there is student work and announcements on the walls, but I’m not sure who really looks at them. At Catholic High, I was drawn in to posters, games on the hallways, and displays as we walked around.

There are even teachable moments on the stairs..

We visited one science class where the teacher was setting up an activity in which students were recording the time it took pieces of paper, folded in different ways, to fall from various heights. The room was loud and there was a lot of movement and experimentation, but what was most noticeable was that every student was actively engaged in the lesson, taking notes on a recording sheet and working with partners.

Students experimenting in groups

When I first came to Singapore I did not know what to expect from the teachers’ pedagogical approaches. I knew there was a standard, set curriculum and a lot of assessments, but I did not know that so many teachers employed student-centered group activities in Singapore. Another class of younger Primary students had just begun taking a test, but it was no multiple choice or fill-in-the-blank exam: there were objects including beakers and measuring cups and water and other things at the center of each table, and the students were required to use them to solve specific problems. We saw a physics lesson that focused on magnification of light on paper, and 35 students huddled around the instructor at the front of the room to see his demonstration of the concept. Then, students returned to their tables to answer some questions will performing different light experiments.

A student reflecting light

This lesson was modeled by the teacher, but then the students needed to figure out the work on their own. Throughout our visits I have thought about how envious our science teachers would be if they saw the perks that the science teachers here in Singapore receive. For example, every lab has a staff person to set up before and clean up after each experiment. In another lab, we saw a group of 9th grade students measuring the volume of small marbles both with an instrument and also by measuring the amount of water they displace in graduated cylinders. This activity appeared student centered, but as Patsy pointed out, the students’ worksheet led them on a path and did not allow for creative experimentation.

After out science visits we saw some math classrooms, but we saw mostly 1st and 2nd grade classrooms. Like in other classes I’ve observed this week, many of the teachers were wired with microphones so students could hear them more easily, and there were about 30 students in each class. For first and second grade students, these children were well behaved and attentive to their lessons. The first grade class was following instructions of the teacher using her visualizer as she displayed some addition and introductory multiplication problems. The students were working together and the class had a nice flow. In the second grade class, the teacher was using a student’s worksheet to model the proper way to use the model method, which is extremely visual. The problem was something like, “Frank had 42 dollars and his friend John had 12 dollars more than Frank. How much did they have altogether?”

The model method explained in a 2nd grade classroom

The student’s work was flawless and meticulously performed step-by-step just as the teacher had instructed them to do it. She covered his second and third steps and showed the first step in which variables are used to represent Frank (F) and John (J). This was nice to introduce variables to second grade students, and next to the letters, the student drew one  medium-sized box next to the “F” and one medium-sized box and one smaller box next to “J.” As the teacher went through the student’s answer, she was asking the class and certain students in particular questions like, “So which box should be bigger than the other,” and “So what does ‘F’ equal and what does ‘J’ equal?” I’m sure in a few short years, the student who did the work would be presenting it himself. I was really floored by the amazing uses of the visualizer as the student’s notebook could be projected onto the mounted overhead using the mounted digital camera. Brilliant. I’m not sure how much they cost, but they make the traditional overhead projectors that many of the teachers at my school still use look like BETA tapes.

I had a positive and enjoyable experience at Catholic High today and everywhere I looked I saw learning. The day is broken up into seven or eight periods, and the day starts at 8:15. Primary school students are finished at 1:35, and Secondary students have class until as late as 3:45 on a long day.

A student's schedule

Lessons for the Secondary school students are 45 minutes each (much shorter than our 64-minute classes) and students and teachers have a five-minute passing period. I would welcome such a time to exhale and go to the bathroom between classes at my school, as I’m sure most students and teachers at my school would agree, but we have only two minutes to sometimes travel four long floors “upstream” through throngs of students. Maybe we can discuss passing time and its benefits with our incoming principal.. Other things that stood out at Catholic High was the giant room where teachers’ desks were located.

In Singapore, the classrooms are not "owned" by the teachers. They plan in a centralized office. This leads to more teacher collaboration.

This centralized room makes the teacher the visitor to classrooms and not the owner, as the students feel more ownership in their classrooms. Also, teachers can plan and work together in this giant, centralized room. Adjacent to the staff office was a staff lounge complete with a plasma tv and comfortable-looking couches (I’m not making this up), which is attached to the staff lunchroom. The students eat their lunch outside in a covered canteen area where there are numerous different food choices on any given day, and all of the food looked healthy and tasty (it’s not surprise Singapore is a skinny nation based on their love of healthy and delicious foods in moderation..).

Not your typical cafeteria with pizza and tots..

Overall, our visit was eye opening even though we did not see as many math classes as we would have hoped for. We have been promised that tomorrow’s visit to the Tampines Primary School (http://www.tampinespri.net/) will include multiple math class observations. Regardless, I have seen enough engaged students working together in groups to solve small projects and activities on this trip to completely dispel my preconceived notion that Singaporean classrooms are cold factories where teachers do not like questions and students have no voice. Tomorrow is my last school visit in Singapore, and then on Saturday it’s off to Thailand, where I hope to visit a school in Chiang Mai the following week.

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Republic Polytech and Kent Ridge

I did not post yesterday (Tuesday) because we had a full day observing students at Republic Polytechnic, and then we attended the opening of a new Invent! exhibit at the Singapore Science Centre. Yesterday we had a full group of six visiting Republic Polytechnic (RP), a school students attend after their tenth year of school.

Day 2: Republic Polytech

Students attend RP for three years, and upon graduation, most are employed or go to university (except all males must perform two years of mandatory civil defense training – Singapore has one of the largest armed forces, per capita, in the world). RP has courses of study in engineering, applied science, IT, technology for the arts, hospitality, and even sports, health and leisure. RP’s curriculum is completely project-based. Teachers do not lecture – rather, facilitators help to guide the students, in heterogeneous groups of five, to their ultimate conclusions.

The qualities of a Republic Polytech student

The day is broken up into parts – at the beginning of the day the students download their problem statement for the day. We observed a first-year (11th grade equivalent) math class, and their problem asked what whale-watching package someone should choose based on its cost and chance of spotting a whale. The problem involved probability, and the students spent the morning reviewing the problem together and starting to answer questions on a worksheet that guides their progression from start to finish.

Students in an 11th grade math class working in groups to solve a difficult real-life project

We observed the second class meeting before lunch at which the facilitator was making the rounds and questioning groups about what answers they had for the worksheet. She was adept at assessing which groups needed more support and which groups needed to be pushed farther. Her questions made the students think about every aspect of probability, and she pushed their thinking along. At RP, all students have laptops, all classrooms follow the same format (students have a math project one entire day, and a physics project another, etc.), and all classrooms are wired so students can present from an overhead projector from their group’s table.

