Children

Teaching Children Thinking

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One year ago in April, MIT was host to a day-long seminar on the subject of "Teaching Children Thinking." The focus of the day's activities was the work of two members of MIT's Artificial Intelligence Laboratory, Professors Marvin Minsky and Seymour Papert. During the 1969–1970 school year, Minsky and Papert were given a seventh grade math class in Lexington, Massachusetts, to teach. Instead of daily lectures in math, they set up computer programming projects, utilizing on-line teletype terminals interfaced with a PDP-1 computer. Using a, special programming language called LOGO and setting their own pace, the children learned to make theories, find counterexamples, generalize and extend theories, face problems, and make decisions—in other words, to think, to exercise their minds.

Professor Papert is documenting these experiences with teaching children to think in the form of a book, as yet untitled, to be published later this year. REASON is pleased to present excerpts from this book, in advance of publication.

INTRODUCTION The most pointed complaint about the use of technology in education is that it often reduces to inventing clever new gadgets to teach the same old stuff in a thinly disguised version of the same old way. When the technology uses computers the complaint is aggravated by apparently high cost and fears of "dehumanization." People who bring these charges are usually thinking of something like the teaching machine dialogue below as a model of how computers would be used in education:

Q.: What is 2 plus 2?

A; 7

Q.: No, Johnny, it is 4. Please try again.

The dialogue shows successive stages in an interaction between an invisible computer (Q) and an invisible child (A) via a device know as a Display Console. Its essential visible parts are a TV tube and a keyboard. It is connected to a computer which can cause words, pictures, or what you will to appear on the tube.

The public image of the computer's role in education is dominated by the Teaching Machine, but this is a false picture of present reality and even more so of future potential. In fact, the Teaching Machine is merely one of many ways in which computers and the science of computation are asserting their claims to an important role in the theory and practice of instruction.

The purpose of this monograph is to provide insight into the kinds of ideas and the visions of education that inspire these claims. A large part of the monograph will describe the use being being made of computers in an elementary school near Boston—the Bridge School in Lexington. This description can be taken on several levels. Some people will read it as a simple picture of children doing some very exciting things and, if they are teachers, might even use some of these models for projects in their own schools. The descriptions are couched so as to make this as easy as possible for anyone who wants good ideas for projects and has no patience for more theoretical and longer term consideration. But there is more to it.

The word "visions" in the previous paragraph was deliberately chosen. Beyond the particular projects described below in precise technical detail is an image, blurred in some places, quite unspecified in others of what the lives of children could be like and what the theory and practice of education could be like. The content of this vision will become fuller and clearer in the course of the following pages. But before broaching the specific content it is useful to say something about the level of aspiration.

Behind much of the thinking described below is an attempt at formulating an experiment to probe the limits of the educational capacities of children. It is crucial to our purpose to realize that there is almost no theoretical or experimental knowledge with a direct bearing on the simplest questions one might ask about the inherent learning capacity of children or about the relative degrees of difficulty of different subject matters. Take mathematics as an example, though any other would do as well. Ask the psychologists, the teachers, or whoever you will whether they think it would be possible to construct an educational system so that 99 percent of the present first grade children would become proficient in mathematics at the level necessary, say, to major in it at a good college or even at the level necessary to do significant research in topology. Of course, it is irrelevant to discuss the desirability of creating a few million topoligists. Is it possible?

Now I maintain that no one is in a position to venture any responsible guess! One can certainly point to the fact that very few actually achieve true competence even at the level of elementary school math. But it would be the crassest empiricism to deduce from this that mathematics if intrinsically difficult or that most children are not "mathematically minded." One might as well deduce that French is intrinsically difficult and that most children are not "Frenchly minded" from the poor competence achieved by most children in school French. Yet we know that these same children would all speak French fluently had they grown up in France. Their lack of aptitude is therefore not really for French as such, but for learning French under the conditions that obtain in our schools. So let's ask the question about mathematics again in a different form. Is there something that would be to learning mathematics like growing up in France is to learning French? The question defines one corner of our vision. This is the idea that one might be able to construct a "Mathland" in which almost everyone would grow up with a true competence in mathematics just as almost everyone seems to acquire true competence in his native language.

