John Mighton writes the 9-times table on the board and asks the Grade 6 students to look for patterns.
The children stare at the numbers 18, 27, 36, 45, 54, 63, 72, 81 and 90 and make a few quick observations: The digits in each number add up to nine. One plus eight is nine, two plus seven is nine and so on.
Within minutes, every kid in the class is using the sum of the digits to determine if a number is divisible by nine. If it isn't, they learn to predict what the remainder will be.
They practise on half a dozen three-digit numbers. Then Mr. Mighton scrawls 121,252 on the board - a much bigger figure than they have tackled so far.
"What is your prediction?" he asks.
"Easy peasy lemon squeezy," one girl says as she copies the bonus question down in her notebook.
Mr. Mighton is not a certified teacher. He's a writer and mathematician who devotes most of his time to JUMP, a charity that helps youngsters learn to think mathematically.
Since he founded it as an extracurricular tutoring program in 1998, he has amassed compelling anecdotal evidence that it helps struggling students. The question now is whether it also works in regular classrooms, where kids have a wide range of mathematical abilities. It's under study, and the way Canadian students learn could ride on the answer.
"There is a perception that JUMP is only for weaker students and that it will hold faster kids back," Mr. Mighton says. This Grade 6 class at the private Mabin school in Toronto shows how JUMP can work for all children, he says.
The teacher, Mary Jane Moreau, started using JUMP last year, when the children were in Grade 5. Beforehand, she gave the students a standardized math-computation test: Their marks ranged from the 37th to the 75th percentile. After a year of JUMP, she says, all but one were in the 91st-to-the-99th percentile.
"It is like they are a gifted class," she says. "But they aren't a gifted class."
One thing that's obvious to an observer is that these kids now love math. Even the shyest children volunteer answers. Some seem giddy.
One class, of course, isn't proof. Ms. Moreau is an exceptional teacher, keen to use what brain scientists have found about learning to help her teach more effectively, which is why she was drawn to JUMP. She also has the luxury of teaching just half her class - nine students - at a time.
But Tracy Solomon, a researcher at the Toronto Hospital for Sick Children, is doing a study that should show if Ms. Moreau's class is an anomaly.
She is comparing 300 children in an Ontario school board: Half are being taught using JUMP methods and half in the regular manner, which stresses problem solving. Like the Mabin-school children, they started JUMP in Grade 5 and now are in Grade 6.
Dr. Solomon's hypothesis is that kids taught with JUMP will have better math fluency than the control group. If that proves correct, she wants to dig deeper and learn what makes JUMP work so well.
"It's an opportunity to marry two things separated for far too long - research and education," she says, "and draw on the substantial body of knowledge from psychology, cognitive science and neuroscience and infuse those findings into education."
(It may seem strange that a hospital researcher is studying math teaching, but Sick Kids takes the view that education is intertwined with long-term mental health.) Recent results from a smaller group of students in Britain suggest that children who are already at grade level can progress at a rapid speed with JUMP. In the Lambeth school district, all of the 74 students in Grades 5 and 6 who were close to meeting expectations for their age were able to perform beyond their grade levels after one or two years with JUMP. By the age of 11, 57 per cent of those students were three grade levels ahead.
Rising in the west
In Canada, JUMP has its strongest foothold in Vancouver, where Mr. Mighton has trained 400 teachers, and is also being used, although to a lesser extent, in Edmonton and Winnipeg. Teachers in Western Canada often have more autonomy to choose programs for their classes, he says.
The program has met with more resistance in Ontario, where it began. Many school board officials prefer the current approach, which helps students discover and understand mathematical concepts through problem solving. Still, JUMP is getting attention there: Mr. Mighton has trained more than 100 teachers in the public and Catholic boards since September.
The JUMP method breaks mathematical operations into small steps that kids practise and master before they move on. In learning subtraction, for example, children might do a whole page of identifying which questions require regrouping (what used to be known as borrowing).