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SCOTT SIMON, host:

The mobile phone industry struck a nerve among teachers this month. An industry trade group argued that cell phones should be allowed in the classroom, saying they can be used as a teaching tool to help children with their math skills; in particular, algebra. Well, we're going to avoid that debate this week, but it did make us reflect - what exactly is algebra? Why do so many people find it hard to learn? So we turned to - who else - our math guy, Keith Devlin of Stanford University, to help us out. He joins us from the studios out there in Palo Alto.

Keith, thanks so much for being with us.

Mr. KEITH DEVLIN (Stanford University): Hi, Scott. Thanks for having me on again.

SIMON: Now, isn't algebra just arithmetic with letters?

(Soundbite of laughter)

Mr. DEVLIN: You know, that actually gets at the nub of why people find it difficult, because they think that's what it is. And it really isn't. To cut straight to the chase, arithmetic is thinking with numbers. It's calculating with numbers. Algebra is reasoning about numbers. So whereas arithmetic, you're actually thinking numerically about the sizes of things and the measures of things, in algebra you're thinking logically and analytically about numbers in general. And that's a very different kind of thinking.

And in fact, the problem is, people spend all of these year learning arithmetic and then they get moderately good or very good at it, and they meet algebra and there's these X's and Y's and Z's that are - at least they're not numbers - so this is just arithmetic. And they keep trying to do it using arithmetic methods. And that isn't the way to do it. You've got to stop doing arithmetic, step back and adopt a whole new way of thinking. It's a very different kind of thinking.

SIMON: Let me bring a question to your attention I don't believe I've asked since I asked it of Karl Geise(ph) at Senn High School in Chicago, one of my math teachers. I said, Mr. Geise, I mean, like, what can you use algebra for anyway? That's exactly how I talked.

(Soundbite of laughter)

DEVLIN: You know, the odd thing is today, in today's society, there's an answer that's staring us all in the face, and that's the computer spreadsheet. It's very hard to do anything these day without a spreadsheet. If you're running a sports competition, you're going to start entering the results on a spreadsheet. If you're keeping track of your finances, if you're running a business, if you're a videogame player and you want to figure out how to equip your warrior character in World of Warcraft and you want to do it correctly and make a good job in the game, you'll start working on a spreadsheet.

And so spreadsheets are ubiquitous. But spreadsheets are all about algebraic thinking. In fact, the thing that the spreadsheet has done is it means we don't need to be good at arithmetic anymore because the spreadsheet does the arithmetic for us. But to put that spreadsheet together so that it does the calculations you want, you have to enter these little instructions, what we call macros, in certain cells that say: Spreadsheet, do the following with these numbers. That's algebraic thinking. You cannot set up a spreadsheet to do anything without doing algebra.

SIMON: And are there different ways of teaching algebra now?

DEVLIN: I think the main thing is the motivation. You know, when I grew up and we met algebra, there were all sorts of weird problems about filling swimming pools with two hoses and the water running out, or putting water in the bath, in the bath. I mean there were all these problems, and you know, I thought to myself, as did all my friends, I will never need to do that. If I need to fill a swimming pool, I'll hire the guy down the road to come and - and run until the water's in, and then he'll turn the tap off.

I mean we all knew that those were fake problems. They were problems designed to provide exercise in the techniques, but they weren't really applicable ones. But with spreadsheets, almost for the first time in history we have an absolutely important self-evident application that's absolutely about algebraic thinking. So the main difference isn't how you teach it now, so much as the motivation.

Kids today, all you've got to do is convince them that spreadsheets are going to be really useful to them in their leisure activities or their professional activities or their home activities, whatever, and then they'll sort of see, oh yeah, I need to learn how to do these things and then they'll put in the effort.

But once you've got the motivation, it's still a matter of - you know, it's the old joke of - how do you get to Carnegie Hall? Well, practice, practice, practice.

SIMON: You know, it occurs to me, a number of years ago when handheld calculators first became well-known, I can remember people saying, well, you know, you can get rid of high school math now, becauseā€¦

(Soundbite of laughter)

Mr. DEVLIN: Yeah. Yeah, it's like computers led to the paperless office too, yes. So what do we do? We all print off our PDF files all the time. No, it just doesn't work like that. What the computers did, and the calculators, is they changed the mathematics we need to learn and concentrate on. It didn't become important to be good at doing arithmetic. You still need to know about arithmetic. And to understand how to deal with spreadsheets, you need to have some competency in arithmetic, but it's not important to be able to always get the right answers in arithmetic.

What is important now is to be able to tell that computer how to do the work for you. So computers turned us from being at the coal-face, being the mechanics who actually grind at the numbers, to be managers. We're all now managers. We now instruct the computer to do the arithmetic for us. And instructing the computer to do the arithmetic means we need two things. We need a good sense of arithmetic, so we do need to still get people to learn arithmetic up to a point. But what we need in spades is algebraic thinking.

SIMON: Is it true - I have to ask you because I think you probably told this to me once - that there are mathematicians whom you wouldn't trust to figure out the tip on a cup of coffee?

Mr. DEVLIN: I'm one of them, Scott.

(Soundbite of laughter)

Mr. DEVLIN: So I probably did say that. Yeah...

SIMON: I think that's why you made me buy it, if I'm not mistaken.

(Soundbite of laughter)

Mr. DEVLIN: No, in fact, mathematicians are notoriously bad at doing everyday arithmetic, because they never do that. Because if you're a professional mathematician, you're working several levels removed from the levels of numbers in algebra. So you never do basic arithmetic. In fact, not only do mathematicians often make mistakes with arithmetic, we often make mistakes with elementary algebra as well, because our minds are on higher things. At least that's the way I'm going to try to describe it.

SIMON: Keith, wonderful talking to you. Thanks so much.

Mr. DEVLIN: Okay, my pleasure, Scott.

SIMON: Keith Devlin, director of the H-STAR Institute at Stanford University, speaking with us from Palo Alto.

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