Computers In Education

Computers In Education

Educational Solutions Worldwide Inc.

Caleb Gattegno

Newsletter

vol. IX no. 5

June 1980

First published in 1980. Reprinted in 2009.

Copyright Š 1980-2009 Educational Solutions Worldwide Inc. Author: Caleb Gattegno All rights reserved ISBN 978-0-87825-300-5 Educational Solutions Worldwide Inc. 2nd Floor 99 University Place, New York, N.Y. 10003-4555 www.EducationalSolutions.com

Most of the articles in this Newsletter were written by users of The Silent Way. They were contributed as papers to qualify for the Diploma of Advanced Study in The Silent Way granted by the Gattegno Institute, a division of Educational Solutions. Many more papers were received, but these few were considered to be contributions from teachers to the ongoing thinking on language teaching stimulated by the seminars of the Advanced Study Program, and beyond their original purpose. This Newsletter may not remain the right channel for such contributions if their number increases considerably, as it seems likely by the caliber of the participants in the seminars that generate at present the opportunity for such writings. A special Silent Way Newsletter will then be contemplated to serve as a vehicle for the reflections and experiments of the contributors.

More and more, one hears that governments which are prepared to cut funding for education, as it takes place in traditional institutions, and to lay off thousands of people involved in these institutions, are ready to find money to see more people come in contact with electronic devices. Teachers and traditional educators find this strange, or even see it as a sign that ignorant politicians heed the advice of manufacturers and not that of true professionals.

Be that as it may, education is becoming more involved in the electronic revolution of these recent decades, and it is the interest of everybody in education to understand the subtle, as well as the overall, impacts of that revolution. This issue of our Newsletter is a contribution to this study, a small one, no doubt, but one that combines findings in several fields and sheds some light on that which challenges all of us today. It is urgent that we emerge from our complacency, experience the demands of belonging to our time, and prepare ourselves for the future which is rushing towards us.

Two book reviews and extensive News Items complete this issue.

Table of Contents

1 Introduction ...................................................................... 1 2 The Computer And Mathematical Education..................... 7 3 Infused Reading ...............................................................17 Book Reviews ..................................................................... 25 1 Earl W. Stevick’s ........................................................................... 25 2 “Issues And Initiatives In Learning Disabilities” ........................ 27 News Items ......................................................................... 29

1 Introduction

Only the specializations of the people involved in the field of computers make hardware different from software. Engineers and scientists use their minds as much as educators do. The first have experience that involves items in their thinking which do not occur to the latter because they are not part of their backgrounds. Conversely, because engineers ban considerations of educational matters when they develop their ideas about the computer and its uses, they do not see what could, perhaps, be evident to them if they reflected upon it.

Clearly ideas like “time-sharing” — which is halfway between the making of computers and what they are used for — although important in the history of the new industry, are not counted as hardware or as software. Neither are the languages, developed to send to the computer commands it can understand and to extract from it what its owners want it to deliver, hardware or software.

Perhaps these two concepts and labels only help a few people a little, and hamper many a lot.

Perhaps the truth is that the way the mind works in this field is always the same, but that the appearance, as seen by some, is interpreted according to what already furnishes their minds. Engineers can take steps to change their ideas, their images, their awarenesses, into items that are experienced as being hard, being material, being tangible and, for these items, they created the word hardware.

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Computers In Education

They fail to see that a tape, or a disk, or a program, may appear to some other people to have a consistency, a reality, which would put it in the class of hardware too.

Hardware is a word devoted to that which does not change, while software is attached to that which is compatible with the hardware but can span any number of activities that can be made understandable to the machine in the way it was conceived to operate.

We can see that, conversely, the machine is compatible with a project which has been thought out to use it, and that together the machine and the program generate another reality, which may be the progress a student makes in mathematics, or a list of writings that refer to a particular topic, or a horoscope, and so on.

In the way we have integrated the somatic components of our hand or our will to make it (the hand or the will?) write, or paint, or play an instrument, we no longer need to say the bones and muscles are the hardware and the will and the skills the software. What we do is form a hierarchy of necessary components and, as each new level integrates the pre-existing ones, we make a new synthesis of software and hardware which represents the new hardware that is necessary for obtaining a particular result.

Because of their common origin in the mind, these products of the mind can only become united.

For the purpose of education, perhaps it will be beneficial to blur the categorical distinctions between the new electronic organization which produces the machine, and the new forms which have been given to old experiences that may have existed for millennia, such as geometry, or languages. Indeed, each new component of the new computers is created, in the minds of the people who work for manufacturers, as an alteration of some existing function, or a different coupling of parts, as a way of materializing a theory, or an adoption of another machine conceived to give greater freedom, greater flexibility to the original one, or to come closer to what one finds in one’s introspection when one does some special mental work, and so on.

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1 Introduction

In forty years or so of creative work on computers, to produce them, improve them, make them error-free or error-sensitive, or to relate to them (as with talking to them and interpreting their responses) we have developed our minds. After having solved all the obvious linear tasks that already existed, and having managed to provide ourselves with aids that either do very quickly or can be made (programmed) to do very quickly, some social jobs in banks, corporations, travel agencies etc., we find ourselves today owning more and more powerful computers (hardware) which cost less and less, and which demand more and more jobs to occupy them. This is the meaning of the demand for software.

Since legions of imaginative and eager people are at work producing programs which are compatible with the existing hardware, there will be need for criteria to know exactly whether or not programs are worthwhile. This is specially true in fields like education, where funds are short.

The most obvious attribute of the computer is its speed. We are becoming used to it, and expect answers to our questions at once. Thus, instead of remaining full of admiration for how quickly we can get a telephone number for a long distance call, or a seat reservation to a destination overseas which requires several changes of planes, or a list of books and articles on a particular topic from a central library, or the details of our horoscope, we become impatient when we are told that we must wait for a while. Taking the speed of the computer for granted must be resisted, particularly since there are challenges which require still greater speeds of operation to be tackled, such as weather forecasting. Manufacturers are engaged in saving billionths of seconds on every step of the computer’s operation, and we all take their great speeds for granted.

