Constructionism vs. Instructionism
In the 1980s Seymour Papert delivered the following speech by video to a conference of educators in Japan.
Part 1: Teaching vs. Learning
Seymour Papert: Hello. Greetings to Japanese educators. I’m sorry I’m not there with you, but fortunately we live in the century of technology, and I can use this magical image-making machine to send my picture, my voice, half way across the world. It’s really wonderful.
What I was going to talk about if I had been there, is about how technology can change the way that children learn mathematics. I said how children can learn mathematics differently, not so much how we can teach mathematics differently. This is an important distinction.
All my work is focused on helping children learn, not on just teaching. Now I’ve coined a phrase for this: Constructionism and Instructionism are names for two approaches to educational innovation. Instructionism is the theory that says, “To get better education, we must improve instruction. And if we’re going to use computers, we’ll make the computers do the instruction.” And that leads into the whole idea of computer-aided instruction.
Well, teaching is important, but learning is much more important. And Constructionism means “Giving children good things to do so that they can learn by doing much better than they could before.” Now, I think that the new technologies are very, very rich in providing new things for children to do so that they can learn mathematics as part of something real.
I think part of the trouble with learning mathematics at school is that it’s not like mathematics in the real world. In the real world, there are engineers, who use mathematics to make bridges or make machines. There are scientists, who use mathematics to make theories, to make explanations of how atoms work, and how the universe started. There are bankers, who use mathematics to make money — or so they hope.
But children, what can they make with mathematics? Not much. They sit in class and they write numbers on pieces of paper. That’s not making anything very exciting. So we’ve tried to find ways that children can use mathematics to make something — something interesting, so that the children’s relationship to mathematics is more like the engineer’s, or the scientist’s, or the banker’s, or all the important people who use mathematics constructively to construct something.
Well, what sorts of things can they make? Let me give you some examples: children in a school in California, the Gardner Academy, in a project called Project MindStorms, the children made a calendar. And this is the work of a fourth-grade child who programmed the computer to make this shape, thinking of squares and triangles and how to fit them together. And because she had to explain all that to the computer, writing programs in LOGO, she was really using mathematics to make something which she liked, which was even commercially valuable because they sold this calendar and got money to improve their project.
Some of the things are just beautiful. For example, this one. I just got this today and I’m so pleased with it. It was sent to me by a child in Costa Rica, way down in Central America. The child programmed the computer in LOGO, using LOGOWriter and made this beautiful thing. It was photographed and sent to me.
Now if you asked this girl while she was making the picture, “What are you doing?” I don’t think she would have said, “I’m programming a computer.” I don’t think she would have said, “I’m doing mathematics.” She would have said, “I’m making a bird, I’m making a picture. I’m going to send it to America.” She would have expressed her excitement about what she was doing.
But if you look carefully at how she did it, you see she had to worry about the mathematical description of a curve like a graph. She had to worry about mathematical descriptions of shapes. She was doing mathematics, like a real person — a real mathematician, an engineer, a scientist.
And this is what we’re trying to do: find ways in which the technology enables children to use knowledge, mathematical knowledge and other knowledge, not just store it in their heads so that twelve years later it’s going to be good for them. Nobody can learn well like that; it’s a terrible way of learning. We all like to learn so that we can use what we’ve learned, and that’s what we’re trying to do with these children.
Part 2: LEGO/LOGO Projects
Seymour Papert: Well, some other things by connecting the computer to this kind of construction set — LEGO. Look carefully under this. You’ll see how the gears are carefully designed so that the horses go up and down as the merry-go-round turns. So, somebody was thinking about technology and how to use it — was thinking about gears, about the relation of small gears and big gears — but all this was part of making something which was meaningful to the learner.
So, in a way, the computer becomes invisible. The computer becomes just an instrument. I said if you asked that child making the picture, “What are you doing?” she would have said, “Making a picture, making a bird.” It’s interesting to compare this — imagine going to a poet and saying, “What are you doing?” You’d be very surprised if the poet said, “I’m using a pencil”. The poet would have said, “I’m writing a poem,” or, maybe, “Just leave me alone, I’m busy.” Of course the poet was using a pencil, but that’s not worth mentioning, and the same should be true of computers.
