Unedited transcript follows….
the following is a videotape module from the learning system. Seymour peppered on logo.
The tape series has two parts. The first new Mindstorms focuses on the process and the principles of. The second logo hurdles focuses on specific technical aspects of logo.
The new Mindstorms module teaching looks at logo as the instrument teachers need to appropriate the computer to their own personal styles of work.
I’d like to read you a favorite passage from mark Twain. Huck. Finn is talking sometimes we’d have that whole river to ourselves for the longest time. It’s lovely to live in a raft. We had the Skype. All speckled with stars. We used to lay on our backs and look up at them and discuss about whether they was made or just happened, Jim.
He allowed they was made, but I allowed, they happened. I judged it would have took too long to make so many. Jim said the moon could have laid him. Was that looked kind of reasonable. So I didn’t say nothing against it because I’ve seen a frog. They, most of them. And so it could have happened. We used to watch the stars that fell too and see them streak down.
Jim allowed they got spoiled and was home out of the nest
he has a frog is to think about stars is a marvelous example of some tonic thinking, thinking about problems, making their age. Gives us a term in between the making of simple objects and just happening in glitches the discussion. And then besides the conceptual side, it resonates with strong images of spawning that form a central part of hacks, personal culture.
I wonder what, how could have done if he’d had a computer. Perhaps something like what I did. I wrote a logo program in which a procedure spawns, more stars than I would have liked to have made one by one by hand
making a stop field like this doesn’t fit the stereotype that’s been established in tens of thousands of classrooms all over the world of what children do with logo and the end of mantra. But the stop yield, isn’t more difficult than drawing squares and triangles. It’s just a different style of programming.
Not better, just different how call it hackathon style, because I’m sure that that profound young philosopher who would have preferred to do it this way as a bedroom fact, when I first wrote this program, it was rather more company. I learned to simplify it when I used it as a theme for a teacher’s workshop.
I wasn’t surprised when teachers showed me a simpler way and I was truly ecstatic when I discovered that this simpler way was rooted in techniques that many children in second grade, and even younger have rediscovered in the course of their first encounter with logo. Let me show you how this works by recapitulating, how somebody might meet the turtle for the first time.
An object on the screen is introduced as the turtle. We’re going to learn the language for telling the turtle to do our bidding, right. Is a command in turtle talk. It orders the turtle to turn that is to stay in the same place, but change its direction. 90 says how much it should turn that much left has exactly the opposite of.
Left 90 will exactly undo what right. 90 did notice the turtle stays in the same place. It changes the way it’s facing forward makes it move to a different place. It’ll move in the direction that it’s facing up there. Pin down. Doesn’t produce an immediately visible effect. Turtle is still there, but now the instruction back 50 back is the opposite of forward.
We’re move the term. And leave a trace a line. So you begin to see how the turtle can be used as a drawing instrument to draw almost anything you can imagine. And then the word clean wipes, the screen clean right? 90 this time I’m doing it right. 90 left, 30, the turtle can turn. And so can I, in fact, I can carry out exactly the same instructions I would give the turtle in total.
You have to do when you learn about angle, you use instruments like set squares and tractors, wonderful instruments. That ought to be part of the culture of everyone. But turtle gives us an extra route and extra set of connections for an idea like angle gives us what you can think of as a pipeline from body knowledge, knowledge of how we move our own bodies into the study of genomics.
This idea is so important that it deserves a name in psychoanalysis. There’s a word egosyntonic, which I’ve adapted, and I call it body syntonic, learning the kind of learning that is rooted in this way and our own knowledge of our own bodies,
a small personal touch in teaching, the ways of the turtle make the turtle bumpy. LT is an abbreviation for left, a child who needs some exploring before hitting on left 30, but that does it. And then forward something here we practice a little problem solving, try anything forward something 20, not enough.
