A version of this piece was published in 1976 as an appendix to a proposal to the National Science Foundation. It was based on a talk delivered at the HUMRRO Conference, Sept 16-18, 1975.
Ten years is in some ways a challenging and in some ways a very awkward period for predicting the impact of computers in education. If you asked me whether the practice of education will have undergone a I mean, there might be changes comparable in spirit and extent to those technology and science have brought to transportation or medicine over the past century. But it is also possible that the practice of low cost micro-computers in every classroom will not have produced deeper changes than have come from all the other odds and ends of technology in the classroom. There seems to me to be little profit in guessing which way things I see this as a design problem. This paper is an exercise in designing a learning environment for children on the assumption that certain technologies are or will become available. My purpose is neither to prophesy that schools will necessarily conform to this design nor to persuade you that they ought to do so. What I would like to learn from the exercise is much more important and generalizable. I want you to see what it is like to go through the experience of So let us go to work. The project is to design a learning environment, let us say for children at the ages presently identified with the elementary school. Where do we start? Consider three possible starting places. - We could start with the present elementary school. If we make this choice we would look at what happens now in the school, try to identify weaknesses and seek fixes for them using the new technologies.
- We could start with the technologies. This choice would lead us to predict what machines would be available and seek uses for them. An extreme example of this "machine-directed design" is the current fad for seeking ways to use the little hand calculators with small children.
- A third starting point, and the one I shall use, is radically different in spirit. I shall start off by selecting a highly successful example of learning (or, if you like, of education); try to identify features which make it successful and then ask how to transfer these features into situations in which learning is not typically as successful. On previous occasions I have used as the "successful model" the child's early acquisition of language or of Piaget's concrete operations. In both of these examples learning takes place not only "painlessly" but also with almost complete success in the sense that all "normal" children learn to talk and, for example, to use such principles as conservation and transitivity. This contrasts dramatically with the way in which, say, children at school "learn functions". The latter process is painful for most children and highly unreliable in that very many children do not in fact acquire any degree of competence despite (or because of?) constant coercion by teachers and parents. I have discussed elsewhere whether the difference is due to deep and non-transferable factors as, for example, in Chomsky's theory that language is not (really) learned but (essentially) innate. I have also discussed whether the difference could be entirely attributed to shallow factors such as the total amount of time spent (rather than the conditions of learning.) I conjecture that the primary factor is neither innate differences nor mere quantity of exposure but rather the nature of the learning process. But the question will eventually be settled not by conjecture or speculation but by conducting experiments (of the sort I am about to describe) in building totally different learning environments. So let us return to our design process whose first step is to select and describe a "success model".
The model I shall use on this occasion is like those already mentioned (such as language acquisition) in its natural-ness and larger degree of painless success. It is different in a number of ways including the possibly very important fact that it is not confined to children only. The model is an organizational form I had the opportunity to study last summer in Rio de Janeiro. It's generic name translates literally from Portuguese as "Samba School" although I suspect that were such a thing to exist in the United States, it would not use the word "school" in its name. It would be more likely to describe itself as a "club", for although it Some of the many ways in which this can be taken as a success model for education are too complex to discuss briefly here as a mere example. So I shall select just one, the simplest and most visible of it's school-like aspects: it's function as a dance school. If you dropped in at a Samba School on a typical Saturday night you would take it for a dance hall. The dominant activity is dancing, with the expected accompaniment of drinking, talking and observing the scene. From time to time the dancing stops and someone sings a lyric or makes a short speech over a very loud P.A. system. You would soon begin to realize that there is more continuity, social cohesion and long term common purpose than amongst transient or even regular dancers in a typical American dance hall. The point is that the Samba School has another purpose then the fun of the particular evening. This purpose is related to the famous Carnival which will dominate Rio at Mardi Gras and at which each Samba School will take on a segment of the more than twenty-four hour long procession of street dancing. This segment will be an elaborately prepared, decorated and choreographed presentation of a story, typically a folk tale rewritten with lyrics, music and dance newly composed during the previous year. So we see the complex functions of the Samba School. While people have come to dance, they are simultaneously participating in the choice, and elaboration of the theme of the next carnival; the lyrics sung between the dances are proposals for inclusion; the dancing is also the audition, at once competitive and supportive, for the leading roles, the rehearsal and the training school for dancers at all levels of ability. From this point of view a very remarkable aspect of the Samba School is the presence in one place of people engaged in a common activity - dancing - at all levels of competence