We’d like the computer to become an invisible part of things that learners do. We’d like mathematics to become an invisible part of things that people do, and then only later, when it’s been intuitively understood, when it’s part of your unconscious mind, then it’s time to be formal, and have formal classes, and teach mathematics as an abstract formal subject. Meantime, we should relate it to everything in the world — to useful things, and to beautiful things.
And let’s look at one other of these constructs that were built out of LEGO controlled by LOGO. That one doesn’t do anything except be beautiful, but it involves the same kind of principles of programming and using gears, and rotation. And so, the same principles of knowledge can be used in many different ways which match the interests and the desires, and the personality, and the style, of the individual children.
One of the things that’s wrong with school, I said, was that what you learn there, you can’t really use. Another thing that’s wrong with school is that there’s one way to do it. And that doesn’t happen in the real world either. In the real world, there are many ways to do things, and this is how creativity develops. This is how people make exciting new discoveries — because they try many different ways to get the results they’re looking for. And here, in all the examples I’ve shown you, we’re going to look at some more more closely, children are using knowledge about computers and about mathematics in personal ways to do personal projects. Each one doing something different, but through these different activities, learning the same sort of knowledge.
Does that seem strange? In school we say there’s a curriculum: everybody must do the same curriculum or else how can they learn the same thing? To see what nonsense that idea is, think of a baby. All babies — well, all Japanese babies I suppose, are going to learn to speak Japanese. But we don’t think they all ought to say the same things to their mother.
Each one says something different. They just live their lives in different homes, and have different toys, and they have different relationships, each one saying what comes from the heart — what they feel, what they think. But they all learn Japanese because they’re using the same language. And they learn it well. But at school, we try to systemize and make everybody do the same thing. I just can’t understand why, except maybe it was because we didn’t have the technological possibility to give children this wonderful variety of things to do.
Now I’d like to show you some examples of children working in schools, using computers, programming with LOGO, but doing very, very different things with it. We are going to see a child who’s making something like a video game, a game on the screen. And we’ll hear this child talk about whether it’s more interesting to play the game or to make the game. And two children will disagree, but what could come out of it was that both are interesting. And it’s even more fun playing the game if you made it yourself.
Well, making a game draws on the kind of intellectual passion that we see in children when they’re glued to the video screen, playing ready-made video games. I have nothing against games, but if the children could make them, or modify them, I think they would learn ten times as much.
Boy #1: We’re making this game.
Boy #2: And we made this car.
Teacher: Is that the car there?
Boy#2: No, these are our two good cars that we made. And this is the car that tries to crash into them.
Teacher: Which one? Where is it?
Boy#2: This guy. Doing, doing, doing, doing.
Boy#1: Okay, come here and you can see it.
Boy#3: So what do you like better, making a game or playing it?
Boy#1: Well, making it makes you feel like you achieved something. Just playing it.
Boy#3: Well, after you’ve made it, and playing it, doesn’t that make you feel like you’ve achieved something else? You made a game that works?
Boy#1: Yeah.
Boy#3: I mean I could make a game that doesn’t work, and I wouldn’t feel like I achieved something.
Boy#1: I know.
Boy#3: Actually playing the game might be the funnest thing. That’s what’s bad about games — if you want to play it, you’ve got to make it.
Boy#1: Games are the best thing, it’s like you play ’em.
Teacher: Is it more fun making the game, or playing the game that you make?
Boy#3: Playing the game that you make.
Seymour Papert: Well, you see, these two children have very different approaches. They both like making the games and playing them, but one’s more one way and one’s more the other way. And what’s great about this situation is that each could follow a personal path and they could discuss it with one another. So they could develop a sense of there being different styles.
When we look at the issue involved here you could talk about consumers and producers of games. These kids are not just consuming a game, they’re producing it as well. And in the next example, I’d like to talk about children as consumers and producers in another area, namely educational software.
Part 3: Educational Software
Seymour Papert: All over the world, huge industries are churning out so-called educational software for computer-aided instruction to teach children this or that or something. Children can make their own educational software, and by making the software, they learn much more than by using it. Because when you make a piece of software, when you teach something, you have to think about what’s really going on, you have to think about the ideas.
