Michelle Jones says her students have been far more engaged since she started using the JUMP Math method at Jarvis Traditional Elementary School in Delta, B.C. Try the quiz at the end of this article to see whether you could solve the problems that Ms. Jones's Grade 6 students are expected to handle.Jennifer Gauthier/The Globe and Mail
In her more than two decades in front of a classroom, Michelle Jones has used five different math textbooks and, until recently, had grown increasingly frustrated in her inability to reach many of her students.
The story-based math problems that filled those textbooks left most of the children either checked out or confused. She’d draw on videos and other materials to supplement her lessons, but it didn’t feel like that was enough to help her students build their confidence in the subject.
Then, three years ago, her board – the Delta School District in Delta, B.C. – piloted a program that incorporated JUMP Math, a resource originally developed by John Mighton, an accomplished playwright and entrepreneur in Toronto. The program, run by a charity established in 2002, emphasizes students rehearsing basic arithmetic operations so they can see patterns and break problems down into smaller parts, gradually raising the level of difficulty. “We were just ready for a shift, to try something different,” said Ms. Jones, who teaches Grades 6 and 7 at Delta’s Jarvis Traditional Elementary School.
John Mighton helps Grade 4 pupils practice JUMP techniques at a Toronto school in 2007, five years after he developed the method.Deborah Baic/The Globe and Mail
For Ms. Jones, using JUMP Math – JUMP stands for Junior Undiscovered Math Prodigies – represented a sea change.
She is now armed with new strategies to teach the subject and has been able to reintroduce some rote learning so that students can engage with the material more quickly. The students use whiteboards, check in with their partners and practise on their own. As a result, she’s noticed they are less anxious and take more risks in class.
“In my experience, I have never seen students so engaged, relaxed and enjoying a math lesson,” she said.
The pilot at Delta has since expanded: In 14 of the district’s 24 elementary schools, most of the teachers are now using JUMP.
Focusing on math fact fluency may seem like an obvious recipe for success, but the way math is taught in schools has been the subject of a long-standing and divisive debate, much like reading.
On one side, some experts and educators believe rote learning creates anxiety and dread, and that children should approach the subject with playfulness and curiosity by learning through problem solving, pattern discovery and open-ended exploration.
Others have advocated for a so-called back-to-basics approach and pushed governments to initiate curriculum changes so students have the ability to quickly recall addition, subtraction, multiplication and division through repetition and memorization. Rote learning shouldn’t be considered a dirty phrase, they argue.
The debate comes at a critical time: Although Canada performs well compared with other countries globally, Canadian students’ scores on an international test administered by the Organization for Economic Co-operation and Development have been slipping for almost two decades – and the latest results from late last year show that slide continuing.
Neil Stephenson, director of learning services at Delta, brought in JUMP Math because he felt something needed to change in his district.
Educators were doing a “hodgepodge of things” to help students meet curriculum expectations, he said, which put an incredible strain on them to find and build lesson plans.
After doing some research and finding JUMP, he approached an elementary school that hadn’t been scoring well on provincial tests to see if any teachers there would try the program. Around three-quarters of them raised their hands – and assessments at the end of that school year showed that several students had progressed multiple grade-levels, and teacher confidence in how they approach the subject rose, he said.
“Absolutely we want kids to be doing creative work and solving interesting questions and synthesizing their knowledge. But there has to be some building up of that knowledge somewhere else first,” Mr. Stephenson said.
In Jarvis Elementary's district, more than half the schools now use JUMP for math education.Jennifer Gauthier/The Globe and Mail
That is heartening to JUMP’s founder.
Mr. Mighton didn’t fare well in math in school and nearly failed first-year calculus in university. But he slowly overcame his own math anxiety and, as a playwright trying to make a living, started tutoring the subject later in life. Teaching children encouraged him to break down difficult concepts into smaller parts, and, in turn, grasp the subject better. He relearned concepts he had missed along the way, and then returned to school in his early 30s to earn a PhD in math at the University of Toronto.
“Math is actually accessible, very accessible,” he said.
He explained that the current method – investigating ideas through problem solving, pattern discovery and open-ended exploration – rushes children past learning math facts in the hopes of making the subject more engaging. It has the opposite effect, he said, because children actually just become confused and disengaged.
His program provides lesson plans for teachers that allows for an incremental approach to problem solving. There’s a workbook for students, but Mr. Mighton said that should only be used after the lessons. “You want to get to those problems, but that’s not where you start. That’s the mistake we’re making,” he said. “We always think kids are experts. And we give them problems that are designed for experts when they’re novice learners.”
