"ALMOST EVERYTHING of value that is taught under the heading of mathematics in school could be learned fairly spontaneously by children in a computer-rich culture," asserts Seymour Papert, one of the most revolutionary figures in contemporary education.

Papert had just flown in from Paris for a whirlwind tour of 10 New York City schools where some of his theories about computers and children are being tried out. He is a professor of mathematics and education at the Massachusetts Institute of Technology (on leave to work on an international computer project in France), and the driving force behind a novel way of using computers to teach math. He is also the inventor of a deceptively simple computer language called Logo.

With the aid of Logo, children as young as 3 or 4 can instruct a computer to design any object line by line on a video screen -- for example, a house, a truck, or a plane. Papert believes that children who play with computers in Logo will teach themselves mathematics as easily and naturally as they would learn to speak French by living in France.

Before going to MIT, Papert spend five years working with the famed Swiss psychologist Jean Piaget, whom he admired greatly. Piaget showed that children develop their view of the world in stages, as a result of experimenting with the objects around them. "Certain knowledge, certain intellectual structures can be built by using the materials that are provided by the culture," Papert says, echoing Piaget. "But then there are gaps -- things that most children don't manage to construct for themselves because of deficiencies in the culture, or even because they're prohibited by the culture. That's why we have to organize schools. And that's what's being changed by computers."

He emphasizes that he is not talking about the rigid kind of computer-aided instruction that has spread through many American schools in recent years. In such schools, computers provide little beyond standard drill and practice in a more attractive format--"electronic flash cards," as some critics call these computers disparagingly. Papert does not want the computer to program the child.

By contrast, he says, "In the Logo environment the relationship is reversed: the child is in control." Even very young children soon find out that there are ways to make a small triangular figure on their video screen (dubbed a "turtle" and actually the computer's cursor) move exactly where they want it to, leaving a trail behind it. After some random exploring, children usually begin to give the "turtle" specific instructions as to how far and in what direction to move: for instance "forward 5, right 20, forward 5." Following these commands, the Turtle traces the appropriate lines on the screen.

This process allows children to learn many elements of mathematics that usually are not taught in school until years later, Papert says: angles and velocity and the properties of squares, triangles, circles, polygons or spirals. They also learn to use addition, subtraction and multiplication.

"An important part of becoming a good learner is learning how to push out the frontier of what we can express with words," Papert wrote in his ground-breaking book, Mindstorms: Children, Computers and Powerful Ideas. "Getting a computer to do something requires that the underlying process be described, on some level, with enough precision to be carried out by the machine." This forces the children to think things through, rather than learn by rote.

With considerable relish, Papert tells how a group of first-graders using Logo at the Lamplighter School in Dallas, Texas, taught themselves far more than their teachers expected. The school is lavishly equipped with computers, he points out -- 50 Texas Instrument microcomputers for 400 children between the ages of 3 and 9. According to Papert, the first-graders were having a fine time making their computers draw fairly intricate pictures on the screen, until they saw what the third-graders were doing: making their pictures move around.

"You can get some very pretty effects if you have a lot of objects moving in different directions," he says. "But setting a heading for each of them, in a controlled way, involves understanding angles and using rather large numbers, like 135 or 270. The teachers thought the first-graders couldn't possibly do that, so they decided to keep them working with static pictures. But that lasted just long enough for somebody in first grade to ask somebody in third grade, 'How do you do that?' "

As a result of this subversive act, the younger children learned to make objects move about on the screen, Papert reports. "The concreteness of the computer made it possible for the third-grader to tell the first-grader something," he says. "Obviously the third-grader was not capable of explaining the idea of measuring directions and headings and degrees, or what the number 270 means. But he could show some very concrete steps to take, and these became materials, incentives for the first-grader to develop his ideas.

"I visited the place a few days later," Papert continues. "The first grader had recruited a number of his friends and they were playing with the machine. He explained to me his way of thinking about it: 'It's a code,' he said. 'The numbers are codes for directions. We haven't yet cracked the code.' But they were working on it. And gradually they reconstructed this piece of mathematical knowledge by themselves, bit by bit, without being taught."

What exactly had they learned from this experience? "They certainly know the idea of degree very thoroughly," Papert says. "They know that numbers can be used to measure direction, and they know which numbers correspond to which directions. Theyyalso got a feel for working with a range of numbers they weren't used to. The teachers quite rightly said that numbers like 270 were too big, because in the experience of a little child, the only numbers that are really meaningful are counting numbers such as 6, or 20 maybe -- the number of objects a child might have. Millions stand for something different. But for most young children in our culture, a number like 270 doesn't really have concrete meaning." The children's most important gain, he adds, was "their sense of having done this themselves -- what they learned about learning."

This incident is just one of many similar ones that he knows about, Papert says. "From its very nature, I think you can guess there must be many more that the teachers don't even know about," he points out. With free access to a large number of computers, children at the Lamplighter School got involved in computer activity which the adults could not watch. "It's got out of hand!" says Papert happily. "It's become a powerful cultural and social process in the community life of these children."