from beginning children who seem scarcely yet able to talk, to superstars who would not be put to shame by the soloists of dance companies anywhere in the world. The fact of being together would in itself be "educational" for the beginners; but what is more deeply so is the degree of interaction between dancers of different levels of competence. From time to time a dancer will gather a group of others to work together on some technical aspect; the life of the group might be ten minutes or half an hour, its average age five or twenty five, its mode of operation might be highly didactic or more simply a chance to interact with a more advanced dancer. The details are not important: what counts is the weaving of education into the larger, richer cultural-social experience of the Samba School. So we have as our problem: to transfer the positive features of the Samba School into the context of learning traditional "school material" -- let's say mathematics or grammar. Can we solve it? To the uninformed mathophobe the problem will appear very (perhaps impossibly) difficult for the "simple" reason that dance is fun and math is dreary. But a point is being missed. What is "Dance" and what is "Math"? Math for the kid often means a I have a firmly held and well elaborated theory. You My theory now says: if you can do mathematics with a dynamic technology instead of with a static one, then perhaps you can do The task of inventing some new mathematics is not a trivial one. But one should not expect designing an educational environment to be trivial. To carry the task through sufficiently we may need to draw new kinds of people into education research; for example, people with better developed skills of mathematical creativity than is usual amongst people concerned with educating children. But before proposing that as an important national (and international) objective some evidence is necessary to make it plausible that some such mathematical nugget lies there to be found. And as an existence proof I cite once again our own contribution to this area, namely Turtle Geometry in all the ramifications which our MIT team is forever extending. If you are a reader who does not know what Turtle Geometry is, I cannot do more than give you a very summary impression and then send you to find out more about it, perhaps by writing to me at the M.I.T. Artificial Intelligence Laboratory or by consulting the references in the bibliography. One of its key ideas is to create an environment in which interesting actions can be produced and controlled by using a mathematical language to "talk to" and to "teach" a computer. The Turtle is a computer controlled robot which will move in whatever patterns you know enough geometry to describe, and Turtle Geometry is a computer language (in our work embedded in LOGO, though it need not be) which can be used to describe movements. The wonderfully rich fact is that Turtle Geometry is at once more powerful, more accessible and more intuitive than the non-computational geometries of Euclid, Descartes, etc.. I believe that this analogy is very deep: Learning Math by talking to Turtles is like learning dancing by dancing with people while learning math by doing pencil and paper "sums" is like learning dancing by rote memory of pencil and paper diagrams of dancing "steps". At this point in the design process we run into some methodological problems and some need for inputs from experiment and possibly psychological theory. The first methodological problem is this: I can (I know from experience and so do many of you) weave what I would call a poetically coherent and even compelling story about mathematics and turtles. But is that a good reason for believing in my analogy as a practical design goal? Is it, for example, a good enough reason for you to take Turtles into account in making your forecasts about the ten year impact of computers on education? Or for you to give me the resources necessary to attempt to translate my visionary dream into reality? In the past I have avoided this issue (which I shall call, so we can refer to it later, the "Poetry principle") by saying: "But there are Well, all that is true and I have written it down in other places in more detail than I can repeat here. So I shall let the previous paragraph suffice for now as a pointer to issues you will want to study more closely if you are, by any chance, led to think further about what I am saying. The aspect I want to emphasize right now is another side of the Poetry Principle. I have just acknowledged that this principle is not I have only How can we establish a link between mathematics and beauty? For those of us who become (through who knows what lucky accidents) mathematicians this bridge has become strong enough for us to see the deepest beauty in abstract mathematics itself. But if we are not to rely on accidents we need the means to link mathematics with aspects of beauty which already touch the aesthetic sensibilities of the non-mathematician. Two outstanding examples of such links are The fact that the computer enables geometry to produce results to which the child Surely I have said enough to make the point that formulating the task as design for education in a technologically rich future leads very quickly into areas of research which are totally neglected, indeed quite unsuspected, by the community of professionals in "education research and innovation." There must in the world be tens of thousands of people struggling to understand what happens in a classroom where children are asked to do sums with pencil on square paper. Some of them try to improve matters by having the children do the same sums on computer terminals. I do not think it is my business to criticize or judge the value of all this. But I cannot help being overwhelmed by the fact that there must be ten thousand or more people doing that for each one person who has the other kind of design process of which I have tried to give you a glimpse. And I suggest that what happens in ten years depends very sensitively on whether our society decides that it can afford a small shift in this ratio. So perhaps the problem is more political than technological. And if the political aspect depends on how well we can convey an alternate vision, then perhaps it is even more poetical than political. |