But, since we are merely asking questions, let us continue the fantasy to ask: why stop at math? Could there be a "land" in which everyone would have an easy competence in "analogies," "generalization," and all the other mental paraphernalia of the "intelligence testers"? Could there be an "IQ-land," "Think-land" in which everyone (supposed in our fantasy to be biologically identical copies of the present population of first graders in the U.S.) would grow up with Stanford-Binet scores above 180?

The vision of education presented in the following pages reflects an increasingly widespread belief that these questions are not pure vanity. It is true that many romantic dreamers have entertained similar hopes. But ancient dreams about flight were no reason to shun experiments on aviation. The point, of course, was that the Wrights and other pioneers recognized the emergence at last of a technology capable of realizing the dreams. There is no proof that we are in the same position in relation to a possible educational technology. Nor will there be unless enough people with talent and access to material resources judge that the thesis is plausible enough to make it worth pursuing with the kind of dedication given by the pioneers of aviation (or any other new field) long before this dedication produced proof that they were right…

GLIMPSES OF MATHLAND To ask whether there could be an IQ-land is a far cry from finding one, and it is scarcely original. Many educational reformers have dreamt the dream and their failure must be taken by any hard-headed observer as at least indirect evidence against the reality of the vision. But I shall argue that we have the technical means to carry out what the earlier reformers only wished they could carry out. We can actually lay down a first sketch of how to construct a real Mathland. Indeed some pieces of it are already built and occupied by children. Naturally our first sketch will not be the final and decisive one; I claim only that it shows we can cross a certain barrier whose importance has been widely recognized by many clear minds devoted to education. To define the barrier and our relationship to our predecessors, let's hear for a moment the voice of John Dewey.

Digression: A Word from Dewey

For Dewey the dilemma of schools is expressed in the following passages contrasting schooling with the way he supposes children learn in less developed societies:

For the most part, they depend on the children learning customs by sharing in what the elders are doing…To savages it would seem preposterous to seek out a place where nothing but learning was going on in order that one might learn.

But as civilization advances, the gap between the capacities of the young and the concerns of the adults widens…Much of what the adults do is so remote in space and meaning that playful imitation is less and less adequate to reproduce its spirit…The task of teaching certain things is relegated to a special group of persons…But there are conspicuous dangers attendant upon the transition from indirect to formal education. Sharing in actual pursuit, whether directly or vicariously, is at least personal and vital…Formal instruction, on the contrary, easily becomes remote and dead—abstract and bookish to use the ordinary words of deprecation.

You Can Take a Child to Euclid but You Can't Make Him Think

The child at the hunt is involved; the child in the grammar class or the geometry class is alienated. That this is not quite always true is a remarkable fact pregnant with hope. Somehow for a few children the contents of the academic subjects come to life; and these children have the marvelous experience of learning ideas at school that are actually relevant to personal problems and interests.But are we to believe that the other children are born academically alienated and doomed to be so? Clearly not and, indeed, a great deal of effort has been expended in trying to present the academic material in a more living, personal way.

I think we need to cut the Gordonian knot boldly. It is often said that elementary school mathematics is badly taught; and dedicated teachers, taking this to heart, work desperately to find ways to teach it better. I suggest that the difficulty is really not that it is badly taught, but that it is fundamentally unteachable. I do not mean to deny the obvious fact that heroic measures of superlative teaching will get somewhat better results. What I mean to suggest is that this scholastic math (new or old) is not a naural route into mathematical thinking! A natural route would probably be more like the participation in Dewey's hunt. I believe (following Piaget) that all children acquire a great deal of mathematical knowledge through activities that lie outside the classroom. I believe that some children go far enough along such routes to cross a threshold of mathematical comprehension which enables them to work in the academic context (until, as often happens, they are turned off by it!)