More important than speed per se is what speed has made, first, possible and now, obvious. The true way the creative mind works is neither analysis nor synthesis alone, but both in unique combinations which correspond to many and complex challenges.

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Perhaps the greatest boon we have gained from the creation of the computer is the dawning of an era in which our minds will not shrink from considering complex and large tasks, whether or not these can be programmed for the computers which are in existence today.

Studies of the minds of young people in various environments concur in telling us that the not-yet-conditioned mind works very differently from the conditioned one. This, mingled with an arbitrary value system, has led adults — who call themselves scientists — to denigrate children’s spontaneous workings and to suggest that we force the pace of the “proper” conditioning through education. Piaget’s work can be bracketed with those of such scientists. They did not ask themselves whether the spontaneous ways of working, which lead so early to mastery of as complex and non-linear a task as learning to speak, invite us to reconsider our biased view of the mind. But the wide adoption of the computer as an aid to thinking will force us to review our positions and attitudes, if we do not want to generate only failures on the scene of education, as we are doing today.

The absurd combination of the swift computer and the lean school curricula which forms the basis of C.A.I. (computer aided instruction) has led to a loss of huge sums of money — which are no longer available for valid research — and of many years, with the consequence that many people no longer wish to believe that there is room for the computer in the field of education.

To return with hope to the computer in education we need to renew ourselves. At this moment, it may be said that such renewal demands 1

that we stop thinking in terms of the pair stimulusresponse and,

2 open ourselves up to the analytic-synthetic way of working we bring with us at birth. When we are uncommitted to the culture around us we work passionately as learners to make sense of the world in which we are born. In particular, we swiftly assimilate a language that took centuries to structure to the point it is now.

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1 Introduction

Since we cannot be as swift and accurate as electronic calculators are, (and calculators may reach a price that most school children will be able to afford) we can stop thinking of schools as places where a few years are rightly spent in learning to compute on numbers. A few hours may be more than enough for the acquisition of the skill of pressing the proper buttons to obtain any numeral needed in a social transaction.

Such social transactions have often been cited as the reason for teaching arithmetic at school. The time saved can be given to the acquisition of awarenesses which characterize those mental attitudes shared by the populations which call themselves mathematicians, linguists, logicians, physicists, etc. If we can save this time in any one of these fields, we will have given evidence that the new era is already upon us and education, at the level of human evolution, is at work, at last, for all.

The computer, by itself, cannot produce this change in our society.

Human beings have to do it. The following two articles aim at articulating some ideas that we can now have since much “brain power� has been released because of the state reached in our modern world as a result of the electronic revolution.

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2 The Computer And Mathematical Education

The computer, as a creation of the mind, displays a number of properties which are owned by the mind. The hardware and software are invented when someone becomes aware of a possibility of putting together items which are present in the mind but do not yet form an integrated whole. For that, these items have to be compatible; i.e. they must have properties the mind recognizes as capable of merging together to form a functional entity. For example: “adding one” and “iteration” are two very different mental operations but can be used in conjunction, yielding the sequence of integers, if we start, say, with “one.” The operation “stop,” used in conjunction with the other two, will generate the individual integers of the sequence, one after the other (for whatever use one has in mind), as well as the notion of “finite” and, by a flight of the imagination, the “non-finite” or “infinity.”

When the mind that has created the sequence of integers applies “stop” to it in different ways, it may produce new iterations, which are awarenesses of subsequences that can be stored in one’s memory and contemplated individually.

This contemplation will produce “multiples,” a new awareness — which can be separated and can become an operation in itself. If we start with “one and one” (which we name “two” for brevity) we get the multiples of three, and so on.

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Thus we have — from very little — produced a lot that is new. The “very little” is made of the very few awarenesses that the mind can objectify sometimes as operations, some other times as instructions which are selections of combinations of those operations. As it creates those combinations, the mind is aware of them. Thereby, new entities are generated.

When mathematicians, like Peano and those of his generation, attempted to find the foundation of mathematics in the sequence of integers, they had a similar intuition. But it did not lead to a total success. This forced mathematicians to look again at the foundations and to find much that was new and very important for them.

Programming computers remains in the vein of that search for foundations, for, only when we are aware that we must use such operations as “stop” or “end” or “go to” or “do” etc., can we make a computer do its work and give us the outcome we expect. All these operations are mental operations, i.e. broader than mathematical operations, which we routinely use in mathematics, in combination with other mental operations which are strictly mathematical.

In the early history of the computer, the hardware was given the most attention because an awareness of what is mechanical in the functions of the mind was necessary in order to produce a machine. A sufficient number of challenges were present in that awareness to require from Pascal to Babbage, two hundred years of trying, in order for the first breakthrough, that encouraged workers coming to these questions, to be reached. Now, the hardware is as much a mental item as the software, and more and more, their distinctions are disappearing. A microchip that is capable of carrying 64,000 or 256,000 bits of random access memory (RAM) can scarcely be conceived of as an object which strikes our senses as hardware generally does.

There are tiers of mental functionings in all the achievements of man which include things that can as easily be considered sometimes as belonging in the category of hardware and sometimes in that of software. Language, logic, can be counted among them. That is why, in all advanced intellectual activities, we lose awareness of what serves as 8

2 The Computer And Mathematical Education

hardware and become aware only of that on which we are working.

Logicians of the past (and probably of today) started from “a universe of discourse,” which they needed for their work, but didn’t consider to be their field of study. Language is part of the hardware of the logician, who only needs to use it to force his awareness of something else, such as consistency, newness, extrapolation, premise and conclusion, definition, proof, and so on.

Linguists must look for their own hardware in order to consider language as that “new” that is being created, and of which they have recently become aware. The brain and memory may suggest themselves as that hardware, and these require other workers to know what they are and how they function.

