Author: Mr. Kaswell

I am a mathematics teacher at Middle School 88 in Park Slope, Brooklyn. This summer I received a grant from Fund for Teachers to travel to Tokyo apprentice with Tetsuya Miyamoto, a master teacher and creator of KenKen puzzles.


services (1)

I’ve done a lot of writing in this space about blended learning: a blend of traditional and virtual learning to give students learning opportunities/experiences they did not have before. In my own practice, this means using the School of One program. School of One is a web-based interface and assessment system with a grouping algorithm behind it. School of One assesses student learning  and assigns students new groupings and lessons based on that assessment every day. Like the students, I also get a new teaching assignment every day, so I have to stay as sharp as they do.

Screen Shot 2015-02-28 at 4.28.18 PM

BetterLesson’s Blended Master Teacher Program is now making blended resources available to any teacher for free. Click on this picture to go directly to the site.

School of One’s technology allows me to work smarter and target my skills so that I have the most impact on students. Instead of teaching one skill to a class of 30 students who are all learning at different paces, School of One will assign me to teach a lesson to a group of 10 students who all need a lesson in that particular skill while my colleagues (there are 5 of them) teach other targeted lessons.

School of One can assign me and the students one of seven possible lesson modalities (five of which are built around teacher-student interaction). It creates different student groupings every day to meet students where they are on their own individualized learning path. Its system allows students to progress at their own pace and truly learn for mastery.

It makes a lot of sense, and because of it, student engagement is through the roof. Students who have gaps in their learning from previous years catch up faster than I ever thought they would. My data show that the lowest performing students are actually making the biggest gains. Students who were behind in past years apparently just needed some extra time on these skills for whatever reason, and a blended model like School of One provides these individualized opportunities to my 300 students every day.

School of One is a great blended model, but it is not the only one out there. I know lots of teachers who are experimenting with different models, many created on their own using Google Classroom and whatever available tech they have. There is no shortage of tech, but with these new tools and trying to navigate a new teaching landscape comes a lot of questions:

How do I setup my own blended classroom?

Which technological tools are effective and which are not?

Do I have to set up the entire system myself or can I use a platform like School of One?

What will the culture in my blended classroom be like?

What is my role as the teacher in a blended classroom?

How do I maintain a strong bond with students in a more tech-focused environment?

These are hard questions. But from my own experience, missteps, and work with other colleagues who are also blending their classroom, I have found some strategies that work. My blended classroom is set up differently from my traditional one yet some of the basics of any classroom – strong culture and strong instruction – are still at the core. But it wasn’t without a lot of experimentation and miscues along the way. This year, I’ve tried to tackle more of these questions with colleagues through a fellowship at BetterLesson. In case you don’t know BetterLesson, it has, for the last 5 years, recruited “Master Teachers” from around the country to share best practices in every area and grade level of teaching in a well-curated format. This year, BetterLesson recruited 11 of us blended teachers from around the country to showcase some best practices in blended learning because, well, it doesn’t exist anywhere else! If you want to start blending your classroom and are looking for some good strategies and tips, check out all of the great resources from teachers of all subjects and age groups at A description is also below. Enjoy.

Screen Shot 2015-02-28 at 4.28.24 PM




I didn’t really know what I was getting into coming to EduCon2015 in Philly. Every conference has a different vibe that is a function of variables like people, setting, location, and x-factors (Sal Khan was at iNACOL 2015 and although he is a person, he’s also an x-factor that makes my geek meter go off the chart and the conference ultra-memorable.).


Educon has a very student-teacher-school-based feel, as it’s hosted by the Science and Leadership Academy, a unique public partnership high school between the Philadelphia DOE and the Franklin Institute. This partnership set the stage for a conference based around innovation and lots of progressive thinking. And since it’s hosted in an actual school, it felt like I belonged there even thought it’s not my school. Sitting in classrooms and having discussions with other educators and stakeholders just feels natural.

EduCon doesn’t have sessions like a regular conference does. It has conversations. I initially thought this sounded gimmicky, but it was appropriate. Basically, it was less lecture and more discussion and sharing amongst educators. Exactly what I was hoping for. The conversations ranged all over from technological to philosophical to anthropological and beyond.

