2012 Lesson Study Immersion Trip in Japan

Beyond show and tell…


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Final thoughts…

So, this will be my final post for the blog. I’ve been back in the U.S. for a few days and I am still buzzing about all I was able to learn and do on the trip. Doing this kind of thing requires lots of sacrifice; I’m horribly behind on email, my research, writing, planning for teaching in the Fall, as well as household stuff like picking out new tile for our kitchen, and my bank account is noticeably depleted from the costs incurred to go on the trip as well as all of the $$$ I spent on irresistible Japanese pens and paper clips in the shape of elephants (the Japanese have a term for this kind of thing – kawaii – meaning “cute”) but it was all very, very much worth it.

I’ve put a lot of thought into this final post. Here’s my big take-away about lesson study: lesson study, in itself, does not result in instructional improvement. The act of collaboratively planning a lesson, teaching it as observers watch, and discussing the lesson afterwards does not, in itself, change teaching practice. What I observed is that lesson study changes the ecology of teaching in school settings, and by changing this ecology, what teachers and administrators in a school recognize as important and valuable shifts. Lesson study, done badly, does little to improve instruction. However, when lesson study is done well, teachers and administrators see their practice with new eyes and sharpen their focus on what really matters for students’ learning. Ultimately, its the teachers and administrators who make the change, but lesson study can provide an environment to make what needs to be reworked in one’s teaching practice more transparent.

I learned that…

In Japan, teachers mention frustrations with unmotivated students, students who don’t do their homework, students who don’t pay attention in class. However, Japanese educational leaders seek answers to these questions by critically examining the content of their course of study through lesson study, asking questions like “How can we pose tasks to spark students’ interest, to see the value in discussing their ideas with others, etc?”

Like their American counterparts, Japanese teachers face preparing students for high-stakes (in 9th grade) and standardized assessments (in 6th grade), earn middle-class to upper-middle-class wages, work long hours (in Japan, teachers are on contract for 11 months). I noticed that on lesson study days, Japanese teachers would stay after school from 3 p.m. – 6 p.m. or later discussing the study lessons, even for the study lessons they observed but were not directly involved as a member of the research lesson team. My impression was that all teachers were dedicated to their jobs.

Technology is not used in Japanese classrooms just because it exists; if technology is incorporated, it usually starts when a school does a lesson study to see whether or not the tool or software promotes learning effectively. All lessons I observed would be very low-tech by U.S. standards.

In reflecting upon what I’ve learned, I realized something interesting: advocates of a more “corporate” approach to schooling that has contributed to the growth of vouchers and charter schools argue that improving education for all children is achieved by running schools in a fiscally responsible manner, firing bad teachers (those whose children don’t do well on tests) and hiring better teachers (some who have less experience or no experience), and adding an element of competition into the educational “marketplace” to motivate “lazy” schools to work harder to become better schools and retain their “clients.”

I have a B.S. in Administrative Management, and learned in my management coursework some basic principles for managing employees effectively. From what I see, the “corporate” approach to education has completely failed to acknowledge the first principle of management: Recognizing that your employees are what makes a company successful. No amount of savvy budgeting, cost-cutting measures will compensate for a staff that is poorly trained and unmotivated. A second principle: Motivating your employees involved helping them understand the company’s purpose and goals, the rationale behind decisions that impact their work, and the value that they add to the organization and its mission – and then “getting out of their way” to allow them to figure out how they will achieve the mission. Lesson study is the means with which Japanese teachers work together to help the school achieve the goals of the yearly research theme, and the change that happens is wholly determined by the teachers that participate in lesson study. Instead of the specter of dismissal looming over their heads, Japanese teachers work in a culture that strongly promotes improvement and change collectively. It’s true that it is very uncommon for Japanese teachers to be fired. They enter their professions with strong content knowledge, and after having passed rigorous exams for certification as well as when they apply to teach in a prefecture. They have much to learn about teaching at this point, but the educational system sees as part of its duty to support the ongoing learning of teachers, recognizing that teachers with ten or more years of experience are far more effective than novice teachers.