After lunch we returned to see one of the final parts of the day – the students’ presentations. Each group went to the front of the class and presented their solution for about 20 minutes. Each student presented a different part of the problem, and the facilitator asked all of them follow-up questions to assess understanding. The facilitator also asked them all to complete an extension problem on the board. RP develops students who collaborate and work well in teams. Our tour guide, “Mervin,” (I do not have his exact name) was quite the gracious host and his school’s approach is not to learn countless formulas from lectures. Instead, his students learn by doing, by collaborating, and by creating. Facilitators are looking at what strategies the students are using, and how they are applying their knowledge.

The first math group to present its work

This group is working on a white board to answer a follow-up question from the teacher

I like the project-based learning approach at Polytechnic, and I employ a similar strategy at my school, however, I have a mini-lesson first to teach the topic for the day. At RP, students were more applying topics that they have already learned. I wonder how groups would fare on a more complicated topic that they have not seen before. A different between my classes and these is that I see my students for one hour each day, so if I were to copy the RP model, I could do it by using Monday to distribute the projects to groups and have them brainstorm. Tuesday would be devoted to working together to solve the problem, students could fine-tune their presentations on Wednesday, and then present and discuss on Thursday, and then there could be a quiz on Friday. Another difference is that all students have laptops, the school has wireless internet, and the students’ presentations are done in Powerpoint. My students generally present at the end of each class on 2 foot x 2 foot whiteboards. Next year we are supposed to get a few new sets of student laptops, so that technology gap could be eliminated.

I was impressed by the students ease at presenting (they do it every day and are obviously quite comfortable, even with visitors) and the facilitator’s probing questions. She knew when to rephrase questions, when to go back a few steps and when to push forward. Even though the groups had five people each, many groups had members working mostly independently, and group members shared ideas and questions with students from other groups. One thing we did not get to see was the facilitator present her model answer after all of the groups presented. Following this summary, in which the problem is solved completely, there is a discussion and then a quiz and a reflection. There is no homework. The RP model is different from most American schools, and even though I employ a similar model in my classroom, I will consider tailoring some projects next year based on this model.

We could not leave Republic Polytech without giving our gracious host some origami

We took the MRT (public transit) a few stops to the Science Center and heard a minister of education speak at the opening of the new Invent! Wing of the Science Centre. I liked his speech as he spoke of the need to encourage future generations to explore and invent more, but I thought the exhibit was only average. There are interactive displays and games, but I would have no interest in returning to it someday. Following the tour of the exhibit, there was a catered meal of local foods that we happily feasted on.

The launch of the Invent! exhibit at the Science Centre

Perla's son Danny mastered a balancing act at Invent!

Today we took the train to Kent Ridge Secondary School, which serves nearly 1,200 students.

I realize the climate in Singapore allows for open-air walkways in all schools. It made me think about students at my school who are not allowed to leave the building.

Strategic Focus of Kent Ridge

It accepts students from all three tracks (or streams): express, normal and technical. The express students are on the fast track to university, while the other two tracks could possibly join the express track, but they often end up at a Polytechnic School. Express students move on to junior college for two years after Secondary 4 (our 10th grade) before entering college. We did not see many classes (we saw 7th grade students on the tech track sing us a song in a music class), but we did get a nice tour of the facilities and had a nice conversation with the principal Koh Chong Mong. We spoke about how the dropout rate in Singapore is much lower than in the United States and how this could be due to the abundance of options students of all ability levels have to find their niche. For example, at Kent Ridge, we saw amazing kitchens for home ec classes, a complete workshop room where student use giant power tools, full dance studios, multiple gymnasiums, and four fully-equipped computer labs with 40 computers each and an additional two smaller computer labs.

These students appeared to be in decent shape, but they are in danger of failing an upcoming fitness test, so they jog around the track while other students in the gym learn dance moves

These students don't need the extra fitness

This is one of many science lab storage areas

On average, the schools I visited had four air conditioned computer labs with 40 stations each

What has blown me away visiting Singapore schools is its clear embrace of technology. All rooms have mounted projectors, good sound systems, many have interactive Smartboards, wireless internet for the school, etc. Perhaps the most impressive technology I have seen in most Singaporean classrooms has been the digital visualizer, which is a mounted camera above the teacher’s work area where whatever he or she is doing is projected onto the screen. The overhead of the digital era..

This teacher was writing in a math notebook. What she does is..

..projected on the screen. Nearly every classroom during my week of visits had this technology.

In Boston, we have a limited computer lab that serves my whole school, and I have commented earlier about our Smartboard situation. And it is not just that these schools have the technology – all students and teachers are proficient in its use and use it every day to instruct.

In our discussion with the principal and his vice principal, we talked about the Singapore value-added model of education. The Ministry of Education, which oversees all things education in Singapore, has fine-tuned data-driven policy decisions. Students PSLE (Primary School Leaving Exam) scores from 6th grade are compared to their seventh grade results, and the schools and parents are informed about the improvement or lack thereof. Because the Singaporean curriculum is uniform through the grades, the ministry is able to assess which schools, and teachers, are adding the most value to students’ learning. Kent Ridge gets students from all three streams, so there is a challenge there of educating the top students and some of the students who struggle the most. The school has close bonds with its parents as parents come to sell cookies and brownies every day at lunch, and the principal meets with parents once a month after school.

Other observations I had were that no students were roaming the open-air hallways during instruction time. Apparently, students in Singapore are better than some of my students about using the bathroom before school and during breaks in the day. The science rooms at Kent Ridge had people whose jobs are to clean and keep the lab stocked with supplies. I know our science teachers do not want to hear this. The labs were big and clean, and the stock room was full of supplies for experiments of all kinds. There was a Responsible Thinking Program room (RTP) where a disciplinarian resides and oversees students who have gotten into some sort of trouble or need a break (At North Light on Monday, classrooms has a chair in the back of the room where students could independently go if they needed a break). This is where in-school suspensions are held, and students complete written reflections about their actions and why they are there. The school has an office for students with dyslexia, and a specialist pulls students out of classes to work one-on-one with them. Most teachers at North Ridge teach for about 15 hours per week. At my school, that number is closer to 18. One thing we do more of at BCLA is meet in content teams, as the math team at North Ridge meets on Tuesday afternoons. All teachers in Singapore are rated on student performance. According to Chong Mong, the ministry looks at teachers in a holistic way at both student results and the instructional process. Chong Mong also said that there are numerous incentive programs that benefit teachers who get good results. The Boston Teacher’s Union has fought such a program in recent years. All Singaporean teachers get a yearly budget of $400-700 for memberships, another computer, equipment, extra classes, etc. I enjoyed our discussion with the principal and vice principal today. I wish we could have observed more math classes, however.