To give substance to this series of expressions of personal belief, I shall describe another context for mathematical work. When we have it as a concrete example, we can come back to the general issues.

A Fifth Grade Child and his "Turtle" on the Fringes of Mathland

As a first groping step to building up an image of Mathland, let's pursue the analogy with learning French in France. This idea leads by an easy step to the fantasy of a companion who would speak only mathematics and do wonderful things with us if we could converse with him. Wouldn't this make leaning to "speak" mathematics more meaningful and involved?

An early attempt to construct this comparison is a cannister shaped object on wheels. It's called a LOGO turtle and is part of the experience at the Bridge School.

LOGO turtles differ in many ways. Their common characteristic is that they are controlled by a computer which in turn is controlled by a child. Let's see concretely how this control takes place.

The child at the console types
FORWARD 100
and watches the turtle move (slowly and deliberately or fast and impetuously) depending on which turtle the child has chosen and partly on what instructions have been given previously).

The command
FORWARD 200
causes the turtle to move twice as far in the same direction. Next the child types
LEFT 90
and the turtle moves around its center through 90 degrees without any other displacement.

The turtle's movements left no trace. But when the child types
PENDOWN
there is a thud as a pen falls down a a tube at the turtle's center and thereafter the turtle will leave a line wherever it goes, until this command is countermanded by
PENUP.
Thus the series of commands:
PENDOWN
FORWARD 200
PENUP
FORWARD 100
PENDOWN
FORWARD 200

will cause the turtle to draw the perfectly dull pattern:

To make the turtle do anything more interesting one has to learn how to use a programming language in order to instruct the computer how to combine the elementary turtle commands to produce complex patterns. Simple flowers and stick men are examples of patterns that require mastery of some very definite and deep mathematical ideas—certainly more than usually goes into a freshman high school algebra course—and yet are within reach of average fifth grade children. Needless to say almost all children find this route into mathematical thinking more meaningful and exciting than learning to solve linear equations!

The turtle is not limited to acting like a slavish draftsman. It can be given more active and flexible kinds of behavior by using its sense-organs. Around its periphery is touch sensitive tubing so that signals are relayed back to the computer when it makes contact with another object. The turtle is not built with any "innate" behavior patterns.

What happens when a signal comes depends entirely on the programs the child has constructed for it. An easy program is to make the turtle reverse its direction whenever it hits an obstacle.

Review: Bridging the Dewey Gap

My first sentence complained about educational technology being nothing but inventing ingenious new gadgets for old ideas. But, to be really objective, one must admit that an educational purpose is served. Perhaps not for the children but certainly for the inventor of the gadget who surely gained an intellectual stimulation and excitement from the experience!

So why not turn the tables and let the children do the inventing?

The emergence of computational technology makes this suggestion seem much less preposterous. The typical product of "classical" technology was a mechanical system with lots of parts that had to fit together rather precisely and stay together if anything interesting was to happen. _rhus making clocks or internal combustion engines requires precision on a level that is unlikely to obtain in an elementary school and, moreover, boring in execution. Even more serious is that such devices do nothing until they work properly. The situation is sharply different when we consider "information machines" in place of "matter machines" or "energy machines." Suddenly there is the prospect of systems with great and interesting complexity, made of parts each of which functions interestingly by itself, and, above all, the coupling between the parts does not require mechanical precision or an understanding of abscure conditions for "matching." In the extreme case there is nothing but "information": the system and its parts are all programs in a large powerful computer. Even when the work with turtles brings in physical manipulations and even in putting together physical parts such as attaching a new sense organ, it remains basically true that the interface between the parts is informational.

