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.”