What if we began conceiving that learning to teach is a lifelong endeavor, and that the district that hires a teacher must take on the responsibility of supporting the ongoing learning of that teacher? Which leads me to one other principle I learned about management: the investment you make in training and supporting the work environment and culture for employees yields both immediate and recurrent dividends. Are we really prepared to play this “corporate” analogy out? If so, its time to recognize how strong corporations support their employees, and from there we will see where the most important change in U.S. education needs to be made.

I won’t be continuing with this blog, but I may continue blogging about lesson study in my work. I’ll post a link to that blog when/if it happens!

 

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Day 10: The final lesson

Greeting us at Hashido

 

 

 

We observed our final lesson in a 3rd grade classroom at Hashido Elementary in Tokyo. The topic of the lesson was division with remainders, and this observation was unique in that the same research lesson was being taught in three different classrooms at the same time with observers in each classroom. This was an unusual structure compared to other research lessons we’ve observed. I suppose in some ways it provides more “data” for teachers to consider in evaluating the merits of the lesson, as well as improving the teaching practice of teachers within the school.

 

 

 

 

In the prior lesson, students had used counters as concrete tools to model dividing an amount into equal size groups (also known as problems involving partitive division). They had also explored how to write expressions for situations involving division with remainder, like 8 / 3 = 2 remainder 2.

In the launch to this lesson, the teacher provided some simple word problems involving division and asked students to write the expression to represent the situation in the problem (but not solve the problem). As students wrote expressions like 15/3, 16/3, 8/4, the teacher kept track of the expressions on the blackboard. After doing four such problems, the teacher asked: “Can someone pick an expression that will give us remainders?” One student picked 16/3, and the teacher instructed students to figure out a way to find the answer. However, he said that they would not use counters today. They would have to find another way to find the answer, and he encouraged students to find multiple ways to solve 16/3.

I saw all kinds of different magnetic paper or even sticky paper used by teachers to organize their board work. Simple magnets were also used, as seen here. Some teachers would write out the problem of the lesson on what looked to be plain white paper, but it was either sticky or magnetic because they would unfold it and just smooth it on the blackboard. This saved time, as well as kept the board organized for students’ notes.

As students explored the problem, many drew pictures to model the situation or even representations of counters. However, some students recognized a connection with multiplication facts (which was the desired result of the lesson). As students worked, the teacher brought magnetic, whiteboard-type sheets to selected students so that they could write their solutions on the sheet. After about 10-15 minutes of working, the teacher posted students’ magnetic sheets on the board and asked those selected students to describe their solutions. A couple of the solutions showed different ways of pictorial representing the problem situation, such as 16 counters drawn and grouped into 5 groups of 3 with 1 remainder. However, one student used the multiplication fact 5*3 = 15 to determine that 16 is 5*3 = 15 + 1, so 16/3 is 5 with a remainder of 1.

When asking which of the solutions was correct, one student responded that none were correct. He said, “I think it is 6 remainder 2, because you can make 6 groups of 3 if you add in two more counters.” This student’s response made me realize that students likely didn’t yet have a strong understanding of what a remainder means. With two different answers provided, the teacher asked students to discuss in pairs whether they thought the answer was 5 remainder 1 or 6 remainder 2. In so doing, he was putting the responsibility back to the students to decide the correct answer.

After a few minutes of discussion, the teacher brought the students back together and asked what they had decided. Most students decided that 5 remainder 1 was correct, but then another student suggested that the correct answer was really 6 remainder 1. At this point, the teacher decided not to pursue this student’s idea, and instead re-directed the conversation to determining which students used drawings to solve the problem and which students used multiplication facts. Since most used drawings, the teacher gave the problem 17/3 for students to work on in class, emphasizing that they use other methods than drawings as the drawings take a long time to create and they should identify more efficient strategies. After a few minutes, the teacher asked a girl at the front to share her work. She said she used the “3 facts”, meaning multiples of 3 to solve the problem. After writing her strategy on the board, the teacher had students consider the similarities between 15/3 and 16/3, and then taught the class the word “indivisible” to describe division problems with remainders.