After visiting Kent Ridge, Patsy, Perla and I took the train to the Chinese Gardens and walked around. We climbed to the top of a Pagoda and visited a turtle zoo of sorts.

Nice view from top of spiral stairs at Pagoda

Nice view from top of Pagoda

Feeding the turtles

There were more turtles and tortoises than I have every seen. After that we went to see Khoon Yoong Wong from the National Institute of Education lead an in-service professional development for math teachers of 7th and 8th grade students. We saw him teach the art of using manipulatives to model how to solve basic algebraic equations. He used bags to represent the variable and pieces of rectangular paper to represent constant terms. This reminded me of how I use cups to represent variables and translucent colored discs to represent numbers. He also showed us a nice computer model of solving equations involving matchbooks and matches that I plan to use in my classroom.

After this workshop, we stopped by the headquarters of the Ministry of Education to visit briefly with a friend of Patsy’s.

Security was tight at the Ministry of Education

I was scolded by a guard for taking this picture in the lobby

A nice gym in the ministry building

She gave us a brief tour, and I was amazed by a few things: the security in the lobby would not let us take pictures of beautiful educational banners they had hanging, and their elevators were technologically advanced and sophisticated – you press what floor you are going to and it tells you which elevator, A through H, will take you. Then it takes you to that floor – Patsy’s friend is a math expert teacher leader and she does not have access to any other floors except the one that had a fully-equipped gym and cafe..

This model, showing four circles cover this sphere, visualizes the surface area formula of a sphere

It has been clear throughout this trip that Singapore values education highly, invests in it greatly, and recruits top candidates to teach in each field, and then gives them the resources, technological and developmentally, to be successful in the classroom. I have been learning a lot at these visits, and I look forward to seeing the opening school ceremony at Catholic High School tomorrow at 7:30. Because of this early start, it is already past my bedtime, so I will tell you all about it tomorrow.

p.s. Apologies for all of the typos I imagine are in all of these posts.. There is no spell check on the computers I use and I’m typing ideas as they come..

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First School Visit and National Institute of Education

So today was the beginning of a full week of school visits around Singapore to witness different types of schools and approaches to teaching mathematics. All week I am joined by Perla, a math teacher at the University of San Diego, and Patsy, one of the organizers of the 5OSME conference and well connected in Singaporean math circles.

Today we started the day at Northlight School (www.nls.edu.sg) for a meeting with the principal Chua-Lim Yen Ching. She was an extremely gracious host, giving us a tour of the school of 820 students that combines academics and vocational skills.

Principal at Northlight showing us one of the non-academic supports offered at nearly all Singaporean schools

At the completion of the sixth grade in Singapore, all students take a high-stakes test that puts them on one of three tracks. Northlight is where students who fail this Primary School Leaving Examination (PSLE exam) go for seventh through tenth grade. After that, graduates of Northlight may continue to the Institute of Technical Education (ITE), an apprenticeship, or straight to employment. Ching said that most students will not proceed to the Polytechnic School or University, but the school is only three years old, and its first graduating class was last year.

Perla, Patsy and Paul at Northlight School

Northlight has a staff of about 110, which is high because of the need for at least two teachers for most vocational program classes. We toured one of the school’s test kitchens and its student-run cafe where we had a delicious lunch; a model hotel room with attached classroom where students were learning how to fold the end of toilet paper rolls; a mock retail store where students were practicing stocking items; and a recreation room where students can exchange positive teacher reports for tokens after school.

Mock hotel room at Northlight

Retail store at Northlight

Test kitchen classroom at Northlight

I liked that four positive teacher comments would get a student one token to play pool or a video game, but if the students showed patience and saved eight tokens, he or she would receive three tokens. We also visited a school store that teachers from other schools in Singapore shop at. All proceeds go to a student fund, and I purchased a Monopoly-like financial literacy game developed by Northlight called “Mind your money.”

Mind your Money financial literacy game produced by Northlight

I hope to use it as a model to create a similar game for my students since financial literacy is such an important subject that is neglected in the Boston Public School system on the whole. We also visited a vegetable and herb garden in the corner of the school where students grow pumpkins and watercress, to name a just a few.

Northlight serves bright students, but they often lack confidence in their abilities and many come from difficult homes and social and emotional levels. I can certainly relate to this student profile. Twenty-three percent of the students receive special education services, and 70 percent of students receive some sort of financial aid. The school is 2/3 boys, and many have “complicated social problems,” according to Ching. Because of this, Northlight conveys positive reinforcement at every turn. I must have taken 15 pictures of different posters of encouragement throughout the school – they are everywhere – reminding students of their opportunities and their abilities.

Motivational writing is ubiquitous at Singaporean schools

Ching said something that I have not heard in an education-related discussion: she spoke about the school’s focus of raising the Emotional Quotient (EQ) of its students.

Northlight quantifies and develops the emotional quotient of its students

At Northlight, a student’s EQ level relates to his interpersonal and intrapersonal relationships, adaptability, stress management and general mood. The school does this is a variety of ways, but one way is by staying front and center in the lives of the students. Every morning starts with 30 minutes of “Class Family Time,” which is a nice way to think of homeroom. Teachers touch base with students and how they are faring in school and at home, and it is a way to ensure that no student is falling through the cracks. They have “Class Family Time” at the last 30 minutes of school on Fridays to remind students about living life in a positive and nurturing way as they set off for the weekend. The school stays open over holiday breaks if students want to drop in, as many come from difficult home situations. There is an on-sight eye doctor twice a week to provide regular check-ups and free glasses. There is a school health center where students can get checkups and have dentist appointments.  At lunch, students and teachers often eat lunch together and have mid-day check-ins. As we walked around the three-story campus that enclosed a rectangular open green space students were smiling as they walked by in their white, purple and grey uniforms, and they were all quite courteous. Our student server at the student canteen where we had lunch was professional and sweet.

A delightful lunch at Northlight's student-run cafe

As Ching said, “We strive for quality relationships and structures to stay connected.” In addition to the vocational options at Northlight, there are numerous extra-curricular activities such as compulsory ceramics, a student-run radio station and sports. Ching said that all students leave Northlight proficient not just in basic computer skills but in others such as blogging. Students have the choice at a variety of modules, which allows students to pursue their interests and ensures that the curriculum is more manageable for the students. Students have work attachments (internships) to practice the vocation they eventually choose to focus on. Vocational options include retail, hotel and restaurant, and once a student has tried at least four vocations for an extended period, they may choose one to focus on, and they spend 1000 hours to master it.