But for neurologists, and those who study memory (perhaps psychologists), there cannot be any doubt that the functions of the brain and of recall, or the storing of memorized items, are not the starting points. From a certain viewpoint the hardware again loses its “hardness,” and a search for bedrock is started once more as soon as software is encountered in what initially appeared to be hard.

Perhaps it would be helpful to us to re-examine those things we have endowed with “hardness,” and thus, to come into contact with awareness and with ways of working with awareness.

When we lose the awareness of which energy remains in the objectified, we produce things that are objects for our minds. But our minds can shift the focus of our awareness, and until we make ourselves remain in contact specifically with the shift of awareness, we lose that which assimilates awarenesses which, to the mind, can appear as very different. The study of foundations is that deliberate effort to know the attributes of the content of the mind which generate differences in that which could also be seen as not being different. ***

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In the computer languages, data stored and instructions use the same devices (bits) and computers are forced to recognize different sequences of bits to mean different things by translating the mental perceptions of the programmers into organizations of the sequences of bits. By doing this a semblance of consciousness is passed on to the computer. A programmer who is using the given makes himself capable of recognizing that which looks different as the same and that which is the same as different.

This essential awareness would serve well in a number of investigations.

For example, it could serve us in treating mathematical mental structures as mental structures and looking at how computers could be made to force awareness of mathematization by explicitly developing programs that handle algebras.

As a mental activity, algebra is defined here as an awareness of the dynamics behind all mental functionings. More especially, it can also be seen as the effect of operations upon operations. Hence, algebra is always present, as soon as the mind is at work. But since the dynamics takes all the forms it actually takes, the appearances will differ and the impressions the minds register will differ too. Is it possible to generate awarenesses of what goes on in the mind so that one will know for certain that a given mental structure has been objectified in one’s mind?

The answer, in many instances, is “yes.” This proves that elementary mathematics is for everyone who has given and gives signs of having spontaneously generated certain number of mental functionings. For example, the ability to speak one’s native language, in the case of nondeaf people. *** Let us look at Logarithms in base 10 as a mathematical entity and see how much we can learn from this about the relationship of

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mathematical structures to mental structures. In the definition: N = log10 of 10N we have the mathematical structure.

Hence, here, exponents precede logarithms.

Exponents (that are integers) are defined by —

an

n times = a x ax . . . . . . . . . . . . xa

and this presupposes: 1

multiplication as a mathematical structure

2 “iteration” as a mental operation 3 “counting” as answering the question “how many?”

4 “stop” as a mental structure that recognizes the end of a process.

Multiplication as repeated addition presupposes: 1

addition as a mathematical structure

2 iteration as a mental operation 3 “counting” 4 “stop” 5 retention of the items stopped at.

Addition as a mergence of two sets (labeled by integers) as 1

iteration of the units in one set, at the end of the numeral that is the label of the other set

2 recognition that all units can be assimilated one with another

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Computers In Education

3 recognition that a sequence of labels (sounds or signs) is available in one’s memory to be involved in the act of counting 4 counting as a pair of activities, one consisting of sequential utterances of the ordered set of labels of the numerals, and one consisting in going through the set of objects to be counted, without repetition or omission 5 stopping when the “last” object has been reached and the corresponding label uttered.

As this short analysis shows, many of these awarenesses are generally taken for granted, because they have been automatized by the process of “learning.” For us here, they are the main elements of the presence of general mental structures, amid the mathematical structures that hold them in our consciousness. This also proves that these mathematical structures are first mental structures, and because of this, can be integrated by them or integrate them.

To present Logarithms we need another mental dynamic which we can call “inverting” or “inversing” because we consider a relationship such as n = 10x and read it as x = Log 10n, (the sign = has here the meaning of is another name for). The definition of a logarithm therefore results from a shift of awareness, from (n and 10) to x. When we focus on n we call in the mental activity of labeling, and introduce the words “logarithm base 10 of n.” Only when we sense the mental dynamics which allows our mind to go from one relationship to the other and back, as freely as we are used to in many other activities, can we say that the definition of logarithms is integrated in the sense exponents are. These, in turn, were handled similarly, when iteration of multiplication was seen as an integrated whole, and a count of the number of iterations was kept in the mind.

So, we do not handle mathematical entities only. The more generally available mental structures are the real stuff of mathematization, thus securing this activity for all. Indeed the purpose of teaching mathematics can be to generate these awarenesses. Knowing mathematics then follows as a natural functioning of the mind that recognizes, recalls retains, connects, and so on.

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Another example may be needed to illustrate the dynamics of the mind.

Let us consider the mental structures involved in subtraction.

The mathematical definition is that subtraction is the inverse of addition. Hence, we have either to relate the two operations from the start and associate with each addition the one or two subtractions that are connected with it (a + b = c, b = c - a and a = c - b), or develop an algorithm for both operations on a set of numbers as two ways of reading the same reality.

Addition, being the bringing together of two sets, requires that we still perceive the two sets in the combined one. In subtraction we still see the initial set or minuend, when we have separated into it the two “complementary” subsets, the subtrahend and the remainder. The simultaneous holding in the mind; not only of three sets (two of which are subsets of the third) but also the shift in emphasis from two to one and from one to two is what represents the mental dynamics that is necessary to comprehend how addition and subtraction are inverse operations.

The mental operation of cutting a given set into two complementary subsets is the source of two perceptions of the three sets generated by the cut. According to the emphasis, we perceive either addition or subtraction in the same situation. But we could also perceive that there are a number of possibilities for the cut to generate the class of complementary subsets of a given set.

If we iterate the “cut” within a given set, we generate a new notion: that of “the set of partitions of a given set.” This is a new awareness. It is triggered by the perception of the possibilities offered by the situation: the awareness of a retention of the results of the cuts previously made, replaced by the merging of those parts and again a new cut whose effect we can now contemplate as before, and so on.

