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The Year Of The Child The Elementary School Years

Educational Solutions Worldwide Inc.

Caleb Gattegno

Newsletter

vol. VIII no. 4

April 1979


First published in 1979. Reprinted in 2009. Copyright Š 1979-2009 Educational Solutions Worldwide Inc. Author: Caleb Gattegno All rights reserved ISBN 978-0-87825-294-7 Educational Solutions Worldwide Inc. 2nd Floor 99 University Place, New York, N.Y. 10003-4555 www.EducationalSolutions.com


In a society where education is compulsory up to the age of 16, all children attend elementary school (on a more frequent basis) until the age of 12, since playing truant is harder then than later. Is there much we need to keep in mind about that age group that could ease their education both at home and at school? We think so, and this issue of our News-letter will provide some of the guidelines which serve us in our study of the self-education which characterizes this age. Let us note that this age has been examined for almost 80 years through extensive testing which, for a while, appeared to be the only way of reaching a correct picture, an objective picture, of that section of the population. Alas, after some time only one thing had become clear: that no one had any idea of what actually characterizes that age. Soon Piaget, whose methods of work had been considered not to be valid because of their slender statistical bases — gained the ear of more and more educational psychologists. Cognitive psychologists were trying to correct what seemed to them to be the main defect of previous workers in the field, who had neglected to take into account that which makes students more than mere receivers of knowledge. But they in turn neglected to take into account obvious attributes of students such as motivation, persistence, endurance and, above all, the true intellectual and affective components of every child either in or out of school. Today, in the great confusion reigning in the field, the light of consciousness and that of the person as a whole being may be welcomed by those who want to serve knowingly, rather than be in contact with abstractions. This issue is written in that spirit. A review of the book “Of Boys and Girls� is included, as well as one of its short chapters. The News Items contain various reports from different parts of the world.


Table of Contents

1 On Piaget ........................................................................... 1 2 The World Of Action ......................................................... 7 3 Some Thoughts On Absolutes ........................................... 11 4 Of Boys And Girls - Reviewed ...........................................17 5 Chapter 5 “Of Boys And Girls” — Filling The World With Dynamics .............................................................. 27 News Items ......................................................................... 33


1 On Piaget

For Piaget, the mind can be explored through a model I have called “algebraic” because it holds as essential what Bourbaki labeled “algebraic structures”* i.e., ones that are formed of operations. Piaget may suspect that there are other components to the mind, but in his writings he tries to reach an analysis of all the notions he has worked on in terms of operations. Having reached that understanding of the mind he gives paramount importance to the presence of a set of propositions which work together as they would in mathematics, or, in fact, in any discipline where algebra is explicitly present. For our readers to gain the meaning of algebra as it is found in Piaget’s studies of genetic epistemology, we need to say a few words. When you look at x + y you understand at once that what you are looking at is an addition, x and y have been written instead of figures so as to force your awareness that it is the addition and not the result that we are concerned with, x - y tells you it is a subtraction and (x + y) x (x - y) that three operations are considered at the same time, an addition multiplied by a subtraction, or operations upon operations. If you note that the terms x and y in one bracket have been kept in the second, it is possible to show that this string of operations can be replaced by                                                         *

In their presentation of mathematics as the outcome of the axiomatic method acting upon three kinds of structures.

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another equivalent one x2 -y2, read as a subtraction (or difference) of two products: x x x and y x y, written in short as x2 and y2 or squares. The recognition that algebra is precisely the set of propositions concerned with operations upon operations makes one understand 1) that there is a universe sui generis for that science and 2) as we shall see, that the model that has guided Piaget in his studies is essentially algebraic. But clearly the mind that has invented algebra and other things cannot be reduced to part of itself without losing the rest. There we find the main weakness of Piaget’s proposals and see the limitations his psychology has imposed upon a deeper study of the mind. Indeed, the empirical mind we want to know is what it is, and not what we want to make it into in order to accommodate our own limitations and only study what we are able to study. If it is true that mathematicians, in their introspection, have found that in certain mental activities of theirs they use operations mingled with other structures, we must acknowledge that mathematical structures are mental structures; but is the converse true? Are all mental structures mathematical? The answer today is a definite no. For example, mathematicians have not yet attempted to come to grips with the challenges proposed by languages: to provide a model for language is too complex a problem for the art or science of mathematics to take on in its present state. New inventions in mathematics are needed before it can come near these challenges, and none that we know of have been offered as yet. Is it strange, then, that Piaget has kept clear of the epistemological study of the advent of language? In his studies the advent of language is taken for granted when he considers children in the pre and post lingual stages. Had he looked into it, he would have found that his algebraic model is either too simple or otherwise inadequate to serve the explicitation of one of the most remarkable achievements of the human mind — perhaps even the epitome of what the human intellect can do in early childhood.

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1 On Piaget

Algebra is present in all mental activities, and these include those involved in perception and action as well as thought. Some of our bodily movements can be expressed in terms of an algebra; our eye movements, for example. Still, there is so much in the mind that an algebraic model cannot account for. To have access to it we need to be concerned with energy and its transmutation: energy that is part of the affective component and energy which is used in minute amounts in moving the eyes when perceiving visually, in triggering memories and in other mental activities. The problems that Piaget gave himself can be described as follows: the philosophers of science analyzing their contemporary science find in it concepts and notions, procedures and methods which are current and represent the background of their thinking. Enquiring how children manage to acquire these notions to the level of their users in the sciences, will indicate how little or how much of it they have done at such and such an age or stage. Hence it is possible to label such studies, “The child’s conception of . . . . . the world, space, time, number, causality, probability” and so on, as Piaget has done. Instead of studying what actually and explicitly mobilizes children for their own purposes, if we study the evolution of their mental constructs in so far as they relate to the culture around them, we shall only find what we seek and not what is real and true about children. In 1949 to ‘50, I translated into English Piaget’s book on “The Child’s Concept of Number” and found some of his proposals fascinating on an a priori basis. From 1953 on I developed a different understanding of that field, working with means Piaget had never used, nor even ever suspected might affect the child’s concept of number. The most important finding in that context was that if we knew how to reverse an accepted order of concept formation, and presented it to children, they would receive it with enthusiasm, absorbing it more easily than the previous order, at least in the field of number. Historically, algebra came much later than arithmetic, and everyone believed that in the curriculum also it should follow the study of 3