Try again, four with 20, but it’s almost there. So let’s use a smaller number this time. Forward 10. Got it. To bring it back home. We need back. How much back 50 BK is an abbreviation for back as F D is for forward,
right? One 50. See, I’m learning to do it in one go children gradually learned through experience, which for me means thinking about and talking about what you do as much as doing and the hands-on. To associate numbers with particular amounts of turn, uh, numbers with particular distances, the amount of turtle talk you’ve seen is actually enough to open the door to the wonderful world of turtle graphics.
I’d many children delight in going on from here to exploring these associations of numbers and angles and distances to make squares and triangles. I put them to. An increasingly complex figures of their own design. In this tape, I’ll be talking about two routes into logo. One that’s become dominant in the turtle graphics literature.
I call the hard hard-edged style. One way into that is by practicing instructions like repeating forward 50 right 90, you get a square and then you get a triangle by repeating. And you get a star by repeating that, and we know how to make a triangle and a square. You learn how to put them together to make a house.
Then you put together houses to make a village and so on and so forth in a while we’ll rejoin this route, the standard one into LoDo. In the meantime, I’d like to take a peep at the other route, the Hudson style. Let’s see what hack matters.
This is the beginning of an imaginary scenario. The Tetra has been set up with a left turn with pen down. It’s about to do forward 50. That could be the beginning of almost anything, a rooftop, a mountain, the Trinity, see another forward 50. We begin to wonder. And in fact, this is not the beginning of a drawing.
It’s the beginning of a more mischievous enterprise. The learner is wondering what happens when the turtle. End of the screen. And another forward 50 is going to tell him that it is going off the screen and came back on the other side. That’s a phenomenon known as wrapping something you need to understand by playing at the computer for children who do so it opens the door to exploring instructions like this forward 2,783, a number chosen only because it’s big, then tenants.
Let’s set the turtle up with the right 37 and do this. Even if you understand the idea of wrapping the actual patent is a little bit surprising. So is the place with the turtle reappeared, let’s do the same instruction again, and I’ll do it in a different color. So you can see the pattern more clearly notes where the turtle is.
And once more, and the early encounters with logo, many children are passing. Uh, these wrapped patterns spend a lot of time with them and some teachers wonder what could a child be learning through all that? I think a child could be learning many things, and it’s very hard to know which what is most relevant to my star story is the amazing fact that repeating one command can produce that surprising results besides surprise in the pattern they surprise in where the turtle then.
Yes, where it would appear next.
Did you guess, right. I guess again,
two factors make this, the kind of situation where as a teacher, when one does weather and how to intervene, one fact is the evocative nature of the situation. It has a passenger. And it could hold a child longer than you think appropriate. The other is the objective interest of what’s going on. There, there is a lot, you can say the question is whether you should let the child explore, whether you should interpret what’s happening, why the patterns come up as they do, how the situation can be used to produce other effects.
Well, it’s a kind of very personal judgment for teachers. I can give you rules, but it is good to have a bag of tricks things, you know, to say, when you think the time opportunity, for example, in this case, it’s interesting to clear the screen and run through the same set of instructions again, this time with pen op.
So you can separate interest in the pattern from interest in the way in which the turtle comes up in surprising place. We do pan up. So the pattern won’t be drawn. We set up the turtle with right 37 as before, and then we’ll do the same instruction forward to 7 83, right? 10 total pops up there and there and there and there and there just as, before this play on the edge between control and randomness is useful as well as evocative.
It shows a way to stop. For example, if we know how to do repeat 12 times this, do this forward and rise to pop up somewhere and then run a procedure draw, which is going to make a star, it could do almost anything. Let’s do it. That star could have been a little procedure. The child wrote could have been a procedure you provide.
Well, that’s an to show you that the stars program is within reach. Of course you don’t understand all the details you won’t until you’ve tried it at the computer too. So meantime, I’d like to tie together some threads of this discussion threads about syntonicity and making, learning personal. I talked about personalizing anger by relating it to your person, your.
That’s body syntonicity. And then I talked about personalizing learning by allowing people to do it in their own style. The hackathon style and the hard edge style of doing turtle graphics are just two examples. That’s closer to the sense of ego syntonicity of psychoanalytic theory. When you do it in your style, it sits more comfortably.
