Wide differences in mathematical achievement among students appear to be natural: In every school in every country, only a minority of students are ever expected to excel at or love learning mathematics.
In the many schools I have visited on several continents, I’ve seen a significant number of students who, by grade five, are two or three grade levels behind. In my home province of Ontario, where children do quite well on international tests of math achievement (like the PISA), only 54 percent of sixth-grade students met grade-level standards on the provincial exams in 2014. And in countries that outperform Ontario, such as Finland and Singapore, whose educational systems are held up as models by the media, PISA results suggest that at least 40 percent of their populations would have trouble holding a job that required fairly basic mathematics.
Many people have suggested that U.S. and Canadian educators should find out how math is taught in the top-performing countries so it can be taught in the same way in North America. I expect this is a good idea, but 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. Answering this question might do as much to help us improve the teaching of mathematics as any efforts to emulate the educational practices of other countries.
I believe that a root cause of many children’s troubles in math, as well as in other subjects, is the belief in natural academic hierarchies. As early as kindergarten, children begin to compare themselves with their peers and to identify some as talented or “smart” in various subjects. A child who decides that she is not talented will often stop paying attention or making an effort to do well. This problem will likely compound itself more quickly in math than in other subjects, because when you miss a step in math, it is usually impossible to understand what comes next.
The more a child fails, the more her negative view of her abilities is reinforced and the less efficiently the child learns.
To create classrooms in which every brain can work efficiently, we must start by dispelling the myth that only a few brains are born with natural talent. In “The Expert Mind,” an article that appeared in the July 2006 issue of Scientific American, Philip Ross examines the implications of a century of research on how experts develop abilities in chess and other fields. His conclusions lend strong support to the notion that abilities can be nurtured in students through rigorous instruction and practice:
“The preponderance of psychological evidence indicates that experts are made, not born. What is more, the demonstrated ability to turn a child quickly into an expert — in chess, music, and a host of other subjects — sets a clear challenge before the schools. Can educators find ways to encourage students to engage in the effortful study that will improve their reading and math skills? Instead of perpetually pondering the question ‘Why can’t Johnny read?’ perhaps educators should ask: ‘Is there anything in the world he can’t learn to do?’”
Research in cognitive science has also uncovered the methods by which teachers can nurture talent in all students. These include scaffolding (breaking challenges into manageable chunks), providing continuous feedback, and giving adequate practice and review. In a randomized controlled study, students taught math using these methods progressed at twice the rate of students in control classes. (See “For the Love of Math,” John Mighton, in Scientific American Mind, September 2013.)
When we compare our present outcomes in education with those that science suggests are possible, it’s clear that intellectual poverty afflicts even citizens of the wealthiest countries. The losses that come from failing to address this problem in mathematics alone are staggering.
Students who do well in math are much more likely to finish school, attend university, and earn a good living than students who struggle in the subject. For young children, math is an even stronger predictor of academic success than reading. According to McKinsey & Company, achievement gaps in subjects like math impose the equivalent of a permanent national recession on the economy.
There is also a deeper loss that’s harder to put a price on. If children are born with anything, it’s a sense of the invisible beauty and elegance of the world. They love seeing patterns, making connections, and solving problems. But the majority of children will lose this sense of wonder and curiosity before they grow up simply because, as a society, we expect so little of ourselves.
Every child has a right to fulfill their intellectual potential, just as they have a right to develop healthy bodies.
We don’t have to wait until we have recruited an army of superhuman teachers or invented some miraculous new technology to guarantee this right. We already have the teachers we need to transform our schools. We simply need to give them the means to teach children using effective methods that are backed by rigorous evidence so we can put to rest the myth of inborn ability once and for all.
John Mighton is the founder of JUMP Math.
Visit www.jumpmath.org for more information.