The important point is that developing programs can provide very young children with an experience much more like that of a research project than anything now available in the schools. This is not meant to suggest that "programming" is in itself the key to a new education. Writing a "machine language" program in "binary" to add a series of numbers is as abstract and, to most children, almost as boring as learning long division. Good programming languages lead to better results and are essential to many of the projects we shall discuss. But programming is a mere vehicle (the tool, the raw material) for what we have in mind. The educational experience is a project involving building a system of programs of a particular kind—we shall later on develop examples of conversational programs, programs to play strategic games, teaching programs, etc., etc.

Dewey complains of a situation in which the gap between the occupations of adults and the means accessible to children is so large that playful imitation cannot capture anything of the spirit. I think the new technology is closing the gap—provided of course that we help by giving children access to it…

TEACHING THINKING AND LEARNING This chapter is about trying to teach children how to think and how to learn. Some of the ideas in it have no logical connection with computation. The idea of heuristics is used in very much the same way as in Polya's books. But I maintain that programming provides by far the best examples on which students—particularly elementary school children—can work to develop a sense of heuristic problem solving. So, though there is no logical connection in this case there is a strong heuristic one.

Other ideas are more obviously related to computation. In particular we shall discuss how programs can be used as models of one's own thinking. This will bring us into direct contact with an important set of ideas from the branch of computation known as Artificial Intelligence. The first sections of the chapter deal with some very general questions about education.

The Don't-Think-About-Thinking Paradox

It is usually considered good practice to give people instruction in their occupational activities. Now, the occupational activities of children are learning, thinking, playing, and the like. Yet, we tell them nothing about those things. Instead, we tell them about numbers, grammar, and the French revolution somehow hoping that from this disorder the really important things will emerge all by themselves. And they sometimes do. But the alienation- dropout-drug complex emerges too.

In this respect it is not a relevant innovation to teach children also about sets linguistic productions, and Eskimos. The paradox remains: why don't we teach them to think, to learn, to play? The excuses people give are as paradoxical as the fact itself. Basically there are two. Some people say: we know very little-about cognitive psychology; we surely do not want to teach half-baked theories in our schools! And some people say: making the children verbally self-conscious about learning will surely impede their learning. Asked for evidence, they usually tell stories like the one about a millipede who was asked which foot he moved first when he walked. Apparently the attempt to verbalize the previously unconscious action prevented the poor beast from ever walking again.

The paradox is not in the flimsiness of the evidence for these excuses. There is nothing remarkable in that: all established doctrine about education has similarly folksy foundations. The deep paradox resides in the curious assumption that our choice is this: either teach the children half-baked cognitive theory or leave them in their original state of cognitive innocence. Nonsense. The child does not wait with a virginally empty mind until we are ready to stuff it with a statistically validated curriculum. He is constantly engaged in inventing theories about everything, including himself, schools, and teachers. So the real choice is: either give the child the best ideas we can muster about cognitive processes or leave him at the mercy of the theories he invents or picks up in the gutter. The question is: who can do better, can we or the child? Let's begin by looking more closely at how the child does.

The Pop-Ed Culture

One reads in Piaget's books about children re-inventing a kind of Democritean atomic theory to reconcile the disappearance of the dissolving sugar with their belief in the conservation of matter. They believe that vision is made possible by streams of particles sent out like machine gun bullets from the eyes and even, at a younger age, that the trees make the wind by flapping their branches. It is criminal to react (as some do) to Piaget's finding by proposing to teach the children "the truth." For they surely gain more in their intellectual growth by the act of inventing a theory than they can possibly lost by believing for a while, whatever theory they invent. Since they are not in the business of making the weather, there is no reason for concern about their meteorological unorthodoxy. But they are in the business of making minds—notably their own—and we should consequently pay particular attention to their opinions about how minds work and grow.

There exists among children, and in the culture at large a set of popular ideas about education and the mind. These seem to be sufficiently widespread, uniform, and dangerous to deserve a name, and I propose "the pop-ed culture." The following examples of pop-ed are taken from real children. My samples are too small for me to guess at their prevalence. But I am sure similar trends exist widely and that identifying and finding methods to neutralize the effects of pop-ed culture will become one of the central themes of research on education.