I was jealous of the school’s open-air feel with a lush courtyard and outdoor eating area. The conference room, like every other room in the school had a ceiling-mounted projector displaying onto a wall-mounted interactive Smartboard.

A typical Singaporean classroom is brimming with technology

Smartboards allow teachers and students to move objects around with their hands and create on the screen. We have three Smartboards at my school, which has no open space at all unless you consider a concrete teacher parking lot an open space, but I don’t.. However, my school’s Smartboards are portable (on wheels) and so whenever we want to use one we need to wheel it into place, apply the brake locks, and then go through the cumbersome process of calibrating the Smartboard for use with our projector, which is most likely resting on a cart or desk as we have no ceiling mounted projectors. The difference in this technology may not seem great, but it is, because teachers at Northlight do not use Smartboards for “special lessons” or “Smartboard lessons,” but they use Smartboards like we use white boards and overhead projectors because they are integrated seamlessly into the classroom environment.

Education at Northlight is the combination of vocational education (46%), instructional education (28%) and character education (26%). Ching said that a student who receives a perfect score for a term in math has an 80 out of 80, and the remaining 20 points for the term are determined by the student’s EQ and character. Each classroom has glossy posters describing positive scholarly habits of mind. We had the pleasure of visiting a 7th grade math classroom that was learning angles. The teacher was lively and animated (the class had 14 students, including only 2 girls – the class size maximum is 20) and she used her Smartboard throughout the lesson.

Math teacher and student at Northlight exploring angles

She was able to construct an angle by dragging her finger across the board, and she had many students come up in front of the room to present an angle or to work on the Smartboard. After about 15 minutes of this, she asked the students to construct angle XYZ, which was 50 degrees. Her students were engaged for the most part, and her expertise with the Smartboard, and her students ease in using the Smartboard made it clear it was used frequently. We only caught 25 minutes of the lesson, but it was clear that the students in the class were engaged in the lesson.

Students manipulating angles on a mounted Smartboard

Ching said the teachers assign homework, but they prefer that students do the work at school.

The similarities between Northlight and my school mostly revolve around the makeup of the students and the fact that many students at both schools suffer from social and emotional turmoil in their lives. My school focuses on college prep and leadership while Northlight focuses on providing its students with the ability to cope with their daily lives and lead productive lives as members of the Singaporean workforce. Ching said that helping these students achieve more than their parents will make them positive contributors to society and to put them on the path to produce children who then move on to college and do better than them. At my school there are students who I know would benefit from vocational training and who are thinking about careers in a trade, but we have no way to support them other than helping them find a summer or after-school program. Also, I don’t think we do enough at my school stressing positive behavior and raising our students’ EQs. I learned a great deal about how a school of students who were mostly written off by their Primary School teachers have risen proudly at Northlight, and the school’s model has proven successful. I feel lucky to have had the chance to be a guest there for a few hours today.

In the afternoon, we took a cab (cheap) to the National Institute of Education (NIE) where we met with Khoon Yoong Wong, former chair of the mathematics department.

National Institute of Education

Patsy made Wong a paper hat

In Singapore, the teacher-training system differs greatly from the system in the United States. In Singapore, the Ministry of Education selects prospective teachers based on test scores and grades and they come to the NIE as untrained teachers. Their education is paid for by the Ministry.

There are different paths that prospective teachers take to becoming a teacher which include: Diploma Program (2 years and paid), Post Graduate Diploma (one year paid), or the Degree Program (4 years and partly paid). Students at NIE must focus on either two or three subject areas depending on whether they want to teach at the Primary Level (graded 1-6) or at the Secondary Level (7-10). Wong said that sometimes students are mismatched, and that occasionally someone with an engineering background will have to focus on math and English. He said incoming students get to choose what subject areas they would like to focus on, but he said the ultimate decision rests with the Ministry of Education. He said that there are few cases of students who come from other careers later in life. At the end of a student’s time at NIE, if she passes, the Ministry of Education would assign her to a school.

Graduates have a three-year obligation to teach. If the teacher fails during the teaching training and drops out, he has to pay for the school. Similarly, if a teacher does not fulfill the three-year commitment, she would have to pay back the Ministry. Teachers of students with special needs would attend the NIE’s Early Childhood/Special Needs track, but Wong said that subject teachers do not get this training. He said once a teacher completes the NIE processes, she is certified for life. Wong said the Ministry is starting to offer cash incentives to teachers who have stayed in the system for at least five years to retain their best teachers, but he said that the number of people who leave the teacher profession, other than retirees, is not large. Teachers are well compensated in Singapore. Patsy said that the difference in teachers in Singapore and the United States is that in Singapore, the Ministry actively recruits the top 1/3 of all students to the profession, whereas in the United States, there is no such policy. Wong said the NIE and Ministry are working to revise the Singapore math curriculum slightly, but he did not give too  many specific details. He said some people are concerned the math syllabus is being watered down and the standards are being lowered. One thing about the Singapore math curriculum that may not be replicable in the United States for logistical reasons is that fact that you can enter Primary 2 math classrooms on opposite ends of the island (it’s not a very big island, but you get the point) and the teachers would be teaching the same content in different ways. In the United States, there is a good chance that if you attended a 2nd grade classroom in Boston and one in Oklahoma City, you would not only see different pedagogical approaches, but the content would likely be quite different. The current state of public education in the United States with its variety of standards and competencies on the state level ensure that students in one state will not learn all of the same math concepts as a student in another state. The Singapore system has continuity and a track record of success, and it is no doubt that its math books are being used in many math classrooms in California.

Another difference in the Singaporean and Boston school systems was that all teachers in Singapore must complete 100 hours of mandatory, yearly in-service professional development of their choice. In Boston, professional development can vary greatly in value, and I respect the ability to choose enriching experiences in Singapore. As a matter of fact, Patsy, Perla and I (hmm, our names all start with the letter P..) will attend a professional development class on Wednesday afternoon that Wong is teaching to prospective Primary and Secondary school teachers about tools to implement and teach multiple representations effectively in the math classroom. The Singapore model of making concrete manipulations more understandable is quite similar to the National Council of Teachers of Mathematics’ process standards that we use at BCLA. Wong showed us a concentric hexagonal diagram of the tools that Singapore math teachers use to implement multiple representations that include: symbol (manipulative), word (communicate), story (apply), real thing (do), diagram (visualize), and number (calculate).

Six mathematical representations taught in Singapore

These representations are similar to math essential question at BCLA: “What does it mean to problem solve analytically, graphically, numerically and verbally, and why is it important?” As an example, Wong reviewed the problem (a + b)^2 and talked about how a Singapore math teacher would teach students how to represent it in six different ways. I look forward to his class on Wednesday.