Below are some highlights, thoughts, ideas, and resources I picked up in the conversations along the way…

General Tidbits to Start With

I’m amazed at how much awesome technology exists and is being developed for teachers. The market is bursting. Zaption is a cool one that embeds prompts and questions into videos that you make (presumably on Educreations or something like it). I recently started using Padlet, an online bulletin/posting board, to have class challenges. Then I use them for discussion. My colleague and I also just collaborated on a Weebly that hosts all of the resources we are using for a 7th grade Ratio and Proportions Unit we are doing this week. I know some might say that students are doing no more learning with these technologies than they were 30 years ago, and that may be true. I don’t think it is, but let’s say it is. Even if it is true, these new learning tools and formats make learning so much cooler, and I think they prepare students for the world in which they live.

Digital Portfolios for Student Work

As students do more work online, there are more and more ways for students to create digital portfolios. And they definitely should. I still have analog portfolios in my classroom filled with old homeworks and projects, which is fine. I still believe there is something to a paper assignment, but what happens to that assignment at the end of the year? Will the students be diligent and save them forever? Probably not. But if they took pictures of their work, it could be saved forever. Google Classroom and Wikispaces are good places to house this work. Safety and privacy are concerns, especially in the larger scope of students having an online presence. But one huge takeaway that I thought was so cool was students using avatars as pseudonyms to protect their identity. So cool.

Beyond just storage, these digital portfolios are being used for so much more. They are becoming interactive portfolios. A big topic of discussion was whether digital portfolios should be a display for products or a documentation process and encouragement of student process and reflection. On the latter, students are annotating their work with screencasts, podcasts, and videos as part of a reflection and growth process. This use of digital portfolios feels like it’s bursting at the seams, and there are so many things teachers can do. Time to start experimenting.

Can We and Should We Assess Character (non-cognitive skills)?

Jonathan E. Martin facilitated a very productive conversation on a topic I feel strongly about. Yes, we should assess character, which means we should be teaching and developing character. A lot of research out there supports this intention with findings that show certain character values correlate to “success” in any field or aspect of life. For clarification, “success” means generally feeling like your life has meaning and purpose no matter what you choose to do with it. One of my favorite books that I’ve read in the last few years is How Children Succeedwhich details these character traits very well. And what these traits are may surprise you. Definitely worth the read.

There was a lot more opposition in this group than I expected. The dissenters would say who are we to say which character traits are important? What if they clash with other cultural values? How do we actually assess it? Although he didn’t work for the company, Mr. Martin was advocating for a product called Mission Skills Assessment, which is a system that helps assess and track character, like a gradebook. But more questions and concerns came up. If we are assessing student character, do we give students a character grade? And if so, can we give an entire class or school a character grade? Can we then compare one school’s character to another? It was a strange road to travel down for everyone involved in the conversation, but I still say 100% yes. All the rest are details to be worked out.

Teaching for Mastery and Grading for Mastery

A fellow NYC teacher at NYC iSchool and Math for America Master Teacher, Sarah Prendergast led a fantastic conversation on mastery teaching and grading. Sarah teaches high school algebra and prepares students for the New York State Regents Exam. And just like my teaching in School of One, Sarah uses a mastery model to teach. This is mastery teaching from her blurb:

Mastery-Based Learning means breaking down a class into smaller, trackable topics and then tracking student progress on each topic. It’s about seeing mastery as the most important goal, and providing students with ample opportunities to show what they know.”

Not only does she teach for mastery, but she and her school grade for mastery, something I admit I don’t do very well at all. 60-80% of students’ grade is based on mastery. 10-30% productivity. 10% contributing factors, whatever those may be and it varies from teacher to teacher. I really struggle with mastery grading because my students work on different grade levels depending on their individualized learning path. My colleagues and I struggle with what to put on a report card for the 7th grade student who is doing very well in his work but is working on 5th grade skills. And what about another 7th grade student who is working on 8th grade skills? My report cards are not really equipped for this.

What I found fascinating and amazing is that by using a mastery tracking system and giving kids ample opportunities to master skills (instead of just moving on), Sarah can predict with almost perfect accuracy all of her students’ regents exam scores. When I heard that, I thought to myself, “Isn’t it amazing how well she knows her students?” Whether the student passes or doesn’t pass any exam is never the most important thing to me, but the fact that she knows the students well enough to be able to predict it is outstanding. And she doesn’t have any super fancy software. Just a really well-thought-out spreadsheet that has evolved into her own excellent tracking tool.

