My Inspiration for JUMP Math
Nothing comes easily to me.
I’m a mathematician, but I didn’t show much aptitude for math until I was thirty. I had no idea, in high school, why I had to turn a fraction upside down when I wanted to divide by it, or why, when I wrote a square root sign over a negative number, the number suddenly became “imaginary” (especially when I could see the number was still there). At university I almost failed my first calculus course. Fortunately I was saved by the bell curve, which brought my original mark up to a C minus.
I’m also a playwright and, early in my career, I made the mistake of checking the papers to see what two of the local critics thought of my first major production. It seems unlikely that they consulted each other before writing their reviews, but one headline read “Hopelessly Muddled” and the other “Muddled Mess.”
I often wish I was more like my literary and scientific heroes, who seemingly could produce perfect poems or solve intractable problems in a blinding flash of inspiration. Now that I’m a professional mathematician and writer, I console myself with the thought that my ongoing struggles to educate myself produced an intense curiosity about how we achieve our potential.
In the final year of my doctoral program, I persuaded some of my friends to start a free, after-school tutoring program called JUMP Math (Junior Undiscovered Math Prodigies) in my apartment. The program’s methods, which can be used by people of any age, are easy to understand and apply, and they reinforce confidence in your abilities rather than assigning you to a particular skill level.
Twenty years later, 200,000 students and educators in North America use JUMP as their main math instruction resource, and the program is spreading into Europe and South America. And after teaching math and other subjects to thousands of students of all ages, and after reading a great deal of educational and psychological research, I am convinced that our society vastly underestimates the intellectual potential of children and adults.
We’re Born With Unlimited Potential
Over the past two decades, research in cognitive science has radically changed the way scientists think about the brain. Researchers have discovered that our brains are plastic and can learn and develop at any stage of life. As well, a growing body of evidence suggests that the vast majority of children are born with the potential to learn anything, particularly if they are taught by effective methods.
A variety of psychological studies—in which people have been trained to develop musical abilities that were once considered to be innate (like perfect pitch) or to significantly improve their performance on SAT tests (by becoming better at seeing analogies)—indicate that experts are made not born. As Philip E. Ross points out in “The Expert Mind,” a research survey published in Scientific American, these results have profound implications for education. According to Ross, “Instead of perpetually pondering the question, ‘Why can’t Johnny read?’ perhaps educators should ask, ‘Why should there be anything in the world that he can’t learn to do?’”
Many people believe that math is an inherently difficult subject—accessible only to people who are born with a “gift” with numbers or who display mathematical ability at an early age—but I’ve discovered that math is in fact the subject in which learners of all ages can most easily unlock their true intellectual potential. Indeed, if every child was taught according to their true potential from the first day of school, I would predict that by grade five, 99 per cent of students could learn, and love learning, math as much as the top one per cent do. And I believe that the significant majority of adults can attain an aptitude for math as well, if they are taught using the methods I’ve developed.
What We Can Learn From Standardized Tests
I remember reading newspaper articles about the remarkable intellectual potential of children and the surprising plasticity of older brains as long ago as the 1990s. Since then I’ve read many excellent books on this topic, including David Shenk’s The Genius in All of Us and Carol Dweck’s Mindset. I wrote about the issue in my own books, The Myth of Ability and The End of Ignorance.
It strikes me as odd, then, that although the research has long been widely publicized, its existence has done very little to change the way that people think about their own intellectual abilities or the way people are taught—at home, at school or in the workplace. Just as the ancient Greeks couldn’t conceive of a world in which every person is born free, it appears that, in spite of the evidence, we can’t conceive of a world in which virtually every person is born with the potential to learn and love learning any subject.
When people complain about problems in North American education, they often speak as if those problems would be solved if students in the United States and Canada were able to perform as well on international tests of reading and mathematics as students from countries that achieve the highest scores. Nations like Finland and Singapore are singled out in the media as having superior educational systems because their students do better on standardized tests of mathematical achievement—like the Programme for International Student Assessment test written by fifteen-year-old students in eighty countries every three years.