You feel yourself.
And then at the opening, I repaired two cultural syntonicity for hackathon arguments from frogs and scorning, a culturally syntonic. They belonged to his culture. They’d well-rooted there. When I think of learning logo, I think of two sides of cultural syntonicity I’d like logo to be supportive. Uh, the learners culture, this is the only way it can be solidly not, but I’d also like it to enrich, to enlarge the learners culture.
This is the only way in which it can be meaningfully learned. The main purpose of logo is not what they call computer literacy. Of course it serves that better than anything else I can think. But the real purpose is not to have better understanding of computers, but through computers to have better understanding of everything else, including I’d like to say.
one way to encourage some tonic learning is to be imaginative, bad, exploring the world around the school farms
perhaps. Uh, rich kind of exploration is the investigation of the people who make it or WIC. For example, who drives a riverboat like this? Basically it’s easier to navigate a small. Because it’s the fact that it is small. It turns quicker. You can stop quicker. If you had something to do with a boat like this, you’re about, you have to be thinking about two miles ahead because if you see something right now, it’s too late.
It just won’t, you can’t. So you have to be looking ahead the whole time you have to figure out, I look way down a river and I see a boat coming up. I have to make plans on what I’m going to do, how I’m going to meet him. So it’s, it’s like almost anything the better you have it. The farther ahead that you plan the better off you are.
You can’t wait till the last minute where the big boat, what fascinates you? Why do you do this job? No, I’m from the central part of Missouri. I don’t know if y’all know where it is, Mexico. It was flat as a pool table there. And it wasn’t even a Creek that water was deep enough to get up to my knee. So I didn’t swim.
I’d never been in a boat of any kind, not even in a rowboat. And they drafted me and put me in the Navy and I fell in love with boats. And so, uh, when I got out of the Navy and I came back to the middle of Missouri, there wasn’t any ocean to play around in. So. Came to work on the river.
if the river is a theme of activity field, It makes sense for logo to be integrated into their work with the rivers and rivers, to be integrated into their work with logo. The picture you see on the computer screen is a logo picture it’s written in logo. It might be a lot of work for an individual student at a young age, but it could be done by a group of students, even by a whole class.
It’s also a game. That can be used for beginners at logo to exercise their first attempt at controlling the turtle. Let’s see how this works. This is a turtle game in which the turtle starts as a starting pier has to find a path to a landing pear where it seeks the treasure represented by the diamond, the user, a child types commands in turtle talk, and the turtle does whatever is typed for.
It’s a good way you see then right. 90 turns it forward 50. Again, the child working at it is practicing the commands, practicing the idea of angle, practicing what it’s like to use turtle commands. Also, the child is learning that you can correct your first guests. You can back off again. You don’t have to be right at the first.
teachers often try to give their students this kind of exercise by overlaying a transparent maze on the computer screen. It’s a little easier, but I think it’s worth the trouble to write a logo program, to give a background for this kind of exercise. There’s several reasons. The first is that we can give the game several levels of difficulty, just like real computer game.
This level of the game is really very different. First, there are no forward commands. The turtle moves an extra blade, so you don’t have time to stop. And think you have to think that you must think on the fly. And then the turning commands are written in this unusual form L 45. Plus it’s not the turtles LT.
It does turn the turtles heading by 45 degrees, but only. As you see from the near misses, we’re taking off care on the captains remark that he has to make his decisions, at least two miles ahead in order to stay at his heavy boat. I find that the kind of real time thinking we need here brings you into a different kind of relationship with the work.
You really have to make the turtle an extension of your. And you have to make the ideas underlying the turtles movements, part of your intuition of the world and of yourself. The fact that this game is a logo program means you have an open-ended project of adding levels, levels of variety or levels of difficulty.
For example, you still know enough to add and without any trouble at all the effects of. And adding the effects of river currents is very instructive. Although more challenging. However, what I think is truly powerful about basing it on a logo program rather than a passive overlay or something like that is that the learner can take charge.