Another possibility opens up when we become aware that if we wish to partition a given set into two complementary sets we have choices,

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whose contemplation generates new opportunities. For example, if we wish to separate one element from the rest there are as many choices as there are elements in the set. Simultaneously, we can perceive that this is equivalent to separating one element from the rest or the rest from one element. This leads to the awareness that two ways of expressing a situation which sound very different provide the mind with possibilities that increase its reach.” * The study for its mental content, of subtraction, could take another turn as soon as we choose another term from the trinity: minuend, subtrahend and remainder, isolate it, and stress it. Contemplating one (the remainder) can be conceived of as contemplating the pair (minuend, subtrahend) that generates it. There are as many such pairs as we wish and with respect to that difference they form a class of equivalence.

We have made a mathematical discovery through an introspection, which is a mental awareness.

We have at the same time made a pedagogical discovery. We can now generate mathematical propositions simply by stating what we perceive in our mind, once we have shifted our lighting from what we had looked at before to something of that which we had ignored.

The new awareness of subtraction can be stated as follows: any number can be considered to be a difference between two other numbers, and this in an infinite number of ways.

Hence the question: find the difference between a and b, can be tackled, not necessarily on the given pair a and b, but on any other pair of that same class of equivalence. This awareness leads to a new algorithm for actually finding the number which is the difference

*

Let us delve for a moment into how easy it is to become more powerful mentally by only shifting viewpoint mentally. Looking at the spread of our two hands, it is clear that we have ten choices of folding one finger. If we ask the very different question: how many choices do we have of folding nine fingers? we may not perceive that we have already solved it, simply because we put emphasis on the different sounds and think it is a new problem. In fact, it is simply another reading of the same situation.

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between two given numbers. Rather than stick to a and b in a - b, we can operate on a and b, replacing them by (a+N) and (b+N) (with the same N) so that the difference we want to find can be read directly.

Of course, this difference is equal to (a-b) - (b-b) where -b replaces N. This absurd looking statement is in fact the basis of the algorithm, for it states that the simplest form of the difference in the class of equivalence is the one that no longer looks like a subtraction and is a single term.

Once we replace a and b by numerical polynomials in a certain base, the algorithm looks different and suggests that we take steps which a b cannot offer.

We can move towards replacing the subtrahend by a number made up of zeros, except for the first figure on the left, by adding to it a properly selected number N. By doing the same to the minuend, we obtain the remainder at once, through one reading which includes a one-figure subtraction which can be done mentally at once.

But we could also choose to first change the minuend by making it into a number made up of zeros, except for the digit on the left, by adding to it an appropriate number and doing the same to the subtrahend. But this time the difference cannot be obtained only by reading. We need to use a second algorithm — albeit one which is very easy to acquire — which allows us to obtain in figures the complement of a given number in any other larger given number (written in any base and written from the left).

At least we now have a variety of ways of obtaining the difference between two given numbers, and can select, according to the given pair, the way that is easiest for us or best suits our taste. Because we allow the problem to guide the solution, we are certainly better off than when we use the same mechanism to solve all problems. We mobilize what is, in effect, asked for by the challenge.

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What this second example may have taught us is that, by delving into the mental structures implied in the most primitive operations of arithmetic, we gain a mental freedom with respect to matters that did not seem as primitive but are in fact, more so, and can be a safer basis for teaching mathematics to all.

The effect these awarenesses have upon the programming of computers for mathematical education in this field must be left for later.

The algorithms we have deduced from our closer look at mental structures show that to work out addition or subtraction on numbers (in any base) we can explicitly use each operation to make the working of the other easier and safer. This seems to be a proper understanding of addition and subtraction as inverse operations.

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How can the computer assist us in the study of that which needs to be done to make sighted speakers of a language capable of reading it too?

This challenge is a multiple one, for until we have solved the problem for a few of the existing scripts used on earth, we shall not know how the form of the items used for writing a language imposes the necessity for new approaches for each of them.

At this time, what matters is to prove that the computer can offer a “better” solution to the challenge than what exists today, even for one single language.

This is the problem we shall entertain in this article.

As seen within the overall awareness of using the swift computer, the flexible and patient instrument it can be when properly programmed, the challenge of presenting the reading of a language to native speakers, in order to make them literate, will only be met when the computer is directed by a primitive flow chart it can understand.

Skilled programmers will take it from there and instructions be provided to users so that, as a result of interacting with the problem on the terminal, one will find oneself a reader.

That is why the project is called “Infused Reading.” Viewers of a monitor, where the successive phases of the act of reading can be called up by them, when they sense they have mastered the previous phases, 17

Computers In Education

will know that they have been taken into account and given exactly as much or as little material as they need to practice in order to move towards a total and individual mastery of all the necessary components of reading.

What the computer brings to them besides the program is the right to move ahead as swiftly as they are able, or to dwell as long as they want on that on which they still need to work.

The format of a set of command keys and a TV monitor in front of the student is the normal one. We have nothing to add here.

The question of what commands are necessary for this specific program has also been solved. The students will either need to move forward and will press a “next” button, or need to return to a stage they sense is less secure than they thought it was and can press a button that “brings back” earlier material. They may need to isolate items, to magnify some, to review a detail. All such demands are routine in computer technology.

Thus, individualizing learning is akin to the normal uses of the computer, and we do not have to concern ourselves with it.

What then are the challenges inherent in the problem of the use of the computer for literacy?

A solution will only exist if, theoretically, going once through the program will be equivalent to meeting all the components of the act of reading.

Actual languages make different demands upon the illiterate, because reading requires recognition of written words and these have a traditional form called their spellings. Only strictly phonetic languages would not present this component, and not make demands of that kind on speakers who want also to be readers of their language.

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Thus there are at least two broad categories of challenges to whoever wants to develop a computer program for reading, those resulting from understanding how to work out a “phonetic” language and those imposed by the demands of spelling. Perhaps it is possible sometimes to tackle both. Only experience will tell.