The Year Of The Child

number, as is obvious from the way elementary school courses are structured. When using the colored rods (which we have now named Algebricks) it became possible to show very young children (5 years old or even younger) what operations were, and to obtain evidence that they could operate on operations i.e. consciously do algebra. It then became clear that the need to follow the historical structure was only a prejudice on the part of adults, and even more so on that of scientists: that to mold curricula on historical development was not the wisest move. Indeed, in looking at the structuring of the mind which Piaget and other cognitive psychologists cherish as their main task, we could see that number implies algebraic structures (and some others which mathematicians know how to distinguish in terms of independent axioms) and that we can help children merge them so as to be as aware of numbers as a mathematician would be. Working systematically we can reach a coverage of the field of number which is as different as could be from the traditional one but which corresponds much more closely to the reality of our world. Although there are an infinite number of numbers, only a small proportion of them are known intimately. As we grow in their study and acquire new tools to reveal their properties, we manage to widen their set. These tools are technically much more sophisticated than the three general ones retained by Piaget in his description of the concept of number: cardinality, ordinality and the existence of a unit. Hence we propose that rather than look at the acquisition of number (as the merging of these three structures), we consider numbers (in the plural) and see the set of those we know expand according to properties we single out as our guide in their study. Thus it is easy to recognize that there are two kinds of integers according to their parity: the even and the odd. It is less easy, but not too difficult, to know that some are composite and others prime, according to whether the set of their partitions contains multiples of other, smaller, numbers or not. It also becomes clear that any child who has learned to speak can acquire numeration independently of the properties of the numbers 4


1 On Piaget

involved. That numeration does not require the postulation of a unit which, when iterated, produces the integers. To generate numbers (instead of number) we cart proceed through the construction of sets of equivalent partitions of lengths obtained successively by the iteration of a given unit. Each length becomes its set of partitions, and by scrutinizing these we learn to know numbers better. At the same time we understand why only a few numbers can really be know. The set of partitions grows exponentially. The study of numbers requires other lightings. For that the concept of number is of little use. What we are suggesting here is that our knowledge of what we do and think conditions our finding of what children do with themselves, and that we must therefore use other words than those which usually appear in the title of books like: “The Child’s Conception of.…” To reach such knowledge we need to know the whole of mankind. So, what we reach in our limited investigation is what we start with, always allowing for a recasting of our finding as soon as a new lighting emerges. What we can say for certain is that unless we start with what children (or for that matter all people) actually do with themselves, we shall only end up with our conceptions, which may be hollow. For example, young children do not use “conservation” as older ones would (so say Piaget and his followers) and this is seen as a lack in their mental equipment. Would it not be more sensible to ask: “Since young children are learning all the time and are guided by what they work on, are there not good reasons why they should not display what we expect of them and to which we may be attached?” or “Is it not possible that conservation is needed in some cases but is a hindrance in others?” Such questions would help us remain in contact with the challenges we give ourselves. Piaget has created his questions and has obtained some answers to them. He certainly has not found what children do with themselves:

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first because he looked at them from the outside; second, because he set out with a preconceived idea; third, because he believed his instruments were the right ones; fourth, and above all, because he was not able and/or willing to truly reach the actuality of the children’s spontaneous work. Had he chosen to be with the spontaneity of children, his enormous output could have been useful to educators everywhere. As it is, it does not really enlighten us, although it can hamper us because it misses the truth of childhood and the reality of children’s actual involvement. Children do not aim at constructing the pre-existing world of the grownups. What they do is to be concerned with their own world and to try to make sense of what comes their way with their own means. To study children’s learning seriously, we must develop other means than those prevalent today. We have come up with the proposal that awareness is an appropriate one, and our crop to date proves it. We do not belittle the people we study and do not distrust their performance. Children are the teachers of those who want to study them. Such a simple concept has taken a long time to become clear to some of us. Caleb Gattegno

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2 The World Of Action

Reference has been made in previous issues of this Newsletter, to the observable fact that every individual, at different stages in his or her life, selects certain aspects of his or her inner and outer milieu and gets very involved in exploring these, giving them priority over any other — although these other aspects may become of interest at another stage in life. It has been agreed for convenience to call “absolutes” these states which on average last for about five years, and to recognize four major successive ones, extending from birth to adulthood: the universe of perception, the world of action, the domain of affectivity and the field of intellectual activity. When I use this perspective to look back at the first, say, twenty years of my life, I find that phase two, the world of action — lasting roughly from the ages of 5 to 11 — somehow seems to be the one that has left me with the clearest sense of being able to say: “I did a good job.” True, I must also have done the job of integrating the universe of perception, otherwise I would not have been able to proceed into the world of action, but my recollection of it is much more diffuse and undefined. This may be because the world of action seems to give more precise and “graspable” feedback on what one is engaged in. My clearest memory of an event which I could label and date as my “passport” into the world of action is the day I first swam on my own. The moment it happened I was, of course, elated, but somehow not

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surprised at the way it felt; I knew I was equipped, and the time I had spent getting equipped had also allowed me to get to some extent acquainted with the new state I was entering and to anticipate some of the feelings it would create. The world of action has, for me, two main aspects. One is made up of the many skills one teaches oneself during that period; the other is the recognition that one is constantly active physically, and constantly looking for involvement in actions of different types. When two or more boys and girls get together, the question they always ask one another is not: “How are you today?” or “How do you feel?” but straight-away: “What shall we do?” As an example of the first aspect I could describe learning to dive as one special challenge one sets oneself after one knows how to swim. During what could be called the preliminary phase of this apprenticeship, I can remember how I would squat at the end of the jetty for what seemed like a very long time (maybe 15 minutes at a time), deeply involved in weighing up the many components of the contemplated action. Drawing heavily on the experience acquired in previous years when I had concentrated on perception, I would watch other people dive and ask myself questions directly related to the action such as: “How hard do they push with their feet against the jetty so that their body hits the water at the right angle? How much of an impulse do I have to give myself so that my arms and head make contact with the water at the right moment?” It was easy enough to visualize that if I did not give myself enough impulse with my feet and leg muscles I would land on my belly, possibly hurting myself; but what would happen if I pushed too hard and landed on my curled up spine? All these variables had to be pretested, so to say, not so much at the rational level but in terms of how to use muscle power. Then there were other elements involved, like judging the distance between where I was and the water, anticipating the feeling of being suspended in the air for a fraction of a second, and some slight sense of “a happy fear,” that could not afford to be very strong since I knew that at one point or another I was going to do it anyhow, just for the sake of action.

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2 The World Of Action

As soon as the first step is taken, the feedback is immediately accessible and is processed at once, so much so that the second dive will be utterly different from the first, at least from inside, even if not visibly different from the outside. From then on, I will proceed towards mastery, in a succession of stages which are precisely and clearly described by Gattegno when he looks at the acquisition of skills. It seems to me that each individual goes through the absolutes mentioned earlier with varying degrees of intensity. The more intensely one has lived through one of those phases, the more the experience gained from it (both in terms of awareness and of facility) will stay with one through life. Someone who, as a child, let himself or herself be totally immersed in the absolute of action is more likely to be able, as an adult, to face with ease the unexpected situations that require body skills, such as sliding one’s way through a crowd, carrying an open umbrella, or getting oneself through a revolving door after somebody else and just in time to use the remainder of the impulse, without having to do any pushing oneself and without being hit by the door. These examples may seem trivial, and indeed they are, but I know for myself that my daily life is full of small instances like these, which I can connect with a general feeling of intimate acquaintance with the way I move in space and with the way different parts of me (my limbs and body) relate to each other. This inner understanding I acquired during those years when action was a priority for me. However, going through something myself does not mean that one also acquires an understanding of it and the capacity to describe the inner workings of the self at different stages of one’s involvement. That is why it was so helpful to me to find, in a book like “Of Boys and Girls” — where so much of what is written becomes obvious as soon as it is expounded — a description of some of the ways in which I involved myself in action in previous years. The reality of this involvement is still with me, but the fact that somebody else can find the words to describe it makes one become aware of it in a different way.

