Gifted Issues Discussion homepage Forums General Discussion A Better Way to Teach Math

http://opinionator.blogs.nytimes.com/2011/04/18/a-better-way-to-teach-math/
A Better Way to Teach Math
New York Times
April 18, 2011
By DAVID BORNSTEIN

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.

<rest of article at link>

Breaking math problems into small pieces may be effective for children of average or below-average intelligence, but it may bore gifted children to tears. The message I draw from this article is that children of different abilities need different kinds of teaching. I'm concerned that many people will assume that the math instruction that is best for the left half of the bell curve is also best for the right tail.

I agree. All students deserve practice to develop their working memory, as well as other thinking skills where gifted kids excel, and that implies different instructional criteria. I do hold tight to the notion that there is a core of "best" math ideas that all kids should learn, to develop both understanding and problem-solving, but they certainly don't need to learn them the same way.

ETA: I especially have misgivings about this part: 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.

Because some studies indicate that some kids are not ready to learn through problem-solving as well as through direct instruction (I disagree-- all kids should be encouraged to problem solve at an extremely young age, and it can be quite guided, plus they don't have to be mutually exclusive), this sounds like Jump Math may remove some vital learning opportunities from gifted kids, even if they're allowed to speed ahead through curriculum compacting.

I guess the technique of breaking something down into little steps can be useful for tutoring, or even for instruction to make sure someone understands a procedure. I'm not sure that all that focus on procedure will lead to deeper understanding in classrooms. This sort of score-boosting method is likely to spread because of its obvious attraction to administrators, especially in lower-performing schools. It reminds me of a news article from years ago of miraculous results of a teacher in an inner-city setting (I believe it was in Chicago) who was greatly boosting math achievement scores by teaching students mnemonic tricks, such as a sing-songy way to remember long division. I wonder how many students who learn that way ever become mathematicians.

Thanks for the post.

I enjoyed the article. The micro steps to building skill jives with my understanding of the brain research that has been discussed recently. Small steps, building brain connections.

I just read through the Introductory Unit using Fractions of Jump Math, and I think it would be a very good fit for DD7, who likes math, but isn't intuitively mathy. It's designed with a lot of "bonus" problems that allow for learning through problem solving.

Breaking things down is great IMO, no matter what the level. I think the issue is to give gifted kids the level of problem that is appropriate (mildly difficult) for them, and then teach them a process/break the problem down.

DeeDee

I've looked at the curriculum and this is perfect for my DD. Breaking things down helps her understand the whys. We worked on 3rd grade level today and she had no problems mastering it. Would I force DD to be redundant? Absolutely not. If she gets it then we move on, but the way in which it is explained, I can see the lightbulb going off in her head.

Here is an lecture about Jump Math by founder John Mighton:

John Mighton lecture


I also read his book 'the myth of ability' and found it really interesting. I really like Jump, and it's Canadian:) DD7 (not terribly mathy, but starting to love it) also likes Jump. I was considering switching to Singapore math because it seems to be more challenging/compact, but I do have some misgivings. I'll be following this thread to see what others have to say.

Annaliisa

I have just downloaded the introductory unit and accompanying teachers manual. I am completely conflicted as I read through. On the one hand I am going to sit down and do the introductory unit with DD1 as I think it is exactly what she needs right now. On the other all the references to not letting the faster kids get ahead, keeping the faster kids busy while you work with the delayed kids, etc just brought all the frustration of being that bored faster kid flooding back.

And I do wonder how well a system like this would work for a "big picture" learner. What about the kids that won't "get it" until they understand the why/how of the big picture?

My DH, and his business partner, were my bosses straight out of school and the two of them were probably amongst the best teachers I have ever had. Both of them would always start out explaining something to you with the assumption that you had all the background knowledge you needed and the smarts to "get it" from a quick outline of the big picture - which was usually the case. But if that wasn't enough they were always quick to break it down a little, and a little more, and a little more, until you really did get it - always with equal respect and enthusiasm as they started out with (in fact often getting more excited as they really warmed up to talking about an idea, both of them loved nothing more than a good white board session).

So I think I want to try this with my DD but I am not sure I would want her school to try it. And that seems crazy!

Some good thoughts here. From the description Jump Math sounded like it was bound to be a good tutoring or single-student option, for getting through tricky-to-remember procedures. I am not against clear explanations of procedure, just worry that it might occur at the expense of broad and deep understanding. The part about holding bright kids back while stragglers catch up sounds worrisome too. But I will probably get Jump Math and Singapore Math so I can abstract the best of both of them, as soon as we can afford them. Up to now DS5 has not really had math instruction at all, except for ad-hoc tiny lessons I've given him as I've thought of them. I need a real curriculum.

We use Singapore Math- it seems to be very problem-solving based. In school, they take timed math tests, so that has forced us at home to do flashcards. But my son really likes Singapore Math. Last year in first grade on the WJ, he tested into 5th grade for math- I don't know if it's due to Singapore Math or if it's because he was in a Montessori for 2 years.
My little one really likes IXL, the computer program. I get bored by the repetition, but he doesn't for some reason. It is a good way to reinforce basic concepts. He gets little online prizes, cartoon pictures, that he just loves. HTH.