On a side note, she’s also doing lots of other great stuff with Maker Education. Those of us who saw her present at MT^2, a TED style event put on by Math for America, were impressed. Check it out below.

If you are someone who is worried about the state of education or that teachers aren’t that good or yada yada yada, go to EduCon next year and see what’s happening. You’ll feel much better. I owe a huge thanks to my principal, Ailene Mitchell and AP Peter Russo for sending me, my amazing colleague Emily Reisman for being a great learning partner there and in the classroom, and the folks at iZone NYC – Alana Laudone and Cynthia Warner for making it all possible for me.












These last few days, it’s been more like Mr. Kaz in Palm Springs, CA for the iNACOL symposium on blended and personalized learning. Yesterday morning I had the privilege of sharing the stage with Vicki Phillips, Director of Education/College Ready for the Bill and Melinda Gates Foundation, as well as three fellow teachers – Brian Johnson, Tanesha Dixon, and Collen Kennedy – who are doing amazing things in their classroom with blended learning.


On stage at iNACOL (L to R) Vicki Phillips, me, Brian Johnson, Tanesha Dixon, Colleen Kennedy

If you’re not familiar with blended learning, it is the formal education that blends traditional teaching with some type of virtual learning. Usually the blending allows lessons and curricula to be personalized to an individual student’s needs. There are many different forms and models that blended learning can take. One popular tool that many teachers now integrate into their curricula is Khan Academy, an online tool which provides virtual, self-paced learning. Khan Academy has even allowed students outside traditional classes in rural places all over the globe to access a world-class education for free. Pretty amazing. The iNACOL conference is about bringing all of the stakeholders in blended learning together.


Hero shot with Sal Khan, founder of Khan Academy

The blended learning model I work in is called School of One, and it is a very comprehensive blended learning model. Possibly the most comprehensive. It starts with this premise: Every one student is a unique individual and learns at his or her own pace and in his or her own style. The School of One package (it is essentially part product part service that a school can buy) includes a user interface and dashboard for students and teachers, content, daily groupings, an assessment system, a redesigned and renovated classroom, amongst lots of other little pieces that create this new model of learning.

School of One starts by assessing each of my 300 students at the beginning of the year and then uses a grouping algorithm to place them in personalized lessons every day. If a 6th grader enters my class on a 4th grade level, that student will start with lessons at a 4th grade level; the same is true on the other end of the spectrum. Every one student has a personalized learning path and is assessed daily to manage each student’s progress on that path. If a student passes the daily assessment, the student moves on to a new lesson on the next skill. If not, the student gets a different style lesson the next day on the same topic. Thus, this blended learning model allows me to be responsive every day to the current learning needs of each of my 300 students, something I struggled with tremendously in my old traditional classroom.

Another reason I call this model comprehensive is that School of One has completely redesigned my classroom to fit the needs of the students in this program. What was once three separate classrooms is now one giant classroom. It was completely renovated and reorganized to meet the needs of a program that has seven different types of lessons that, in theory, could all be going on at once: Live Investigation, Task, Small Group Collaboration, Peer to Peer Collaboration, Virtual Instruction, Virtual Reinforcement. Thus, there are live instruction centers, collaborative centers, and virtual instruction centers.

Screen Shot 2014-11-05 at 7.48.04 PM

A Live Instruction center

Screen Shot 2014-11-05 at 7.48.12 PM

The whole room with lots of different types of lessons going on all at once

Whatever the model is, the goal of every blended learning model and technology is to allow students to learn in ways they never were able to before. It is to reach students in ways they were not reached before. As I wrote before, I am able to meet each of my 300 students individualized learning needs every day with my blended learning tools. Again, pretty amazing. We have finally acknowledged that students are not a product moving down a factory line to be packaged up by batches, usually grouped by age. They grow non-linearly, and we finally have some good tools to respond to that.

This sounds exciting, but you may be asking: are these models really working?