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I have noticed that the children with whom I relate best are precisely those who fall within the span of the action years. Various types of action seem to be the easiest element for me to introduce into a given situation, and therefore the suggestions for activities or the spontaneous involvements of children that age make sense to me more readily. Conversely, the suggestions I may have to make or the attitudes I may take make sense to them and they take them as one more component of the situation they are working on. I would be inclined to think that this has to do with the different levels of intensity mentioned earlier. The more intensely one has experienced one stage or another, the better one is going to relate, later on, to people who, in their lives, are going through similar phases. Readers will see if there is anything in this proposition that holds true for themselves. Clermonde DominicĂŠ

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3 Some Thoughts On Absolutes

What struck me most in my reading of “Of Boys and Girls” (Gattegno, 1975) was the depth and breadth in which the following questions were investigated: “What are the singular properties which characterize the elementary school years? What must children learn at that age which help them make sense of their lives? What must they become aware of in order to occupy themselves meaningfully and in order to grow steadily?” The book had the power of taking me back to my elementary school years. With care, and in great detail, Gattegno discusses many of the activities we involve ourselves in: playing marbles, hopscotch, cards, tug of war, Softball, cars, shooting archery, jumping rope and many more. He also raises the questions of why children draw, watch cartoons, tease each other, and climb trees. These activities, and other topics such as virtuality, symbolism, finesse, balance, partnership, morality, are all integrated into a study of the elementary school years: “The age of stressing action as a way of knowing, knowing oneself, as well as the dynamic universe in which one finds oneself.” It was immediately clear to me that the activities studied in “Of Boys and Girls” were the ones which occupied me as an elementary schoolgirl. After finishing the book I commented to a colleague: “No wonder I have so few memories of my elementary school years — I was too busy living! But at the time I didn’t think I was educating myself; I only thought I was doing what was fun.”

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On reflection, these words revealed the precise description of a person in an absolute, which led me to ask myself how absolutes function in our growth. The memories of how I spent my elementary school days, in being activated, offered me some insights into an understanding of absolutes; my living today also assisted this investigation. Gattegno seemed to be saying that a stress on action as a way of knowing during the elementary school years, grows out of the fact that there is a great deal to learn about oneself as a system endowed with muscles and a skeleton. For example, one has to learn how to integrate complex physical behaviors with seeing, so that sight guides the instructions that one gives to voluntary muscles. In developing physical behaviors, one must also know how to take into account certain attributes of the outside world, such as gravity or mass. Thus, living in an absolute requires that consciousness be present, informing the self that one is, or is not, doing what is needed to grow in that aspect of life. However, one is not necessarily aware that one is educating oneself. Investigating a vital universe, whichever one it may be, is synonymous with living at a particular age. At any age, we are usually clear about what absorbs us, what calls for our attention, what we prefer to do with our time. But when we are in an absolute, we are in it; we don’t necessarily ask: “What am I going through? What is vital for me at this age?” In fact, we usually don’t ask these questions. I remember when I learned to water ski at the age of ten. When the opportunity presented itself, I knew that water skiing was something in which to become involved. There was no hesitation in me: I knew, from the inside, that I was equipped to do it. It didn’t happen at once: I fell forward, lost my balance, pulled back too far on the rope, and the skis rushed out from under me. But I was neither scared nor doubted that I would learn: I simply knew that I had to get “the feel” of what to do with myself. “Getting the feel” for what there was to do when skiing was my specific education. To describe what this meant in terms of muscles, bones, tensions, attention, energy, sight, balance, and the integration of all these and more, would require pages. In spite of these complexities, I 12


3 Some Thoughts On Absolutes

ended up knowing how to water ski, and the consequences of that learning are still with me; that is, they are integrated in my functioning and are available to be recalled at any moment. By 15, I had lost interest in water skiing, as well as in other similar activities. In understanding the role of absolutes in growth, then, one needs to know why we come out of them, as well as why we get into them. My learning to water ski seemed to involve a general education, as well as the specific ones. What I learned from it and from other involvements of the elementary school years was how to give myself to an activity, so that the dialogue between my soma and the dynamics of the activity informs me of what I needed to do in order to obtain a new knowledge of myself and to master new relationships with the environment. This way of relating to unknowns in the physical realm is still with me. Since I know it is available, I can give my time to new aspects of life. I recalled having the opportunity to learn to snow ski for the first time just a few years ago. As soon as I put on the skis, it was obvious that the only similarity between snow skiing and water skiing was the word “skiing.” I had to learn everything. Since I was able to give myself to it, in the same way I had at an earlier age, I learned quickly. After a few hours, I was able to come down an intermediate slope. Learning to snow ski at 25 and learning to water ski at 10, however, were qualitatively different. At 10, when the absolute was the universe of action, learning to ski was how I wanted to spend my time. At 25, learning to ski was an opportunity to study myself learning something new. Studying my learning was more important than mastering skiing. And after a short time, when I had had a glimpse of what learning this complex skill entailed, it was clear that other aspects of my life were more vital and consequently were where I preferred to spend my time. In pursuing my understanding of the role of absolutes in growth, I asked another question: “Do I know which absolutes I’m living at this time in my life?” i.e., “which are the aspects of life that I’m investigating with passion, absorption, and abandonment?” Some characteristics of absolutes became clearer. For example, while

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absolutes are associated with periods of life, they do not correspond strictly to a certain age. While many adolescents enter the absolute of the intellect as early as 16, this realm did not become an absolute for me until I was about 30. In addition, it seems that a person can be living more than one absolute at a given period of their life. I thought of the three year old daughter of a friend who is simultaneously immersed in perception as a way of knowing, and action as a way of knowing. In attempting to identify the absolutes in my life today, I discovered that since I am aware of awareness, this colors all that I do. I tried to understand, for example, my recent interest in jogging. Although the details were not clear, I knew that jogging today is essentially different from the running which used to be a way of life at 7, 8, 9 and 10. Jogging today and running 25 years ago both serve my involvement in knowing myself and in knowing the dynamic universe in which I live. For example, at 10, I’m sure that I investigated the following: “What is pacing? Which pace is correct for which circumstances? Which muscles are involved and how? How do slight changes in the environment — wind, type of surface, gradient — affect what I need to do with myself?” But at 10, I was absorbed in running. While awareness was at work, sorting out questions such as those above, I was not aware that my awareness was at work. Today, jogging is an occasion when I can be aware of awareness at work. Some of the questions I am asking are similar to those I asked at 10: “Which pace is right for me? Which muscles are being exercised which I did not know were required for running? What are the effects of warming up?” Other questions seem to come more from the absolutes of this period of my life: “How is it possible that I feel less tired after running? Why do a hat and gloves seem to help so much in keeping warm on cold days? Is exercise related to the maintenance of health? Where is the evidence?” The most absorbing element in all of this, however, is that I am aware of my awareness at work in the investigations.

