Fifty parents and a handful of teachers have gathered in the library at Bayview Public School in Ottawa to hear Marian Small tell them how to change their children’s math fortunes.
Dr. Small is a lively speaker with the firm “eyes on me” tone of a teacher. She lobs math questions at the hesitant audience (some things never change) although she promises not “to call on anyone who doesn’t want me to.” Her talk is also peppered with practised catchphrases: “You can Google answers,” she recites. “You can’t Google thinking.”
Flicking through her PowerPoint presentation, she explains, “There was a day when people thought the only way a kid could understand something is when we show it to them. Now, teachers know that. if we give kids a little space, they can figure it out for themselves.”
More than a few parents in the audience are scribbling notes.
If you have children between Grade 1 and 8, there’s a fair chance you’ve actually seen a textbook penned by Dr. Small, the former dean of education at the University of New Brunswick and now a professor emeritus and private consultant. She has written, or co-written, more than 85 books about math and is in demand for professional development days with school boards from coast to coast.
“If Marian Small was deciding math curriculum in this country,” one math-education researcher gushes, “we’d all be happy.”
Well, not everyone.
In the latest – arguably fiercest – of the “math wars” to break out in Canada, she would be Public Enemy No. 1 for those who think kids are fast losing their number sense because of the “fuzzy-math, basic-skills-lite” teaching Dr. Small and many of her contemporaries promote.
In December, this group got its proof: The latest international rankings revealed that 15-year-olds in Canada had finally slipped out of the top 10, after a slow, decade-long slide, and were now far behind their peers in such math powerhouses as Japan and South Korea. (The trend in provincial scores, Quebec excepted, has been equally deflating.)
The poor showing led to grassroots petitions in Alberta and Ontario to abandon the “progressive” practices that, purportedly, leave Grade 9 students still using their fingers to calculate six times seven. An advocacy group founded by mathematicians became a champion of the bring-back-the-basics movement, after persuading Manitoba to add more rote learning to its curriculum.
Math anxiety spiked to such a fever pitch that former federal minister John Manley, now president of the Canadian Council of Chief Executives, declared to The Globe that the results – Canada placed 13th among 65 countries in the Organization for Economic Co-operation and Development’s Program for International Student Assessment, or PISA – were “on the scale of a national emergency.”
We should worry: Canada is stumbling just as research shows that student performance in math matters more than reading, both for academic success and future job prospects, two goals that loom ever larger for parents alarmed by bleak job predictions for the next generation. Meanwhile, the country is producing too few engineers for its high-tech economy and nowhere near enough mathematicians and scientists to leap ahead on the Next Big Thing.
But go easy on the teenagers.
Math may be the the backbone of our greatest achievements – supersonic flight, quantum computing, finding the Higgs boson – but the debate over how to teach it has been flaring up with the certainty of a repeating decimal since at least the launch of Sputnik, which pushed the Soviet Union to the front of the space race and sent North America’s math panic into the stratosphere.
A swinging pendulum, however, goes nowhere. What Canada needs is to calculate what Grade 3 kids now will actually need to know by the time they graduate high school in 2026 – to say nothing of their children a half-century from now.
By then, technology will have advanced exponentially, giving everyone a Siri in their pockets (or glasses or who knows where) to tell them in a millisecond the answer to 4,235 times 7,935.
The big questions on today’s blackboard is how to make math relevant for tomorrow, says Eric Muller, a professor of emeritus of mathematics at Brock University and a fellow at the Field Institute for Research in Mathematical Sciences at University of Toronto.
“At the beginning of the 20th century, Latin was a required subject – it was seen as fundamental,” he says, to show how, as society changes, so does what it values. “By the end of century, Latin was gone. What will mathematics be by the end of this century?”
Included in Dr. Small’s presentation is a look at “what has changed” – where she explains how elementary students are no longer taught, step by step, one way to do arithmetic, such as borrowing for subtraction and carrying for addition.