And the next example we’re going to see is an example at the Hennigan School in Boston, where there’s a project called “Children as Software Designers”. And in this project, children spend two or three months, three or four hours a week, working on a long project to make a piece of software. And the child we’re going to see was making a piece of software to explain fractions to the viewer. It’s a piece of software explaining something about fractions, and I’m going to give you some little peeks at how one girl did this.
Narrator: To the right of the screen, at the back of the classroom, sits Ebonique, all by herself. This overweight girl spends most of her time in school in her own socially-isolated cocoon. Self-conscious and insecure, she rarely risks participating in classroom discussions, but when she does, quite often her worst fears are realized.
Teacher: Ebonique?
Ebonique: Why are the numbers on top smaller than, um, the numbers on the bottom?
Other Children: Not always
Ebonique: Sometimes
Teacher: It’s something that she’s wondering about sometimes. OK, so why are the numbers… what’s you’re question again?
Ebonique: Why are the numbers on top smaller than those on the bottom?
Narrator: Outside of the classroom, it’s the same sad story. Ebonique is not hanging out with the other kids. With the instructional software design project, we did not expect to transform Ebonique’s personality.
Ebonique also experienced genuine intellectual excitement with fractions. Starting the project by creating simple representations and dividing geometrical shapes, she suddenly seemed to develop a personal relationship with fractions. She then felt free to play, and it dawned on her that she could see fractions everywhere. She transferred this insight into an idea for a teaching screen, and began intensive planning in her designer’s notebook.
She became obsessed with this design, and it took her many hours to finalize and implement it on the computer. This screen is the product. It reads: “This is a house. Almost every shape is 1/2! I am trying to say, that you use fractions, almost every day of your life. All the parts are fractions! Not just the shaded ones”
The caterpillar turned into a butterfly. Ebonique came to be known for her good ideas, and enjoyed feeling creative and successful. Other children wanted to see or play with her software and gave her positive responses, “I love it” or “This is fresh,” they would say, then ask her to teach them how to do things. “How did you ever make these colors change?” This representation became part of the culture. A few weeks later, Tommy’s house appeared, and then Paul’s.
Seymour Papert: I think the key point about Ebonique, and the key moment, is the transition when fractions stop being teachers’ knowledge and become her knowledge. She appropriates fractions. She relates to them. You see her talking about 2/3 as a hard fraction. You see a screen image, which is a typical teacher textbook representation of a fraction as 2/3 of a pie, a circle divided into sectors. This is somebody else’s knowledge. Then, all of a sudden, there’s a connection. Ebonique is now thinking about fractions, and she’s thinking about her thinking about fractions.
Ebonique: 1/2 is one whole.
Narrator: Ebonique believed that if a shape was divided into halves and 1/2 was shaded, the unshaded part was nothing: it was not a half, it was not a fraction. When she discovered that this was not the case, she worked on ways of teaching this to her software users, telling them, “All the parts are fractions, not just the shaded ones.” After the project ended, she felt much more comfortable when talking about fractions, and she overcame many of her misconceptions.
Ebonique:This is a whole and if I want to split it in half, this is all I have to do.
Researcher (Idit Harel): Good. Which one is the half? Which one is the half?
Ebonique: These two sides are the halves, and if I take this out, it’ll just be a whole.
Seymour Papert: We’ve seen Ebonique do something with computers and fractions. What she was doing with fractions does not look like schoolwork. She was explaining ideas like, “Fractions are everywhere all over the world”.
What’s that got to do with adding and subtracting and multiplying them? Well, an amazing thing is, it has a lot to do with it. Before this project, Ebonique was at the bottom of her class, almost, in mathematics. She was in the weakest math group. After this project, she was in the top math group, and she stayed in the top math group, not only that year, but the rest of her time at the school.
What was going on? How did she get an improvement in how to add and subtract and multiply fractions from doing this? Well of course she was still going to her school classes. She was still being taught. But because she developed a good relationship with fractions, because she was thinking about fractions, and she thought about it as her knowledge, not teachers’ knowledge, she could now listen to what was happening in the class, and she could learn from it.