That’s a complicated question since there there are so many models being implemented. It’s also still relatively early in the process. But Vicki Phillips shared some encouraging interim research yesterday that just came out through the RAND study. Twenty-three schools were studied (my school is not included in this study). In a nutshell, the research suggests (albeit with further research necessary and ongoing) that those twenty-three schools who implemented blended learning practices show significantly higher gains in reading and math than those in the control group. Of course, there are caveats and concerns about bias. But read the study and form your own opinion. (Full disclosure: The Gates Foundation funded this study and is also a partial funder of School of One. It also brought me out to Palm Springs to speak about my blended teaching practices.)

In my classroom, I have seen many students – especially those on the low end of achievement, gain 1.5 and sometimes 2 grade levels in a single year. And kids are engaged and excited to be in School of One every day to boot. Rarely are they bored or overwhelmed. I don’t want to get ahead of myself, but it sounds like success so far to me.

The iNACOL conference gives me a lot of hope about where education is going. I have recently been thinking that it may very well be possible that my own kids (should I have them some day) may not even need to attend traditional college. With online and personalized learning tools, will it be commonplace for students 25 years from now to get a high-quality degree while traveling the world? Will college classes will be fully blended? Whatever it is, education is in a transformational phase and my classroom is meeting more student needs than ever and is more exciting because of it.


Final Thoughts on the Eve of School


Aside from these being quality dry-erase markers, you can actually buy refills for them. Why can’t we have that in America?

New York City teachers report to school tomorrow, and I can feel the wave of seeing colleagues and preparing for the first day. I have my Japanese whyteboard markers ready to go, and I just bought a 72-pack of Dixon Ticonderoga pencils (in my opinion, the best standard pencil on the market). But the big question still lingers: How do I incorporate what I experienced this summer into my own classroom? I’ve had this question stewing on my back burner since I got home, and I’ve been waiting to articulate some intentions. I guess you could say I was slow cooking this stuff in my head. Here are some thoughts:

KenKen Program: It was always my intention to start a KenKen club after school, and I plan on doing so. One big takeaway from my time in Miyamoto sensei’s class was his use of one puzzle at a time as well as a timer. I will keep a point system as he does and post the rankings. I’m very curious to see how the students respond to this.

Great Lessons/Problems/Puzzles: I will always consider the fact that there is no substitute for a great question, problem, or lesson. Sometimes all it takes is 1 and you can spend 45 minutes on it. With a great problem or puzzle, the management often takes care of itself.

Say Less: This may sound silly, but I will try to say less this year. If Miyamoto sensei can say next to nothing, I’m sure I can trim down what I have to say significantly. I think this comes from being extremely confident in your ability, your material/lesson, and your class systems.

Super Challenging Puzzles: I will use puzzles that are intentionally much harder than the students are used to. I won’t help them or give them hints. I will really let them struggle, and I will be tough on them to keep trying.

Competition: I will have a quantified reward system where students can compete as opposed to just prizes and rewards for good work. As I have gotten older, my sense of competition has faded. I’m much more into cooperation rather than competition. But I have seen in many places, especially Miyamoto sensei’s class, that young people thrive on friendly competition. I’m sure I can teach some good sportsmanship in the process.

Patience and decorum: Every student in Miyamoto sensei’s class displayed extremely good patience and decorum. If a student had their hand raised and Miyamoto sensei was turned around, the student waited until he saw them. No questions asked. Despite the fractured and impatient world we live in, I still see these values as very teachable. It will take strong conviction, but my experience this summer has greatly strengthened that. I have started a ‘How to be a good student‘ document that I am considering giving out this year, and I would love any and all feedback. It is intentionally direct and somewhat harsh, but I believe this is necessary to get the point across. Feel free to comment directly on the document.

Buy-In and Excellence: All in all, the reason the students give 110% and raise their performance in Miyamoto sensei’s class is they buy into Miyamoto sensei himself. They believe in him, his problems, his process, his classroom. They believe they will be excellent under his tutelage. This buy-in is one of the biggest keys to an effective classroom. I know the students believe in me and School of One, so it is just a matter of me taking it to the next level.


Miyamoto sensei helping me achieve excellence


There was so much that happened this summer that I’m sure I’ll have more revelations and connections to this summer as the year goes on. Thanks to everyone for reading. I hope it was as rewarding for you as it was for me. For all the teachers out there, apply to Fund for Teachers and make your professional development dreams come true!