Examples of Pop-Ed Thinking

(a) Blank-Mind Theories. Asked how one sets about thinking, a child said, "Make your mind a blank and wait for an idea to come." This is related to the common prescription for memorizing: "Keep your mind a blank and say it over and over." Many adults admit to thinking this way. In my sample the ones who do tend also to complain of an inability to remember poetry!

(b) Getting-lt Theories. Many children who have trouble understanding mathematics also have a hopelessly deficient model of what mathematical understanding is like. Particularly bad are models which expect understanding to come in a flash, all at once, ready made. This binary model is expressed by the fact that the child will admit the existence of only two states of knowledge often expressed by "I get it" and "I don't get it." They lack—and even resist—a model of understanding something through a process of additions, refinements, debugging, and so on. These children's way of thinking about learning is clearly disastrously antithetical to learning any concept that cannot be acquired in one bite.

(c) Aptitude Theories. Most children seem to have and extensively use an elaborate classification of mental abilities: "He's a brain," "He's a retard," "He's dumb," "I'm not mathematical-minded." The disastrous consequence is the habit of reacting to failure by classifying the problem as too hard or oneself as not having the required aptitude, rather than by diagnosing the specific deficiency of knowledge or skill.

(d) Caterpillar Theories. The theory that explicit formulation harms performance seems to be itself a central part of pop-ed. It is akin to the Blank Mind Theories and is felt by children to be confirmed by examples of skills they can perform although they cannot (in their opinion

and probably in reality) describe them.

The Computer vs. Pop-Ed

I do not believe that much good can come out of merely preaching to the children about these bad ideas. Such a widespread set of beliefs is bound to reflect deep aspects of the children's intellectual structures. In particular these are largely determined by the poverty of our culture in means of conceptualizing and discussing complex processes of any sort, and mental ones in particular. This must be remedied by exposing the children to more than verbal contact with the new ideas we wish to give them. We must find ways to provide a set of activities through which children can develop an easy fluency in the new concepts and integrate them into widespread structures of concept and intuition and attitude. I see the primary use of computation in this process as providing suitable activities. Secondarily, it will provide children with explicit models of some cognitive processes.

In a good Piagetian sense I'd rather say: you cannot give someone an idea; education consists of creating the conditions for him to invent it himself.

So Is It Bad to Think About Doing?

People usually withdraw the "half-baked theory" objection once they have been made to think about pop-ed. Views on the millipede objection to explicit verbal formulations are more obstinately held, I believe, on the basis of the fallacy that confuses the plainly true assertion "bad verbalization is harmful" with the contentious "no verbalization is good."

To emphasize the point a little let me use the millipede as a mythological example. I believe (mythologically speaking) that the beast might really have become paralyzed, but for a slightly different reason. The psychologist asked him, "Which leg do you move first?" and his mistake was to let himself be browbeaten into believing that the question is meaningful, i.e., that there does exist some leg that he always moves first. Naturally he can't find the answer, because there isn't one. The proper description (let us suppose!) of how he walks if "Move any leg, then move another leg thus far down along the body, etc."

The moral of this story is very important to our theme. For it says that if we are going to give descriptions of processes, we should be careful to have the means to find and express the good ones or else we will paralyze ourselves! And the means to express such descriptions are nothing other than those needed to write programs.

Learning and Describing

35
35
610

Asked whether 35 bucks and another 35 might get up to 600, the kid who did the sum said, "Not a chance" and removed the 0 to give 61 as the answer. When / said "What did you do the first time?" he said, "I didn't carry"and made a new revised estimate of 70.

Some people might say that the kid finally "got it right." But what does "getting it right" mean? Surely not the physical act of writing the number "70." In this case the fact that the first revision was 61 and the second 70 is almost certainly the result of a purely random process. It seemed very likely (from observing the child) that he knew a couple of things to do—like those two corrections—and beat around trying them until I was satisfied.

