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.
April 18, 2011
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.”
steps and assess each student’s understanding at each micro-level before
moving on.
April 18, 2011
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.”
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& Holtz v. Maura
Larkins defamation
SDCOE
CVESD
Castle Park
Elementary School
Law Enforcement
CTA
CVE
Stutz Artiano Shinoff
& Holtz
Silence is Golden
Schools and Violence
Office Admin Hearings
Larkins OAH Hearing
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Teaching Math