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AP MEMBER FEATURE EXCHANGE ADVANCE FOR MARCH 29-30 -- In this March 7, 2014 photo, Nate Studley works on solving a 5x5 Rubik's Cube at Freetown-Lakeville Middle School in Freetown, Mass. Math teacher Nate Eleuterio teaches his students to follow a series of steps to solve an equation, also known as an algorithm, to master a Rubik’s Cube. (AP Photot/The Standard-Times, John Sladewski)John Sladewski/The Associated Press

At one time, it was mandatory for students to memorize their times tables and learn to add and subtract without counting on their fingers. But it fell out of fashion years ago, displaced in most provincial curriculums by "discovery learning," which encourages children to come up with their own creative approaches to solving real-world math problems. Or, as is often the case, not solving them.

Formal math training and rote learning were jettisoned, victims of a creeping fear that children would be turned off math because they found drills stifling. As it turns out, for kids learning math, there's something even more off-putting than boredom: a lack of knowledge, and struggling to solve real-world problems because they lack a strong grounding in math fundamentals.

Without a firm grasp of math basics, even the brightest students can fall behind. Discovery learning may be popular, but it doesn't necessarily work. One seminal paper, published in 2006 in Educational Psychologist, which reviewed more than 100 empirical studies on discovery learning, concluded: "After a half-century of advocacy associated with instruction using minimal guidance, it appears there is no body of research supporting the technique." Students may like making up their own rules when it comes to math, but they don't learn much doing it.

That's why Ontario and Alberta are right to be changing course. Last week, both provinces signalled subtle but significant changes to math instruction that show the tide is turning against discovery learning. Alberta's Education Minister, Jeff Johnson, instructed his ministry to ensure reciting the times tables and recalling other basic math facts be brought "front and centre" in the classroom starting this fall. Ontario's Education Minister, Liz Sandals, followed suit: "We expect kids to know their basic math facts," she said. "That's actually a great homework assignment: Learn your multiplication tables."

To the casual observer their statements may sound like time-tested truisms, but to close followers of the "math wars," they represent a stunning climbdown for both provinces, and proof of the so-called PISA effect. The term refers to sweeping policy changes that tend to follow in the wake of the results from the OECD's Programme for International Student Assessment, which compares how 15-year-olds in 65 countries perform in math, reading and science.

Last December, the survey revealed nine countries outperformed Canada in math – not a particularly terrible result. But what's worrisome is the trend line: Canadian students are getting worse, not better. Our math performance has slipped since 2006. When it comes to math, Canada was once held up as a global example of excellence. Today, it looks as if we are headed to become a case study in how to go from top of the class to epically average.

The good news: Alberta and Ontario policy-makers finally seem to recognize there's a problem, and have shown themselves willing to make the changes necessary to prevent Canadian students from falling further behind. Canada is also lucky in the sense that it can learn from laboratories within its borders, and from its own past. Quebec students did noticeably better than those in the rest of the country on the latest PISA results, and scored on par with top-tier Asian countries such as Japan. Why? The province has more rigorous teacher training. Quebec also essentially ignored the fad of discovery learning, while the rest of the country embraced it.

If Quebec is held up as a model of math education, Alberta offers a glimpse of what not to do. In the early 1990s, Alberta was spurred into sweeping educational reforms aimed at bringing its students on par with their peers in countries that showed outstanding academic outcomes: Japan, Germany and Hungary. The province, under pressure from both business and parents, urged policy-makers to go "back to basics" in the classroom. Alberta implemented rigorous testing, invested heavily in education and lifted its standards for teacher training. Student results improved. But once the province fell under spell of discovery math – around 2008 – many of those gains were lost.

By 2012, 15.1 per cent of Alberta's students failed to meet baseline levels of math proficiency, according to the PISA survey. And Alberta produced fewer high-achieving students – 16.9 per cent of students in 2012, compared with 26.8 per cent in 2003. Over a nine-year span, Alberta posted the second-largest decline in math scores in Canada, right behind Manitoba.

It would be wrong to single out discovery math as the only culprit to blame for Canada's declining math scores. Teacher selection and training and investment in education also play major roles. But it would be even more egregious for education policy-makers to pretend discovery math has been a boon for learning outcomes. It hasn't. Canada's sliding PISA scores show the pendulum has swung too far in favour of discovery math, and Canadian students are paying the price. Ultimately, so are the rest of us. Math is the foundation for engineering, finance and the sciences. If Canadians want to compete on a global scale, our students' abilities in math matter.

When other countries faced poor or falling PISA scores, they instituted sweeping reforms to reverse the trend. Poland boosted middling reading results by dramatically increasing the number of hours spent on language instruction. South Korea has emerged as an education powerhouse in a relatively short period of time, with an ambitious plan to digitize classrooms and trade in traditional textbooks for interactive ones. Alberta and Ontario's small nods to curriculum change are welcome. But only if they signify the first steps toward broader reform that dials back on discovery learning.

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