Posters of English names for numbers and shapes in the 3rd grade classroom

 

 

 

 

 

 

 

 

Post-lesson discussion in the gym

 

In post-lesson discussion, the major point raised by Prof. Fujii, the outside commentator from Tokyo Gakugei University, was whether it was wise to not let students use counters in this lesson after having only one day to explore division with the manipulatives. He argued that the counters provided students with a concrete way to model the situation, and they may not know enough about division yet to be able to just work with abstract representations such as numbers. This discussion reminded me of the principles of Cognitively Guided Instruction, which came from research on elementary students’ problem solving conducted at the University of Wisconsin in the 1980s and 90s. In Japan, they regularly use manipulatives as a way to help students model and make sense of problem situations. Manipulatives are not just seen as a tool for the teacher to use to illustrate mathematical relationships during instruction. Rather, one aim of Japanese education is to help students be able to use tools such as counters, measuring sticks, tape models, area models, and so forth to model problem situations.

Coming up next: I’ll wrap up the major insights I learned from this trip, particularly misconceptions I had about Japanese education that were dispelled on the trip as well as new things I learned.


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Day 9: Learning about Angle Bisectors at Koganei Lower Secondary School

Only one more lesson study to observe. I am already sad to leave Japan, but very much looking forward to apply all that I have learned.

So, think back to your school mathematics experience: what is the definition of angle bisector? From what I remember, I learned that angle bisector is simply the line that divides an angle into two smaller angles of equal measure. From this definition, I had no idea about the similarities between angle bisector and circles – in the Japanese curriculum, they define angle bisector as the set of points equidistant from two given (intersecting lines). Brilliant! Students can relate this definition to other geometric objects, like a circle (the set of all points equidistant from a given point), as well as parabolas, etc…

We observed a 7th grade lesson written to help students understand how to construct angle bisectors. Students learn how to do constructions using compass and straightedge beginning in ….. 3rd grade! They study circles in 3rd grade by constructing circles. In this lesson, students were asked to generate as many methods as possible for constructing the angle bisector using a compass and a straightedge. The lesson plan itself featured 6 different ways. After 10 minutes or so of exploration, the teacher had students share their methods for whole-class discussion.

Although the teacher guided the students in a spirited discussion of whether the methods that were presented on the board were in fact different or not, the lesson itself did not push the students to think deeply about methods for constructing the bisector. Maybe I’ve been sounding like a broken record, but the real heart of a lesson is in what students discuss about their solutions, strategies, or thinking about the problem. In this lesson, although students were showing correct constructions (for the most part), the teacher did not ask students to explain how they know that their construction methods yielded an angle bisector. Since the strategies of the students who were asked to share were not actually the same, there could not be a meaningful discussion of the mathematical similarities between strategies for constructing that were clearly different. “Why?” can be an incredibly powerful question, but it is one that is asked far too infrequently in math classes.

One aspect of lesson study that I have only briefly mentioned is the work of observers during lesson study. Typically, the observers are fellow teachers, members of the research team, outsiders invited to offer commentary during the post-lesson discussion, and administrators or visiting professionals from the Ministry of Education. I especially appreciated the visibility of administrators from the Ministry of Education; regularly visiting classrooms grounds policy makers in understanding the status of public school education. In this lesson, we were made privy to what observers were instructed to monitor as they watched the lesson and students’ work.  Specifically, observers were to note which of the anticipated construction strategies students used, and whether they came up with any unanticipated strategies. In general, the focus of the observers’ work is on documenting student thinking, instead of primarily focusing on the teacher’s moves during the lesson. This focus on student thinking is the hallmark of the lesson study professional development approach.

