This story is part of a series on Canada's ongoing debate about how best to teach math in our schools.
The lesson starts simply, just a basic six-by-six grid marked with the Shanghai Luwan First Central Primary School – and several nearby snack shops.
Nie Xiao, the teacher, points to one.
"How can we find it?" she asks. "Four hundred years ago, scientists already figured out how. … Do you think you can learn how, too?"
The class of third-graders snaps to attention.
"Hao!" they cry in, unison – "Yes!" – and Ms. Nie explains to them how to identify a location with a grid, matching horizontal and vertical axes. She starts at 0,0, then works her way out, introducing 3,4, then 5,2.
They may not know it yet, but these students are already on their way to becoming global math elites. No country does better in math than China. And the city of Shanghai is to math what Edmonton is to hockey – an outsized producer of gifted protégés. In the latest round of tests by the Program for International Student Assessment, the city's students were about three years ahead of the average among member nations in the Organization for Economic Co-operation and Development.
These sorts of scores have won China attention – and produced an epidemic of hand-wringing everywhere else. When the same tests revealed that Canada's math scores, while still above average, are slipping, former deputy prime minister John Manley said the problem was "on the scale of a national emergency." In British Columbia, a group of Chinese-educated tutors has called on the province to look to Asia to improve its performance, saying local math skills are "weak and getting weaker." Alberta and Ontario are introducing more drills, to make its math classes look more like China's.
Britain has gone a step further, dispatching Education Minister Elizabeth Truss to Shanghai for a recent fact-finding mission – "its skyscrapers, and its ambitions, are all built on maths," she observed – and to recruit dozens of Chinese teachers to its own schools. The Global Times, a Communist Party-run tabloid, called the teacher exports "weapons of math instruction."
But figuring out exactly what China is doing right that everyone else is doing wrong requires a complex calculation: Part of China's success stems from cultural factors – not educational methodology. And within China, education experts are only too eager to criticize the failings of their system – which can drill students until their pencils crack – even as other countries try to replicate it.
The East-West way
In fact, in the past decade China has taken a series of steps to make its classrooms feel more like those in the West.
"Chinese teachers and principals are now apt to adopt elements of Western education to better protect children's spirits, so they can grow up in a happier and freer study environment," says Lao Kaisheng, an education professor at Capital Normal University in Beijing.
Indeed, in Shanghai's classrooms – at least the ones city education authorities are willing to show Western eyes – something surprising emerges: Math here is undeniably engaging.
Back in Ms. Nie's classroom, in a quiet downtown neighbourhood, a few dozen students sit quietly while she talks. But when she asks a question, a forest of hands pops up.
"Do you like checkers?" she asks her eight- and nine-year-olds.
"Yes!" the class shouts again.
On the projector screen, Ms. Nie displays a half-filled board. A single well-placed piece will win the game. It falls to the class to use number pairs to describe where it goes.
Then it's time for Ms. Nie to bring the class's fun and games home. She displays a National Geographic map of China with a star for Shanghai's location. This is their home. But it's not just a spot on a map, she explains, it's a plot on a grid: in this case, 31.2 degrees north, 121.4 east.
"So this is an example of number pairs," she says. "And this is how scientists invented the GPS to help us travel."
In less than an hour, her kids have practised a skill as fundamental to map-reading as it is to tracking the performance of a hedge fund.
"We have, I feel, a wider view on math education," says Gu Hong-da, an educator at the centre of how Shanghai kids learn to manipulate numbers. "Math is fully connected to life, to science and technology and the economy – and to how to use tools to solve problems in those fields."
Mr. Gu, 72, has been part of Shanghai's math scene for more than 50 years. He began as a math teacher, worked as a principal, directed educational research, served as president of the local education college, and has organized math competitions. He was a student before the Communist Revolution, and worked in the system after it.
"I have experience in all of the phrases of educational reforms," he says during an interview in downtown Shanghai. "And I'm also the one who carried out the policies."
He carries around a simple set of tools to illustrate how they have changed: photocopied pages of complex sketches in early math textbooks; now, photographs of bridges and skyscrapers. The meaning is clear: The sketches are eye-glazing abstractions; the pictures are a chance to see numbers at work in brick and steel.
Out, then, are theoretical sine and cosine curves; in are exercises using trigonometry to recreate McDonald's Golden Arches or calculate the height of Shanghai's famous Oriental Pearl Tower. Also in are teacher-mandated shopping trips to practice adding up grocery bills and subtracting change for elementary students.
"Shanghai, as a developed Chinese coastal city, has built the most advanced bridge for mathematics to solve real problems in life and production," Mr. Gu says.
