Excuse me, mind if I observe your class?

For the students in Junko Takagi's ninth-grade math class, this day may have made the Top 10 list of classroom nightmares.

There was Ms. Takagi, at the board as usual, beginning to say something about arcs. But standing up along the back and sides of the classroom was a horde of other math teachers, all watching the lesson, the students, and the props Takagi was using.

"I was a little bit nervous at first," Takagi says, "but the kids helped, as they always do." The students were well behaved, aside from a little wise-cracking, and Takagi's "master class" went off without a hitch.

"One thing I learned is the fact that we can teach in class without textbooks," she says. In an education system where the central government determines the curriculum and where critics charge that learning is often confused with preparing for exams, Takagi's statement is a sign of change.

Japanese education is in a rocky period. Rote learning and memorization were once considered ideal, but now teachers are being told they must emphasize creativity and problem-solving. At the same time, maintaining discipline is increasingly difficult as students become more rebellious.

And like teachers everywhere, educators here need ways to keep their commitments to teaching fresh and to develop new ways to teach old lessons. One partial answer to all three problems is master classes - opportunities for teachers to study teaching.

Master classes "help teachers maintain a high level of motivation," says Takaaki Matsuoka, a curriculum and guidance official who serves the school board of one of metropolitan Tokyo's 23 wards. "It's not so easy for teachers to change their styles of teaching unless they see something new ... to become a student sometimes is important for them."

Although much of Japanese education is rigorously systematized, master classes are put together somewhat informally and have been developing for decades. Sometimes individual principals create such programs in their schools; others are organized by local or regional school boards. A nationwide teachers union also holds master-class conventions to discuss big issues - the main topic at one recent convention was the eroding discipline in elementary schools.

Takagi, who teaches at a public school in Tokyo, volunteered as part of a master-class program on teaching geometry to middle-schoolers. She and a colleague prepared a lesson on arcs using an umbrella, a worksheet, and a gizmo that allows students to see the arc described by a falling umbrella. Getting it all together took about a year, Takagi explains.

Teaching the lesson in front of her usual class and two-dozen colleagues, Takagi also engaged students by getting them to vote for what they thought was a correct answer and repeatedly and randomly calling on them. Instead of calling out names, she distributed cards with numbers as class began and then called out the numbers.

In a review session after class, math teachers from several Tokyo middle schools watched videotaped reports about two other experimental lessons -one involving computers and the other wooden threadspools and chopsticks - and talked about what they'd seen.

Discussion focused on the importance of cultivating a "let's try" attitude among students, the need for teachers to be flexible, and the effectiveness of creating a playful atmosphere in class.

One experienced teacher praised the educators who'd developed the lessons for using objects relevant to daily life and for making math more accessible. Another teacher sounded impressed with what he'd seen. Takagi "got the students to think," says Hiroto Okamoto, who teaches ninth-graders at another middle school in Tokyo.

Toshihiko Banba explains that there are only two math teachers at his junior high school -"It's a limited world," he says. He wanted to see Takagi's master class and the other presentations because, "There are a lot of things I want to study as a teacher."

Teachers also take master classes as a way to show their commitment to the profession if they want to be promoted to administrative posts, but in general the programs are voluntary. "They have operated this way for years and years," says an official at Japan's Ministry of Education. "The primary objective is self-enlightenment."

For teacher Takagi, the point was to expose "how students can discover the joy of learning in math class."

(c) Copyright 1999. The Christian Science Publishing Society

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