Today was a long day. I took a nap after the school visits and then went back to the sushi place I went to on Saturday night. I went with Perla and her son Dan, who is entering his senior year at High Tech High in San Diego (the complex of schools featured on Oprah, I’m told). We had a nice dinner, and now I must go to bed for a busy day tomorrow. We are spending the whole day at Republic Polytechnic (www.rp.edu.sg), which is a project-based school for students who have completed secondary school (10th grade). Dan spent the day there today shadowing a student and their assignment for the day was to take six hours of a videotape of a conference and condense it into a five-minute, well-edited program. How cool is that? I still think back fondly to my year of student teaching at Fenway High School in Boston where they have a Project Week every April. Dan’s description sounded like something that would be offered there. I still hope to get a Project Week off the ground at BCLA, and I look forward to learning best practices at Republic Polytechnic tomorrow. At 5:30 tomorrow we are attending the opening of the iNVENT! Exhibition at the Science Centre (tie required – I nearly choked from the humidity this morning before I loosened my tie).

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Day Two of Folding Convention/School Visits Tomorrow

Yesterday the folding convention concluded and the class I would like to talk about was the last of the day. I was really taken by the skill and instruction of my teacher, Cheng Herng Yi, a local high school student t a school with a focus in math and science.

Our simple box instructor, Cheng Herng Yi

The class was simply called, “A simple box,” and as a novice folder with now a handful of days worth of experience, it was refreshing to work on origami that was less complex, but also highly practical for my geometry classroom.

Yi, wearing his polo shirt with the name of his high school was extremely calm and clear in his presentation of the directions. He started the presentation by telling us that he came up with the fold pattern independently based on a well-known folder’s similar shape. Upon further research, he realized that this folder had also developed the pattern that he created. I was extremely impressed that this 17-year-old was developing his own patters, even if they had already been documented by someone else. It seems to me that with practice, many people are able to become proficient at copying existing models. However, to develop your own folding patterns to create something takes more ability and conceptual understanding.

Yi showed us a model of one of his boxes, and then he took it apart into its different pieces. He then unfolded each piece to show us the outline of its folds.

Yi's instructions were clear

He also drew on the white board what the diagram of the paper looks like folded. He was a very visual teacher, and his instructions were clear and concise. He waited until everyone had reached the same point in folding before moving on. The folds involved in making the “simple box” are not overly difficult, but what was hard was fitting the pieces together so they fit snuggly.

Some pieces of the box

Here I am folding..

Part of my box

This took time, but with other repetitive tasks, it became much easier with practice. We also folded tops to our boxes using paper that was slightly shorter. Overall, it was a great experience, and what was also nice was that the activity lasted about 50 minutes, or time to teach and practice in one school period.

I envision that many of my students will struggle initially with folding because it will be new for most of them. I will start with straightforward activities like examining what happens to a square piece of paper when it is folded by its edges or its vertices. As I mentioned in an earlier post, I can use this activity to teach vocabulary, and it will also be good practice for my students to practice the two most basic folds. During this introduction to folds, I will also review the difference between valley folds and mountain folds (if you put the paper on a table, the paper would prop up and the fold is on top, like the peak of a mountain). The valley fold is the opposite.

The construction of a simple box is a good activity for volume and surface area, and I plan to use it when teaching these concepts.

At the conference and folding convention I bought some books, “Origmics: Mathematical Explorations through Paper Folding,” by Kazuo Haga, and “Origami Games,” by Joel Stern. I also received the names of other Origami books by Tom Hull and Nick Robinson to buy for the development of lesson plans and projects involving origami.

Last night I had dinner with friends of a friend at a sushi restaurant in the basement of a mall that is only about three minutes from my hotel. I had not explored in that direction, and it was surprisingly my first experience in a Singaporean mall. Singapore is known for its malls and shopping, but I have preferred walking around neighborhoods like Little India and Chinatown to malls. I was a little skeptical about a Japanese restaurant in the basement of a mall, but the sushi was good (and cheap) and it made its way around a conveyor belt. There were also sushi chefs taking more specialized orders. Perhaps the biggest quirk of the place was how to order things not on the sushi carousel.

Sushi carousel

You walk around with a cylindrical container that you might put pencils in on your desk, and you peruse little descriptions of Japanese dishes on assorted bins. If you want one of the dishes, you take a popsicle stick from the bin with the food’s description and put it in your cylindrical container.

Popsicle sticks for ordering sushi

Once you have taken all of the popsicle sticks you want, you give them to the server, who brings your food to the table. A fascinating system. The dinner was good, and it was nice to have a long conversation with locals who have a few years of stories to tell. One story that caught my attention was about a failed plan here many years ago to offer tax relief to married couples who each have college degrees and have a child. On the flip side, apparently there was some sort of incentive for women who did not go to college to be sterilized. Creepy. Anyway, the couple likes living here, and they like the ability to hop on a cheap, short flight to exotic destinations.

Today I had a free day and it rained, so I went to the Asian Civilizations Museum by the river.

Don't worry, they are bronze..

I spent a few hours there learning about different cultures ranging from headhunters on remote islands in Indonesia and the different Chinese dynasties. The museum, on three floors, was impressive, and its collection was varied and interesting.

One of many cool artifacts at Asian Civ Museum

For example, there was a skull that was found on one of the headhunter islands with carvings on it. There were also a lot of interesting weapons, jewelry and statues. I lucked out and latched on to a guided tour when I arrived, and the guide was quite knowledgeable. Singapore is a melting pot of people from all over the region, and it was interesting to hear the stories of why people have come here and where they came from.

At 6 p.m. I met Patsy, who is taking a few of us from the conference on school visits this week. We walked to the Peranakan (means “child of” or “born of” and refers to people of mixed ethnic origins) Museum, but it was closing, so I plan to come back on Wednesday afternoon when there is no school visit. Then we ate dinner at True Blue Cuisine, an authentic Peranakan restaurant across the street. We shared dishes that were spicy and mostly contained shrimp. We had a salad with bananas, a whole fried fish, tender beef, and a pot with chicken and interesting nuts that were stewed and cracked. You scoop out a marrow-like black paste from inside the nut that is quite tasty. Dinner was nice, and we talked about the origami conference and teacher training and education in the United States. Perla, who teaches college math in San Diego, is the only other person attending every school visit this week. Robert Orndorff, whose presentation I attended and who was the instructor for the modular brick class, was also at dinner. Robert and Patsy agreed that one reason they believed that American schools have sometimes struggled with math education is that its teachers are not always mathematicians. I agree with this idea, but in my opinion this will not change until education is valued more in the United States and there is more of an incentive for highly qualified math minds to forego careers in science, business, and engineering (to name a few) and enter the cracked system of public education in America.