The component of spelling may defeat the trials to solve the first problem, because, ultimately, text in a non-phonetic language will remain closed to the scrutiny of the newly trained person who can only tackle words of a certain kind (in terms of spelling).

Still, the true challenge of using the computer is to give people the skill of reading. This is the primary problem and we may leave the spelling problem for later. Can we prove that speakers of a certain language can become conscious readers of that language when exposed to a complete computer program? And can this be done by a reasonably short program that would attract illiterates?

This is precisely what we expect will happen when the project we conceived is given form by the programmers who are considering it.

For our readers these words only state that we have made one move from the theoretical stage (reached in September 1972, when we saw “infused reading” as compatible with the powers of the mind at work in reading any of the ten scripts used by a number of languages) to translating the reading of Spanish into a computer program.

It is not impossible that speakers of Spanish may go through the whole program in one hour and become literate in that short time. Even if only one person could do that we should be very pleased, for we would have proven, 1) that the program is capable of eliminating all doubts in the transmutation of looking at a script into speaking, and 2) that the program proposes a valid solution that could perhaps be transferred to all sorts of written languages (a colossal job which requires collective support).

Let us sketch the solution of “infused reading” of Spanish that makes it computer programmable.

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*** If a text can be created which can be shown as one whole on the monitor screen and be legible to knowledgeable readers, and if that text contains samples of all the signs that trigger all the sounds of Spanish, it can serve our purpose.

The illiterate student is facing the monitor lit by pressing a “start” button and showing the complete text (in color when possible, and if only a few colors can be used, only vowels will be colored). Silence goes with that text and we shall call its appearance on the screen, the showing of the “cell.”

The essence of the project is a succession of approximations to that text from within. Each approximation contains the previous one and adds something new. The cell and its approximation are shown alternately.

This means that by design of the program the viewers will meet the cell many times, but each approximation only once unless they order a repeat.

Another feature of the program is that in the alternate view of the text we call approximations, the signs that are shown are exactly in the places they occupy in the cell. Sounds are only provided for the items introduced in the successive approximations. If students listen to each item when it is introduced, they will recognize a sound of their language, and it is expected that the signs triggering that sound will be looked at; also to be recognized from that moment on.

The studies of reading we have undertaken since 1957 (for a score of languages) have brought us to the realization that the recognition of vowels in words is a key to swift decoding. We therefore devote a good fraction of the program, at the beginning, to the practice of the vowels in all the words of the text. Starting with a (a single sound in Spanish) but with two spellings (a and ha) we can scan, from top to bottom and left to right, all these signs as they are made to appear in succession, leaving time for the viewer to utter the sound.

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Once the set of these signs as it belongs to the text is completed, the viewer has the choice to go over the same ground or to press the “next” button and see the previous scene integrated in the cell. Pressing “next” again will make the cell disappear and all the u’s (one sound, two spellings: u and hu) appear in turn exactly where they were on the cell and with their sound given. The “next” pressed will reproduce the cell but the “next” one will show both the a’s and the u’s as a second approximation. Students will take time to go over these two signs and say what they know. In particular they will see ua appear contiguous when they exist together in words of the cell. Whether they pronounce them correctly or not may require a special awareness of what happens to the mergence of u with other vowels in Spanish.

The “next” showing is of the cell integrating the above.

Similarly i (one sound, three spellings i, hi, y) appears on its own first, then in the cell, then integrated with a and u before all are integrated in the cell.

The last two vowels e (one sound, two spellings e and he) and o (one sound, two spellings o and ho) will have given five approximations of the text through vowels which make what seems, at the fifth approximation, to be half the text.

We have met only five sounds, eleven spellings, very few words (a, u, o, he, ha, y) a few diphthongs (ua, ahi, hay, two of which are also words) but we have acquired those aspects of the act of reading which are essential, such as scanning from the left, from top to bottom, combining sounds for contiguous signs, allowing for blanks, changing vowel sounds when their forms change — except those forms met in one color which represent permissible spellings. We are sure that vowels can be sounded on their own and that they are parts of words since they have so often been shown as integrated in the words of the cell. We also know that in words there are things other than vowels.

From now on, the successive approximations will include one consonant each. This will be added to the last integrated set of vowels

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which has been mastered and is used to reveal the words as they get completed by the addition of the consonants they contain in the cell.

The sound associated with each consonant is introduced through the syllables it forms with the previous vowels or diphthongs in the text.

Thus, more and more words are encountered, but more as a random distribution in the selected text than as a system. Hence, only if they are scrutinized and properly met will they be recognized in the text when the cell appears on the monitor without any sound accompanying it.

Since the viewers are the ones who direct the appearance of the “next” scene, they can take as much time as they wish to locate words they read and to scrutinize them among all those sets of signs that are not yet words.

As more and more consonants are introduced, fewer and fewer words remain to be completed, and instead of single words we discover phrases, sentences, clusters of phrases and even of sentences which make sense and provide meaning to the paragraph on the cell. It may be possible that incomplete words be read through guessing and then be confirmed when introduced explicitly.

Finally a scanning of the text will yield all it contains. The student is witness that very little was given to him or her and that he or she did all the rest.

With this confidence that one has mastered the act of reading, the “next” images are a succession of tests of mastery and transfer of the acquired skill.

First, phrases and sentences are extracted from the cell and presented one by one in isolation to ensure that they are known for themselves and not only recalled by rote.

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3 Infused Reading

Second, a new text is presented, made essentially with the phrases and sentences of the original, text and the student is asked to give a reading that can be recorded for examination.

Third, an entirely new text (of “the same level of difficulty�) is proposed on the screen to be scanned and sounded. The recorded tape will tell whether reading is now indeed infused.

Here stops the present proposal. Its extensions are obvious and may be pursued if the means is available.

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Book Reviews

1 Earl W. Stevick’s “Teaching Languages — A Way and Ways” (from Newbury House Publ. Inc. Rawley, Mass. 1980) I received a copy of this book as a compliment from the publishers.

