Greater competition from private schools in Quebec could partially explain why the province's public schools outperformed the rest of Canada in a 2012 international math test, a C. D. Howe Institute report suggests.

The report, published Wednesday, analyzed Canada's results in the 2012 Programme for International Student Assessment (PISA), which tested 15-year-old students in 65 countries on math, science and reading with a focus on math that year. Canada ranked 13th in math internationally.

Both public and private schools in Quebec, which has the highest percentage of private school students in Canada, scored several points higher than the Canadian average. While most provinces saw a significant decline in their math scores since 2003, the last time PISA focused on the subject, Quebec's average score dropped by just one point.

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"I suspect that there is some competition going on here where the principal of a public school wants to keep students and sees that the parents are making a choice between public and private," said John Richards, author of the report. "A modest amount of competition is probably beneficial. This is my cautious summary."

About 20 per cent of Quebec's students are in the private system, he said, and the province subsidizes up to 40 per cent of their tuition. British Columbia, which performed the second best in math, also subsidizes a smaller chunk of private school fees and about 10 per cent of its students attend private schools.

"You don't have to be particularly rich as a family to decide to send your child to a private school," Mr. Richards said, which amps up the competition.

But Mr. Richards said private schools shouldn't become the focus of education reform.

"You do not want to get into a situation where all of the wealthy families say we don't care about the public system because our kids are doing OK in private schools," he said, adding a moderately low public-private ratio similar to Quebec's or British Columbia's is a good example to follow.

Private schools in Quebec did about 62 points better than public schools in math but students from wealthier, better-educated families tend to score higher anyway, Mr. Richards said. The difference wasn't statistically significant once adjusted for those social advantages.

Mr. Richards's report also compared Canada's overall results to the U.S., suggesting better-paid teachers might contribute to Canadian students' higher math scores.

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On average, Canadian teachers were paid about 150 per cent of Canada's GDP per capita, about 50 per cent more than teachers south of the border.

"That means you can encourage better students to study to become teachers and that's valuable," Mr. Richards said.

The report also pointed towards more pre-school education for socially disadvantaged families as a policy that appears to boost students' test scores.