Lesson Study, Japanese Style

Today, I will try to give you the flavour of the Japanese lesson study process, and tomorrow I will wrap up with a discussion of how gradual long-term improvements add up to real change. The excerpt is from a description of one session during which a group of lower primary teachers were planning the introductory lesson for a grade 1 unit on simple subtraction with the minuend larger than 10. This planning process went on for many many weeks.

"During one of the early sessions, the Japanese teachers decided to use this problem at the beginning of the lesson: "___________ (student's name) collected ______ ginkgo leaves. Then he/she drew _____ pictures of his/her family on the leaves, one member on each leaf. How many leaves did not have pictures?

"The teachers agreed that it would be good to use one of the students' names in the problem, though they hadn't determined which student. Also still unresolved was the question of what numbers to use in the problem. This question led to great deal of discussion. Ms Tsukuda, the teacher who had proposed the problem, began with the following comments, as related by Yoshida:

"Not long ago, the Vice-Principal (Ms Furumoto) showed me several textbooks. All of those textbooks used 12 and 9 (i.e., 12-9=) and 13 and 9. What most of the textbooks said was, they started out by introducing the Subtraction-Addition Method. In the case of 13-9, first subtract the nine from ten (10-9=1), then add what is left over in the 1s position (which is 3) to the number (1+3=4). I thought if you narrow it down like that (introducing subtraction with borrowing by teaching the Subtraction-Addition Method), it's not very interesting. So on Saturday I suggested using 15-8 or 15-7. I thought that these are a little harder than 12-9 and 13-9. Using these numbers will bring out a lot more ideas or ways to solve the problem. But after reading a lot of different books on the subject, because kids can conceptualize in their heads about up to the number 6 at this age, I thought we should go with numbers like 11-6.

"The teachers agreed that the choice of numbers would influence which strategies the students would try when solving the problem. But they had other concerns as well. For example, one teacher wanted to use 12-7, because one of her students, who was a low achiever, happened to have seven family members. Everyone agreed that this was a good idea. They also liked the number 12 because, since none of the students had fewer than three people in their families, subtracting the number of family members from 12 would involve decomposing ten, which was, of course, the point of the lesson. They briefly considered the number 13 instead of 12, but decided against it, as shown in the following dialogue.

• "Tsukuda:  Well, I was thinking. I also thought of using 13 minus 7, but it's really hard to break down 7 into 3 and 4.
• Maejima:    I see, you mean conceptually.
• Tsukuda:    Right, conceptually it's easy to break 6 down into 5 and 1, and it's easy to break down 7 into 2 and 5, but it's really hard for first-grade students to break 7 down into 3 and 4.

"Once the numbers were agreed on, they wondered how they could make it seem natural that students should start with the number 12. They decided to begin the problem by asking students to select their 12 favorites from among the leaves they had collected. These would be the leaves students would use to work on the problem.

"From there the discussion turned to the different strategies that students might be expected to generate. The teachers consulted some of the teachers' manuals and found five common ways of solving simple subtraction problems with borrowing. Each method was labeled with technical terminology that seemed quite familiar to the teachers. Ms Furumoto, who was the vice principal and who had been in the school for only one year, named a particular student who appeared to use only the subtraction-addition method. She said this concerned her, because she found it difficult to move students from this particular method into using more sophisticated methods.

"And so the discussion continued, for weeks, touching on all the topics listed above [the problem, the materials, the anticipated solutions, the questions to ask, the kinds of guidance to give, how to use the space on the chalkboard, how to apportion the fixed time of the lesson, how to handle students' individual differences, and how to end the lesson, considered a key moment] at a level of detail similar to that manifested in this example. This kind of planning is decidedly intellectual in nature; these teachers are thinking deeply about the options available to them and the way the experiences they structure in their classrooms will facilitate students' understanding of mathematics. There is real excitement as this process unfolds, an excitement that is obvious to those who observe the weekly meetings of a lesson-study group."

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