Like many people who struggle with math, John Mighton believed that he simply wasn’t someone who was naturally good at the subject.
“I thought you had to be born with the talent and I wasn’t sure I had it,” he told Yahoo Canada Finance.
He recalled that when he was growing up in the 1960s it was commonly believed that IQ was “immutable,” so if he wasn’t good at math, why try?
“I was always afraid to work hard because I was afraid that I would meet the limits of my ability. I had a very fixed mindset.”
Mighton’s struggles got so bad he almost failed first-year calculus and abandoned the subject for many years.
But he came back to it in his 30s, turning to tutoring as a financially-strapped playwright and eventually earning his PhD in mathematics at the University of Toronto. It was this experience of training himself to overcome his “math anxiety” that inspired him to develop a new method that is drawing praise for its ability to keep students engaged.
JUMP (Junior Undiscovered Math Prodigies) is being used to instruct more than 150,000 kids to in Canada, 15,000 in the U.S. and another 12,000 in Spain.
The program’s results have been good enough to attract a $2.75 million grant for cognitive scientists at SickKids hospital and the University of Toronto who are testing it on 40 classrooms and 1,100 kids. They’re aiming to confirm the findings by the same researchers that found that children from 18 classrooms advanced twice as fast as those receiving typical math instruction in 11 other classes.
How it works
Despite what many people believe, Mighton says that math can be one of “easiest subjects” — if it’s taught well.
And in his mind, the best way to do so is by using a method called “guided discovery.”
Mighton said this involves giving students lots of opportunities to figure problems out on their own while teachers provide guidance and feedback.
The technique uses challenges that are broken into “manageable steps.” After the teacher finds that students are ready for the next level, the bar is raised incrementally to get them excited about new challenges.
To demonstrate how a math problem in a JUMP curriculum might look, Mighton provides the following example:
To teach long division, a teacher could ask how three friends could share seven dimes and two pennies. Students would be instructed to draw three circles for each person and use Xs to indicate how many dimes each of them would receive.
Students would then draw two Xs in each and have one left over.
The teacher could then follow up by asking how many dimes were given away and how many remain. Then all that’s left is for them to divide is the leftover dime and two pennies.
“So … the kids can discover it themselves if the teacher asks some good questions,” Mighton said.
What’s wrong with current methods?
Mighton said in a typical math class instead kids might be expected to understand all of these steps right away or to develop their own methods, rather than being guided along through a series of questions with more limited answers.
“Sometimes the teachers will teach whole procedure at once, or encourage kids to figure out their own procedure, which is fine too, but if you want them to develop a method they can figure it out for themselves,” he said.
These standard math teaching methods rely “discovery-based learning,” which Mighton suggests can cause children to suffer from “cognitive overload” as they’re “asked to absorb too much new information” and aren’t given enough time to practice and get a good grasp of concepts before moving on.
Discovery-learning techniques tend to place less emphasis on following a general rule and more on tackling complex problems based on real-world examples that may allow for more than one approach or solution.
While the goal is to encourage students solve realistic problems, many kids don’t have the knowledge base to uncover the answers.
“Often kids are being challenged to do too much without enough guidance, or prompts or hints,” said Mighton.
He said problems need to broken into more easily digestible steps for students who should be assessed immediately as they try to progress.
“If you give them more incremental challenges, you also get them excited at their victories and you raise the bar incrementally, so you make it look harder and harder, then they learn to persevere and eventually you can let them struggle more,” said Mighton.
The other issue with the standard way of teaching math, according to Mighton, is that educators often stress the importance of bringing up the class average, rather than tightening the range of good marks.
The reason this is key, Mighton explains, is because children start comparing themselves to their peers as early as grade one and decide who is good at math and who isn’t.
“And as soon a child decides they’re not smart in math, their brain stops working,” he said, noting this creates a sense that students who are successful in the subject have a natural “gift or talent for math.”
“They stop engaging, working hard [and] remembering things.”
Mighton said if classes instead focus on bridging the gap in performance between high achievers, the middle and those at the bottom, as well as bringing up the average, all of the students improve.
“When you take care of the students who struggle or who are turned off math, the whole class benefits and even the faster students go further because the whole class moves further [as] everyone’s excited about math,” he said.
Mighton said there are some exceptions, as some may need extra help and others extra work, but a “very high percentage” of children can move at about the same rate.
Why it matters
It’s not a contentious statement to say many people struggle to learn math. Nearly one quarter of university graduates born in Canada have a low level of numeracy and more than half of millennials have below “desired” competency levels of the subject, according to the OECD.
And this has had a damaging effect on our economy, according to Mighton. He said these levels of innumeracy make it difficult to fill high-skill jobs that require math, such as those in STEM fields, which have among the highest average salaries in the country. It also means people have trouble understanding risk, their personal finances and how to develop sustainable economies.
But ultimately the biggest damage is felt by kids who miss out on the opportunity to enjoy math.
“I’ve seen kids cheer for math. I’ve seen kids beg to stay from recess for math. Kids are born with a sense of wonder and curiosity, and they love solving puzzles, seeing connections and making discoveries,” said Mighton.
“But they gradually lose that sense of wonder through failure, and that’s the deepest loss to our society.”