David Bornstein writes in the New York Times
in "A Better Way to Teach Math
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.
"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.Â ...
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?"
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."
In other words, the secret to better math education is to Have the slow kids go slower
. Don`t introduce the Pythagorean Theorem to everybody in second grade, as is common lately. Instead, make the not so bright kids chant their times tables until they`re burned into their memories. Use educational tricks on the dumb kids like "Imagine you`re playing a game for money and you lost seven dollars and gained five. Don`t give me a number.Â Is that a good day or a bad day?" that would put smarter kids to sleep.
Of course, these methods would be disastrous for the smarter kids, so the bottom-line macro implication is: Track, track, track.
(A second order implication is that individual tutoring, which tends to work better than less labor-intensive ways of teaching math, should be handed off to computers that can customize each lesson and quiz for the individual student. On the other hand, notice that Steve Jobs`s Apple products were heavily aimed at the educational market 30 years ago, but almost ignore schools today. Most educational software in 2011, sadly, comes from small firms that deserve to be small.)
Of course, all this subversive wisdom about not ignoring cognitive differences has to be phrased as being part of the Holy War on Charles Murray.
I suppose this kind of subterfuge is, on the whole, better than the current orthodoxy, which is toÂ accelerateÂ everybody in math to avoid the soft bigotry of low standards, which leads to lots of kids who could have mastered arithmetic counting on their fingers as they fail algebra.
Arithmetic really, really matters in real life: arithmetic skills are an important hurdle in determining who moves up from carpenter`s helper to carpenter and from carpenter to contractor. But elementary and middle schools put less relative emphasis arithmetic today and more on "rigorous" math because Studies Have Shown that kids who aced Algebra I in 7th grade are more likely to graduate from college. (It might also be useful to teach more people how to Think About Statistics.)
Still, the need to lie all the time, especially about bell curves, means that practically nobody in the Education Biz ever learns any broadly applicable lessons even from success stories. How many readers of this story will figure out the real message? Two percent?