The latest analysis of international math scores will have some disturbing news for Canadian professionals spending loads of cash on tutoring and enrichment for their kids: Their offspring were outmatched by the children of janitors in Shanghai.

Ever since the PISA exam scores were announced in December, parents and education experts have been fretting over Canada's 13th-place ranking in math. But when parental education is taken into account, it turns out the children of the country's doctors and lawyers fall even further in the rankings: They placed 22nd when compared to their similarly advantaged peers around the world.

Canadian students with parents working in the least-skilled jobs, such as cleaners and couriers, may have answered, on average, fewer questions correctly than the better-off students in their class. But when ranked against their global peers, they did much better – placing 10th. (One caveat: The sample size of students by category varied between countries, sometimes significantly – Leichtenstein, for instance, recorded a very small number of students from this group, so wasn't counted.)

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The good news: Canada has one of the most equal-opportunity education systems in the world, according to the OECD study.

"We do a very good job, and put a lot of energy, into being average," says Miles Corak, an economics professor at the University of Ottawa, who studies equality. "This is good because in not letting the least advantaged kids – in terms of family resources – fall behind, we have an overall higher score, and frankly in the long run, a more inclusive society."

At the same time, Corak observes, "average is increasingly not good enough."

The 2012 rankings of the PISA exams – which tests 15-year-olds in 64 countries in math and reading – raised alarms in Canada because students had continued a nearly decade-long drop in math scores, falling out of the top 10.

The latest study shows that, generally, kids from more advantaged backgrounds outperformed their less well-off counterparts, especially in math. But global comparisons were revealing. In Shanghai, which came first in international scores and where 15-year-olds outperformed all countries in every category by parental education, students from the least-skilled families were good enough to place 10th among all students with professional or managerial parents – significantly ahead of teens in countries such as Canada, Britain and the United States.

The study reveals an important story hidden within the overall rankings. For instance, while Finland outranked Germany overall in average math scores, this was because the Scandinavian country has low inequality in its education system. By contrast, while German students with parents working in manual occupations performed "very poorly," the study found that the children of professionals in Germany were among the highest achievers in the world.

The studies concludes that the fact that "students in some countries, regardless of what their parents do for a living, outperform children of professionals in other countries shows that it is possible to provide children of factory workers the same high-quality education opportunities that children of lawyers and doctors enjoy."'

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Since the December results, there has been a lot of debate about the validity of comparisons of diverse countries, such as Canada, to more cities such as Shanghai, the financial centre of China. The fact that China's results are divided up by city-region on the PISA scores has been controversial, as this Brown Center on Education column points out, even though the head of PISA has stated in previous years that rural results, which are not released by China, are in line with the public results.

Many education experts have pointed out that the high scores of Asian countries are capturing a "shadow education" in which the vast majority of students, even those from low-income families, participate in private tutoring in addition to regular classes. (The Shanghai results also include a smaller percentage sample of all the 15-year-olds in the city, many of whom don't attend public schools because of passport-type licensing system for families called "hukou" that restricts access to certain municipal services.)

But experts have also noted a key difference in the learning culture of places such as Shanghai, where achievement is consider to be the result of work, and North America, where achievement has tended to be considered more based on ability.

And for all the caveats, these results should spark a discussion about Canada's math rankings that step outside the narrow domains of classroom and curriculum. When the average janitor's son in Shanghai outperforms Canadian students with every advantage, it's time to take a hard look at the big-picture cultural messages our kids are getting about resilience, grit, and the achievement to be found in hard work.