Screen Shot 2014-09-01 at 8.39.42 PM

Q&A with Miyamoto Sensei Part III


Miyamoto sensei reviewing a problem

It’s now Monday afternoon, and I’m back in Brooklyn after a long trip home yesterday. Saturday was my last day sitting in the back of Miyamoto sensei’s class, and instead of doing our normal debrief/interview at school, I invited him and my translator to my apartment roof that night for a summer fireworks show (It was happening coincidentally. I didn’t arrange a fireworks show for the occasion, in case you were wondering.) and a celebratory dinner. We did the debrief there. Yesterday was all about travel, so here I am trying to catch up. Neat fact about traveling back from Japan: I departed Tokyo/Narita Sunday, August 17 at 5pm. I flew for over 12 hours and landed at Newark Liberty on Sunday, August 17 at 4:55pm. Yep, it took me 12.5 hours in a plane to fly back in time 5 minutes.

After doing some reflecting about the whole experience in Miyamoto sensei’s classroom, I realized I hadn’t written anything about what the classroom actually looked like. So in case you were curious, the room is about 15 x 15 and bright with floor to ceiling windows along about 1/3 of the walls. The classroom is on the 12th floor so it gets quite a bit of light and a nice view, not that anyone student is looking. There are five tables of three seats each on either side of the room with a walking aisle on both ends as well as a center aisle in between. Miyamoto sensei loves to pace around the room while the students are working.

There is a long chalkboard (with multi-colored chalk and a long eraser) up front where he lists the student’s names and keeps score of the daily performance for all to see. There is no technology except for a magnetized timer he uses throughout the session. It’s pretty old school.

In the back corner of the room where you enter is his office area with several computers, an enormous monitor, a copy machine, and other personal items like some cookwear, a refrigerator, CDs (many Queen albums) and a few extra shirts. As you may remember from my last post, he spends quite a bit of time here working on puzzles and preparing for school – not just teaching – and he needs some personal stuff from time to time.

On the side wall, there is a bulletin board with the daily student rankings that many students check when they enter the class. These rankings are huge. There is also one poster advertising the Japanese Math Olympiad. No other decorations. No “You can do it” or “Keep Trying” or “Work Hard” posters. Just a ton of math books and magazines and my guess is he has a system for where everything goes. There have been a few occasions when I was interviewing him that he ran over to a bookshelf and pulled out a random volume just to show me something.

IMG_3428 IMG_3429

It is also pretty cold in the classroom, which is a big contrast from the outside heat. It definitely keeps you awake and just slightly uncomfortable, which I think this is all part of the plan. I don’t think he minds if you feel just a little bit uncomfortable. The combination of the temperature and lack of any kind of comforting gestures or signs is something you need to cut through to maintain your focus. It’s as if you’re forced to develop the ability and the confidence to handle that type of environment for 2.5 hours at a time. This is the Zen of Miyamoto sensei.


Twin dragons painted on the ceiling at the Zen Buddhist temple Kennin-ji in Kyoto, Japan


This last interview I tried focus on some of the history of his classroom as well as what lies ahead in New York. In case you did not know, he announced several months ago that after 30 years of teaching in Tokyo, he will move his class to New York next year. Once again, I did not record this interview. I took notes based on what my translator, Tom, told me.

Q: Can you tell me about the evolution of the Miyamoto Mathematics School? Was it always in the format that I see today?

A: Yes, the format has always been the same. I had a few jobs before I became a teacher, but I did not find them fulfilling at all. I was not overly interested in profits, and I realized that I wanted to create something that would last. This is when I had the idea of becoming a teacher. So I got a job as a juku teacher at one of the best companies – TAP. They are no longer around. They have been replaced by Sapix. But after a short time there, I realized that I could not teach in the way I wanted to. That’s when I had the idea for my own school, and it was born. I have always created my own materials, which is the basis for my classroom. I worked extremely hard the first few years generating my own materials, but the school format then is exactly the way you see it now.

Q: When did you start creating puzzles? Was it at the same time your school started?