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3 Some Thoughts On Absolutes

This initial investigation into the role of absolutes in growth leads me to yet another conclusion: that becoming aware that I am in an absolute changes the nature of the absolute. I know that I am in it, because the dominating interests of the self are broad enough and deep enough to be perceived. If I am aware of the absolute, however, I am also clear that the way I see the world is not the only way of viewing it. When one is aware of absolutes, one can notice also that others are living them. What engages others can become as accessible as what engages oneself. Becoming aware of absolutes also makes relativity a possibility in relationships. Katherine Mitchell

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4 Of Boys And Girls - Reviewed

I read “Of Boys and Girls” by Caleb Gattegno about four years ago. Recently, I read it again. I was on the last but two pages in my reading when a friend walked into the room who had read it too. During our brief conversation, one of my comments on the content of the book was: “Gattegno deals with everything in this book.” The remark expressed the feeling overwhelmingly aroused in me while reading this slim book (95 pages). The feeling had to do with the total approach to the complexity of life which the author manages to maintain while he studies the activities in which boys and girls aged 5 to 11 engage. Gattegno considers the activities of this age-group singularly significant, and essential to children’s learning experiences. In his own words: “I shall present the construction of the functioning self that results from the acts of living that mainly show themselves in children of this age. The complexity of life remains the field of his study as he views — and inspires his readers to view — boys and girls from the vantage point of the ‘self,’ which he describes as free energy consciously engaged in the process of objectifying itself in time. In the Preface, Gattegno states: “…the life of human beings (is a) continuous unfolding of a consciousness at work on pinpointed tasks as well as on a grand design.” It is apparent that while engaged in studying the spontaneous activities of elementary school age children, the author keeps in mind — and reminds the reader — that each age is a “psychological landscape” to be explored and understood for what it actually is, none better than another, only different, each equally significant, equally rich in its content. Each age or stage is lived as a process of individual 17


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evolution and is therefore significant for its own sake; yet at the same time, each is lived as evolving human consciousness and is therefore a part of the larger whole. In still another way the author makes apparent the unity of continuity in the life of each human being. While this book is concerned with a segment of life — the ages of 5 to 10 or 11 — the active inner dynamics which unify one’s whole life are kept in sight all along. In the chapter Interest and Lack of Interest Gattegno says: “Children’s interest is only a symptom of a deeper involvement. Inter-est (which means: to be inside, to be with) would be a more precise description of involvement. To find what holds children’s attention we need to find the springs of growth.” On the following page he goes on to say: “Children are moved to be interested in exactly the same way as adults. The difference lies in what will mobilize the self in each. For boys and girls of elementary school age, it is the universe of action. …” The book invites the reader to consider why it is vital for boys and girls to relate to the world through action. As one reads on, one begins to see children’s involvement in action as a way of knowing themselves as well as the world around them. Children adopt this way of knowing at this point in their lives because they receive the intimations to do so from the self within. It is the guidance from within that makes it vital for them not to postpone entering the universe of action. “Action seems to stress the outside world,” says Gattegno, “but in fact it cannot exist without the self and its inner workings. So we are concerned here with inner shifts, inner dynamics, movements of awareness.” One intuits from reading this book that each individual life, at different stages, is devoted to making an inner world through the workings of inner dynamics; — an inner world which “agrees with” the outer world because the reality of both keeps on being “real-ized” through the interplay, interaction, and dialogue which is constantly taking place between them. Gattegno has evolved a model which he uses as an instrument for understanding the complexity of living. The various components of the instrument are outlined in the Introduction as being: 18


4 Of Boys And Girls - Reviewed

that the self as energy knows itself during the process of knowing itself through the activity of its own dynamics; that the knowing takes place in time as time gets transformed into new structures, new functionings, by the process called “objectification;” that an integration process is observable which produces changed individuals but maintains the uniqueness and singularity of the person; that there exist temporal hierarchies in the process of growth, i.e., experiencing in time obeys a certain order; that “time” as a linear mental construct can be seen as past, present, and future; but in actual living a unity in time prevails as one’s past (composed of the existing structures and functionings) participates in the actualization of the present process of living which, in turn, is impregnated with elements that represent the future. The components of the instrument, listed above, exist and may be used concomitantly. An intuitive understanding of their active co-presence can enable one to comprehend the complexity of living. The following diagram is my attempt at portraying their co-existence: (see figure 1 on next page)

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Figure 1

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4 Of Boys And Girls - Reviewed

With this model as an instrument for study, Gattegno examines the activities which boys and girls get involved in, quite spontaneously, and which they drop as spontaneously when their purpose, related to their inner life, is over. Such activities include children’s games, drawing, fantasizing, daydreaming, group activities etc. Children, according to the author, engage in action to sharpen their perception of the world. Their sharpened perceptions, in turn, improve the quality of their action. As children act, they constantly look for the criteria which let perceptions guide actions. Their actions, as feedback, lead to selfcorrection. In the chapter on children’s drawings the author explores the question: “Why do children draw?” Evidence tells us that the majority of children engage in the activity of drawing for a period of time and then drop it. What inner movement is it that guides them to take up this particular activity and to give it up? The answer in the author’s words is: “if we go on spontaneously drawing for about four years between the ages of five and ten and suddenly give up the activity — unless we take it up as an expression of our whole self and become artists — are we not saying that drawing, like playing certain games, is a way of knowing? Of knowing what it is to see? It is a way of knowing which speaks of a double movement: how we are affected by what we know as reality, and, how reality is constructed in each one of us. In order to follow this epistemological career the child who works on reality in order to construct his reality — the one that will permit him to dream as well as to be at peace with his environment — draws as well as plays.” The author of this intense little book tells us that he has collected and studied children’s drawings over a number of years. He sees in them the evidence of children learning to find out how inner reality is constructed. Their concern with detail while drawing, say, a face, their focus on one detail or another of the features, their attempts at handling the fact that the surface on which they draw is flat while the reality perceived is not, indicate that “a child is undertaking particular studies and delving more deeply into the investigation he is entertaining.”