They, no doubt, were instructed by the author to send it to me.

Although this book is, in part, about my work, and Stevick, in it, kindly suggests that he has been affected by my work, I felt the impulse to write this review myself, rather than ask a friend to undertake that task for this Newsletter.

Stevick is influential among language teachers not only because he is one of them, an articulate expositor of intricate matters, to a great measure an impartial examiner, a sensitive person moved by compassion, understanding and scholarship, but also because the English language, at his hands, becomes an instrument that pleases, guides, delights, touches, permeates the mind and creates a conspiracy of good will which keeps one going. Going, as a reader of this considerable piece of literature and as a teacher experiencing a new hope.

Stevick knows how to arrange a banquet for many many guests, so that all find nourishment commensurate to their appetites.

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Computers In Education

He knows, also, how not to press his views and opinions, without, for that, diminishing their chances of being adopted by a good number of his readers. A paragon of eclecticism, he sets the scene to show how a mergence of opposites is possible, to show where to find resemblances between that which can also be seen as irreconcilable. In that, he shows himself to have been affected by the thinking of those who prefer to conciliate, to be kind, not to rock the boat. He remains an individual when he says: “it sets only one way — only one man’s way of looking at the methods and techniques. No one else will see exactly in this way……” (page 297), but he writes to consolidate the communal feelings he cherishes, and which seem to correspond most closely to his deepest personal traits and inclinations.

The climate of the chapters, the style of writing, the presence of his affectivity, are functions of whether he reaches the real springs of what moves him consciously and unconsciously, and they give away his real preferences. Once again I was struck by the fact of how the individual in him supersedes his community self. Because this tension, created by Stevick himself, occupies so much of the background of his thinking and therefore of his writing, it will appear to his careful and attentive readers to affect the argument which seems only indirectly to be language teaching or learning.

Perhaps this view comes from my unique way of reading his book. Most readers will extract the information it contains and find that it is considerable and detailed. From where I am, the writer and his ways of handling the tasks he gave himself, seem to be justifications for a close reading of this compact book, which, on many occasions, succeeded in engaging me in an inner dialogue.

C.G.

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Book Reviews

2 “Issues And Initiatives In Learning Disabilities” (published by The Canadian Assoc. for Children with Learning Disabilities. Ottawa 1979.)

The editor Edward Polak and the Canadian Association for Learning Disabilities have done a useful and important job in publishing these papers read at a 1977 conference in Ottawa. Speaker after speaker, reviewing the field from some particular angle, has stressed that much remains to be done, although a great deal has been attempted since the term L.D. (Learning Disabled) was introduced not quite 20 years ago.

Reading the various chapters which rarely repeat subject matter, what comes most forcefully to the fore is the human concerns of specialists who, in their professional lives, spend so much time with the “learning disabled,” their parents, teachers and various advisors, medical, psychological and pedagogical. Not only do efforts at circumscribing the field not lead to a clear definition which can help education, doctors, and legislators, but the immensity of the group of individuals classified as L.D. defeats those same efforts. Each speaker in turn stressed the shortcomings of what is being attempted and the difficulty of finding a synthetic approach that will cause the various aspects to illumine each other.

Many worthwhile, close examinations of initiatives have placed these initiatives where they belong, indicating how much they contribute to the overall encounter of the challenge and how much they, justifiably or unjustifiably, claim. Aware of the vastness of the task confronting them, the speakers (who appear generous, cautious, informed, sensitive and active) have put in front of the serious reader enough material and enough criticism to keep him or her busy for a long time before deciding how to attempt to contribute to the field. Unless one is sure of maintaining the human component at the center of one’s thinking, the chances are that one’s contribution will be futile.

Some chapters, more than others, dwell upon that vital human component and indicate its supremacy and urgency among all other

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Computers In Education

components that the specialists who offer us their concerned and concerted experience have examined. Although it is clear that there is a technical side to many of the questions they raise in examining segments of the field where they are called (or have chosen) to work, they warn the reader that no single restricted suggestion can serve more than a small population and that, often, only temporarily.

The strongest impression I was left with is that a concentration on finding the synthetic view remains the primary task in that field, as it may be in others, too.

C.G.

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News Items

1

April was the month that brought us a little closer to the realization that Educational Solutions’ solutions are beginning to strike the imaginations of those people who seek practical answers to educational challenges.

Readers of the April issue of this Newsletter learned about our impact here and there from people living and working in Argentina, Australia, Britain, Canada, France, Japan, Spain and Switzerland. During a short trip to Europe that month, Dr. Gattegno discovered that there are educators and servants of education who are now assessing the impact the subordination of teaching to learning has in making a distinctive difference in the cost of education, first in poor countries and later in the newly impoverished countries which are saving money by taking it out of public education.

Time has ripened in an unexpected manner. What seemed to require perhaps fifty years to become acceptable to the conservative sectors of the population, which are teachers and their teachers, may now become part of the fabric of education by the year 2000.

While jobs in schools are becoming fewer and fewer because of budget cuts, the reduction of the numbers of students of compulsory school age, of larger classes, and of technological innovations, parents are becoming more demanding, more militant, and more vocal. They demand a better education for their children, and point at the teachers and administrators as not giving them the proper returns for their

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Computers In Education

financial investment in the public schools. To meet these pressures, some people are stating that there are educational solutions which have not yet been widely attempted, and advocate the abandonment of social strife between rival adult factions: parents and their elected boards on one side and teachers and their unions on the other.

What is news is that the work of our international team is being mentioned by name here and there and supported by voices to which people listen. We, at our headquarters, supplied the impetus in the fields of research and development. Others are willing to supply social support.

Educational Solutions may now consider itself also “Social Solutions.”

In our “Problems and Solutions” Newsletter Vol. # VIII of 1978, we discussed at length the temporal hierarchy formed by the existence first of a valid educational solution •

concerned with learning and teaching that generates its own technology

•

required so that it can become available, to be incorporated in the advancing social solution. For years, we felt it our duty to secure the first, without which there is no chance for the second to be contemplated. We can report today that because of the climate of crisis which exists in the world of today, the second stage of the solution is starting to occupy the minds of responsible community leaders.