Math professor Anna Stokke feels that methods of teaching introduced in the 1980s have done a 'disservice to children' in the decades since.John Woods/the Globe and Mail
Anna Stokke, a mathematics professor at the University of Winnipeg and a vocal proponent for schools to once again focus on fundamentals, said the change in how math was taught began in the late 1980s under the school of thought called constructivism. The theory suggests students should not passively acquire knowledge through direct instruction but rather learn through experiences and interactions. At the time, the National Council of Teachers of Mathematics in the U.S. released a set of standards where problem solving became the focus of instruction, she said. The movement then spread to Canada.
Prof. Stokke said the change in instruction has been a “disservice to children” because students should be practising math procedures and memorizing facts before they can grasp more complex problems. “I’m a mathematician and, believe me, I know how to solve complex problems. And you can’t do complex problems without having a web of knowledge in your brain.”
The result of this change has been a widening equity gap, she said, where families who have the means provide tutoring for their children, while others continue to struggle in the subject.
However, Jason To, a math co-ordinator at the Toronto District School Board, said the argument that schools are teaching one way over another is misplaced. He worries that some experts are latching onto international test scores and insinuating that inquiry-based instruction is dominating the education space. But teachers, he said, are doing both: instructing their students on math fluency and immersing them in complex problems.
“This debate to me is you got to do one versus the other, and it’s not productive. It’s more like, how do these co-exist?”
Math fluency, and the way it is measured in standardized test, can be polarizing subjects in the world of education.Justin Tang/The Globe and Mail
Janelle Feenan, a teacher and peer support co-ordinator at the Delta school division, echoed the sentiment. For years, she and her Grade 3 teacher colleague would spend an evening a week researching and pulling resources to help their students with math fluency and to develop a more comprehensive understanding for concepts.
“We were struggling a little bit to make sure our students were understanding what we were doing. We’re going through the motions, but we just didn’t feel that they were where they needed to be,” she said.
They raised their hands to participate in the pilot that introduced JUMP Math to students.
Having worked with the program, Ms. Feenan found that there’s a place for both the structural approach that JUMP provides as well as allowing for problem solving and conceptual understanding. She uses JUMP as her main lesson plan, and then supports that with games and visual aids to deepen understanding.
“Neither of those approaches alone would be adequate to prepare kids for success in math,” she said. “I think you have to supplement lessons with activities and resources that are fun and engaging to build their understanding and enrich their learning experience.”
Pop quiz: Test your math skills, JUMP-style
These are Grade 6-level problems from JUMP Math assessment and practice books. Get out your calculator app and give them a try!
c. If the pitcher pitches on the first game (or on the second, or on the third), she will pitch a total of 10 games, ending on the 46th game (or 47th, or 48th, respectively).
Photo: Jon Blacker/The Canadian Press
d. The lake with the longest shoreline is Huron, at 6,164 km. The shortest is Lake Ontario, 1,146 km. The difference is 6,164 – 1,146 = 5,018 km.
a. Avril’s grade sold 10 + 15 + 25 + 10 = 60 tickets in total. Of those 60 tickets, 30 (half) are adult tickets and sell for $5 each, and the other 30 sell for $3 each. So Avril’s grade raises (30 × $5) + (30 × $3) = $150 + $90 = $240. Since the bus costs $320, there is still $320 – $240 = $80 needed.
c. Round 3,128 to 3,000, and 4,956 to 5,000. So 3,128 × 4,956 is approximately equal to 3,000 × 5,000 = 15,000,000, i.e., 15 million.
b. 821 × 4 = 3,284. To calculate mentally, multiply the digits separately.
c. The perimeter of the field is 921 × 5 = 4,605 m. The farmer needs 4,605 – 4,500 = 105 more metres of fence to surround the field.
Photo illustration (source: Ina Fassbender/AFP/Getty Images, JUMP Math
b. Add the digits and check if the sum makes a multiple of nine.
c. 40 per cent of 20 = 8, and 25 per cent of 20 = 5. Since 8 + 5 = 13, there are 20 – 13 = 7 green fish.
a. $7.21 × 3 = $21.63. To multiply mentally, multiply the digits separately.
Photo: Kham/Reuters
d. 84.8 mm ÷ 4 = 21.2 mm. To divide mentally, divide the digits separately.
b. 220 kg ÷ 4 = 55 kg.
c. 15 × 8 = 120, 120 ÷ 100 = 1.20. They will pay $1.20 in taxes.
d. Three quarters of 12 is nine, so nine green balloons have writing on them. Sixty per cent of 15 is nine, so nine blue balloons have writing on them. So, 9 + 9 = 18 balloons in total have writing on them.
Photo: Vadim Ghirda/AP