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Another phase of children’s drawings contains evidence of their investigation of moving objects, the feeling of motion, the moods and feelings of people. They take these up and work on constructing them. They express what they perceive by handling the medium of drawing in specific ways. In three sentences from the book the purpose of children’s drawings can be summed up as: “Drawings are spontaneous actions which make children practice holding a pencil so that it obeys commands from the self — drawing is a way of knowing sight as the instrument of the self rather than as an organ anatomically and physiologically endowed to see everything all at once— drawing is used by every child to provide himself with evidence that his consciousness is involved in seeing, and in seeing more analytically.” As I read the chapters on the games children play, I was struck by their significance for the self. The author dwells at length on how the gamelike experiences Lived during childhood endow the self in special ways. The experiences are over in time but what is left behind — in the form of special mental constructs and functionings — is integrated by the self and is available to the self all through life. Gattegno calls “games” those activities which are felt as challenging. “Would it be a game,” he asks, “if there were no successive broadening of the challenges, each proving that the previous one had been mastered and was available to be taken on to the next?” Games obviously are “disciplined activities that yield specific improvements of functionings” and one enjoys playing them in all seriousness and with due respect for the rules. Children are attracted at a certain phase by games which are mainly somatic in nature, that is, those which involve their somatic functionings. Specific games, described in the book, allow children to work on specific functionings of the soma to attain specific skills and to educate themselves as users of those skills. The mastery of these skills enriches the functioning self. But this is just one aspect of the education that is taking place. By being willing to enter new challenges and new games, children educate themselves to meet the unknown. By being ready to throw themselves into uncharted activities, children discover and live their sense of adventure. They learn to know themselves as adventurous beings. By being at peace with their clumsiness in the beginning while nonetheless remaining

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4 Of Boys And Girls - Reviewed

persistently interested in what they are doing, children strengthen their capacity to form criteria for improvement through practice. It is mainly through games calling for somatic involvement that children educate their integrative power, which in turn keeps them interested in making the games more and more difficult, and sustains their courage so that they can meet new challenges. Their contact with this integrative power gives children the sense that they can “do anything.” Childhood games provide opportunities for us to know ourselves as undaunted by obstacles and inspired by the unknown. By being involved in all kinds of games children learn the significance of mistakes. Since there is constant feedback from the self’s functionings to the self, games are opportunities for becoming aware of mistakes, working on them and correcting them. Children play with structured, as well as unstructured toys. These games they fill with their fantasy and imagination. Contact with these mental powers is significant, for it is fantasy and imagination which carry children to the virtual plane. Through their active power of imagination children become conscious of their ability to “make the impossible possible;” they come to know themselves as people who can alter the outside world by virtue of their active imagination. Relating to fairy tales is very much a part of this phase of childhood. Action on the plane of the virtual is another kind of action which makes symbolic living accessible to children. “For much of this period,” says Gattegno, “living is a kind of dreaming where the actual is modified by the presence of the flexible and extendable realm of the virtual. Living the dream is in no way living the unreal. On the contrary, it is the way the self finds to give full humanity to itself at this age.” Games are opportunities for children to become aware of the phenomenon of change. From within, they know themselves to be changing as they become more and more capable of doing different things. Their actions, coupled with their imagination, allow them to know at the same time that the world is changeable and that they are capable of bringing about change.

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The Year Of The Child

Children play on their own, with their toys and with other children. They play games which involve the element of luck and of chance. Children play with others and come to know what it is to be friends. They learn to know themselves as losers, winners, leaders, followers, competitors and contributors to a common cause. They learn what it is to be fair-minded and to be mean. They learn to reflect on their actions, to develop plans and to design strategies. In the course of playing, children educate themselves to accept with equity the consequences of actions, their own and those of their companions. They grow socially and in their moral sense. Action in games inspires children, directed as they are by the self and dedicated to knowing themselves through the process of objectivation of energy into action. But ‘‘. . . . . beyond the layers of objectifications of action there are other layers, invisible and transcendental now but known as immanent since they affect the consciousness. . . . . . . . . . . . ” “As boys and girls grow, many of their springs can be activated by new elements from the immanent, and some of their interests change as these elements descend into their lives. The stress shifts without destroying the past, and the involvements generate new appearances.” Thus the author takes us to the age called preadolescence, the last chapter of this book. The overall message that I see contained in “Of Boys and Girls” is twofold: 1) one must abandon the simplistic view of children if one really intends to understand what they are living, and 2) one can become a fair observer of children by learning to observe oneself impartially. This book does not offer any statistical evidence in support of the author’s findings. This could be considered a weakness by those who are inclined to look for evidence of a certain kind in order to be convinced of the validity of a statement. On the other hand, the absence of such evidence may encourage some readers (I happen to be one of them) to verify the author’s findings and insights by looking into what they themselves can observe both, of themselves and of the children around them. In such a case one would not need to agree or

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disagree with the author, but would further investigate what interests and inspires one. As I proceeded in my reading I kept expecting to come across some suggestions regarding educational activities for teachers to experiment with in their classrooms. Inwardly, children are prepared to accept new challenges belonging to the universe of action; but where school curricula are concerned there is a dearth of activities which facilitate self-education, I was under the impression that the author intended to include some of these in this book. At one point, for example, he says: “There is room in this for further education, as we shall see later, this time occasioned by the intervention of educators who can offer new opportunities which make sense at once.� At other points too there are indications which suggest that the author had a Part II in mind for this book. I hope it will soon be made available for the benefit of parents who are bringing up young children, and for that of the teachers who are entrusted with their education. Shakti Gattegno

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5 Chapter 5 “Of Boys And Girls” — Filling The World With Dynamics

When we allow ourselves to be touched by the reality of another being we find that all that pulsates in us is also present in the other. We can call this “knowing-through-love,’’ but even people who love each other may fall into the trap of only having schemas of each other. Knowledge of others as they actually are requires a discipline of which non-interference and total openness are the essence. In the past science could only be about generalities and therefore could not apply to knowing people in their reality, only as stereotyped abstractions. What we are trying to do in this book is to restore to boys and girls their right to be met in their acts of living, even if this can only be done in a very limited way because the literary genre used here is that of a scientist rather than a novelist. The boys and girls who people my mind are not only images, many of them nameless; they are myself as a boy surrounded by boys and girls of my own age brought to life by our acts of living, our gift to the moment and to the fulfillment of ourselves at that moment. What I see, in the many boys and girls in the many elementary schools where I worked is the passionate search for truth as it appears to them in their life, the dedication to knowing the world (both inner and outer) as far as they can grasp it with their present instruments. No different, in fact, from the way I see myself in my world (inner and outer).