A: I got my first puzzle published in 1995 by Tokyo Shuppan. In 1997, I was able to get my puzzles published in one of the top mathematics magazines here in Japan. By 1999, this publisher was able to publish 2 books of my puzzles. In 2003, a top executive from Discover contacted me because her daughter had been enjoying my puzzles, so they decided to publish some books. Unfortunately, they did not sell well because they were too expensive. But, they did publish my book “The Art of Teaching without Teaching” and that was a big success. 2006 was when I started working with Gakken, the largest education publisher in Japan. With them I created four categories of books of KenKen: easy, medium, difficult, and expert. The books with Gakken now only cost Y600, and they sold well. Later in 2006 I was contacted by a very popular program on NHK, the public station in Japan, to do a piece on me. At first I did not have the best experience working with them, and I actually turned them down. But they came back to me – which never happens – and the piece finally aired on 12/10/06. This was the point where things really took off. I started getting recognized in the grocery store and things like that.

Q: What do you envision for the future of your school in New York City? How will it be different?

A: I plan on keeping it just the same as it was in Tokyo. The difference will be that the first year I will teach only 3rd, 4th, and 5th grade students in Japanese. I have a goal of improving my English enough within one year that in my second year of the school in New York, I can have an international 3rd grade class conducted in English. I will continue to build my international classes from there.

[Because I just had to ask] Q: Do you ever have disruptive students? 

A: I try to give problems that are so challenging and consuming that there is absolutely no time for distraction. But there have been a few times here and there when I have had a disruptive student. There was one student who was doing something distracting with his pencil so I told him I would subtract 10 points from his score. Same goes for a student who I knew was cheating. Deducting points from their score was enough of a deterrent to make them stop.

If you would like to read the previous interviews, click the following links: Part I  Part II


This being the last interview with Miyamoto sensei, I thought I would end by sharing another one of my favorite problems from the day’s classes. I always come back to the fact that there is no substitute for a great problem that completely captures you. I worked on this for a while until I finally got it. How would you solve it?

48 x A = 54 x B = C x C x C

Find A, B, and C.



Q&A With Miyamoto sensei Part II

This past Tuesday I went back to Miyamoto sensei’s class. 2.5 hours in the morning with the 6th graders, and 2.5 hours in the afternoon with the 4th graders. In between I had a great sushi lunch at Tsukiji Fish Market, but that’s another story. If you’re in the neighborhood, I highly recommend going.





I am still amazed at the amount of concentration that Miyamoto sensei himself displays during class. He is straight-faced, pacing, checking, writing (on the board), and saying, for the most part, only two words – Maru or Botsu (Good or Wrong) – for 2.5 hours straight. Sometimes he says nothing at all when he checks a student’s work. This forces the student to really re-check their work. It’s not as surprising to me anymore that he gets the same level of concentration back from the students. In a way, they all seem like an orchestra playing together for 2.5 hours. Miyamoto sensei is the conductor, and the students play and play and play until he says stop. Why do students run to the bathroom? The orchestra doesn’t sound as good without them. I asked Miyamoto sensei several questions about his planning process during my interview, and his answers sounded like that of a musician or performing artist. More on that below.


My biggest takeaway from this session is that there is no substitution for a great lesson or problem. You can be the most gifted teacher, but if you don’t have a great lesson or problem that captures the students, you are dead in the water. Miyamoto sensei believes this so strongly that he doesn’t do any direct teaching at all. He merely gives excellent problems and expects the learning to come from the hard work and perseverance that is necessary to solve them. I myself was enthralled with one of his problems for about 30 minutes, and I eventually created a great spreadsheet on excel to help me figure it out. I probably should have been able to solve it by hand, but that’s where I went. How would you do it? 

The number of boys in 1st grade is 2/3 of the amount of girls.  5/12 of all 1st graders wear glasses. 72 of the boys wear glasses, and 5/9 of the girls do not wear glasses. How many 1st graders are there?


Like last time, I did not record my interview. I only took notes based on what my translator, Tom, told me.

Q: How do you plan which questions to use in class?

A: I always start my class with review problems from the previous class. After that, I use a set of 10 problems that get progressively harder. I have created all of these problems myself and spent much time arranging them. I am very satisfied with how they have come out.

Q: You told me previously you wake up very early on school days. Why is that and can you tell me more about your routine?

A: It is true I wake up very early on school days. I usually wake up at about midnight, ride my bike to the school, where I then sleep for a few more hours. This starts to bring my focus to school. After some more sleep, I wake up and start preparing my materials. In this time, I am also building up my focus for class, which takes quite a while. I do a lot of visualizing of how the class will go, and my focus steadily increases right up to the beginning where I am finally ready.

