It’s hard to believe, but today is the final day of the 2007 Lesson Study Immersion Program. This morning, we met to share what we learned from the experience (more about that later). Then in the afternoon, we visited Kyuden Elementary School in the Setagaya Ward of Tokyo to observe and participate in a district-wide public research lesson. All of the schools in the district dismissed their students early, except for one class per school, to hold public research lessons in different subjects. The mathematics lesson study group (there are 50 such groups in the Tokyo area) was holding its public research lesson at the Kyuden school so many teachers that were interested in mathematics came to observe. Other schools held public research lessons in other subjects. Later, we spoke to a principal who held a public research lesson in art at her school.
We observed (there were over 100 observers) a lesson on finding patterns in a number chart. The teacher began the lesson by posting a large paper showing a hundreds chart (a square with the numbers 1 to 100 in rows). He had a square magnetic frame that he could place anywhere on the chart creating a square with nine numbers inside. He asked the students to find the sum of the numbers as quickly as they could with a calculator (see example below).
11 12 13
21 22 23
31 32 33
At the same time, he asked Dr. Takahashi to figure it out without a calculator. Dr. Takahashi found his answers quickly and the students began to wonder if he was using some kind of trick. So the teacher posed the following problem: “Let’s come up with a strategy to calculate the total of the 9 numbers efficiently and explain the strategy.
Students first began solving the problem on their own. After several minutes, when the teacher noticed that many students were unable to think about a strategy, he called students who needed help getting started to the floor at the front of the room to give them hints. After several more minutes, he asked students to share their strategies.
The first strategy presented was (1+2+3) x 3 + (10+20+30) x 3. This student said that the ones digits in each column are always 1, 2 and 3 so since there are 3 columns, the sum of the ones digits is (1+2+3) x 3. Likewise, when the ones digits are removed, each column has 10, 20 and 30, so the sum of all the tens is (10+20+30) x 3. The teacher had arranged that the ones digits (the problem was on a large paper on the chalkboard) could be removed to illustrate this solution method. The kids remarked, “Our teacher is really prepared for this lesson!”Another student explained that by decomposing the numbers, you could make all the numbers in one column the same (e.g. move 10 from 31 to the 11 so all three numbers in the column are 21). Therefore, the problem could be solved by 21×3 + 22×3 + 23×3.
The teacher then asked the students that if by looking at these methods, they could come up with a better strategy. Many students quickly came up with the idea that by decomposing the numbers, all of the numbers could be made equal to the middle number so you could just multiply the middle number, 22, by 9. Next, the teacher asked if this idea could be used to find the sum of numbers in other parts of the chart. Most students were able to quickly find the solution to the next problem. Afterwards, several students shared what they learned aloud. (I would like to add that I really liked Mr. Tsuruoka’s teaching style. Whenever he asked a question, he would wait, even when many students had their hands up. He wanted all students to think and it was obvious that students were used to this type of inquiry-based, problem-solving lesson, and it was not just something he was doing for the sake of this public research lesson.)
During the post-lesson discussion, one teacher acted as the facilitator, another acted as recorder, and final comments were given by Professor Nakamura. During his comments, Prof. Nakamura emphasized the importance of careful observation and careful note taking during the research lesson observation. A good post-lesson discussion is the result of careful observation. He showed his notebook that had 7 pages of detailed notes that were color-coded with four different colored pens (see photo). The different colors were used to record different aspects of the lesson such as math expressions, student reactions. Another interesting aspect of how he observed the lesson is that he focused on one student, writing down what the student said and what he was thinking (aloud), misconceptions, etc. He said that while you are teaching, you cannot focus on how one student is understanding the lesson. This is the beauty of being a lesson study observer—you are able to focus on details that you would not normally be able to do in your classroom teaching. Afterwards, I asked him how he selects the one student he will observe. He told me that he listens carefully to what students are saying to themselves and chooses a student who is “thinking out loud.”
After the lesson, we had our final “enkai” (big party) with the teachers, professors, administrators, district superintendent, and others. Mr. Toki, my good friend and former principal of the Greenwich Japanese School (GJS) in Connecticut also came. (I had the privilege of working on a research lesson on the area of plane figures with Mr. Toki and several GJS teachers in 2003 and it was definitely one of the highlights of my career. Mr. He is now a principal in the Setagaya Ward.) I must say that this was one of the best enkais that we have had. Many people made speeches, there were many kampais (toasts), and I was even asked to say a few words. My final act in Japan was to put on my “indoor shoes” I had brought along to wear during school visits and ran outside and jumped up and down! (In Japan you must remove your shoes and wear “indoor shoes” or slippers. Now, all of the shoes I own are dirty!)
Well, what can I say? The 2007 LSIP is over but in many ways it is just beginning. We now need to take what we learned back to our schools and figure out what to do next. This will be very different for every one of us. In our morning reflection meeting, we talked about how important it is to keep in touch and for the lesson study communities in North America to network and support one another. Many questions were also raised such as, “How can we make lesson study work in North America without having the underlying support system for lesson study that exists in Japan?” In Japan, everyone—universities, professors, administrators, teachers, students, superintendents, ministry of education officials—value and support lesson study. In the U.S. and Canada, many of us are, as one LSIP participant remarked, like “underground freedom fighters.” Maybe part of the answer is, in the words of the famous New Orleans musician Dr. John, to just simply “keep on keeping on.” But now we can do that—continue lesson study, form new lesson study groups, improve upon what we have been doing—with new knowledge and renewed enthusiasm and commitment.
Lastly, sayonara to all the wonderful friends I have made from the U.S. and Canada. Y adios a mis Buenos amigos mexicanos, que gusto conocerles y compartir con ustedes en el idioma celestial! Let’s all keep in touch!
Tokyo, July 4, 2007
I am now off to Guatemala to spend a few weeks vacation with my wife and kids whom I miss very much and who have sacrificed and supported me on this trip. I will be thinking about you all from time to time as I lay on a lounge chair sipping some kind of tropical drink with an umbrella in it. ☺ God bless you all and enjoy your summer!