In future Newsletters we shall share with our readers the implementation of such projects when and where they are on the way.

2 The math weekend in Paris (April) was highlighted on the last day, by two demonstration lessons. Two children, aged five and six, were invited to come in order to show the seminar how easily children of that age can learn subject matter considered difficult and therefore postponed — sometimes for years. An hour and a half later two older students (14 and 10) were involved in

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News Items

work that took both well beyond their level of performance at school and at home.

The younger ones were given an entry into numeration in the common base. The 5 year old child boasted knowledge of counting up to 30. The 6 year old said nothing but clearly matched that level. Still, when asked to count backward, the younger one could not do it at all, not even if she started from 10. The other child could, and soon the younger one managed it too. We extended that activity to 20 and then engaged the children in the game of counting alternately first from 1 to 20 and then backward. Only the 6 year old could do this. His numerals were written under the corresponding digits that had been written on the board on a top horizontal line from 1 to 9.

Thus the unwritten teens, which were those the 5 year old had to name, could not be seen and read, only evoked. Soon that was mastered and we could move on to the names of the “ty’s” of which 20 and 30 were known to the younger one. With the help of the older one the column 20, 30.… up to 100 was read by both as it was written on the left side of the board and underneath the empty space for 10. This too was written so that the board showed in red the digits 1 - 9 at the top and on the left, alternately in black and in red the “ty’s” leaving room for a few beyond 100 (which were later inserted as 110-120-130-140-150). The second line in black, only showed the odd “teen’s.”

With this instrument in front of them the two children could generate the names of the numerals at the intersection of the rows for the “ty’s” and the columns for the units. French is more complicated than English, but very soon both children had mastered the naming and the writing, when asked for it, of two digit numerals they had not seen.

Once this was ascertained, the lesson shifted to three digit numerals.

The older one named and wrote, in its proper place, 109, like that, indicating that that was not a problem for him. When the five year old was asked to name and write the numeral with coordinates 130 and 5, first she wrote 1305, but when shown what the boy did for 100 and 9, she placed the 5 on top of the 0. After practicing a few of the numerals on the double-entry table and soon after, the three numerals 53 and 42 31

Computers In Education

and 68 were written one after the other (the first and last written sideways, one on the right edge, the 5 below the 3, and the other on the left edge, the 6 above the 8, and on top, upside down and reversed 42).

The boy read 53 as 35 and was corrected by the girl who also read the other two and was confirmed by her classmate. He was asked to read 197, which he did spontaneously and quickly as if he had known it already, then 298, then 599. The girl could have repeated those sounds.

To avoid this: 197 was read by the child slowly as 100, then 90 then 7 (although in French it sounds like 100, 4x20 and 17). Because of this awareness both children learned to name a three digit numeral, including 90. Three such numerals were written in one row, the first three digits on the right, the next three digits to their left a small distance away and three more digits close by. Soon after the children had read these numerals the space between the one on the right and that next to it on its left was pointed at and, the word thousand announced (as mille). At once, the children read the six digit numeral.

When the third three digit numeral was followed by the sound million, which applied to the space between the last three digit numeral on the left and the others, the reading of 9 figure numerals was achieved.

Transfer to a second example was immediate.

Thus, in about one hour, this way of working made possible the handling of all the demands of the reading of numerals (in the common base) of up to nine digits. The writing was tested only on 3 digit numerals. The only things the teacher told were “mille” and “millions;” the rest was generated from what the children knew.

The older students had been witness to that lesson and accepted Dr. Gattegno’s way of working. Without telling but with time given to sort things out, squares of integers up to 20 were generated with those above 81 being evoked and not written. They were retained at once, the 10 year old girl explaining later how her retention had been eased by an observation in the behavior of the names of those squares. Square roots were introduced and exercises given in which products of fractions of square roots were used without further ado.

The mental work that was done then and there, for the first time (as was ascertained later), proved easy and enjoyable. The 30 members of

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News Items

the seminar (most of whom knew the French system of education from inside) said in their comments that such activities have given hope to those who feared that the damage done by the “modern math curriculum” (now scrapped) was irreparable. In France as elsewhere, youngsters’ math is more verbal and a sense of reality of numbers almost non-existent.

3 Within the renewed interest of so many at different levels in education, we sense that our having organically linked teaching to learning has had the effect we expected.

Of course, there is still need for much work to coordinate the good will at work in those various circles with the wider mass of educators who are scattered all over the world. Our role is to be awake to the possibilities which emerge and to provide the educators with what they need so that those possibilities become part of the fabric of education everywhere.

The French group which is active outside Paris is particularly promising because it pays in person and, unobtrusively, leads by example. All through the year they offer workshops, courses, and seminars in at least two cities: Lyon and Besançon, they publish a newsletter that goes to subscribers — found in a large area in the southeast and east of France — and books, which are transcripts of weekend or summer seminars. These books are particularly effective as a means of keeping up the spirit of the group that works, several hundred strong, in that region. Indeed, scores of them see in print how much they have participated in helping the conclusions reached at these seminars, concerned with difficult topics (such as time, intuition and affectivity) and educational challenges at all levels of schooling, to evolve. For more than five years, the group experimented with such a format for their publications, and they now feel it recommends itself as proper and valuable.

That group sensing its responsibility in the world at large, dares to take action in matters which are generally considered to be outside its professional field. Thus, two years ago, it opened the first video language school in France, and purchased mathematics films needed 33

Computers In Education

by colleagues in the secondary and college levels of schooling, in order to eliminate the excuse that if these films were needed the Authorities should make them available.