So this is the amazing result of Constructionist learning: that by doing very simple things, the children improve their ability to learn. Ebonique was learning by making software in which she talked about fractions. And I think that’s an important thing. At school, children do not talk about mathematics. She did. The two boys with their game were talking about the product of doing programming.
Seymour Papert: In our last example, we won’t be talking about mathematics, we’ll be doing some more technical mathematics. And I’m going to show you some programming in LOGO that uses more advanced mathematical ideas to get some very beautiful results.
When this procedure is run by this instruction, the procedure’s first action is to note that :SIDE is 50, so that FD :SIDE will become FD 50, and the turtle’s action will be FD 50 RT 90. The procedure’s next action is SQUARE 50, which will start the cycle over again. SIDE is of course still 50. The turtle does once more FD 50 RT 90. And you might be asking yourself, why do we need such a fancy thing as recursion to draw a square? Surely REPEAT would be good enough?
Indeed REPEAT would be adequate, if our interest were in the product. But if our interest is in exploration, recursion allows us to make such changes as this. I replaced SQUARE :SIDE by SQUARE :SIDE +10, and this small modification will give rise to the most surprising and interesting mathematical result. SIDE is now 60. FD 60, RT 90 is going to bring the turtle down below that line. We will now do SQUARE 70. SIDE will be 70, FD 70 RT 90. You guessed it, SQUARE 80. SIDE will now become 80, FD 80 RT 90. And where’s it going to lead? A full screen version shows the pattern: forward a distance, right 90, increase the distance, repeat.
We got this quite interesting result by making a small change to the procedure for SQUARE. Let’s follow that rule. Make a small change to this — instead of 90 as the angle, let’s try 93. Notice how we get this effect of twisted squares. Notice that curved line that appears, an emergent phenomenon, quite interesting.
So let’s try to do the same thing with triangles. First straight triangles, using 120. Same process. 123 FD a distance, RT 123, increase the distance, repeat. A very interesting result. And since 90 and 120 gave something interesting let’s try 180 — it’s sort of in the same family. But the result, as a product anyway, doesn’t look so interesting. Think about the process, though. Maybe if you rotated that as it went up and down, for example by trying 177 instead of 180, look how it turns as it goes backwards and forwards.
I see this as a result that’s interesting in lots of ways: visually, mathematically, and as an example of what happens when you follow a powerful heuristic. I think it’s pretty enough to try again without being cluttered by all that text on the screen. It’s worth thinking about too.
In all these spirals, there’s a common pattern. You draw a line, you turn, maybe 90, maybe 93, some other angle. We’ve been exploring what happens when you vary the angle, but you could vary something else. Instead of a line, you could have another figure. In fact, in the example I have on this other computer, the figure is a triangle. What’s going on in this program is, “Draw the triangle, turn, draw a slightly larger triangle, turn, draw a slightly larger triangle.” What comes out looks like a seashell.
I chose spirals as an entry point to recursion because such simple, such small changes can so often produce interesting, surprising, and beautiful results. The possibilities are endless, like recursion.
Part 5: Conclusion
Seymour Papert: Well, I’d like to end by saying something about what this means to you. What I hope you will do after seeing these images and listening to me talk. Well, what I hope you will do is think. What I hope these examples will do is get you thinking about how mathematics and how all learning could change. I didn’t show you these examples because I think you should copy them, because I think this is what the future will be like. These are just little steps. I’d like you to be part of inventing a future. Nobody knows how computers will be used in 10 or 20 or 30 year’s time. What we do know is that they’ll be everywhere, as much as pencils. Everybody will have them all the time.
And with everybody having computers all the time, it is inconceivable that learning will be like it’s been in the past. There will be new ways of learning. But it’s up to you, and me, and all of us, to invent that future. So in the meantime, we can do little things. We can do a little project here and a little project there. We can have some children write a piece of software. We can build a merry-go-round. We can make some pretty spirals. All these are not theanswer, they are not the way computers are used, or LOGO is used, to change education. They are just examples to provoke thinking, to get more and more people engaged in inventing the future of learning. And so I hope I’ll get another chance to talk to you and to come in person. And right now I’ll just say goodbye and good luck with the rest of your conference.