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As a boy I was as complete as I am now many decades later. I had not accumulated the experiences of the following years but I had days as full as I now have, moments as challenging as today’s, though of another kind. In my sense of relativity I can think about my present condition and also back to that in which I found myself then. If I did not know relativity then, if I could not imagine what I would become, I could still be aware of what went on in my mind and what kind of a person I was. This insight into myself neither reduces my chances of knowing others nor makes my life a model for all boys and girls. In fact, I developed the tools for investigating the content of everyone’s childhood when I found — 1

the role of relativity in psychology understanding of its role in physics;

from

my

2 the meaning of evolution in psychology, being simply that we are all in time and that all phenomena are temporal; 3 the continuity of awareness, at work from conception but shifting its focus from building the vital structures in the self to their use under minimal supervision by the self; 4 that if we are all similar because we all are made of molecules, and of cells, and display common behaviors, we are nevertheless unique because our will generates out of the raw material of life a constellation of uses of our soma and psyche with a nil probability of duplication, even if we are someone’s twin; 5 that it is possible to reconstruct the true course of life for anyone if I made it for myself at every period of my life by determining the temporal hierarchies available to me. This is why I see the age of childhood as being devoted to making its world an inner dynamic entity agreeing with the outer world, visibly a function of time. I see the boy and girl as epistemologists knowing what there is to know and how to achieve that knowledge as legitimately as Locke or Hume or Kant, or anyone else among those who asked themselves: “What is there to know?” and embarked on finding a 28


5 Chapter 5 “Of Boys And Girls” — Filling The World With Dynamics

satisfactory answer. The keen minds of boys and girls seize the fact that the world is a world in constant change. They may have heard of the static models proposed by their elders, but since nobody asks for their opinions on these matters they pursue their quest unperturbed. There is day and night, changes in the weather, the beginning and the end of many involvements, be it to take a meal or a nap. They see themselves grow and become capable of doing what was not possible earlier. They mold mud, clay or dough between their fingers and see forms change, come to life and disappear. They witness the transformation of grain to flour and to bread, or of cloth to clothes, and so on. They break things and cannot put them together. From all this they know that the world is a place where things happen, where a few changes are reversible and many irreversible. They know that in some areas they are allowed to act and that nobody pays attention to what they do. In these areas they are as if they were in command and can compare their functionings in the outer world with those in their inner world and find some continuity, some similarity. They have studied how twigs break, how some pieces of wood resist any pressure from them; they have studied a number of materials and learned to know them by weight, density, cohesion or viscosity, even if not one of these words is known to them. They have little interest in anything which has to remain intact, although they teach themselves to respect it in order to stay out of trouble from people capable of interfering with their peace. Whenever they can alter the environment they do it with delight, so long as it does not represent hard or routine work. Everyone can count on their cooperation if the alteration can be done easily and quickly, but will be disappointed if they expect the volunteers to be around to do the same thing spontaneously again and again. This is because there are other things to do with one’s time, more exciting things, always different for the self aware of its functionings even if, from outside, the appearance is of repetition. Indeed, a learner knows whether mastery has been reached or if there is need for further practice, and a new trial is entered upon to produce greater familiarity with the task.

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What a child sees in a task is his involvement. Observers cannot reach the invisible. They have to assume it and look for evidence of its existence. Seeing a child watch cartoons on TV for five hours at a stretch may lead to a conclusion drawn from his passive presence that belies the conception of his active self. Ask him to watch documentaries or love stories for five hours and at once you will know that this special attention is for something sui generis belonging to the cartoons. Tell him that they are as uninteresting, stupid, empty and repetitive as they appear to so many grownups and he will protest, “I do not have to find them stupid because you do not like them. They are very interesting to me.� This contained activity in front of the TV set is, in fact, a proof of the capacity of children at this age to endow the slightest mention of action with the whole of themselves. It is this gift that animates their world. We can easily live at two levels at the same time, particularly if one is virtual and the other actual. Just as we know when we shut our eyes that we can evoke what we were seeing, and know the difference between the evoked image and the seen reality because of a difference in energy content, we know that we are engaged in receiving impacts from the outer world and processing them into mental actions. Only exceptionally do some people suffer the delusion of only being concerned with one world. Playing in a park or garden, riding a stick, jumping over a wide river which is actually a narrow path or a narrow stream, climbing a mountain while only lifting oneself onto small boulders or rocks, pursuing an entirely imaginary army in defeat — all this is ordinary currency for boys of seven or eight. It is also the way our ordinary world is made worthy of the greatest adventurer. When a few children come together they must accommodate to each other; the younger ones let the older ones lead. The words that are spoken, the orders that are given, may be filled with different meanings by all of them, but the surrender of the younger ones and the imagination of the older ones blend to provide each with what he can accept at this moment. The older children may place a younger one as a 30


5 Chapter 5 “Of Boys And Girls” — Filling The World With Dynamics

sentry to watch for enemies that may never materialize while they climb to their fortress to prepare for battle, standing on a rock looking down on their obedient sentry and the surrounding fields. The thrill of belonging to an army that has a captain fills the soldier with pride and he holds himself erect and alert so as to be worthy of his election. There is nothing in the world that cannot be transformed, and if Don Quixote were a child there would be nothing strange in his changing sheep into soldiers and windmills into fortresses. Indeed, what Cervantes attributed to his hero knight is attributable to boys, without the delusion. The process is exactly the same: an attribute of the actual suffices to generate all the virtual attributes compatible with it. Children provide themselves in this way with a dynamic universe holding in its content futures that are indeed pregnant with invisible possibilities. Are not the visionaries in our societies operating in a similar manner, extending the appearances of reality to include what they see to be compatible with them? Is it not much easier to endow a horse with wings and let him gallop over the clouds than to solve all the problems which lead to aviation? Or to take refuge in a whale and explore the deep sea in one’s mind than to produce the submarine? The sense of adventure would not be found in adults if the capacity of the minds of children to reduce obstacles through the virtual did not exist universally. The long familiarity with the virtual at this age of childhood leaves its marks on everyone, including pusillanimous and cowardly adults who can only dream acts of courage. The readiness to attempt to open doors that others have found cannot be opened owes its existence to this sense — “I can do anything” — which is only true in the virtual. Although the movement of the mind is only in one direction, making the impossible possible, the exploration of the universe of action teaches the limitations of action and leads to a realistic attitude which nevertheless remains tinted with daring, with hope, and with incentive, that tries to break through the perceived boundaries. We gave ourselves to this education as boys and girls; we end up with a universe susceptible to change that we hope will meet our desires because we continue to see it as a universe that involves us

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and the workings of our minds. The boy or girl in each of us has given us a dynamic and expanding universe in which to live as spiritual beings. ***