The Swiss group is more particularly active in the fields of reading and of languages in general. A member of this group, Colette Rohrbach, who has kept trying for 15 years to invite people to subordinate their teaching to the student’s learning, is now wholeheartedly behind providing help for French speaking teachers to have the materials for reading (La Lecture en Couleurs) which have proven valuable to her and her students since 1967. The new edition, revised and expanded, will be ready this fall, and is being tested in six classes this spring in a scattered area including Geneva, Besançon, and Lyon.

We are gathering more news from friends introduced to you in the previous Newsletter, whose activities in the social context are essential for the implementation of the solutions found in our research.

4 Dr. Gattegno’s April visit to England included a presentation of the Silent Way to the staff and graduate students of the EFL and ESL departments of the University of London, Institute of Education. Dr. Gattegno was there on the invitation of Professor Henry Widdowson who, unfortunately, could not attend the presentation because of a death in his family. His colleagues were gracious hosts to a speaker who, 34 years ago, was on the same faculty in a different capacity. Now, his work on language learning and teaching, rather than on mathematics and psychology, was the object of the lecture.

To avoid making the audience think only of what was already in their minds, the Silent Way was presented as a set of instruments created specifically to meet specific challenges to language teachers. The Sound-Color Fidel provides acquaintance with the components of the spoken language that are not related to meaning. The complete Fidel meets the demands of spelling. The pointer focuses on items on the charts, and through its movements, on the time sequences for sounds 34

or words. The set of rods creates controlled linguistic situations. The word charts provide the vocabulary which serves as the scaffolding for all the structures of English and the spellings and sounds associated with the words that form that vocabulary. The pictures and the associated worksheets work to expand vocabulary, which is taken further through three books of which “A Thousand Sentences� also serves to give a taste of how a culture may express itself through the English language.

The discussion that followed resembled what happens everywhere.

Those who were identified with their prejudices showed that they could not see the need for any investigation of new ways which did not confirm their views, and dismissed the techniques and materials as unnecessary or even harmful. But these were very few among a number of people who were curious to know more and to know it from the originator himself.

5 In London, as in Paris, the new mathematics films were considered in meetings with interested people who proved their desire to be involved by purchasing the series. For the first time in 40 years it is possible to state that the value of teaching geometry or trigonometry through films has at least reached a sufficiently wide audience to justify the heavy investments our new series of films demanded. There are now a dozen centers where the films are used or available for use, when a year ago there was only one, our own.

This is a topic on which it seems that we shall report progress at an accelerated rate, J.L. Nicolet’s intuition has been vindicated and his memory honored as it should be. Geometry is regaining ground it lost over the last 15 or 20 years and our films are helping its revival and enjoyment.

6 Our readers would like to know what users of our video tapes series share with us of their experience.

Computers NewsIn Items Education

Exxon International Company has eight petroleum tankers which are manned by Korean seamen. “We are using the Silent Way Video Series to help the Korean officers on these tankers improve their English skills. The training course is conducted over a two-week period. We have just (February ‘80) completed a two week course in February, and the next one will be held in two months.”

Mr. Leroy Willoughby, Dean of Faculty Bunka Gaukuen English Language School, Japan, “……we are finding the Silent Way Video Tapes a great help and may even set up some independent study programs with less teacher time and let the student progress more rapidly through the series. We are also teaching it to classes of about 60 students and have been having some good results.…”

From France we received a long report which we shall summarize in the September ‘80 Newsletter and from which we extract only these words. “The 16 persons who took the whole course to date (February ‘80) declared that they were satisfied that the results matched their expectations. . Only one person out of 35 did not find this way of working to her liking… Very quickly the viewer students generate ties with the students on the TV set and feel for them when they do not seem to perform to their satisfaction . . . As a student of the Silent Way of teaching languages I am constantly struck by the resourcefulness of the (invisible) teacher who manages to suggest exercises that meet the students’ needs and makes possible an efficient way of correcting themselves.”

7 We can now inform our readers that the Silent Way Video Co. is marketing the video tape series English the Silent Way (in NTSC) under three packagings — •

The original 3/4”U-matic series of 140 half hour tapes at U.S. $14,000.00;

•

A 1/2” version of 35 two-hour tapes at U.S. $8,500.00 either on VHS or Betamax;

•

A mini series for teacher education made of a selection of 10 tapes plus a one hour taped interview

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News Items

with Dr. Gattegno, in 3/4”U-matic at U.S. $1,500.00 and in 1/2” version at U. S. $1,000.00. (VHS or Betamax) Rental of the series at $1,000.00 per month is also available for inhouse crash programs when needed, and can be credited towards a later purchase of the series. (All shipping charges are in addition to the above prices stated.) Available in 3/4” only. *** This issue of the Newsletter completes Vol. IX. If you wish to continue receiving the issues — the next Volume X commences in September ‘80 to June ‘81, send your check to us immediately.

For the United States, Canada and Mexico send U.S. $8.00, all other countries U.S. $12. 50.

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About Caleb Gattegno Caleb Gattegno is the teacher every student dreams of; he doesn’t require his students to memorize anything, he doesn’t shout or at times even say a word, and his students learn at an accelerated rate because they are truly interested.

In a world where memorization, recitation, and standardized tests are still the norm, Gattegno was truly ahead of his time.

Born in Alexandria, Egypt in 1911, Gattegno was a scholar of many fields. He held a doctorate of mathematics, a doctorate of arts in psychology, a master of arts in education, and a bachelor of science in physics and chemistry. He held a scientific view of education, and believed illiteracy was a problem that could be solved. He questioned the role of time and algebra in the process of learning to read, and, most importantly, questioned the role of the teacher. The focus in all subjects, he insisted, should always be placed on learning, not on teaching. He called this principle the Subordination of Teaching to Learning.

Gattegno travelled around the world 10 times conducting seminars on his teaching methods, and had himself learned about 40 languages. He wrote more than 120 books during his career, and from 1971 until his death in 1988 he published the Educational Solutions newsletter five times a year. He was survived by his second wife Shakti Gattegno and his four children.

www.EducationalSolutions.com