It's a pity he didn't (wouldn't, couldn't) look at what he had actually done and try to justify it instead of correcting it. For what he did do could be described as the procedure:

Get "units" of sums by adding units of numbers.
Get "tens" of sums by adding tens of numbers.
This works for 23 plus 23:
Units of sum : 6
Tens of sum : 4
Sum :46

So 35 plus 35 should give us 6 10 and what's wrong with that? Whose fault is it that the idiotic decimal place rotation won't allow us to write 6 10 without confusing it with 610?

Perhaps my general thesis can be stated crudely as follows: .if you can't think things like the previous paragraph, you shouldn't be doing that kind of arithmetic; if you can think such things effortlessly, you will find the arithmetic equally effortless. The educational problem (for arithmetic) is found in helping children attain that kind of sophistication. The problem is not to get them to understand numbers as such (if there are such things as numbers as such). It is rather to develop this ability to think about people doing mathematics and especially about themselves. The components of this sophistication are in turn things like the following:

• The idea of a procedure and, especially, the idea of following the procedure literally.

This distinction is crucial. Most children will say that they do use the little procedure for adding digit by digit. By using a procedure they mean using it with the appropriate additions of good sense. Consequently when they get into trouble by using it literally, they are unable to account for their difficulty by blaming the bugs in the procedure.

• The idea of representation and, especially, feeling free (and being able) to make up a representation when one with some special property is wanted.

In my little wishful thinking about what a child might have said to justify his 610 I casually introduced the notation 6 10 for 6 tens and 10 units using the space between the 6 and the 10 to preserve some essential features of place notation while freeing myself from the annoyance of a finite number of digits.

• The idea of making a theory to explain one's behavior.

The question: "Why did you do that?" taken by children as demanding an excuse rather than a causal explanation.

• A certain attitude of objectivity in looking at oneself and mathematics and at oneself doing mathematics. This includes freedom from the puritanical dichotomy into the "right and good" and the "wrong and bad." It includes a willingness to find oneself interesting enough to think about.

• The notion of a program that fails to do what was intended nevertheless does something. One can only study its behavior and understand exactly why it does what it does. The term "bug" (as opposed to the morally charged "error") and especially the use of an active verb "to debug" reflect the elements of objectivity in this…

THE COMPUTER AS ASSISTANT The theme of this chapter has a slightly paradoxical overtone illustrated by the following science fiction fantasy. A robot from outer space on a visit to Earth encounters the phenomenon of schools for the first time. On its own planet biological life vanished long ago, leaving its race of robots with enough intelligence to maintain and advance their level of technological and scientific knowledge. In particular the robots can reproduce themselves in the fullest sense of making new ones complete with all established knowledge and all known skills programmed into them at the time of manufacture. So there is no need for institutions like schools where individuals carry on activity that looks like work but is done to learn rather than for the product of the work. The robot, which we thereby see to be intelligent but not infallibly so, mistakenly supposes that schools are a kind of sweat-shop in which child labor is exploited to carry out computations. As a parting gift, it presents every human child with a miniature computer capable of doing all this work for it. The gift actually was motivated by kindness. Nevertheless some historians maintain that the robot's real intention was to sabotage the educational system so as to inhibit the development of human science to a competitive level.

The question we have to face is whether something like the robot's gift would be sufficiently beneficial to children to warrant our giving it to them without waiting for his visit; or whether it would be so harmful that we must at all cost prevent its development.

The argument for the second conjecture is easy to state. Children work at school to acquire skills. Giving them mechanical aids would be like saving a track athlete in training from the drudgery of his early morning jog by giving him a car. But such analogies cannot be pressed too far. it is sometimes advantageous to give athletes mechanical aids. The use of lifts and tows for training skiers is an example. One might object to the proliferation of these monsters on esthetic grounds or one may find walking up mountains a more rewarding experience than becoming a specialized downhill ski racer. None of this contradicts the utility of ski lifts as an educational aid for teaching skiing.