Before dinner, Patsy gave us a copy of our schedule for the week. Instead of retyping it, I will paste it below.  I am excited to visit a range of schools that teach students with varying skill levels. It will be helpful to see how algebra and geometry are taught, and it will be nice to visit a primary school (grades 1-6) since I have never observed such a level.

Here is the schedule:

Tour of Singapore Schools     19 – 23 July 2010

Monday, 19 July: 1. Arrive by 9:30am at Northlight School (http://www.nls.edu.sg/). It is a secondary school, which opened three years ago to accommodate students who struggled during their primary school years. A teacher will demonstrate use of the smart board. 2. Arrive by 2pm at the National Institute of Education (www.nie.edu.sg), the sole teacher preparation institution for the country, to meet with Khoon Yoong WONG, former chair of the mathematics department.

Tuesday, 20 July: Arrive by 9am for all-day visit to Republic Polytechnic (http://www.rp.edu.sg/), which is unique. It its a totally project-based school for students who have completed secondary school. 5:30pm: Opening of iNVENT! Exhibition at Science Centre (are you interested?)

Wednesday, 21 July: Arrive by 9am to Kent Ridge Secondary School (gr. 7-10; http://www.kentridgesec.moe.edu.sg/). It is a neighborhood school. I conducted a lesson study workshop at this school on 3 June. The students are average, with not very high scores on their Primary School Leaving Exam (PSLE, taken at the end of gr. 6, which determines where students are eligible to go for secondary school). Afternoon open.

Thursday, 22 July: Arrive by 7:30am at Catholic High School (http://www.catholichigh.moe.edu.sg/) that is both primary and secondary. Afternoon open.

Friday, 23 July: Arrive by 8:30 am at Tampines Primary School (http://www.tampinespri.net/), which is a school of distinction. I met the principal in 2000 at a mathematics conference in China.

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Folding Convention

The 5OSME conference offered numerous theoretical insights into applications of origami in the classroom, and the folding convention, which is winding down today, has given me the chance to get some experience folding models.

Yesterday I attended a modular brick class and a starburst ornament class. Both classes were labeled “lower intermediate,” but I certainly struggled at times… The modular brick class was interesting, as we constructed bricks that fit into each other. First, we made folds based on a crease “cheat” sheet that showed us where to fold.

Modular brick made from "cheat sheet"

I was able to follow these directions relatively well. What was much harder for me was starting from scratch with a regular sheet of paper and folding it into columns and rows and then making the correct folds from those columns and rows.

Making the folds without the crease sheet is more difficult

Some of the more advanced participants at the class made five or six bricks by the time I had made my first one.

More experienced folders worked quickly

This is what it looks like when you put the bricks together

Robert Orndorff, who teaches origami in the Seattle Public Schools, led the modular brick class, and I received a lot of help from a friend, Dirk, from Germany, who is a theoretical chemist.

Robert helping James Morrow with the folding steps

This class really showed me how much of a cooperative learning opportunity origami provides. Even though I was confused at times folding the creases on a blank sheet of paper, I was never discouraged, and Dirk and Robert helped me along.

The second class I took yesterday was the starburst ornament construction class with Charlene Morrow of Mt. Holyoke College. Charlene made it clear at the beginning of the class at 3 p.m. that she would stay until the last person finished, and that was me, at 7 p.m.

Charlene showing off a finished star

I worked for four straight hours folding 30 separate squares, in six different colors, and then attaching the created pieces together.

Six different colors and five sheets of each

I'm in the early stages of folding the 30 pieces of my star

For this activity we used clothespins to hold certain parts of our models together as we worked.

Clothespins holding 30 parts together

At 5 p.m. we had to vacate the nice air-conditioned room at Singapore Management University and continue in the hallway, and this change slowed me down because the humidity in the hallway (it is open air) started to bend and curl my squares.

Humidity is not the friend of a paper folder

I counted 9 separate folds per sheet, and there were 30 sheets, and the humidity really slowed me down.

The finished product was a 20-sided polyhedron with parallelogram faces. The paper we used was shiny, so the ornament resembles a sparkling star from afar.

One piece to go..

And it's finished!

I was really proud of my completed work, and I will be taking it back to Boston with me. Even though I was the last person to finish, I never doubted my decision to complete the project. This activity was more repetitive than the modular brick folding, and I found myself in a zone, folding the creases and manipulating the paper. I was calm and not thinking of anything else but my next fold, and where each of the 30 completed pieces was going to go. Charlene and her husband James were incredibly gracious and supportive, and Charlene made me a box and cover to put my ornamental star inside. I took at least 20 pictures of the process from the beginning until the finished product, and I look forward to sharing them with you once I upload pictures from the trip (this may not happen until I return to Boston).

One takeaway I had from the experience yesterday was that I never felt panic or dread no matter how new or difficult what I was doing was, and I learned quite a bit in a short amount of time. I felt gratification when I finally finished the star. I do not think I will use the modular brick model in my origami unit at school, but I could see myself teaching my students how to make the ornamental star. The lesson would be rich in vocabulary like vertex, vertices, edge, symmetry, parallelogram, polyhedron, etc., and it would be great for developing my students’ fine motor skills and confidence in math. I got lost in the project and it did not feel like I spent four straight hours folding and manipulating paper, and I think my students would similarly enjoy the activity.

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5OSME Conference Reflections

First off, I appreciate all of the concerned emails from friends and family after I did not post a blog entry on Wednesday. Let me assure you that I am all in one piece, I am not awaiting trial for jaywalking or spitting gum on the sidewalk, and I have not fled to Indonesia or Malaysia. My international origami conference, 5OSME (Origami in Science Math and Education) commenced yesterday, and it was quite the busy and productive day.

5OSME kicks off!

The conference kicked off with a keynote address by the brilliant (and quite funny) Erik Demaine, a professor at M.I.T., who designed and sold puzzles and board games with his father at an extremely young age, and who attended or completed college at the age of 12. I forget which it is, but you get the point. . Among other things, he spoke of the great innovations in the burgeoning field of Origami, which is going through a Renaissance, or Awakening of sorts. I admire Erik’s seamless ability to discuss extremely complicated mathematical theory in a user-friendly and inviting tone. I especially liked his talk about optimizing wrapping with the least amount of paper. He used the spherical Mozartkugel chocolate candy as an example of how, with the help of computer modeling, the size of the wrapping paper could be reduced to save .1% of material. As he said, this may seem like a small amount of tin foil, but when you consider how many Mozartkugels are produced in a year, he joked that he could be on to something here – perhaps the cure for global warming. He got laughs from the audience of about 200 conference participants, gathered at the School of Accountancy at Singapore Management University, but all jokes aside, origami, the art of folding paper into various models, has numerous potential applications from designing airbags that fold to the smallest area and foldable telescopes, to name a few. I am attending the conference to learn about how origami relates to mathematics, and how I can integrate the art form into my instruction to develop my student’s confidence, spatial relation skills and geometric competencies. I was not disappointed.