Q: I have certainly learned in your classroom that there is no substitute for a great problem, and you have many of them. Where does your inspiration come from to create these problems?

A: Students need great problems to capture their attention. It is much like reading a great novel. When you are reading a great novel, it does not feel like you are even reading. Time will pass, and you won’t even realize it. The same is true with a great problem or puzzle. I have been doing this a long time – 30 years – and I have built up a large knowledge base over that time. At this point in my career, I have enough experience to create interesting problems without it taking too much time.

Q: I have noticed that sometimes you write the problems on the board and other times you give a worksheet. Which do you think is better?

A: I believe using the board is better. When students have to copy a problem, they always show a higher level of concentration because of this extra work. When the problem is already there for them, the do not show as much focus on the problem.

Q: In my own classroom, I occasionally allow the students to use an answer key to check their own work so that 1) I can use many different level worksheets at once; and 2) so I don’t have to run around the room to check everyone’s work. What do you think of this practice?

A: Truthfully I have never thought about using this practice [laughs]. I love pacing around the room and seeing student work. I also have never thought about giving different levels of problems to the students based on their ability. The ability level in my classroom does have a wide range, yet I believe that every student should try the most difficult problems. It is true that very often my students do not find the solutions [side note: for the problem above only a few students out of about 20 solved it], but that does not matter. What matters is the hard concentration and effort that all of the students show in their work. I could understand that parents might not be happy with this method, but since all of the parents know my program, they never question it.

Q: I place a lot of emphasis on divergent thinking, multiple solutions to problems, and sharing with the class. When you check student work, do you notice many different types of solutions, and do you ever share them or have them share their solutions with the rest of the class?

A: Yes I notice many different types of solutions when I check their work. But often there is a lot of work all over the place and probably not the best to share. Once in a while, if there is a very interesting solution to a problem I will share it with the class. But generally I do not like pushing one student’s thinking on another. Every student should think for himself and create his own ideas.



One more class on Saturday, and then heading home on Sunday. Stay tuned for Q&A Part III.



The Little Differences

It’s now over a week into the trip, and I’m definitely starting to feel like I live here. I’m tempted to say I feel like a local, but when you can’t speak the language except for thank you very much (oregato gozaimas), I don’t think I can qualify. But the neighbors in my apartment building know me and the hipsters at the funky clothing shop downstairs of my building wave to me at this point.

This weekend I got to enjoy some touristy and non-touristy things around Tokyo. Tokyo is so much larger than I ever realized. The city of Tokyo itself has over 13 million people (4 million more than NYC), and the metropolitan area has over 32 million; it’s the biggest metro area in the world! With so many narrow streets, the population density here is staggering. There’s masses of people everywhere, and not surprisingly, more restaurants per capita than anywhere else. In Tokyo, you could never be without food. Where it comes from or where it goes, I have not totally figured out.

As I walked around this past week, I got comfortable in knowing that they mostly have the same stuff here as they do in the United States, but there are some little differences. Here’s a few in no particular order:

Electronic toilet with bidet: Not only do almost all the toilets here have bidets, but they are all electronic. There is a control panel on the wall that covers all functions. That means 1) there needs to be an outlet near every toilet; 2) there is serious wiring for a toilet that I usually only save for installing surround sound stereo; and 3) with all this effort going into the toilets, everyone must use them, right? I still have not, and I’m fine with keeping it that way. Although the button to automatically raise the seat is much appreciated.




Sideways traffic lights, driving on the left side of the road, walk signals: I get driving on the left side of the road. I still have to look both ways when crossing, though, because I can never remember which way to look. Luckily, EVERYONE here waits for the crosswalk symbol, even if no cars are coming. The crosswalk symbols have very convenient countdown “bars” so you know when the light, which is always sideways, is changing.


This is one example. Sometimes there are configurations of five and six lights that I still can’t figure out.


Still got some time left before I can cross.

Stickers: So many shops have their own branded stickers to put on merchandise that’s been purchased. My guess is it lets the staff know that you paid, although crime doesn’t seem like too big of a problem here – at least not where I’ve been hanging out. Here’s a pic of the water bottle I got from Natural Lawson this morning with the sticker on it.


