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A student works on a problem in class at Montreal’s École Secondaire Mont-Royal on Dec. 5, 2013. (Christinne Muschi for The Globe and Mail)
A student works on a problem in class at Montreal’s École Secondaire Mont-Royal on Dec. 5, 2013. (Christinne Muschi for The Globe and Mail)

Math wars: The division over how to improve test scores Add to ...

Parents signing petitions. Governments forced to defend their positions. A declaration that Canada’s problem is on the scale of a national emergency.

Welcome to the Math Wars, a battle that’s been brewing for years but heated up last month when this country dropped out of the top 10 in international math education standings.

The battleground is fractured and the sides aren’t clearly drawn, but at the centre of the debate over so-called discovery learning is this question: Should the teacher be a sage on the stage, a guide at the side, or both?

Parents in provinces such as Alberta, Saskatchewan and Ontario look at their children’s math homework and see little, if anything, of the fundamentals they were taught just decades ago. Gone are the days, in much of the country, of long division, mad-minute multiplication, addition with a carry and subtraction with a borrow.

Today, children in provinces that have introduced the Western and Northern Canadian Protocol (WNCP) curriculum – a vast swath of the country – learn instead by investigating ideas through problem-solving, pattern discovery and open-ended exploration.

“If you look at what’s been happening, predominantly over the last decade, there’s been an unprecedented emphasis on discovery learning,” said Donna Kotsopoulos, an associate professor in Wilfrid Laurier University’s education faculty and former teacher.

Robert Craigen, a University of Manitoba mathematics professor who advocates basic math skills and algorithms, said Canada’s downward progression in the international rankings – slipping from sixth to 13th among participating countries since 2000 – coincides with the adoption of discovery learning.

“The word ‘emergency’ suggests a suddenness, but I don’t think there’s anything particularly sudden about this,” said Prof. Craigen, referring to comments made in December by John Manley, the head of the Canadian Council of Chief Executives, that the results of the OECD’s 2012 Programme for International Student Assessment (PISA) were “on the scale of a national emergency.”

“What we’re seeing is the final demonstration that things have been going downhill,” Prof. Craigen said.

And with Canada’s slip on the global stage comes an anxiety at home, one that’s palpably sweeping across the country as governments tout different solutions to an almost universal problem. Parents in Alberta, Ontario and British Columbia, for example, launched petitions over the Christmas holidays, calling on their governments to revamp curriculums with a greater emphasis on basic math skills.

But the governments themselves are taking different approaches, free to do so since provinces have jurisdiction over education and there are no national standards or strategies. Ontario has no plans to change its curriculum and is instead banking on ramped-up teacher training. Manitoba is watering down discovery learning with more “back to basics” fundamentals, while British Columbia appears to be heading in the opposite direction as it revises its own curriculum.

Meantime, Quebec, with its intensive training and teachers who apparently refuse to shirk algorithms despite reforms, enjoys the best scores in Canada and is now at the centre of math-education research.

And then somewhere in the middle of conventional math and discovery learning is JUMP Math, a Toronto-based non-profit whose curriculum reaches 100,000 Canadian students and counting.

“In all the debates that are going on, we think it’s a bad idea to throw [discovery learning] out, but the other side is right also,” said JUMP founder John Mighton, a mathematician and author whose vision has caught the attention of The New York Times. “The parents and those who want to go back to basic math are right in some sense: You need to combine the discovery with guidance.”


There is no national strategy for improving math scores because provinces have jurisdiction over education. Here’s what the provinces are doing – and whether they plan to make curriculum changes.


Landscape: The province withdrew from the Western and Northern Canadian Protocol (WNCP) for financial reasons in 2011 and is currently revising its curriculum. The ministry of education dictates what must be taught, but not how to teach it. Here’s an example: A Grade 4 student is required to learn mental math strategies for adding two-digit numbers, but the teacher chooses whether to teach the strategies by adding from left to right, or top-to-bottom with a carry. Some critics argue the current math curriculum is too conceptually based, with parents in the province launching a petition calling for greater emphasis on basic math skills. JUMP Math, which is being touted as a “third way” that emphasizes rehearsing the basics and breaking problems into small parts, reaches roughly 10 per cent of B.C. students, mathematician and JUMP founder John Mighton said.

PISA 2012 ranking, when provinces are included: 12

PISA paper-based math score change between 2003 and 2012: -16

Outlook: As the province plans for a major curriculum overhaul that will put a greater emphasis on “personalized learning” across all subjects – a focus on concepts and processes rather than factual content – the ministry says math will likely change the least out of all subjects. The ministry, however, maintains that students still must be strong at elements such as mathematical algorithms and memorizing times tables. While the new curriculum is still in draft stage, expected changes include a greater emphasis on financial literacy and interdisciplinary thinking. The province is also reviewing teacher training.


Landscape: Alberta’s current math curriculum, based on the WNCP and discovery learning, is under revision. There are mandatory learning expectations for Grades 2 to 6 “that address the understanding of addition, subtraction, multiplication and division with an emphasis on mental mathematics,” an education ministry spokesperson said. That means Grade 3 students are being asked to add and subtract two-digit numbers and multiply to 5 x 5. By the end of Grade 5, students are expected to know their multiplication tables.

PISA 2012 ranking, when provinces are included: 17

PISA paper-based math score change between 2003 and 2012: -32

Outlook: Based on the PISA scores, Alberta’s share of low performers has doubled over the past decade. “It tells me we’ve got some work to do,” said Jeff Johnson, the province’s minister of education. Parents and teachers are pushing for a better balance between the WNCP learning strategies and students knowing basic math facts. Despite a petition calling for Alberta to focus on fundamental skills, the ministry contends the curriculum already places emphasis on addition, subtraction, multiplication and division. Changes to the math curriculum won’t materialize until 2016.