I was immediately excited that I would have more exposure to teachers using origami in their classrooms than I had expected. If you’ve read my previous post, “Origami Conference Workshops,” I narrowed down education-related workshops that I hoped to attend. To my surprise, I was able to attend all of them. The presentations were each 30 minutes long, and I saw 19 of them over the past two days! My favorites were the ones that most closely related to my goal of using origami as a medium in my classroom to provide a fun tool and entry point to learning geometry. I had discussions with many of the presenters at lunches and during breaks, and I got their contact information to receive detailed essays about their work, lesson plans, and even quantitative studies about the effectiveness of origami on improving spatial relation reasoning.

One of many lesson outlines involving origami

I took detailed notes during all 19 presentations, and also during both keynote speeches, including the one Thursday by the brilliant origami trendsetter, Robert Lang. If anyone wants a more detailed account of the two days, I would be happy to provide them. In this space, I am going to summarize the key ideas and takeaways I have from the past two days.

I learned that origami is being used to teach math (not just geometry, but advanced algebra and much higher level calculus), art, and ELA (English Language Arts) and ESL (English as a Second Language) to students at the Seattle Publics Schools; at schools in Heidelberg, Germany; at schools in Israel; at Mt. Holyoke College; in New Zealand; at the Chicago Public Schools; at Richard Stockton College in New Jersey; in Hong Kong; at middle and secondary schools in Cumbria, England; at kindergartens in Barcelona; in elementary schools on Long Island; and even in my backyard at the O’Bryant School of Math and Science in Boston. Of course, origami is being used in many other school districts across the globe, but these are just some of the places that I heard about at the conference. My question at the conclusion of the conference is, why is origami not being used in all school districts?

One teacher in the audience may have answered that question at the close of Robert Orndorff’s presentation about bringing fun back to the Seattle Public School system’s math curriculum by volunteering his time there to work on explorative math projects using origami. She sadly said that her principal observed a math class in which she was using origami and scolded her for using valuable classroom time (which presumably could have been used to prepare for a state high-stakes test) to do a silly activity like folding paper with students. Orndorff and others in the audience, mostly die-hard origami enthusiasts, all sighed and said that this was a sad story, but also a reality in many districts. Part of the problem with using origami in the classroom is perhaps that few quantitative studies exist extolling the positive and enriching effects it can have on students’ spatial relationship skills, ability to follow directions, problem solving skills, reasoning and proof abilities, verbal and written skills, and confidence.

Math concepts taught through origami

Norma Boakes, a professor at Richard Stockton College in New Jersey, has taught four 25-student semesters of math using origami, and she has data, albeit with a small sample size, that all of her students have improved their spatial relation skills from the start of the coarse until the end. She has also noticed that it does not matter the student’s baseline spatial relation skills – both the best and worst at spatial relationships at the start of the semester improved their abilities at a similar rate. As she said, this shows that origami is a valid tool for learning.

Folding a box is not enough

As an added bonus, teaching using origami focuses on expanding students’ persistence and frustration tolerance, ability to be creative, and it is a relaxing and calming activity. Anyone who has taken a square piece of paper and made a book fold (made by placing one edge on the opposite edge and making a crease) and two diagonal folds (made by placing a vertex on the opposite vertex and making a crease) can quickly see the immediate applications paper folding has to teaching important geometry terms like square, triangle, trapezoid, edge, vertex, vertices, midpoint, diagonal, symmetry, congruent, right angle, right isosceles triangle, Pythagorean theorem, and vertical, complementary and supplementary angles. This can all be taught using a set of square sheets of paper and three folds. Obviously, this is just the beginning to the hands-on, tactile, kinesthetic learning opportunities which origami presents in education. The majority of my students receives special education support and has special education plans, and many of them eagerly look forward to hands-on activities in which we measure things or construct shapes. Origami is a new tool that I look forward to using, starting this year, to not only develop their geometric understanding, but also to bolster their confidence in being successful at school and being proud of their creations. In the process, origami will present a friendly access point into geometry and improve their fine motor skills. Orndorff called what he does in the Seattle schools, “stealth math,” as many students do not even think they are learning math concepts and principles as they are engrossed in folding, either during a free creation period or when following directions or working in a group to construct a model.

Some origami project ideas

Matching the math concept to the appropriate model

I was surprised to learn that there are far-reaching origami applications that extend beyond math and into ELA and ESL instruction. Boakes assigns individual and group projects in which her college students must fold various models of their choosing with specific themes. The group aspect encourages creative cooperative play and respecting team members and roles in a group setting. Her students must keep journals and write essays that describe, step-by-step their constructions, and they must also intricately describe each piece. She has the students organize and present an art show at the end of the semester in the form of a gallery, and each student creates his or her own collection. She also requires her students to record themselves on video cameras describing how they constructed their models. These videos all appear on origamitube.com (I had not heard of that either..). I was encouraged to hear that others are already doing this, because I look forward to developing an origami unit at school this year that culminates in a gallery show of my students in which they describe their constructions and the geometry imbedded in them. They will also write descriptions of each work. I spoke with Boakes after her presentation and have her contact information, and she said she would be more than willing to send me project outlines and ready-made math lessons using origami.

Rich lesson ideas

Boakes was not the only presenter who incorporates both math and verbal skill building into instruction involving origami. Shrikant Iyer of Stonybrook University in New York uses “Storigami” with elementary students. This involves the telling of stories as he creates origami with his students. He has found that this approach improves the memory and listening skills, symmetry, ability to follow directions and social skills. Christine Edison related narratives of successes she has had teaching low-income students in Chicago. She found that students who joined her after-school origami club performed better on math tests that the rest of her students (Boakes had a similar experience with students she pulled out of a traditional math class – she taught the concepts through origami and the students performed equally well on an the next assessment). Edison said that origami provided a bridge between her and some of her more challenging students who would shut down in class and not engage in anything. She reasoned that origami’s playful appearance makes it less intimidating than a traditional math lesson and students were much more at ease engaging in the activities without the pressure of putting students on the spot about understanding prior concepts.

