Friday, Oct. 19, 2001

Miho is a math whiz. She uses algebra to solve complex problems in her head. Ayako can't multiply and still struggles with two-digit subtraction. But because the two girls are in the same third-grade class, they study mathematics at the same pace. At Japanese elementary schools, students of differing abilities do not receive different lessons.

This seemed very odd to me, coming from the American system where children are generally grouped for lessons according to ability. At the school my children attended in the United States, the 75 third-graders went to three separate classrooms for math. Students take a pretest before each unit, so a child might go to the most advanced group for division but to a lower group when learning how to tell time.

The advantage of this system, when it works, is that students get the right level of instruction. Advanced students get more challenging work; struggling students get help.

The disadvantage is that students are very conscious of how the classes are divided up. Although teachers today are very careful not to label groups as "smart" or "slow," children who are frequently assigned to the less-advanced groups come to believe that they are stupid.

How, I wondered, can Japanese teachers use just one lesson to effectively teach 30 to 40 children of different abilities? Aren't the advanced children bored? Don't the slower learners fall behind? Doesn't this system promote mediocrity?

I'm not the only one with such doubts. Many Japanese critics of issei shido (whole-class instruction) pose the same questions. But this system has been used in Japan for many years, and Japan consistently ranks in the top five in international comparisons of math ability.

One of the keys to effective whole-class instruction, Japanese educators say, is structured problem-solving. At the beginning of many math lessons, Japanese teachers give students a problem and let them wrestle with it, either individually or in small groups. Sometimes a teacher will let the students work on one problem for an entire period.

Why spend so much time on a single problem? Because when students are allowed to struggle with a task themselves, they become motivated to discover the most efficient solution to the problem.

I saw how this works when I watched a class of second-graders begin a unit on measurement. The teacher had the children divide themselves into random groups of four or five. Then she taped to the blackboard four large strips of colored paper of different lengths -- one for each group.

The assignment? Each group had to devise a method to make a strip of paper that was the same length as their strip on the blackboard. The rules were simple: The children could not take the strip off the blackboard, nor could they take paper from their desks up to the blackboard.

The teacher let the children tackle the problem for about half an hour, providing almost no assistance. The classroom was filled with noise as the groups debated possible methods. After 10 or 15 minutes, each group had agreed on a method and started making strips.

Toward the end of the period, the teacher asked each group leader to stand up and describe the method the team had used.

One group had a boy go to the blackboard and place a hand at each end of the strip. He tried to keep his hands in that position as he hurried back to the desks for his team to measure the distance between them.

Another group used a pencil case as a measuring tool. When they found that the pencil case wasn't quite as long as the strip, they figured out that adding three fingers at the end of the pencil case gave them the right length. Back at their desks, they used the pencil case and their fingers to mark off a strip of paper.

The third group used one member's forearm as a measuring tool, marking on his skin with a pen. The fourth group had one member move her hand down the length of the strip, counting off the hand widths until she got to the end.

After these presentations, the teacher asked each group to select their best strip, the one that they thought was closest in length to their strip on the board. With great drama, she took the chosen strip of each group one at a time, and taped it to the board under the target strip.

The first group groaned in disappointment when they saw that their best strip was way too short. The second cheered when their strip was almost the same length as the one on the board. The third and fourth groups' strips weren't far off, but the second group definitely came the closest.

The teacher asked the children for their conclusions and then summarized the lesson. The rest of the unit went smoothly, she told me later, because the kids' interest had been piqued: They were given a challenging problem and allowed to devise and test their own solutions.

"But it's harder to devise lessons like that for the upper grades, where you have greater differences in ability within the class. And this kind of teaching is not appropriate for everything the kids need to learn in math," the teacher explained to me.

In short, not all Japanese math lessons are as fun as the one I observed. Teachers do lecture. Kids do complete worksheets. There is repetitive drill to make sure students master basic number facts and skills.

But the whole-class instruction I witnessed was great teaching, by any measure.

Alice Gordenker is a Tokyo-based writer and the mother of two American children attending Japanese public elementary school.