teacher intervenes: "Then I'll draw it for you so, okay?" After considerable help from other students and the teacher, the class together arrives at a solution. "Okay, then applause. Wonderful."

Teacher Summarizes Solution and Presents Another Problem

The teacher then announces that since it is hard to see the solution he will make it clearer. He summarizes the students' method of solving the problems and polls the other students about which method they used.

He then presents another problem. "Without changing the area [of a quadrilateral drawn on the board], please try making it into a triangle. Okay, then, . . . please think three minutes and try doing it your own way."

Student:

Teacher, can we open our textbooks yet?

Mr. Yoshida:

The textbooks? First try thinking about it by yourselves, okay? You know that it was in the textbook, huh? [You're] sharp.

The process of working on the problem individually, in small groups, and with the teacher begins again. After about another 20 minutes of work, the teacher summarizes the results for the whole class. He draws the figure on the board and works through a solution. Toward the end of the solution, the bell rings to end class 49 minutes after it has begun. Concluding quickly, the teacher gives as a homework assignment the problem of converting a pentagon into a triangle with the same area.

Mr. Yoshida:

You worked very hard, amazingly hard. Okay? . . . Then let's say the farewell properly.

At which point the students rise, bow to their teacher, and leave the room.



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