Narrow windy streets: The streets here have no rhyme or reason and they are narrow! You think you’re cutting through from one main dori (street) to another and you end up somewhere else. Turns out that narrow street wound the wrong way.

Screen Shot 2014-08-12 at 10.42.43 AM

A map of my neighborhood Jingumae. The star is where I live.



Katie walking down Harajuku St.

Department store basements: The department stores here have everything that we do in the US except one thing: Their basement levels are the food department. That includes a ton of desks (like cosmetic desks) selling everything from chocolates, sweets, meats, fruit, alcohol, prepared foods, unprepared foods, and a full grocery store to boot. It’s as much fun walking around down there as it is overwhelming. Ironically, with all the great food there is no place to sit down and eat it, and eating on the run or in a random place seems to be frowned upon. It seems people buy their food and take it home. No pic will even come close to doing it justice.

Smaller doors: Generally, standard door frames here are smaller. It feels like I’m living in a slightly shrunken world. Works for me because I’m kind of a small person. Here’s me walking into my apartment.


Cheering/Umbrellas at baseball games: I was able to score some great last-minute seats to see the Yakult Swallows play the Hanshin Tigers last week at Jingu Stadium, which is only a 10-minute walk from my apartment. First off, I got the tickets at the local Lawson (a Walgreens type store), which actually made a lot of sense. Especially if you’re the Mets of Tokyo. More access to tickets hopefully means more tickets sold. Baseball is as huge here as it is in the US, and I could go on about the little differences in style of play. But I’ll limit this one to my observations of the fans. Turns out my amazing top-dollar (¥4600) seats were actually kind of lame. I was really close to home plate but all of the action was happening in the bleachers. Left side of the bleachers was all Hanshin fans; right side was Yakult. Think college football student sections. Every time Hanshin was up to bat, their bleachers went crazy with chanting and singing the whole time plus a full horn section to back them (student marching band?). They took turns as their respective teams came up to bat. And every time Yakult scored runs, which was often (they won 13-4), they rose umbrellas in unison to celebrate. I found out that this is a Yakult thing but I think every team has their special celebration.


The dancing umbrellas


Hanshin fans in yellow in left field bleachers. Yakult fans in green in right field bleachers.

Trays to pay: Whenever you buy anything, there is a tray to put your money in. Or credit card. Don’t hand your money directly to the cashier or the taxi driver. Put it in the tray.


Taxi pay tray

Numbered subway stops and exits: I always thought NYC had a crazy public transportation system, and then I came here. There are so many different lines, lines that connect and turn into different lines, and almost none of them are owned by the government. They are all owned by various companies: Seibu, Tokyo Metro, Japan Railway Company, Tokyu, Toei, New Red Arrow, and more. Thankfully, you can buy a Suica card which is a refillable MetroCard of sorts that gives you access to all of them and they seem to connect and work with each other pretty well. Google Maps is still the best map app, and going anywhere on the subway is as easy as putting it in there. It will give you full instructions including which platform to stand on. But in case that isn’t enough, every subway line numbers its stops. I’m at G-11 (Nihombashi) on the Ginza line at the moment. Also, the stations can be so big that they have conveniently numbered the exits. It has been very helpful!

IMG_3371 IMG_3374

Vending machines still reign supreme: Sure, we still have vending machines in the US, but they are everywhere here. Good thing too because I need a new bottle of water pretty often. The first week here it was 95 degrees, sunny, and humid every day.


Sliding glass doors: So many shops have sliding glass doors. Some are automatic and others you have to push a button, but this is definitely the door of choice here.

No trash cans: There are very few public trash cans everywhere, so I find myself carrying my trash around until I get back to my apartment. I would think this might make people litter, but the streets are very clean.

No napkins at meals – only tissues occassionally: This one kind of surprises me. There aren’t too many restaurants that give out napkins. They always give out a towel of some sort at the beginning of the meal to clean your hands. But what happens when I inevitably drop food on my lap?

Face masks: Many people here wear face masks just like your dentist wears. They are going about their normal daily business: going to work, out to eat, walking around, all with a face mask. I have been told that it is worn mostly by people who are sick so they don’t spread their germs. And yet, I see people driving alone in their cars with them on. Why wear them in your car too? I would expect to see that person with it around their neck.

Fun stuff on the other side of the world. Next post back to more serious matters.