So, for my next post, I’m going to share reflections on the final observation, and I have a list of general observations from my time in Japan to share. I’m actually a day (or two) behind in posting, and I return to the U.S. on July 5, but I will try to catch you up on everything as soon as I can!!! Thanks for reading…


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Day 8: Grade 9 lesson on Square Roots at Sengen Junior High

Entrance to Sengen Junior High

Our visit at Sengen left many of us saying “Now this is more like schools in the U.S..”  Sengen is a public school within the Tokyo Prefecture, and today’s lesson was planned by a research team consisting of teachers from 6 different schools in the district. The goal of convening this team is to improve the practice of teachers with between 5-10 years of teaching experience.  Like the U.S., Japan’s teaching “corps” has experienced generational turnover in recent years. As experienced teachers retire (usually around age 65), there has been a great need for new teachers to fill positions. However, there are many concerns that younger teachers are still too inexperienced to be effective, and the hope is that lesson study will support teachers, particularly those with < 10 years of experience, to improve their practice.

As we began to set up for our observation, students entered class chatting and giggling with their friends. As the teacher called the class’s attention, the typical formal routine we were used to observing was noticeably absent. Usually there is a greeting at the beginning of class where students and teacher bow to each other, but no such routine was executed in this session.

The problem of today’s lesson, “Does sqrt (5) times sqrt (2) equal sqrt (10)?”, seemed straightforward for a ninth-grade class and perhaps not sufficient for a 45-minute lesson.  However, students had not yet learned in class any formal rules for multiplying expressions with square roots. The teacher began the lesson by drawing a rectangle with dimensions labeled sqrt 5 and sqrt 2, then asking students how they would find the area of the rectangle. A student responded that the area is sqrt 2 times sqrt 5, and then the teacher asked students to think about what the product of sqrt 2 times sqrt 5 might be. One student responded “I think it is sqrt 10, but I’m not sure why.” The teacher introduced the problem sqrt 9 times sqrt 4, and they worked the problem as a class to see that the result, 6, was equivalent to the sqrt of 9 x 4. At this point, the teacher handed out calculators and suggested that students investigate the answer using calculators and think about why the result makes sense.

In contrast to other lessons we’ve observed, students tended towards more off-task behavior, such as making up English phrases to whisper to their neighbor while looking at the observers,  rather than digging into the content of the lesson. The teacher would politely remind students to keep working on the task. I’m not sure students had any idea of what else they needed to do; most students simply found the approximate values for sqrt 2, sqrt 5 and sqrt 10, and then computed that sqrt 2 times sqrt 5 was approximately equal to sqrt 10 to convince themselves that sqrt 10 was correct.

When the teacher called the students back to whole class discussion, it was clear that she hoped students would be able to explain why sqrt 2 times sqrt 5 equals sqrt 10. However, the teacher’s approach at this part of the lesson was somewhat troubling to me. During the discussion, few students were able to explain why this was true using their knowledge of square roots. The teacher ended up showing students that (sqrt 2 x sqrt 5)^2 = 10 using the distributive property.  From here, she deduced sqrt 2 x sqrt 5 = sqrt 10.  What concerned me about this approach was that 1) this method for justifying why the statement was true was not a result of students’ thinking and 2) it seemed to assume that students already knew that if a^2 = b then a = +/- sqrt b, for all real numbers a and b. As the teacher summarized discussion, she wrote a general form for multiplying square roots – sqrt a times sqrt b equals sqrt (ab). It wasn’t clear to me whether the class will revisit this formula to explain why it is true for all real numbers, or whether they will have been convinced by a couple of cases and just take the formula the teacher provided as fact.