Take calculators: Unlike most of China, Shanghai allows them in university placement tests. "The benefit of this method is to allow students to save time calculating and instead spend more time probing the math world and improving their thinking style," Mr. Gu says.
At the same time, teachers are working to decrease pressure on students. Shanghai schools have lately grown obsessed with whittling down homework, encouraging teachers to be more intelligent in the way they teach, and the work they require of students.
At the Shanghai Luwan primary, several parents say their children routinely have no math homework at all. Chen Lili has her son, in Grade 5, play piano, guitar and drums.
Hours of homework just don't wash, says another Grade 5 parent, Bao Yinglei, whose son plays basketball and practises computer programming rather than spending all his time on math drills. "This generation won't do it. When we were children, studies were a priority for our parents. Now, our children have their own ideas."
"Actually," she adds, "I feel Chinese families are quite interested in fostering their children's art sensibilities and skills."
Even Gu Chao, a Shanghai youth who took the gold medal at the 2013 International Mathematical Olympiad, was enrolled in a primary school that emphasized language education. "I deliberately left math to him for his own probing," says his mother.
The city also obsesses over its instructional staff, holding regular city-wide "elite teachers training" seminars where the best get together, and teach others. The process happens inside schools, too, where math teachers are organized in teams that meet weekly to share best practices and mentor younger educators.
Teachers are expected to mark everything overnight, providing quick feedback for students. And they face their own ongoing testing requirements. Mid-level teachers are expected to complete 240 hours of further training every five years; for upper-level teachers, it's 540 hours (including 300 hours of research). Each five-year period is capped with performance assessment.
"If your scores don't reach a certain level, then you lose your job," says Deng Weihong, vice-principal at the Shanghai primary school.
A new pressure cooker
It's a reminder that, for all the effort to file away the harsh edges of China's education system, the stakes for math students are high – and the country remains brutally competitive. Teachers may cut back homework – but for many students, any free time is more than compensated for by extra work assigned by parents. An OECD study found that 71 per cent of Chinese students use after-school math tutoring (in Canada, it's 27 per cent).
Despite talk of putting kids in bands or basketball, says math whiz Mr. Gu, in China "I am afraid few students go out for fun on Saturday." When he was younger, he spent some time at a home-stay in the United States. He was struck by the fact that students there didn't leave school to check in with a tutor.
"They might do sports on Saturday, and go to church on Sunday," he says.
In China, the math competitions start at primary school, where marks take on punishing importance. That's because students aren't just preparing for university placement tests – they have to write high-school placements tests, too. And in each of those tests, they are scribbling the script for rest of their lives. Education remains the primary lever for upward social mobility in China.
Parents, too, imbue school performance with great importance. A child is meant "to bring glory to its ancestors, or retirement support for parents," says education professor Mr. Lao. "It deeply affects China's culture of bringing up children, which creates huge pressure on children when they are little."
The problem: The exams, and the teachers who teach to them, actually do a poor job of measuring a student's ability. "Our current exam policies only test very limited factors, such as memorization, comprehensive capability," Mr. Gu says. Left untested are creativity, social and communication skills.
Another gap in the Chinese system is realizing the full potential of that early dedication to math. Once the elementary math tournaments are done and the university placement tests written, the incentives for excellence run dry. Students do "nothing in the much more critical higher education stage – that is the real flaw in their education system," says Zuming Feng, who is head coach of the U.S. team at the International Mathematical Olympiad.
Take Mr. Gu: Now in university, he figures he spends 20 to 30 hours a week on math studies – less than the amount he spent in middle school.
For countries desperate to match China's success then, Shanghai offers something less than a silver bullet. The city's methods do suggest that for the sorts of skills tests can measure, basic math exercises (the sort of "rote" material that has been actively eroded in Canada in recent years) are vital. But so is supporting high-performance teaching that can bring numbers to life, and draw meaning from the dreaded drills. "Repeated exercise can be very helpful if it is not simply repeating – rather, a lot of variations are inserted," Mr. Feng says.
Underlying Shanghai's stellar test scores, though, is something far more difficult to transplant elsewhere: what happens outside the classroom. Chinese math performance, for better or for worse, is driven in large measure by a cultural commitment to pouring hours into math, eschewing soccer games for quadratic equations.
Chinese students "just work hard. That's all," says Ken Wang, academic director at UltiTutor, a Shanghai-based tutoring agency. "There's nothing else to say. There's no special tricks or gimmicks. We're just hard workers."
With assistance from Globe and Mail researcher Yu Mei.