It’s worth looking at the results of these tests, but more for what they reveal about our beliefs about children and their potential than for what they prove about education. On the PISA test, a score at level 5 or 6 in mathematics is required to take courses at university; a score at level 3 or below suggests the test taker would have trouble holding a job that required much more than a basic knowledge of math. In 2015, only 6 per cent of American students and 15 per cent of Canadian students scored at level 5 or 6, compared with 12 per cent in Finland and 35 per cent in Singapore. However, in Finland almost 55 per cent of students scored at level 3 or below and in Singapore about 40 per cent of students scored at these levels.
While it would be a good idea for North American educators to find out how math is taught in those top-performing countries—as many people have suggested—we might also want to find out how countries that produce such strong students still manage to teach so little to almost half their populations.
Learning to Love Learning
Wide differences in mathematical achievement among students appear to be natural. In every school in every country, only a minority of students are expected to excel at or love learning mathematics. In the many schools I have visited, on several continents, I have always seen a significant number of students who are two or three grade levels behind by the end of elementary school. In my home province of Ontario, where children do rather well on international tests, fewer than 50 per cent of grade six students met grade-level standards on the 2018 provincial exams. And the same differences can be found in other subjects, particularly in the sciences.
However, in my work with children and adults, I have seen a great deal of evidence that mathematical ability is extremely fluid and that teachers can produce dramatic improvements with very simple interventions. One example from Toronto is a fifth grade class in which the teacher, Mary Jane Moreau, incorporated strategies from JUMP Math. This meant teaching concepts and skills in steps that were much smaller than the ones she normally followed, constantly asking questions and assigning exercises and activities to assess what her students knew, giving frequent practice and review, and most importantly, building excitement by giving students incrementally harder series of challenges where one idea builds on the next.
Before beginning the program, Moreau tested her students on a standardized test called the TOMA (Test of Mathematical Abilities). The average mark for the class was in the 54th percentile, with the lowest mark in the 9th percentile and the highest in the 75th. This range of marks would represent about a three-grade-level difference between the top and bottom of the class. (A fifth of this class were diagnosed with learning disabilities.)
After a year of JUMP, Moreau retested her students. The average score of her students rose to the 98th percentile with the lowest mark in the 95th percentile. This teacher was able to shift the bell curve in her class so dramatically because she made all of her students feel like they could accomplish roughly the same things. In her classroom, students worked to compete against the problem, not each other. They got caught up in the excitement of their peers, and this excitement helped them to engage more deeply, remember what they learned and persevere in the face of challenges. They were encouraged to learn and love learning for its own sake, not because they were afraid of failing or wanted to be ranked higher than other students.
Curiosity Is the Key
Inequitable learning environments are extraordinarily unfair but also they are inherently inefficient. They’re not good for any learners—including the ones at the top of the academic hierarchy—because they train learners to give up too easily or to exert themselves for the wrong reasons. They destroy our natural sense of curiosity and make our brains function in the most inefficient ways possible.
In “The Business Case for Curiosity,” psychologist Francesca Gino presents evidence that curiosity produces a wide range of benefits for organizations, leaders and employees. For example, in a state of curiosity, we are less susceptible to confirmation biases (looking for information that confirms our beliefs rather than evidence suggesting we are wrong) and to making generalizations about people based on their race or gender.
According to Gino, higher levels of curiosity among employees can lead to more innovation on the job and to reduced group conflict (curiosity encourages members of a group to put themselves in one another’s shoes and take an interest in one another’s ideas). As well, a culture of curiosity creates more open communication and better team performance, since curious groups share information more openly and listen more carefully.
Many people believe, based on their experience of learning math at school, that math is a rigid and sterile subject that stifles curiosity and leaves no room for creativity. But progress in mathematics has actually been driven by remarkable flights of imagination. Math can be an ideal tool for nurturing curiosity in learners of all ages.
Learn more about John Mighton’s book, All Things Being Equal.
Excerpted from All Things Being Equal by John Mighton. Copyright © 2020 John Mighton. Published by Alfred A. Knopf Canada, a division of Penguin Random House Canada Limited. Reproduced by arrangement with the Publisher. All rights reserved.