steps and assess each student’s understanding at each micro-level before

moving on.

A Better Way to Teach Math

By DAVID BORNSTEIN

New York Times

Is it possible to eliminate the bell curve in math class?

Imagine if someone at a dinner party casually announced, “I’m illiterate.” It would

never happen, of course; the shame would be too great. But it’s not unusual to

hear a successful adult say, “I can’t do math.” That’s because we think of math

ability as something we’re born with, as if there’s a “math gene” that you either

inherit or you don’t.

School experiences appear to bear this out. In every math class I’ve taken, there

have been slow kids, average kids and whiz kids. It never occurred to me that

this hierarchy might be avoidable. No doubt, math comes more easily to some

people than to others. But the question is: Can we improve the methods we use

to teach math in schools — so that everyone develops proficiency?

Looking at current math achievement levels in the United States, this goal might

seem out of reach. But the experience of some educators in Canada and

England, using a curriculum called Jump Math, suggests that we seriously

underestimate the potential of most students and teachers.

John Mighton teaching a grade five class at Brock Junior Public School in

Toronto.Peter BreggJohn Mighton teaching a grade five class at Brock Junior

Public School in Toronto.

“Almost every kid — and I mean virtually every kid — can learn math at a very

high level, to the point where they could do university level math courses,”

explains John Mighton, the founder of Jump Math, a nonprofit organization

whose curriculum is in use in classrooms serving 65,000 children from grades

one through eight, and by 20,000 children at home. “If you ask why that’s not

happening, it’s because very early in school many kids get the idea that they’re

not in the smart group, especially in math. We kind of force a choice on them: to

decide that either they’re dumb or math is dumb.”

Children come into school with differences in background knowledge,

confidence, ability to stay on task and, in the case of math, quickness. In school,

those advantages can get multiplied rather than evened out. One reason, says

Mighton, is that teaching methods are not aligned with what cognitive science

tells us about the brain and how learning happens.

In particular, math teachers often fail to make sufficient allowances for the

limitations of working memory and the fact that we all need extensive practice to

gain mastery in just about anything. Children who struggle in math usually have

difficulty remembering math facts, handling word problems and doing multi-step

arithmetic (pdf). Despite the widespread support for “problem-based” or

“discovery-based” learning, studies indicate that current teaching approaches

underestimate the amount of explicit guidance, “scaffolding” and practice

children need to consolidate new concepts. Asking children to make their own

discoveries before they solidify the basics is like asking them to compose songs

on guitar before they can form a C chord.

Mighton, who is also an award-winning playwright and author of a fascinating

book called “The Myth of Ability,” developed Jump over more than a decade

while working as a math tutor in Toronto, where he gained a reputation as a kind

of math miracle worker. Many students were sent to him because they had

severe learning disabilities (a number have gone on to do university-level math).

Mighton found that to be effective he often had to break things down into minute

steps and assess each student’s understanding at each micro-level before

moving on.

Take the example of positive and negative integers, which confuse many kids.

Given a seemingly straightforward question like, “What is -7 + 5?”, many will end

up guessing. One way to break it down, explains Mighton, would be to say:

“Imagine you’re playing a game for money and you lost seven dollars and gained

five. Don’t give me a number. Just tell me: Is that a good day or a bad day?”

This graph shows the percentile rankings of Mary Jane Moreau's grade 5 class

in 2006, which was before she taught JUMP curriculum, and her grade 6 class

after a year of JUMP work.Courtesy of Mary Jane MoreauThis graph shows the

percentile rankings of Mary Jane Moreau’s grade 5 class in 2006, which was

before she taught JUMP curriculum, and her grade 6 class after a year of JUMP

work. CLICK TO ENLARGE

Separating this step from the calculation makes it easier for kids to understand

what the numbers mean. Teachers tell me that when they begin using Jump they

are surprised to discover that what they were teaching as one step may contain

as many as seven micro steps. Breaking things down this finely allows a teacher

to identify the specific point at which a student may need help. “No step is too

small to ignore,” Mighton says. “Math is like a ladder. If you miss a step,

sometimes you can’t go on. And then you start losing your confidence and then

the hierarchies develop. It’s all interconnected.”

Mighton saw that if he approached teaching this way, he could virtually

guarantee that every student would experience success. In turn, the children’s

math anxiety diminished. As they grew more confident, they grew excited, and

they began requesting harder challenges. “More than anything, kids love

success,” he says, “and they love getting to higher levels, like in a video game.”

As the children experienced repeated success, it seemed to Mighton that their

brains actually began to work more efficiently. Sometimes adding one more drop

of knowledge led to a leap in understanding. One day, a child would be

struggling; the next day she would solve a problem that was harder than

anything she’d previously handled. Mighton saw that if you provided painstaking

guidance, children would make their own discoveries. That’s why he calls his

approach “guided discovery.”

This graph shows the percentile rankings of Mary Jane Moreau's grade 5 class

in 2008, which was before she taught them JUMP curriculum, and her grade 6

class in 2009, after a year of JUMP work.Courtesy of Mary Jane MoreauThis

graph shows the percentile rankings of Mary Jane Moreau’s grade 5 class in

2008, which was before she taught them JUMP curriculum, and her grade 6 class

in 2009, after a year of JUMP work. CLICK TO ENLARGE

The foundation of the process is building confidence, which Mighton believes

should be the first goal of a math teacher. Confidence begets attention, which

begets rich learning. “I’ve never met a teacher who will tell you that a student

doesn’t need to be confident to excel in school,” explains Mighton. “But I’ve

never seen a math curriculum that follows the implications of that idea

rigorously.” Math is well-suited to build confidence. Teachers can reduce things

to tiny steps, gauge the size of each step to the student and raise the bar

incrementally.

When math is taught this way, surprising things happen.

Consider some of Jump’s results. It’s been used for four years in the public

schools in Lambeth, one of the most economically depressed boroughs of

London, England. Teachers placed into Jump the students who were struggling

most in math. Among the 353 students who entered the program in fifth grade,

only 12 percent began at grade level. Most were at least two grade levels behind

and the vast majority were not expected to pass England’s grade six (KS2)

national tests. But 60 percent did.

In rural Ontario, Jump was recently evaluated in a randomized controlled study

involving 29 teachers and about 300 fifth-grade students (controlled studies of

math programs are rare). Researchers from Toronto’s Hospital for Sick Children

and the Ontario Institute for Studies in Education arranged for a control group of

teachers to use their district’s standard curriculum while another group used

Jump. Each set of teachers was given two days of training relevant to the

materials they would be using.

In five months, researchers found substantial differences in learning. The Jump

group achieved more than double the academic growth in core mathematical

competencies evaluated using a well known set of standardized tests. (The study

has not yet been published.) “Kids have to make pretty substantial gains in order

to see this kind of difference,” explained Tracy Solomon, a developmental

psychologist in the Research Institute at the Hospital for Sick Children who is the

study’s lead author. “It’s impressive over a five-month period.”

Solomon believes that the key to Jump’s effectiveness is the way it “breaks math

down to its component parts and builds it back up.” And she notes that this “flies

in the face of the way math is typically taught.”

& Holtz

Education Report

Teaching Math