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Sat December 24, 2011
To Make Algebra Fun, Rethink The Problem
SCOTT SIMON, HOST:
Schools across the country are on break this week, meaning that millions of students don't have to think even about algebra - or are they just missing the algebra that's all around them? We're joined now by our Math Guy, Keith Devlin of Stanford University, who joins us this week from member station KJAU in Boulder, Colorado. Keith, thanks so much for being with us.
KEITH DEVLIN, BYLINE: Hi, Scott. Nice to be here.
SIMON: Well, nice to join us electronically. I bet you're pretty happy you're in Boulder for the holidays though, aren't you?
DEVLIN: That's right. I came out here for a white Christmas and right now it looks as though we're getting one.
SIMON: Oh, all right. Now, I think a lot of people think of algebra as kind of arithmetic with letters. You say that's wrong.
DEVLIN: That's right. Arithmetic with letters is still arithmetic. Algebra's is actually a very different way of thinking. With arithmetic, you actually take some numbers and you calculate a new number. With algebra, you think about numbers. You end up naming an unknown number - you called it X or Y - and then you reason, not arithmetically so much as logically. So, algebra is really logical thinking about numbers as opposed to arithmetic, which is calculating with numbers. And, in fact, it's because people, I think, when kids don't realize it's a different way of thinking that they find algebra was so hard 'cause they try to solve algebra problems using arithmetic and it doesn't work.
SIMON: But why was algebra invented? And I recognize it may not have been invented by just one person but what need in the world was being addressed when algebra was created?
DEVLIN: What we think of as algebra - and it goes back into the ancient Babylonians and the Greeks - but it was really in the Muslim empire in the Ninth and 10th centuries where it really developed. In fact, there was one particular individual called Al-Khwarizmi who wrote a textbook in the Ninth century, which essentially lays out modern algebra. It wasn't symbolic. He wrote it out entirely in words because he was actually telling stories about how to reason with number. It was trying to describe to people how to think logically about numbers in this method called algebra. But that book that he wrote not only established modern algebra but it also gave us its name. The name algebra is an Arabic term, al-jabr. He also wrote a book on arithmetic, how to do calculations with numbers and that's why we have this word algorithm. You take al-Khwarizmi and it becomes algorithm for rules, procedures for doing numerical calculations.
SIMON: And was this done to assist this is the trading for which the Mid-East was the center of the world then.
DEVLIN: Oh, yes. Yeah, in fact, one of the things I think that's typical of the work done in mathematics in the ninth, 10th, 11th century in the Arabic-speaking world, is they were not interested in theorizing. They were very practical people and they developed algebra to be more efficient traders, more efficient commercial people, to be better engineers.
In fact, Baghdad and in the ninth century is the equivalent of Silicon Valley in the 20th century and the 21st century. That was the center of new technologies for many centuries as a result of developing that algebra.
SIMON: How do package this story for students these days?
(SOUNDBITE OF LAUGHTER)
DEVLIN: It's very difficult actually because the revolutions, both in arithmetic and then later algebra, was so pervasive and so fundamental that once people got used to it, what had been regarded as this brilliant breakthrough was regarded as dull and routine. We see it today with technologies.
To me, the iPad, the iPhone, those are incredible breakthroughs. But to anybody under the age of 15 or 16, that's just part of life. It's no big deal for kids when they have these things, and that's a measure of how fundamental a major change is.
SIMON: Keith, do you think schools sometimes make a mistake in the way they try and convey algebra to students?
DEVLIN: Oh, I think they make a terrible mistake. First of all, students typically will ask this question: what is a useful for? And if a child is asking that, then it has been introduced in the wrong way. I think it will be much more effective to begin with a bit of the history. Why did people develop this stuff? Algebra didn't come and it wasn't just sort of discovered hidden in a box somewhere. People invented to solve real-life problems.
Now, in the ninth century people literally had to solve those problems themselves with a paper and pencil. Today, we literally don't have to use algebra because we have devices in our pockets; we have spreadsheets in our computers that implement the algebra for us. But we are actually better users of technologies when we have some idea of what goes on underneath the hood.
SIMON: Keith, I hope you'll have a wonderful holiday.
DEVLIN: And the same to you, Scott.
SIMON: Our Math Guy, Keith Devlin speaking with us from Boulder, Colorado this week. Transcript provided by NPR, Copyright National Public Radio.