Pop question — no Googling: How many of Japan’s Nobel laureates were awarded medals for their work in physics?

The answer: 10, or nearly half of the total. You could deduce from this that Japan is good at physics. Furthermore, you could deduce that Japan is good at math, which is, arguably, the bedrock of physics. And math is something Japan does very well.

If you wanted to create an arbitrary division of nations, you could start with division — long division and short division, and multiplication. And fractions, algebra and geometry: some of the stuff that = math. At the top of the pile would be a cluster of East Asian nations, such as Singapore, South Korea and Japan — countries that repeatedly score high in international rankings. Meanwhile, at the bottom of the class lie Israel, Hungary and, notably, the United States. As much as math itself is a puzzle, so too is the reason behind why Japan, along with other Asian countries, continually outperforms countries in the West in math.

Since 2000 the OECD club of developed nations has been tracking and testing 15-year-olds in dozens of countries in math, reading and science every three years in what are known as the PISA (Programme for International Student Assessment) tests. Japan has never dropped out of the top 10 in math. In the last round of tests, administered in 2012, Japan was placed second in mathematic performance and first in both reading and science amongst the OECD countries.

This summer, American journalist Elizabeth Green wrote an essay for The New York Times Magazine titled “Why do Americans stink at math?” It could just as easily have been headlined “What can Japan teach America about teaching math?” since much of the article was given over to the experiences of a Japanese math teacher, Akihiko Takahashi, who trained and taught in Tokyo before moving to Chicago in the 1990s, ostensibly to continue teaching math. His other motive was to continue his research into the pioneering work of a group of math educators in America he had first encountered as a novice teacher in Japan.

Green’s essay was a primer for her book “Building a Better Teacher,” published in August. In the book, Green outlines how after transitioning to America, Takahashi was alarmed to observe that students on the whole were being subjected to a stifling form of math that most readers will probably be familiar with: “I, We, You,” a ritualistic series of steps in which the teacher dictates a problem to the students, the class works together on similar problems, and finally the students work through more of the same problems. Japan, Green says, had traded “I, We, You” for “You, Y’all, We,” in which the process is altered: Students begin with solving a specific problem, then work in peer groups and finally altogether.

The other idea Green hit upon in her explanation of why math teaching in Japan may be more effective is *jugyōkenkyū*, in which teachers are routinely observed in order to help hone their craft. Observation lessons are standard practice in schools in Japan; however, this is not universally the case elsewhere, where teachers tend to view the classroom as their domain, off limits to prying eyes.

The focus of Green’s book is American education policy and practice, and while it explains some of the differences in teaching between Japan and the U.S., superficially and otherwise, it still does not get to the root of why, on the whole, Japan excels at math. Is it the teaching methodology that differs or the attitude to learning? Or is it how much is spent — in time and money — on education, publicly and privately?

To find out, I went back to class. First, I brushed up on statistics.

Students in Japan spend nearly 235 minutes a week learning math, according to Miki Tadakazu, an education analyst with the OECD, only about 20 minutes more than the OECD average.

In PISA’s 2012 questionnaire, Japanese 15-year-olds reported spending an average of just over half an hour a week in a commercial after-school learning environment — read *juku* — which is in line with the OECD average. In fact, the Japanese polled came in *below* the OECD average in time spent on all other forms of after-school work, whether it was teacher-set homework or study assisted by a home tutor, family member or computer.

And one more statistic before class finishes: Japan spends less on education than most OECD countries, allocating it less than 4 percent of its GDP. So, if quantity is not the key to Japan’s math success, could it be quality?

In researching this article, I attended a mixture of private and public schools — a private elementary school and three public junior high schools — to observe math classes and interview math teachers.

While waiting in the cafeteria of Ritsumeikan Primary School in Kyoto, third-graders were busy wiping down the tables. A few students pushed their cloths towards me, more in curiosity than in an effort to clean. I asked one boy, in English, what his favorite subject was.

“Math,” he replied immediately.

I wanted to laugh: Was this an omen or was he a plant? But 50 minutes later, I could see why.

All the classrooms at Ritsumeikan Primary School are open; the wall where the door should be is missing, so if one class was to erupt in noise, it would cause a disturbance in all classes. At Oike Junior High School, a public school in downtown Kyoto, it was slightly similar: All teachers kept their doors open during their lessons. The idea, I think, is to magnify disturbances, or “acting up” as it was called in my time, but at both schools the only noise came in the form of excitement — excitement for math.