Math educators say such tactics were created when people had no choice but to be their own calculators. Instead, students today are encouraged to try “alternative” strategies to find the method that makes the most sense to them – such as breaking an equation into smaller numbers, or making calculations on a number line.
Dr. Small is showing a third option for two-number multiplication when a father raises his hand and asks: “But what’s the most efficient way?”
“What’s your definition of efficient?” Dr. Small responds. “I think it’s probably the calculator.”
When a few parents chuckle, she clarifies, “that was only half a joke.”
The fact that she is even half-serious enrages mathematicians such as Anna Stokke. An ideal spokesperson for the “basic skills” camp, she teaches at the University of Winnipeg, has three advanced degrees in math and is married to a fellow mathematician. She also has two daughters in elementary school, so when she says there is a problem with their math homework, people pay attention.
After hearing about frustrated parents scouring websites to homeschool their kids in Grade 6 fractions or paying for classes at Kumon so their teens would memorize the 12-times tables, Dr. Stokke co-founded the Western Initiative for Strengthening Education, or WISE Math, and started teaching free classes, both for gifted students and those who need extra help.
Dr. Stokke and WISE co-founder Robert Craigen, a mathematician at the University of Manitoba, are familiar with Dr. Small’s presentation. They sparred with her when she spoke in Winnipeg last fall. Their main beef: the idea that kids can deprioritize traditional exercises and rote memorization; they argue that students need those basics, so they don’t stumble later when math becomes more abstract.
But so it goes. The one side says, “drill and kill.” The other says “drill for skill.” Basically, though, just about every mathematician and math education researcher who was interviewed for this story agrees that the perfect math class should have a mix of skills and problem solving. They just can’t agree on the amounts of each, when to add them, and what to skip.
It’s that lack of clarity, says Dr. Craigen, that’s hurting students: “Our next generation is not a shipment of laboratory guinea pigs,” he says. “If anyone did this sort of thing with an unproven medical innovation they would be subject to criminal charges.”
There isn’t firm research to prove that the new way of teaching math works in the long run – at least, not yet – but its proponents can persuasively argue that the traditional math class didn’t exactly produce a nation of mathletes. By using word problems that have to be solved by creative reasoning rather than rules a teacher has written on a blackboard, math becomes a more elegant mental exercise – and, if done properly, more fun.
It is easy, though, to see why many parents would be baffled by this. For instance, one of Dr. Small’s presentation slides demonstrates: “25 x 44 can be solved by splitting 44 into 4 groups of 11 and there are 100 groups of 11.” The answer: 1100.
Dr. Stokke, as it happens, cites the very same example as the weakness in this kind of teaching: it over-complicates multiplication. “At the end of the day,” she says, “you can absolutely not be using methods like that when you are working on algebra.”
And what happens, when the numbers don’t work so nicely, when you are multiplying not 25, but 37, to 44?
Both sides like to use a music analogy to make their case. The “basic skills” camp asks: Can someone become proficient musician without learning the scales and where the notes sit on the staff? The “progressive education” side counters: What’s the point of drilling young musicians on scales, if they want to give up the instrument as soon as their parents will allow?
Ultimately, the argument about basic skills versus conceptual thinking reduces math to a process – and often a grade to be made – rather than a complex exercise in thinking, that can be transferred to other areas of learning.
As Eric Muller points out, “The best mathematicians are the ones with self-reflection, who learn to ask themselves, ‘Am I doing this right? Am I on the right track?’ ”
So if our current binary debate is missing the point, what conversation should we be having about math in the classroom?
A national voice on math would be a start. Unlike the United States and many European countries, Canada lacks a central watchdog for math education. We have provincial associations for math teachers. And the little-known Canadian Mathematics Education Study Group brings together mathematicians and math educators once a year for discussions. But despite several attempts to change its mandate, the group doesn’t propose guidelines, or speak out on policy.
That means there is no group even to help build a consensus on what Canada can learn from the PISA tests, with their vast troves of data.