In general, observing this lesson brought up a couple of questions for me: 1) Does elementary mathematics lend itself more to interesting, problem-based lessons than secondary mathematics? Many of us were thinking that it is a little more difficult to take a topic like multiplying square roots and devise a thought-provoking lesson around such a task. (However, the post-lesson commentator showed an excellent way to use the area model and proportional reasoning to explore the result of (sqrt a times sqrt b)^2.) and 2) How can educational systems around the world address similar persistent, institutional constraints to improve secondary mathematics education?  As I’ve mentioned earlier, lesson study is not a part of professional development for grade 10-12 teachers. The focus of Japanese secondary education is on preparing students for the rigorous exams to enter university, which often determines a student’s long-term career trajectory. Thus, instruction tends to focus on mastering skills and procedures so that students can pass these exams. Some students in this class at Sengen have been attending “cram schools” to prepare them for the exams that place them into high schools (with the rigor of the high school influencing your chances of success on university entrance exams). At cram schools, they learn formulas – and some students had already memorized the formula for multiplying square roots. Thus, faced with similar pressures as schools in the U.S. in terms of high stakes tests and little ability to mandate attendance, Japanese schools address such pressures in remarkably similar ways.  Although I did not go on this trip hoping to find that Japanese schools also have problems, I find it exciting to imagine how we can collaborate with educators around the world to address educational issues that are truly global in nature.

Coming up next: another 7th grade lesson at a laboratory school. Get ready to learn about angle bisectors.

FYI – If you are interested in the lesson plans for any of these lessons, let me know.


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Week-end sightseeing in Tokyo

Sights from our weekend spent in Tokyo sightseeing!

**Sorry for the picture formatting – my Mac doesn’t play nicely with wordpress

A cleansing ritual at the beautiful Meiji Shrine.

A triangular cone! The Japanese think of everything.

Look at the signs on each step telling you how many kCal’s you’ve burned climbing each step – at the famous Tokyo store (and truly undescribable) Tokyu Hands – a must-do while in Tokyo.

Harajuku girls!

The intersection at Shibuya subway station where all lanes of traffic have a red light at the same time, allowing pedestrians to walk in any direction. Can you spot me? 🙂

View from the observation deck of the Tokyo Tower


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Day 4: Grade 5 lesson on nets of solids at Tokyo Gakugei University Laboratory School

Back to Tokyo!! Today, we observed a lesson study on the campus of Tokyo Gakugei University in the laboratory school.  Tokyo Gakugei has a large teacher preparation program, and is home to Project IMPULS (International Math-teacher Professionalization through Lesson Study) directed by Prof. Fujii of Tokyo Gakugei and co-sponsor of this lesson study immersion trip.

Entrance to the lab school

One thing that has impressed me in all of the lessons has been the use of a simple yet engaging task, and today’s lesson was no exception. Today’s task asked students to consider the number of edges that needed to be cut in a cube to open it to be the net of the cube. All of the students were given cubes constructed from paper and tape to use to test their conjectures. As students began cutting cubes, most were realizing that they needed to make 7 cuts to form the net of the cube. The teacher prompted students to justify why 7 cuts were needed. During the class discussion, students found all 11 possible configuration of nets and were able to see that 7 edges would need to be cut to form each of these nets. In essence, this was proof by exhaustion. But, the teacher pressed students to consider why this was the case. After students discussed their ideas in pairs, he solicited their ideas and a variety of correct explanations were provided.

The research lesson was held in what looks to be the cafeteria. Lots of video cameras in the room to capture the lesson.

(Aside – in general, I haven’t witnessed students sharing wrong answers or explanations in the lessons we’ve observed, which suggests that teachers do attend closely to students’ work during their explorations and call on students they know are on the right track).