The next pages will provide some examples of how computers can be used to perform routine tasks for children in the spirit of freeing them thereby for further advancement in more interesting activity. No attempt will be made to provide a complete list. The examples chosen are meant to indicate the possible range and raise the key problems for discussion.

An Editorial Assistant

The kind of assistance the computer can give to a child is certainly not confined to performing arithmetic for him. In our first example the computer will be used in a secretarial and editorial capacity. To provide the proper mental context for this idea, try to imagine a child who has just completed an essay. On reading it through he notices a badly structured sentence somewhere in the middle. Will he re-write the sentence? Unfortunately this is likely to mean re-writing the whole essay. So, he lets it stand! The harm done is worse, much worse, than the presence of a bad sentence in a child's essay. The real harm is the inhibition of the habit of experimental modifications of the text in the spirit of trying several versions to see which pleases most.

Contrast this situation with another, fantastical one in which the child has a super secretary who will instantly retype the essay with any changes he wishes. It is admittedly difficult to know what the consequences will be. Surely the child would be more experimental. Surely a better essay would be produced. I conjecture firmly that the child will acquire a deeper and more sensitive feeling for language and for the organization of thinking and exposition. I conjecture a little more tentatively that he would eventually become less "lazy." This last claim will seem perverse to those who think that the supersecretary would "spoil" the child by making him "lazier" than before. Both outcomes are possible in principle. I base my claim on the assumption that the child will eventually acquire the taste for literary experiment to a sufficient degree to motivate rewriting the essay ten times by hand if the supersecretary happens to be unavailable. But that is a matter for experiments. The prior question is whether we can give the child a supersecretary.

Well, presumably not a human one, but we can make a machine perform a large part of this function. Indeed, such machines exist and are used to perform just this kind of task for people whose time is recognized as being valuable enough to justify labor saving devices. But instead of describing any particular existing example, I shall describe a hypothetical one tailor made to fit the special needs of children.

So now imagine that the child has written his essay by typing at a console. He decides to replace the word "written" by "composed." So he types
D: written I: composed (D for delete, I for insert)
and instantly the change is made. He doesn't like it. So he types
R (for Restore)
and the text goes back to its previous form. The example is trite, but illustrates the way the machine works.

The essay exists in the machine's memory. At any time the child can see any part of it by typing appropriate commands. He always sees it in a tidy form with margins and spacing neatly fitted to whatever pattern he has requested. If he wants a copy on paper it can be produced instantly—though possibly he will never require it since teachers and fellow students can read the essay at their consoles.

It would not be difficult to program the computer to notice unlikely spelling and even some unlikely syntax. Thus if the child types "dificult" the machine would observe that this is not an English word but is very close to one. So it might indicate this by displaying the word in a brighter form on the console. The child would have the option of asking it to be changed or (as would be appropriate here, since I meant to write "dificult"!) leave it as it stands.

I am sure many computer experts will exclaim, but that's much too difficult!" It is indeed too difficult to achieve right now if we want it to be infallible. But the task is much easier if we think that it would do a lot of good by very often picking on a child's mistakes and only seldom picking on a nonmistake.

An important function to automate is that now completed by using a dictionary. It really is boring and/or distracting to leave off writing to look up a word in a dictionary—particularly if the dictionary is large and cumbersome. For the child composing his essay at his console, the automated dictionary reference is very much easier. At his command a summarized dictionary entry appears on the screen. If he wants more information on any part of it, he says so and that part is elaborated.

And as an extra bonus the machine can print out for him at the end of the day or week a list of all the spelling mistakes he corrected, the dictionary entries he referenced, etc. If he or his teacher happens to like that sort of thing, the machine could even be made to subject him to a "review quiz" on this material…

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