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News Items

1 In March a group of eight Korean officers and petty officers from Exxon’s tanker fleet worked intensely for six days, more than six hours a day on learning English the Silent Way, using the video tape series described in Vol. VI. # 4-5. The course was organized by the Training Department of Exxon Int. Corp. as a way of testing the series for use by crews on tankers on the high seas. The participants were selected either because they were complete beginners or because they needed to gain greater facility in English in order to interpret messages received from headquarters when at sea, or to send messages to headquarters, from any location, which could not be codified as routine communications and therefore be taken care of in a ready-made coded translation bank. Most of the studying was undertaken by simply going through the tapes one after the other, and immediately afterwards testing how much of the material covered had been retained and could be applied to new situations. The students had been told, in Korean, to say what the students on the tapes were saying, and a few injunctions in Korean were left hanging on the walls to convey to them that they were advised to relax, not to worry if they missed something, not to give up, to ask for help when in need, to stop the video player if necessary, to repeat a lesson or go over a segment if they felt they did not find it easy, to work together since they were together. They were also told that they would

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learn English well if they did what was asked of them. On the walls there were Silent Way charts: the sound/color Fidel and Word Chart #12. Through a comparison between a Korean color/sound chart made for the occasion — and the English equivalent, it took the participants very little time to realize that most of the sounds present in Korean were also part of English, and they were quickly able to form strings of sounds that were words for English speaking people. With this preparation, tape # 1 was shown in which statements are also made at a very early stage and can be heard and repeated by the viewers. This established the rules of the game which were to be applied through the viewing of the series. The tapes on numeration came next and were studied in two hours. This included a test which took two forms: 1) students were asked to write their own numbers down in figures and then read them, submitting to their classmates for approval or alternative suggestions.; 2) a number was uttered and the class was asked to write it in digital form, which they generally did correctly even when six or more figures were needed. The tapes on the sound/color Fidel were not used in view of the original lessons, so tape #16 was shown next. In that half-hour all the English for asking and telling time was covered, and the test which followed showed that it was available to the students. In tapes 17 to 60 — which took up five of the six days — a great deal of English is put into circulation, while much time is given to practice and sorting things out. On two occasions the students asked for a repeat; otherwise one viewing, followed by a testing session, seemed to be sufficient for them to acquire the language content of each tape. The group was representative in that it contained a wide spectrum of abilities, backgrounds and maritime functions. The participants had been invited to take the course by their employers for ends which were well understood by the company, but which were known only to one or two of the higher ranking officers present. Despite this, the progress registered in that short time by every one of the students can only be described as good to spectacular. They were aware that their tongues had loosened, that their organs of phonation were less tight, and that

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News Items

everything they had done made sense to them. Involved not only in repeating what they heard, but also in making sense of how the sounds they heard and uttered connected to the situations shown on the screen, they took the initiative during breaks of proposing similar situations to each other, setting these up themselves with the set of rods which had been made available to them. The students’ own assessment of the course was that it had been most helpful to them. The observers who were there on behalf of Exxon International Corp., were of the same opinion. What we can tell our readers after the first experiment in teaching with the tapes (which included the presence of one of us as a continuous observer and monitor) is that the purpose for which they were created has been fulfilled: viewers can learn English (both spoken and written) by simply viewing the tapes and doing what is recommended with their content. A sensitive monitor may be helpful but the quality of the tapes, and the formula of only showing learners learning, do most of the work and achieve what no teacher can hope to. The viewers were relaxed and concentrated. Whether they repeated aloud or in petto what they heard, they were affected by the work done by the students on the screen, and always found enough time to sort things out in the way the students they were looking at did. Often they were faster to reach the proper conclusions and to extend a statement as far as its structures permitted. They enjoyed joining a relaxed class of students, who laughed occasionally and worked in a concentrated manner in long stretches through the half-hour lessons. At the final feedback session the class was unanimous in saying that the six intense days had gone very fast and that what they were able to do at the end of them with English was something they would never have thought could have happened. Sensitive to their learning, they became sensitive to the teaching and could assess it as being advantageous to them and of a high standard, although their jobs were so different from teaching: one was a 35


The Year Of The Child

pumpman, one a steward, cook, one an electrician, others second and third mates. With this clear proof of the teaching power of these tapes we can now embark on informing a wider public of it. Mr. Joseph Locetta of Exxon International Corp. of Florham Park, N. J., who was responsible for this experiment, has expressed his willingness to share his observations on the tapes and on the learning that took place over the six days of the experiment with any interested party. Note: Visitors to our premises who come to look at our ESL video series have found that, in addition to their main purpose which is to ease language learning in viewers, the tapes can serve well in teacher education also. 2

Boston TESOL Conference

During a week of study groups and plenary sessions, a complex gathering of more than 3,000 people from all over the world saw, among other things, that the Silent Way has been recognized as a solid contribution to the teaching of English to speakers of other languages. The words “Silent Way” no longer sounded strange and mysterious to most people. On the contrary they drew very positive responses and were associated essentially with beneficial results. One demonstration of the results of the Silent Way occurred during the conference when Dr. Gattegno conducted a six-hour workshop in Arabic. The purpose of the demonstration was to show that through the Silent Way, a supposedly “hard” language like Arabic can become easily accessible to anyone willing to give themselves to the study. Four native Arabs among the observers expressed amazement and delight at seeing their language being taught so efficiently and apparently being learned so effortlessly. Another native Arab teacher said that the students in the demonstration class had managed to learn in six hours

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News Items

what students in her classes worked at for three months. These teachers were determined to investigate the Silent Way more deeply. A rap session one evening brought together a mixture of newcomers as well as beginning and seasoned Silent Way teachers. In this gathering many misconceptions about the Silent Way were expressed, even by the users. Dr. Gattegno, who had been invited to add his authority to that of the two conveners, only came in after much airing had already taken place. His comments helped to remove doubts and to put things into a proper perspective. It was obvious that in the three years since the 1976 New York TESOL Conference, attitudes had changed: no one was treating the Silent Way as a passing fad. On the contrary, it had a place in many of the addresses as if the public were now more aware of what it has brought of value to the field of language learning and teaching. The TESOL Conferences can be characterized by their fragmented format. So many little points considered in the hundreds of meetings seem so important to those engaged in them but also contribute to their losing sight of the overall challenge. In fact, no meeting seemed to have been arranged to give an impulse to the thousands of people looking forward to being uplifted and inspired. Scholarly reviews of the field bring the university back to people who are already well acquainted with it but who already know that it is not the locus of the greatest inspiration. Will anyone veer the conference towards a function that can truly affect the lives of people? It needs it. 3

QACLD

At the Quebec Association for Children with Learning Disabilities annual conference in Montreal, March 21-23, Dr. Gattegno was given the opportunity of inviting educators to look at their problems in a new light. Readers of this Newsletter will more than once have seen the statement that only awareness is educable in man and that selfeducation is the only true education. To most of the public present at the second M. Sara Rabinovitch memorial lecture however, it sounded very new. The bilingual keynote lecture of the conference, delivered 37