What I really want to talk about in this post is the features of the post-lesson discussion that I have observed across several lessons. Prior to going on the trip, I had thought the post-lesson discussion involved having the teacher and observers share out things that they noticed in students’ thinking during the lesson and the implications this evidence of student thinking had for the determining whether the lesson was successful in achieving the intended goals. What I’ve noticed so far is that many of the comments from the observers are related to the lesson goals, but there is little reference back to the goals or research theme during the post-lesson discussion. While the post-lesson discussions can vary somewhat in structure, most seem to have a very formal agenda. They begin with the moderator of the discussion, which is often a lead teacher or the head of the research team, describing the research theme and the agenda for the discussion. The moderator then yields the floor to the teacher of the research lesson, who provides their comments about the intent of the lesson and some reflection about what they thought were strengths and weaknesses of the lesson. Unlike all of the lesson studies I have known about or participated in, the teacher of the research lessons we have observed actually writes the lesson plans with some consultation from the research team. After the teacher’s comments, the observers have a chance to offer their comments about the lesson. These comments vary widely – sometimes they are compliments to the lesson, sometimes they are simply reporting observations of student work, and other times they are critique and suggested improvements. We’ve observed that a good moderator summarizes comments for the entire group after each of the observers’ remarks. Finally, after about an hour of discussion, an “outside” commentator – a university mathematics education professor, or a representative from the Ministry of Education, or another expert – provides their critique of the lesson as well as the plan and process of the study lesson that day.

There has been a common theme among some of the commentators’ remarks – the disappointment in how the post-lesson discussion does not focus more on issues of content. For example, the post-lesson discussion of this lesson on nets of solids involved many comments about the emphasis on individual understanding instead of more use of group work. The commentators critique an over-emphasis on pedagogical techniques such as group work. Instead, they argue, that the focus should be on the kind of justifications students could be expected to generate to the question “Why are there 5 sides that remain intact?” or whether students needed to see the different types of nets to be able to justify why 7 edges should be cut to form the net. I definitely see the merit to deeply considering issues of content in a lesson, but I wonder how focusing solely on issues of content will help develop teachers’ capacity to support sharing of ideas among students or to facilitate students to question each other’s reasoning during the whole class discussion. I can see that there is room for discussion of both content and pedagogical issues, provided that the issues focus on substantive, “deep,” , and not surface-level, features. For my own work, I will definitely take away the importance of having a more formal structure to the post-lesson discussion

I have so appreciated all that the organizers of the trip have provided in the way of introduction to the Japanese culture. After the research lesson, we were treated to a traditional Japanese drum performance by students of Tokyo Gakugei (check out: http://youtu.be/W3UlQNxYmZw). They even let us try!

  


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Day 3: An Unforgettable Day at Oshihara Elementary School

I’m trying to figure out how to limit the length of these blog posts, but our days are filled and I’m learning so much! Here goes…

Our second day in the Yamanashi prefecture began with a short tour of a traditional Shinto shrine…

Entrance to the shrine

Traditional cleansing ritual before entering Shinto shrine

After a brief visit to the shrine, we headed to Oshihara Elementary School in the small town of Showa City. We were greeted at the entrance by a sign declaring the “International Mathematics Class Research Conference” – meaning the lesson study that was to take place that day – and the Assistant Principal who so kindly took us on a tour of the grounds and school, which featured many innovative environmental and ecological learning features.

Grounds of Oshihara, with a stream constructed so that students can conduct a variety of biological and ecological research projects on site. The grounds also included a garden that I witnessed students tending to at the end of the school day.

The first of several shots to follow of the inside of the school. Yes, this is an elementary school! When built in 2004, it was designed with many features to make it an environmental and sustainable building.

Laptop stations

A space outside connected to the library on the second floor. Yep, that’s part of my finger in the shot, because I’m a professional photographer.

Never seen before…a radiant cooling system that utilizes cold water pumped from below ground to cool the air in the 2nd-4th floors

But, literally, the best part of the day was ….LUNCH WITH THE STUDENTS! They treated us like kings as we sat with them in their classroom to eat lunch. These students were 4th graders. We talked about our favorite foods, video games, animations, our favorite subjects in school (math, of course) and I even played rock, paper, scissors with them – apparently a universal way of making important decisions. {I wanted to post a picture, but it shows students faces a little too clearly to protect their anonymity.}

After lunch, we prepared for the research lesson. Today’s lesson focused on developing children’s ability to do mental calculations with 2-digit numbers. The problem of the day was: How can we calculate 53 – 28 using mental computation strategies?