At Ritsumeikan, Kunito Ito, a pleasant coach-like teacher, started his class with the customary *aisatsu* (greetings) and followed this with a problem he had put up on the board — that day they were tackling solving equations with multiple fractions — instructing his fifth-graders to tackle it. So far, so predictable.

But then it got interesting. The first student to finish shot a hand up. Ito walked over, glanced at the problem and circled it, to signal it was correct. The student was then up and out of his seat.

Another hand shot up. But this time the first student had taken the role of teacher, or corrector. Ito was made redundant from the get-go as students darted around the class, checking and aiding their peers.

Throughout the 50-minute class, Ito subverted the “I, You, We” ritual. Students were called on to work in groups, individually, to stand up and present their answers at their desk and to come to the board and present their answers. He particularly enjoyed it when students arrived at different answers, or different routes to the same answer. As a class, they discussed how they arrived at the same answer through disparate routes.

Looking back on my own math education, we rarely, if ever, treated math as a discursive subject; but both at Ritsumeikan Primary and Oike Junior High, the teachers had students routinely work in pairs or bigger groups and talk about the problems. It seems so obvious in hindsight: Math is also a type of language, so why wouldn’t you discuss it like we do English, Japanese or social studies?

After the class, Ito told me: “If you teach what you learn, you will remember about 90 percent. If I stand at the board and just lecture, through listening to the teacher the students will retain far less — say, 40 percent — so it’s far more effective to have them discussing problems and teaching each other. Also, it’s important that there is very little downtime or rest time. You need to keep motivating them.”

These sentiments were echoed at Oike Junior High School. Tanaka-sensei’s third-grade class began with a group presentation using the electronic whiteboard. The four boys had two minutes to summarize and present the findings from the previous class, using a case example.

“It’s hard for them,” Tanaka said afterwards, “as they only started doing this in September of last year.”

His class of around 20 students was more or less identical to Ito’s: a continual mix of group problem-solving, discussions and presentations (although granted, the primary-schoolers were a little more enthusiastic).

“If it’s only me up there teaching in front of the class, I’m not helping students to get high scores in PISA tests,” Tanaka said. “But if you think about how to get students to think by themselves, you need to do a lot of research for this.”

Jugyōkenkyū can help, especially with novice teachers. However, from my interviews with math teachers, personal research seemed more important and effective.

“In a way, jugyōkenkyū is important,” conceded Shingo Fujinawa, a Kyoto University graduate and math teacher at Ibaraki Nishi High School. “It was a good opportunity to be inspired and recognize my teaching skill at that time. But I felt as if it had been a kind of ritual for a beginner teacher.

“Personally, my present teaching skill comes from my everyday experiences with my students as well as other media such as books, TV, which are much better than two observation classes in themselves.”

Other teachers told me of how they tried to stay abreast of new and different ways of teaching using teaching books and DVDs, as well as attending seminars and through informal discussions with colleagues. Investing so much personal time in your occupation is not unusual in Japan, where teachers often have an outsized role in addition to that of teacher: as counselor, surrogate parent.

“Japanese teachers work very hard for their students,” Tadakazu from the OECD told me via email. “They spend lots of their own time engaged in extracurricular activities. Teachers in Japan play a wider variety of roles for students than other countries’ teachers, whose main task is limited within their lessons. This perspective may support the fact that the dropout rate of Japanese students are very low.”

Of course, the elephant in the room is juku. In each interview, I asked teachers if they thought there was a link between Japan’s high standings in PISA and the fact that so many of their students attend juku. Even at a fee-paying school such as Ritsumeikan, where annual tuition costs are over ¥1 million, more than 50 percent of students attend juku. This figure can peak at as high as 90 percent in schools across the country in the final year of junior high and senior high, as students cram for entrance tests to get into high school and university.

Generally teachers are receptive of jukus and saw the complimentary role they play, especially in getting students past those all-important tests. It’s also worth remembering that a lot of teachers went to juku themselves and quite possibly taught there during university.

“Juku fills a role in preparing students for passing exams. However, school teaches you more than one answer and it allows for more creativity. Juku will show you the answer and the most efficient way to get it,” Ito said.

The fact that the math teachers I observed could spend so much time teaching instead of attending to matters of discipline may also impact on student ability and scores. Add to that teachers who have an active interest in their subject and their students, and this may go some way toward a theory of why Japan does math so well.

*Learning Curve covers issues related to education in Japan. Your comments and story ideas: community@japantimes.co.jp*