小学数学难倒大人

The Way You Learned Math Is So Old School

SCOTT SIMON, host: Here's a multiple choice math problem: Let's say you have a 5th grader([美](中小学的)...年级学生) who asks you for help with her homework. Her assignment is to create a stem and leaf plot of the birthdays of each student in the class and use it to determine if one month has more birthdays than the rest. If so, which month? Do you, A.,  stare blankly; B., just Google stem and leaf plots; C., say, why do you need to know that, honey; D. - sounds good - d., just shrug and say, I must have been sick the day they taught it in my math class.

Of course, your children's homework can be confounding these days. Maybe we can blame it on changes in the way children are being taught math, which can make you feel like you're not very good with numbers.

Our math guy, Keith Devlin, is very good at math. Although, Keith, you say you have trouble balancing your checkbook sometimes, right?

Professor KEITH DEVLIN (Mathematician, Senior Researcher, Stanford University): I use machines to do that for me, like most other people.

SIMON: And, of course, ordinarily Keith joins us from Stanford University, but he's visiting us in our studio this week. Keith, thanks so much for being with us.

Prof. DEVLIN: Sure. Nice to be here, Scott, in person at last again.

SIMON: Yes. How nice. How are youngsters being taught math concepts today? Like, like things to multiply. We both have children and I know I'm at the point where I can't help our second-grader anymore.

Prof. DEVLIN: Yeah, the point is the way that mathematics now, the way that arithmetic's been taught in the elementary schools now is different. And that's largely to reflect the different needs of society. When you and I were at school, we really did have to learn to do our arithmetic quickly, fluently and efficiently in our heads and paper and pencil because that's how we had to do it, and that's how people have been doing it for hundreds of years.

No one ever in their real life anymore needs to - and in most cases, never does - do the calculations themselves. We use computers to do them. Most people who are running a business or a sports club or something would use a spreadsheet. In that spreadsheet, all the calculations are done for you on an entire column of numbers instantly. But you have to write the macro. What's that's known as is algebraic thinking.

The emphasis now in mathematics teaching is on getting people to be sophisticated algebraic thinkers. You cannot become good at algebra without a mastery of arithmetic, because arithmetic is the gateway to algebra. But arithmetic itself is no longer the ultimate goal.

SIMON: There's some parents who believe that it's still a good mental exercise and almost a character exercise, to be able to learn your multiplications tables(乘法表).

Prof. DEVLIN: Oh, yeah. And in fact it's kind of myth that modern education doesn't require you learn your multiplications tables - it does. But the way it's taught now is you get to the multiplication tables by understanding the number system and understanding what numbers mean.

Sooner or later, and I would always recommend soon as possible,you actually do have to sit down and learn the multiplication tables. There's no alternative to learning them. From what we know about the way the brain works, we have a strong reason to believe that the only way to actually master the multiplication tables is to learn them linguistically, almost like the chanting that you and I probably had to do.

But if all you do is master them as a chant, you'll never be able to make sophisticated uses of numbers.

SIMON: I've never quite asked you this, but now is as good a time as any. Is there such thing as a math gene?

Prof. DEVLIN: Almost sounds like a book club. But that was a book I wrote 10 years ago, 11 years ago now - in 2000, called "The Math Gene."

SIMON: Seriously? I wish I could tell you I gave it as a holiday gift to everybody. I didn't know that.

Prof. DEVLIN: Well, there's your Christmas present coming up, Scott, it'll be a copy of "The Math Gene," signed by the Math Guy.

SIMON: Boy, did I tee up ([高尔夫]把球放在球座上；(引申)详尽安置、准备) the ball for you? Yes.

Prof. DEVLIN: But the whole point was it was an account of how the human brain acquired the ability - in evolutionary terms, how we acquired the ability to do mathematics. But the message was: Everybody has a head for figures. Anybody in the world, except for about two or three people with a brain disorder called dyscalculia, can master basic arithmetic to the degree where they will get problems correct 98 percent of the time. All sorts of people, even what we would call uneducated people have that ability.

The interesting thing is if you take those people and you watched them performing arithmetic in their everyday world - whether they're shopping or buying things - you'll measure 98 percent accuracy.

If you present those people with the same mathematical problem they've just solved in a real world context, 98 percent accuracy, you present it to them in a traditional paper and pencil format, the mean performance drops from 98 percent to 37 percent. People have a head for figures. What we definitely do not have is a head for doing mathematics and arithmetic using a paper and pencil. There's the distinction.

SIMON: So you will attest our children are brilliant, right?

Prof. DEVLIN: Oh, actually children are always brilliant. Though the only trouble is that parents and teachers, with the best will in the world, sometimes tend to screw things up a little bit.

It's actually, you know, a friend of mine once said: There's nothing elementary about elementary mathematics education. And boy, is that correct.

SIMON: You make me want to sue my first grade teacher.

Prof. DEVLIN: Teachers have a very difficult task, and the task they have now is even more difficult, because in previous generations they could assume that in many cases the parents could help.

SIMON: Keith, this has been fascinating. Hope you come back to the studio again sometimes.

Prof. DEVLIN: I always like coming down here, Scott. It's very nice looking across at the face, rather than the blank wall at Stanford University.

SIMON: Yeah, well... ...they have nice walls at Stanford, though. He is Keith Devlin, our Math Guy, thanks so much.

Prof. DEVLIN: Thanks, Scott.

(Soundbite of "Sesame Street" song, "12")

CHORUS: One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, Eleven, Twelve...

SIMON: The Pointer Sisters but we need the Counter Sisters.

You're listening to WEEKEND EDITION from NPR News.