Origami narratives

More narratives

Of course, those concepts would need to be accessed and developed, but origami provided the benign access point to this learning. She said a lot of her students told her things like working with origami was the first time they felt smart, and she said the origami lessons transformed students who have not experience success at school – ever – into eager learners. She said her work strengthened her students sequencing and understanding of order of operations (and not just PEMDAS, but how to follow steps to reach an end goal). According to Edison, an ESL teacher in Chicago forced students to write the step-by-step directions of how they made a construction, however simple or complex. The teacher also required students to write short stories describing what they made. These assignments transformed a disengaged group to an excited group. The ESL teacher had a student who went to Mexico for a month and returned with a basket of models that she created, with the help of others, and she had accompanying stories and directions written for each one. As a special education teacher, Edison said that she noticed origami’s calming effect on her frequently hyper students, and she said working with origami also appeared to relieve her students’ stress and helped them focus on the task at hand.

Dr. Charlene Morrow of Mt. Holyoke College has run an origami summer camp, Geome-gami, for high school girls for 20 years to build their confidence in math. I spoke with her on the walk back to the hotel last night and she said that an experienced math teacher at the O’Bryant School of Math & Science in Boston has helped some of her students get scholarships to her camp, and she said the teacher also started an after-school origami club at the O’Bryant. I look forward to contacting her when I return to Boston to pick her brain about what has worked and not worked in her use of origami with BPS students.

I also learned about Origametria, a program in Israel in which students are taught first and foremost to think. This was a common thread of all of the presentations about origami in teaching: students need to be the learners, working independently or cooperatively to solve problems and figure things out on their own. Folding paper to build novel creations or recreating a model through reverse engineering, students are forced to become innovative math thinking and develop and use critical thinking skills. They are forced to become more independent thinkers and get out of the habit of providing quick answers and then giving up if they are incorrect. James Morrow, Charlene’s husband and co-director of Geome-gami , said that the goal is to create “the innovative mathematical thinker.” “It’s not about how many formulas you know,” he said in reference to developing the math mind. Creating origami teaches students the ability to synthesize complex, abstract problems. According to James Morrow, the goals of Geome-gami are to help students develop strategies for:

*Thinking critically and creatively and becoming an innovative mathematical thinker

*Communicating effectively

*Posing and solving problems flexibly

*Asking better questions

*Becoming more independent

Outcomes of origami in the classroom

Orndorff said his philosophy is that students must complete a task three times correctly before he is confident the student is starting to get the grasp of it. He said the second time is the hardest. In this day and age of information and digital technology a click away at students’ fingertips, origami appears to be a leveler and calming agent that forces students to struggle with difficult problems and concepts, and then eventually arrive at an answer. Too often my students want to give up easily at the first sign of a mistake or failure, but from what I’ve heard at the conference, origami is not an intimidating medium, and it can be extremely helpful in developing problem solving skills and increasing frustration tolerance in students: skills that I try to develop every day in my classroom.

In addition to learning about Origami activities that I plan to replicate and develop from teachers around the world, I have started to learn more about other countries educational systems. On Wednesday I had a nice conversation with the headmaster of a local primary school (grades 1-6) who told me about the national push in Singapore to increase students’ exposure to the arts and physical education. A television news reporter who I spoke with about her experience in the Singaporean school system was shadowing him. Last night at the banquet dinner, I sat next to an art student studying in Australia who had mixed opinions about the Singapore school system. She said that students are severely tracked at a young age (around age 10) and put on one of three tracks, only one of which points to university. She said the stress level to succeed here can be extremely harsh (I saw 6th grade test prep books stacked by the register at the Banana Leaf Indian restaurant Tuesday night by the cash register – I can’t remember seeing middle school math books anywhere in Boston..). The TV reporter said she had tutors in high school.

One of the presenters at the conference spoke of the German school system and how it is converting from a 13-year system to a 12-year system and how it is vigorously tracked as well. Students there either attend Gymnasium (if they did not have grades below B-), which puts them on a track to university, or they follow a different educational path. Hearing about these “high-stakes” tests and grading systems in other countries made me think more about the United States’ educational system. Not one educator at the conference supports “high-stakes” testing, and on the contrary, the majority were outspoken opponents of it. The reason is not surprising, and is illustrated by the anecdote of the teacher who related the story of a strict, unyielding principal who scoffed at her attempt to integrate origami into her classroom because he did not think it was valid or results oriented. The field of Origami has been evolving exponentially in the past ten years and I look forward to hearing about more quantitative studies like the one that Boakes has started in New Jersey to prove Origami skeptics wrong. In the immediate future, I hope that my new headmaster (my previous headmaster is moving on to lead two schools in Boston that specialize in ESL instruction) is more understanding about the benefits and utility of weaving origami into the framework of my classroom.

So, I have not included all of my observations from the past two days, but I have attempted to distill 19 seminars worth of rich knowledge into this post. If you would like to hear more, or if you have any questions, feel free to email me at prcloth@gmail.com or post a comment below. The two-day folding convention begins tommorow bright and early, and I have two full days of folding classes to move from the theoretical to the practical. Wish me luck.

On a side note, we have been fed the past two days at the conference, and I have had the good hotel breakfast (as described in a previous post) both days. Last night we had the conference banquet (I sat at the vegetarian table because it was served and the others had to wait in along line for the buffet..), and tonight I ate with two new friends from the conference at an Indian hawker stand in the center of town. Delicious chicken tikka masala, saffron rice and garlic naan, all for about $6. There is a giant street festival a block from my hotel this weekend, so I am looking forward to that. There is a cool artistic sign on the main road nearby as well. There is scaffolding set up and giant square letters and a crew of about ten eager artists. There is a number to text what you want the sign to say, and they will change the words around to say what you want. Too bad I left my cell phone in Boston. Also, I noticed that there is a food festival in Singapore starting Friday through my last day here next Friday (before I head onward to Thailand and Cambodia and possibly Vietnam). Not bad timing on the festival.. I could definitely see myself living here some day. One thing I could have done without was the chain of a weight machine in the hotel “gym” snapping this morning at 7:15, causing the bar to come crashing onto the back of my neck (I am fine, no need to call the hotel anyone..). I did run 5k for the third straight day and hope to keep the streak alive tomorrow.

But first the two-day folding convention, an off-day Sunday, and then five action-packed days of school visits next week. Patsy Wang-Iverson, the co-director of 5OSME and quite a remarkable person, told me today that she confirmed a visit Monday afternoon with either the current or former math chair of the National Institute of Education. I welcome questions anyone has for him, or for the people at the teacher-training institute, or for any of the teachers (of all levels) whom I will be meeting next week. -30-

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