I don’t to talk about the steps that could lead a beginner and absolute beginner with no knowledge of. From playing the game in order to learn the fundamental actions of the turtle to making it let’s look at the scene it’s made up of simple parts. That’s one part that line, top bank, and that’s another part.
And then these river objects apart, a first step for beginner could be to add a new pot. And then when you program that. You had the foresight to program it in such a way that it stopped between the drawing of the scene and the navigational action of the turtle. You give the beginner learner a chance to jump in in order to add something new.
For example, suppose that the learner wants to add a raft, I’d set things up. So that logo commands appear in the center of the screen for visible. Show Ted or makes the turtle appear. Now we’ll position the turtle to drive it over there. We’re going to place our raft left 45 forward a hundred Ft is an abbreviation forward, right?
45, straightens it pen down. So it will draw and has the instruction that draws a square repeat four times four, 20 right. 90. And we’ve got a raft. The commands. We’ll place the turtle in the starting position for the navigation game and we’re ready to go. The logo technique used in adding this raft is called driving the turtle because the turtle is driven one instruction at a time, so much forward so much, right?
And so on turtle driving can produce quite fancy effects. For example, as soon as you master the use of color and logo, you can fill in the rest. I’ve put the turtle back at the raft. I’m going to give this instruction to drive it into the raft. We now get into set a color that we’d like to fill it with, put the pen down and fill the square.
So we’ve got a color draft hide the turtle HT, and there is a pretty raft. The next step into logo beyond turtle. Brings us to the most important intellectual contribution of the computer to contemporary thought the idea of program in logo. We introduced the idea of program through a metaphor, the metaphor, teaching the turtle or teaching logo, a new command.
We just so have to make a raft by a whole sequence of logo commands. Suppose we’d like one command raft to do that. This is what we tell logo to make the word raft into a command. We have to do several things. First, we typed two raft. Then we taught some instructions. These are the very same instructions that drew the raft.
And when we give the command raft, these are going to be carried out and means is the end of the lesson on the teaching now. Well, the end of the procedure that defines the command raft. Think of this by analogy with a recipe you might say to bake a cake, sift a pound of flour, separate six eggs and so on.
Now, in order for this to become a command, we have to do one more thing. We have to do a certain, I suppose, Hackford would have called it an incantation. You do it by typing certain keys that differ from version to version of logo. So I leave you to find out about it by looking at the study guides and I will get onto using this command.
But first had I tidy it up, open a hole there and put in pen up home home is the position where we found the turtle. And it’s good practice. When you write this kind of procedure to leave the turtle in the state in which you found. Let’s see how to use such a command game is the command that caused the whole show to happen of the navigation game.
And it has two parts, a sub procedure river. This causes the river to be drawn, swim. As you saw, already causes the navigation action to begin and the true power of having this procedure. Comes when we see how to insert raft in another procedure, let’s make a whole move, swim down, put draft in there. Now, when we give the command game river will be drawn wrap to be drawn, swim.
We’ll make the navigation action begin. What’s an ankle got to do with the two. Well, I’m sure you’ll admit that angle has got a lot to do with the turtle, but I bet that a lot of you didn’t know that the word ankle and the word angle are etymologically the same word, both derived from the ancient Greek for band in preparing for this tape.
I explored a number of such lighter connections between turtles angle, logo and elements of the culture. As I suggest you should. When you think about teaching logo in your classes, the one that astounded me most was the relationship between angle and English or England. I knew that people called angles had something to do with the name.
England. What I didn’t know is that the angles are supposed to own their name to the shape of their case.
The scavenger hunt led on from the etymological dictionary to an Atlas of old Europe. The country of the angles is shown in red. Some members of your class might be skeptical about the dictionary maker’s story. Others might want to defend it. Great. Nothing’s better for learning than a good. You might be asking what’s his angle.