Inside the research classroom for the day…Mr. Koike’s 3rd grade classroom

[Aside – I’m realizing that I haven’t really talked about the logistics of arranging a research lesson in a school. The lessons, conducted several times (or more) per year, are held on days that scheduled in advance as early release days. The lesson is taught during the last period of the day, with the teacher (sensei)’s students staying in school for the lesson. On this day, the school made special arrangements for our visit and it was not a scheduled early release day. In the photo, you see all of the teachers in the school are observing. We found out later that while the teachers were observing, their students were working independently in their classrooms. We didn’t hear anything from those other classrooms, but we saw the students busily working at their desks. It’s astounding what children, even from a young age, are capable of!]

Mr. Koike’s lesson showcased how inventive and thoughtful children can be. He skillfully engaged students in reasoning about their mental calculation strategies, and showed a tremendous amount of respect, empathy, sensitivity, and genuine admiration for his 3rd graders. I could say lots about the lesson itself and the post-lesson discussion, but I have two things I’ve been so anxious to talk about: 1) handling unexpected students’ responses and 2) the idea of “once-in-a-lifetime opportunity” or making every moment count in life (and in teaching)

As you may remember from the previous post, I talked about how the teacher had to deal with a student response that came at an undesirable time in the lesson. In Mr. Koike’s lesson, this kind of situation arose again – as many teachers know, this can be a frequent occurrence! In this lesson, Mr. Koike began the lesson by posing the task (modified for ease of display): Which of the following would be easiest to calculate: 53 – 28; 68 – 28; or 89-28? Sensei was hoping that students would say the expressions with 68 and 89 would be easier to calculate than the expression with 53, as that expression was to be the focus of the lesson (because the algorithmic approach of subtraction with regrouping would be tedious to do mentally). Guess what? The first student called on responded that it would be 53.   Without skipping a beat, Mr. Koike continued to solicit other students’ thinking, and eventually all three possibilities were up on the board for consideration. He had students provide reasons for why 68-28 and 89-28 were easy to calculate, leaving 53-28 as the problem which necessitated more clever mental calculation strategies. What Mr. Koike showed in his teaching is that skillful teaching follows students’ thinking, instead of telling it where to go. I believe part of developing teaching expertise is to allow the process of students’ learning to unfold and have patience in doing so.

The second thing I want to discuss is an idea that Dr. Takahashi mentioned in his opening talks on the first day of the immersion that I have been reminded of as I watch each of the lessons. He discussed how the Japanese think of  even the smallest, most “everyday” sorts of moments in life as “once-in-a-lifetime opportunities”.  I believe this idea is analogous to making every moment count, and Dr. Takahashi described how Japanese teachers take this to heart when considering the moments they have with students in class. Every moment with a child is a moment to help them learn something new, to help them grow as individuals, so no moment should be wasted. Again, this is a foundation of lesson study – refining the work of teaching, even improving a single lesson, reflects a core belief that every moment of a lesson should provide children with the best learning experience possible in each and every moment. These moments are ongoing – after a student has provided an unexpected response, as a student starts to erase their work as they question their thinking while problem solving, when a child goes to write a note about the lesson in their notebooks. In these small moments, how can teachers help children to make the most of their learning? Consider note-taking for example – do children learn more from a moment of copying the teacher’s work on the board, or from a moment where they write in their own words what the teacher or fellow classmates have said? By bounding the research of teaching to one single lesson, it allows teachers to consider all of these little moments that happen and assess how to engage students in these moments in ways that promote learning.

We received small gifts from the students at Oshihara, in bags that students constructed themselves. The bags from Mr. Koike’s classroom had “Don’t forget” written on the outside. We will never forget the fascinating lesson taught by Koike sensei, and the children, faculty and environs that make up Oshihara Elementary.