The Year Of The Child

alternately in French and in English (each being spoken for a few minutes at a time), seems to have brought new light to many hundreds of conventioners who struggle day after day, with challenges which they find both substantial and demanding. The title of the lecture: “Where do we go to get new light?” in itself gave an indication that what was to be offered to the audience was a new way of looking at the relationship between student and teacher. Our proposal was that what the student had already achieved in any of his or her learnings is to be counted in his or her favor, and used skillfully by a helpful teacher. Because these students’ performance baffles parents and teachers, they generally end up being isolated, and often abandoned, by those whose job it is to provide them with the necessary assistance. Now here was someone who knew how to take advantage, through a pedagogical technology, of as much of the already successfully completed learning as was necessary to allow students to make sense of the school tasks imposed on them by the school curriculum and its proponents. The audience was asked: “Has anybody thought what could make sense to someone who has no idea of what a field of study can be? for example, that of spelling, that of grammar, that of geometry? Could anyone to whom only one item is shown correctly guess what its place and significance was in a whole he or she does not perceive?” It seemed that such questions made sense to the audience, and instead of creating doubts, stimulated people to seek how to acquire and master such attitudes in order to implement the subordination of teaching to learning — which also made immediate sense. For the three days of the conference, the climate created by the content of the address continued to be felt by a good number of participants, who again and again referred to its impact on them. The following day, at the workshop on Absolute Visual Reading, those of the audience who had attended the first lecture understood more easily why the film they were being shown had been made as it had. The education of a deaf person’s awareness in order that he or she may 38


News Items

conceive of language for what it is, without having heard words in the environment, seemed to illustrate the lecture, and this in turn shed light on the common sense in learning to read through visual means alone. At the Montreal Oral School for the Deaf, the following morning, this way of meeting students’ problems was presented to a group of teachers and student-teachers who were specialists in the teaching of deaf children. The presentation went smoothly and was very effective. This may sound strange since the word “oral” contrasts so clearly with “visual,” but it is understandable in the context of the enormous effort both teachers and students are prepared to make when the enterprise is the mastery of reading. In the afternoon of Friday a panel which included two neurologists, a professor of reading and Dr. Gattegno was asked to define dyslexia and briefly to explain how to handle it. Although the neurologists were prompt in giving elaborate definitions involving the functioning of the brain, the other two were either unwilling to do so or unconcerned with definition, although they were able to make contributions on the subject of diagnosis and remediation. Generally speaking, this was a conference whose qualities can permit it to be rated as excellent. It moved smoothly, it had the support of all layers of society, from the Provincial Government to some anxious parents and a few students. Experts in a number of relevant areas in the field made their contributions quietly and effectively. The numerous volunteers, dedicated beyond the call of duty, made the more than 3, 000 participants welcome, and put them in contact with whomever they felt the need to meet. Serious and light was the tone of this whole conference which gave such valuable opportunities to so many to come out of the enclosed atmosphere of the workrooms where fresh air is mainly what is needed. That so many people were ready to entertain the suggestion that without the instrument of awareness little can be done to meet the enormous challenges of the school work and schooling which have 39


The Year Of The Child

generated the term “learning disability,� was the most encouraging sign that the choice of theme of the address had been a happy one. As a result of this conference we can certainly say that at least a theoretical stress on awareness has to be immediately recognizable as profitable, and that this recognition is capable of moving people towards adopting such an approach, hence towards the source of one of the lights in education. 4 We have a new Animated Geometry film. The seventh of the new computer-made series. Its content is Epicycloids and Hypocycloids: curves generated by a point in the circumference of a circle rolling on that of another (fixed) one, respectively externally and internally. The result is a lovely visual experience which can start people on the road to becoming deeply touched by mathematics and perhaps to adopting mathematics as a career. The film explores one dimension of the field: what happens to the locus of points generated by the rolling of the moving circle, and illustrates this by taking one point and tracing its destiny. A whole family of curves is generated whose study provides the substance for subsequent classroom discussions. There is a great deal to do after seeing the various segments and, as usual, this is the pedagogical value of the film. According to the level of competence of the students various difficulties perceptible in the loci can be tackled: 1) numbers of arcs, 2) cusps, 3) equation of the locus, 4) length of the arcs, 5) curvature, 6) areas enclosed, 7) simultaneous generations and mutual intersections, and so on. This film could be considered the last of those recasting the original series which J. L. Nicolet bequeathed the world of mathematics educators. We now have a collection which has preserved all the wonderful qualities of the original series: simplicity of treatment, aesthetic handling, profundity of the subject matter and accessibility to

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News Items

everyone on earth. But it is technically more up-to-date, and therefore more worthy of being distributed and placed where it belongs in schools, since no one will be able to complain that it is blemished. All those involved in making it a beautiful, marketable product are proud to have collaborated on it. 5 Last month our colleague Cecilia Bartoli went to Paris and Rome for a series of workshops. In Paris, Cecilia was invited by the Faculty of Law to work with the language teachers there, who have the difficult task of preparing students for a very complex exam in English Law or Economics in a course of 15 to 30 hrs. By the end of the seminar many teachers had realized that our way of working could make them more effective. Many saw that if they stopped trying to cover the content of the exam, virtually an impossible challenge, and started working on their students’ awarenesses, taking into account where they are, they would elicit their students’ collaboration and in turn make them more responsible for the work that needs to be done. In Rome, two seminars were given at the Foreign Language Faculty of the University for about 45 teachers. These included elementary, high school and university instructors. Most of the participants were candidates for the position of teachers of Italian in a program designed to teach this language to about 400 pre-university students from Somalia. These students take language instruction for four months and in this time need to know it well enough to be able to take university courses in Italian. The Somali University in fact, for the time being, uses Italian as the language of instruction. The first seminar was designed to give the participants an introduction to the “Silent Way.” The second was intended only for those interested enough in the Silent Way to wish to implement it in their classes. More than 30 people showed up for the second seminar, and many others

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regretted not being able to come back. About half the participants came from out of town and had to ask for special leave from their schools. The response on the whole was very positive. Some participants saw immediately that the “subordination of teaching to learning” could be applied to other fields of instruction. These two workshops may lead to a more comprehensive collaboration between the Comitato Tecnico (the Italian advisory body to the University of Somalia for language teaching) and Educational Solutions. There is a possibility that they may wish to start a pilot project in which 4 to 6 Italian classes for the Somali students will be taught entirely in the Silent Way, at least for the first 100 hrs. of instruction. 6

Using the tapes - A note from our French friends

In Lyon, a few of us (both old and new members of the group) have started a course with the Hebrew tapes. I cannot find words to describe the enthusiasm and the joy with which we all participate. I have seldom had a chance to be part of a group as integrated. It is the first time that we find ourselves learning a foreign language without a teacher being physically present in the room. And I can say halfway through the course, that this absence has certainly not been felt as a lack, so far, and that the learners have shown that they are capable of getting themselves out of trouble even in delicate situations — for instance when confusion occurs at the level of sounds or at the level of meaning.

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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

The Year Of The Child - The Elementary School Years  
The Year Of The Child - The Elementary School Years  

Newsletter vol. VIII no. 4 April 1979

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