Landscape: Saskatchewan’s ministry of education follows the WNCP curriculum. In 2012, the government responded to concerns that basic math was being overlooked in favour of new concepts. It was announced that work would be done to help parents understand new math, while there would also be improvements in teacher training.

PISA 2012 ranking, when provinces are included: 22

PISA paper-based math score change between 2003 and 2012: -10

Outlook: Following consultations, the ministry ultimately said its curriculum was “in line with what is taught in jurisdictions across North America and will continue.”


Landscape: Though the province is still part of the WNCP, it has started moving toward conventional learning. This past fall, the government responded to a push from parents and announced curriculum revisions for students in kindergarten to Grade 8. The government wanted to “ensure that there’s a strong emphasis on giving kids basic math skills,” Education and Advanced Learning Minister James Allum said in an e-mail. The province set clearer expectations around counting and memorizing math facts. Students are also now taught all four standard methods for arithmetic – addition with a carry, subtraction with a borrow, long multiplication and long division. The curriculum also stresses that children in kindergarten through Grade 3 not rely on calculators. The Manitoba government has also added JUMP Math to its recommended resource list, Mr. Mighton said.

PISA 2012 ranking, when provinces are included: 35

PISA paper-based math score change between 2003 and 2012: -36

Outlook: Besides the curriculum changes, the province has reduced class sizes in kindergarten to Grade 3, and is piloting a new program at the University of Winnipeg to strengthen teacher education in math.


Landscape: In the late 1990s, research into discovery learning drove changes to the math curriculum, which was last revised in 2005. Students are required to be able to multiply by 9 in Grade 4, but there is no requirement that they memorize multiplication tables. They aren’t required to learn basic algorithms such as long division or adding a column of figures, either. Instead, they are encouraged to break problems down into smaller parts to work through them, or use physical materials to help them understand.

PISA 2012 ranking, when provinces are included: 19

PISA paper-based math score change between 2003 and 2012: -16

Outlook: The PISA results have got Ontario worried, with parents launching a petition and Education Minister Liz Sandals vowing to tackle the problem. The province is currently in the early stages of consulting experts on math education, said Lauren Ramey, spokeswoman for Ms. Sandals. But asked this week whether the province would revamp its curriculum, Ms. Sandals said “no.” On Wednesday, the government announced it will spend $4-million this year to help pay for more current teachers to take advanced qualifications courses in math and upgrade their skills. In 2015, the province will also move from a one-year teachers’ college program to a two-year program.


Landscape: The province is the Canadian leader in math, scoring with the likes of Japan and Macau. While Quebec adopted the “discovery learning” method during major educational reforms in the early 2000s, the approach was already in the works as early as the 1980s. That may have given the province the benefit of a longer lead-time in implementing it, said Stéphane Cyr, a University of Quebec in Montreal math-education professor. But some educators say Quebec is succeeding in spite of its curriculum. Nathalie Morel, vice-president of the Fédération autonome de l’enseignement, a major teachers’ union, said educators have insisted on teaching and testing children on math fundamentals. Still, the province hasn’t abandoned rote memorization – the curriculum, for example, calls for children to learn their multiplication and division tables by heart, starting in Grade 3.

PISA 2012 ranking, when provinces are included: 8

PISA paper-based math score change between 2003 and 2012: -1

Outlook: Few studies compare why students in Canada have such different math scores, but researchers have started focusing on Quebec’s intensive teacher training and its curriculum, which balances traditional math drills with problem-solving approaches. Montreal’s McGill University is taking part in a study on math teaching across Canada, and early findings suggest Quebec’s four-year math-teacher course may be a model to emulate. Grade school teachers, for example, must take as many as 225 hours of university courses in math education, whereas in some Canadian jurisdictions, the number can be as low as 39, according to Annie Savard, a McGill professor of math education who is part of the national research team.


Landscape: The Atlantic provinces have adopted or adapted the WNCP math curriculum, said Robert Craigen, a math professor at University of Manitoba. Newfoundland and Labrador, for example, several years ago decided to launch a new curriculum, adopted from the WNCP. In 2012, the Nova Scotia government announced the province would adopt Alberta’s math curriculum, which is the WNCP’s, explained Michael Zwaagstra, a Frontier Centre for Public Policy research fellow who specializes in education policy.

PISA 2012 ranking, when provinces are included: New Brunswick, 25; Nova Scotia, 31; Newfoundland and Labrador, 37; PEI, 46

PISA paper-based math score change between 2003 and 2012: New Brunswick, -10; Nova Scotia, -18; Newfoundland and Labrador, -27; PEI, -21

Outlook: PEI Education Minister Alan McIsaac said his government is focusing on interventions in the early years; for example, investing in a play-based curriculum for preschool. After Nova Scotia ranked in the bottom half of the provinces in PISA 2012 scores, the government issued a press release entitled “Nova Scotia Students Perform Well In International Assessments.” The release noted the math results “are a concern,” but the education minister noted “math is a priority area” and that a “new curriculum is being introduced.”

Sixty-five countries participated in PISA 2012. No data were collected in the three territories, which are part of the WNCP.

With reports from Kathryn Blaze Carlson, Adrian Morrow and Caroline Alphonso in Toronto; Andrea Woo in Vancouver; Allan Maki in Calgary; Ingrid Peritz in Montreal.

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