Canadian 15-year-olds, for example, actually performed pretty well when it came to the easy “basic skills” questions: The PISA test is broken into levels, and about 86 per cent of Canadian students mastered the first two, described as the math “a person needs to be a citizen in the modern world.”
Their weakness is higher-level, more conceptual math – only 4.3 per cent aced the highest level, compared with 30.8 per cent of those in Shanghai. Students in the Chinese city not only outscored everyone, according to OECD data, they spend barely half the time in math class as Canadians, who at five hours and 14 minutes a week, get more teacher time than in any other survey country.
How does Shanghai do so well? They devote an average of 14 hours a week to homework (versus three for the Canadians) and 70 per cent have parents willing to pay for extracurricular math classes (versus 28 per cent in Canada). And those students who seem to spend so little class time on math also have teachers trained more rigorously and subject to greater supervision.
The problem is that it is easier to teach math when it comes down to following step-by-step instructions. To be creative with math requires a teacher who understands the subject at a fundamental level, who loves it, and who is well trained on how to teach it. Currently, future elementary teachers (who may not even have taken math at university) receive less than 40 hours on how to teach math in some cases.
For students, this can translate as teachers who – regardless of official shifts in curricula – are not comfortable with abstract math. “I would bet my last dollar, what’s going on in elementary schools is anything other than [problem-solving, student-centred] math,” says David Robitaille, a professor emeritus at the University of British Columbia. “I would bet it’s a teacher giving a lesson, then seat work, followed by homework.”
In many of the high-ranking Asian countries, even the youngest students learn math from specialized teachers. In Shanghai, according to an OECD survey of principals conducted in conjunction with PISA, math teachers receive significantly more feedback from students, fellow teachers and external assessment than Canadian teachers, and their top performers get pay hikes and bonuses.
To make the grade in math, we need to properly instruct teachers, even in early grades, on how to balance “concept-based” math with basic arithmetic, so that the nobody spends math class colouring pretty pictures, and the time tables get their due.
What they teach is also worth thinking about: top-performing Asian countries typically cover fewer subjects more deeply, especially in the early grades. A 2004 study found that Grade 1 teachers in Canada were expected to cover 18 topics versus just five in Hong Kong, where even textbooks may be hundreds of pages shorter.
Some math educators also propose revamping the high-school curriculum, expanding courses that align with the future needs of the country – subject areas such as modelling, visualization, statistics and finance – and challenging the value of calculus for university-bound students.
We should also take a serious look at the role of calculators and computers in math class – and try to capitalize on our strong showing in the technology-assisted math component of PISA, which has been virtually ignored. (This was the first time PISA tested students in computer-based math; Canada placed eighth in the world.)
While teaching and curricula are easy targets, however, the problem with math education goes beyond classrooms: studies show that students in places such as Shanghai are also more likely than North American students to believe that math ability is the result of effort, not inherent talent. And even with their relative advantages, Canada teens born to two professional parents don’t match the scores of the the children of Shanghai’s least educated families.
We can design the best curriculum, create great textbooks and give keen teachers good training, but if those newly inspired students don’t go home to families enthusiastic about math, who see it not as an arduous necessity but a positive, essential intellectual exercise, what is the point? We are right back in 1957, watching Sputnik’s twinkly light zip across the sky, feeling a dull sense of missed opportunity.
“If we want math to be the thing that we are good at, then we have to strive for it,” says Egan Chernoff, who teaches math education at the University Saskatchewan, “We have known for a long time that people wear their lack of school mathematics on their sleeves, and so now it’s being thrown in our faces.”
Canada has never been particularly great at creating math-literate, number-loving citizens, as the current generation of math-phobic adults demonstrates: Would you ever say that you “suck at reading”?
That’s why, toward the end of her presentation to the Bayview parents, Marian Small gives her most forceful piece of advice, one that would certainly find favour in every mathematical school of thought.
“If you don’t like math, keep it to yourself.” Don’t tell your kids, you were bad at algebra or hated fractions, she explains, cause you’re giving them permission to be the same way.
“Do you get that?” she asks, no longer smiling. “It’s really bad.”