It’s exploring the idea of making connections and idea that you might pick up by declaring an angle day on which your students will report the results of their own research on finding angles in every subject. English is rich in them besides etymology their idioms. For example, what’s his angle or the boast.
Hey, I got a new angle on that. Or the complaint. What you’re saying now is 180 degrees from what you were saying before. You’re contradicting yourself in the same spirit. There’s collecting jokes. For example, two wrongs don’t make a right, but three REITs do make a left.
A new angle on geography is measuring the angles between. And looking at the distribution of these angles. Why is it so different from the distribution between the angles at intersections in a city? And now I’d like to demonstrate some activities related to maps and children’s games.
The children read this. Kevin Johanna Cruz. Find the tree house and take a bearing 30 degrees east of a certain tree.
We’re not turtles. Uh, turtle has built in procedures to handle 30 degrees. Children draw their experience. When uses affect about her body. We could go 30 degrees because my fist is 10 degrees wide. One.
Three. And then we would have 30 degrees in a better way.
Most people can recognize 90 degrees. The proposed. It’s based on recognizing 30 as a third of 90 and drawing on experience in dividing a pie size into three equal parts. And then we take, and it in about a 90 degree angle. It’s not an accident that pay often provides the best connections between concepts and experience.
Let’s put it at about 30 degree angle there. You can’t. Why don’t we make it so difficult? Why don’t we just use a compass?
The last connection takes us back to a, we started this tape. Hack-a-thon was looking up at the heavens. I’d have to go to the computer and show you a program that brings a little piece of astronomy down to earth.
I’ve made a micro world in which the turtle isn’t. He’s watching the sun go around him. It’s a turtle centric world. He’s interested in the size of the sun. He’s also interested in how long it’s going to take to set. So time it from there when it attaches the horizon to there, when it’s completely sad, you probably missed it, but maybe you can get it on the rise.
It’s now not is waiting for the sunrise. When the sunrise. He’s going to freeze the sun in place and use an instrument he’s invented for measuring the angle of an astronomical body that it’s rising. How long is it taking it’s there? The turtle faces the sun. He turns on his instrument. There’s its counter.
The instrument is nothing but a simple logo printed. It does forward a hundred back a hundred and then write one so that it scans the angle of the sun. Each time it steps the counter. That’s an angle of nine of 10, of 11, 13, 14, 17, 18, 19. And it looks like the size of the sun is pretty close to 20 degrees.
How can we measure the angular size of our real sun? If you had a Sexton, a real world version of the turtles instrument, you could do it. Just talk the turtle dead. But if you don’t, you can use these second method using a watch, timing it. Have you ever wondered how long it takes the sun to rise? If you knew you would calculate how many sons would fit around the whole sky, like this necklace of sons grown by another simple logo procedure,
the title used the necklace to confirm his measurements. If each sign is 20 degrees, wide, 18 should fit into the 360 degrees of a wholesale.
I do can see that the title son would take 18 times as long to go all the way around as it takes to rise or set. What are these numbers for the real son?
I’m a mathematician. For me. And I think for human history, mathematics has played the role of intellectual glue, making connections between diverse chapters of human knowledge. I don’t think we succeed very well in using it like this in our classrooms. In this tape, I’ve tried to show how a teacher can use logo to play the role of being slave to glue the role that mathematics has played.
I don’t have to end by some reflections, unpacking the intuition that every teacher has, that it’s good to make connections. Well, why there’s a cognitive side, connections help you understand, you understand the new by referring it to the old they help you remember, but this is deepest. When that has to do with how you feel about knowledge and how you feel about yourself, connecting new knowledge to things, you know, and love and things you think you can do makes you feel good about it makes you take it in, in a form that is your own by taking in knowledge, in a form that feels to you as you.
You change your feelings about yourself as well. You no longer think of yourself as somebody who can do math, but doesn’t really understand poetry or can draw, but doesn’t have a head for numbers. Instead, you appropriate or knowledge in a form that’s yours that you can do that you can love and through loving what you know, you love yourself.