Teachers don't have to provide math problems for the children to work on in this kind of setting, he notes. "Very occasionally, a teacher might point out something that would be an interesting project for a particular child, in the same way that a thesis adviser might tell a research student that here's a good problem," he says. "But you don't need to do exercises when you have a mathematical medium where you use math to produce results which you like."

In the South Bronx, where he had just visited a school, "the kids and the teachers have exactly the same enthusiasm and sense of discovery," Papert says. "They're excited by the idea that with the computer, you can start with something vague in your head, and then you work and work until it turns into something that you can see and show other people."

Papert maintains that far more than mathematical knowledge is at stake in this new style of learning. "Learning to comunicate with a computer may change the way other learning takes place," he writes. He believes that children who are exposed to computers and Logo will become better thinkers -- more logical, better able to write as well as compute, more confident in their own powers, better planners and skilled at breaking problems into manageable bites. In addition, he suspects, they will be less dogmatic, because in the Logo world "the important question is not whether something is right or wrong, as in the traditional classroom, but whether it can be debugged or fixed."

Although Papert admits that he is "an educational utopian," he does have some evidence of the powers of Logo from a few experimental projects, such as the National Science Foundation project which was conducted in one Brookline, Massachusetts, elementary school in 1977-8. All the sixth-graders in this school had between 20 and 40 hours of experience with Logo.

"We saw in Brookline that all kids could learn to program -- even kids at a very low level of school performance," he says. "Many children who had done very badly in school really took to the computer." Since the end of the NSF project, seven more elementary schools in Brookline have bought computers and started working with Logo.

Now the New York Academy of Sciences is sponsoring a Logo project in 10 New York City public schools. It has trained 60 teachers in the method and lent the schools some computers.

"We believe that of all the educational technology developed in past centuries, computers offer the best hope for changing the educational structure of our schools," says Dr. Morris Shamos, president of the Academy. "We selected Papert's program because he combines, in one person, a profound understanding of computer languages and an understanding of how students learn. We have not yet done any test of its effectiveness, but when you go into the schools and watch the youngsters, your spirits soar! You see something is obviously going on. Subjectively, it seems enormously effective."

Just as in the open classrooms which were so much in vogue a decade ago, the children in this project can do anything they please when they get their hands on the computer. Papert is not fazed by the comparison. "With the computer, we're getting another shot at the open classroom," he says.

The major weakness in the concept of open education in the past was its lack of appropriate materials for such traditional subjects as "the whole of formal mathematics, and the formal side of language," Papert says. "In kindergarten and first grade, it did provide those blocks and Cuisenaire rods that concretized certain aspects of mathematics. But to go beyond that, nobody had a material that would lead to algebra and geometry. Yet society places a tremendous value on that kind of knowledge. . . . So the open classroom couldn't succeed. But the computer really does change the situation."

How far can one go with Papert's approach to computer learning? And how much deliberate teaching will still be needed to fill in the gaps that are left by it? Papert is not sure yet. "In order to develop the uses of computers for human development -- not just math, but a better environment for preschool children, for people who need to adapt to new kinds of jobs, and for people in the developing countries -- much larger-scale research is needed than has been done anywhere up to now," he says.

Although Papert ran a sizeable research project under the wing of MIT's Artificial Intelligence Laboratory, he was never able to start the large multi-disciplinary research center in Cambridge he had dreamed of. "We never had a critical mass," he says. "Then the outlook for such a center became even worse after the change in administration in Washington."

This is why he and some MIT colleagues moved to Paris last year, lured by the ambitious plans of the French politican and author, Jean-Jacques Servan-Schreiber, who talked the French government into creating a "World Center of Informatics and Human Resources." The Center is designed to show off French prominence in new technology. Armed with a budget of some $2en0 million a year, it has begun a major program of what Papert calls "action research." For example, it is introducing microcomputers into Senegal, the former French colony in West Africa, and has assembled a team of Senegalese linguists, writers, scientists and educators to translate Logo into Woloff, one of the major dialects of Senegal, so it can be used with ease by children in local schools even before they become fluent in French, the official language.

Meanwhile, Papert is increasingly interested in the social aspects of interaction with computers, and he is looking at how children from various backgrounds differ in their approach to them. Ideas about the role of computers in the future tumble out of his mind at a furious pace. He is deeply involved in writing a book on the subject--to be called The Computer Manifesto -- which he expects to finish in Paris this spring.

Not only will computers make science and mathematics "more compatible with the cultures of Africa and the rest of the third-world," says Papert, but he hopes that they will also help to re-unite the two cultures of science and the humanities. "What we are seeing with the computer is how people who belong on the wrong side of the cultural divide -- that is, wrong from the point of view of those who would normally go into science -- are able to take control of this machine, feel it as a non-alien thing, and use it to develop themselves in their own way."