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A New Braille And Other Topics

Educational Solutions Worldwide Inc.

Caleb Gattegno

Newsletter

vol. X no. 1

September 1980


First published in 1980. Reprinted in 2009. Copyright Š 1980-2009 Educational Solutions Worldwide Inc. Author: Caleb Gattegno All rights reserved ISBN 978-0-87825-305-0 Educational Solutions Worldwide Inc. 2nd Floor 99 University Place, New York, N.Y. 10003-4555 www.EducationalSolutions.com


We begin Volume X of this Newsletter with an article on a Reformed Braille. The proposal it contains has been worked out in the case of one language, French, although it applies to any language, including nonalphabetic ones like Chinese. The second article reports on a seminar on energy held in France last July. The third is the first report from a monitor in charge of the first video Silent Way language school in France. Four writers contribute articles forming extended News Items. One is about a practicum held in New York City during July for ESL Silent Way teachers and three report on mathematics education conferences held in Berkeley and in Quebec City. Also included is a short News Item on the progress of our Math Mini Test Project and a Book Review on “Chinese Medicine� written by Dr. John H.F. Shen.


Table of Contents

1 Teaching Reading And Writing To The Blind: A Reformed Braille .......................................................... 1 An NSF Award ....................................................................................8 2 Seminar On “Energy And Energies” .................................. 9 3 Notes On The Use Of The English Video Series In France. .......................................................................15 Book Review ....................................................................... 23 News Items ......................................................................... 25 1 International Congress on Mathematical Education ................... 25 2 More Comments On The ICME Conference ................................28 3 Among Mathematics And Math Education Professors At Laval University .....................................................................30 4 The Practicum — For Improving Language Teaching................. 32 5 The Math Mini Tests .................................................................... 36 6 Introduction Of The Silent Way In The Netherlands .................. 37


1 Teaching Reading And Writing To The Blind: A Reformed Braille

This article proposes to transfer to the teaching of the blind, ideas that have been operative for the sighted. Although Louis Braille had to wait a long time for his proposal to be accepted by teachers of the blind, his contribution is universally accepted now. Hence we may expect that our suggestion of a new way based on principles differing from those now in circulation, will be received coolly and find that its fair consideration will be slow to come. Nevertheless, it will become obvious that our proposal is guided by the learning which is required of the blind by their condition and the tasks involved in reading and writing. Since this proposal was developed in France and was discussed with French educators, one of whom was born blind and had experience teaching the blind, the examples worked out here are in French. This does not make the principles less obvious for those who do not know that language. The complexity of French, on the contrary, guarantees that the transfer of this proposal to most other languages will be an easy operation. It seems right to reserve to this Newsletter the first mention of a solution to a specific educational problem which may be considered significant even if its beneficiaries form only a small proportion of the 1


A New Braille And Other Topics

populations speaking and writing the numerous languages of the world. *** Braille’s proposal — as it is used today — is “written” with configurations of dots in relief representing the letters of the alphabet of a given language. By scanning the lines with one’s finger (usually the index), one finds the words of one’s language to which specific dot configurations have been given instead of a visible sequence of signs; blanks are left between words. In this way dots reproduce what sighted people see in their written language when the script is used. Braille attempted only to provide a way of doing with one’s finger what sighted people ordinarily do with their eyes. Sighted people are as capable as blind people to read with their finger if they learn the one to one correspondences of the written words and the dotted reliefs. But “writing” is another matter. For the blind, it is still putting down on paper the words of the spoken language observing the traditional spelling and grammar. The only difference is that instead of forming letters, configurations of dots are produced by punching. The sheet of paper rests upon a metal sheet containing a regular set of dots which leave their track in relief on the paper when punched. The “writer” knows which configuration of dots has been selected to represent which letter of the alphabet and punches these dots out of a set of six dots as in this rectangle

The operation of “writing” must be done from right to left since the finger reading is from left to right. Hence the blind must have two images for each letter and each word and use one for writing and one for reading. Such demands are never made of sighted people. And we call the blind handicapped. 2


1 Teaching Reading And Writing To The Blind: A Reformed Braille

*** The reformed Braille we propose must keep the inevitable principles that result from using dot configurations in relief to be felt with one’s fingers. But instead of representing letters by dots we use those to represent sounds. The same sounds in various languages can retain their dot configuration and only the sounds that belong to a language and not another will have to be learned. This may be another advantage of our proposal upon the traditional alphabetic Braille. Direct access to the written language as a phonetic system is given to the students to decode and encode without the bother of an historic fact unrelated to the problem we are working on. Still if it is required — and made a condition for the adoption of our proposal — we have in reserve a second proposal to take care of spelling. At this stage of our proposal it seems an unaffordable luxury which must be postponed. *** Our code. Let us look at an enlarged rectangle in which 9 dots are enclosed.

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A New Braille And Other Topics

They are clearly distinguishable since no two dots fall in the same place is different from

for the sighted as well as the blind. Hence we have 9 representations available for nine sounds and most languages do not require more than that number to be selected for their set of vowels. French requires 17 and English 23. Therefore we cannot meet that need with only one dot for each vowel and we must for the French vowels make some signs with two or more dots. Here is our systematic choice of the possible signs. We selected 7 two-dot signs, and added a three-dot one because the last two are double sounds and we want to make our students aware that these can be made with two merged vowels.

then the rest are as follows:

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1 Teaching Reading And Writing To The Blind: A Reformed Braille

For French we still need gn (n/y) x (k/s) and x (g/z) to which we give the combined signs as follows:

*** Methodology. With such a choice available, we can now think of methodology: in order to make sure that all blind people will learn to read with ease and, when this is done, to help them to write. With one consonant and the 17 vowels we would be able to form twosound words (or syllables), using as many of the vowels as produce words that are part of French.

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A New Braille And Other Topics

leaving out only three of the vowel signs. We can practice these in small groups until they are mastered and use them in sentences such as “mimi ment” or “mimi me ment” or “mais mimi ment,” “mimi M’a ému” or “mimi a émis mes mots” or “mon mot est mou” “ma main mime” “mon ami mumu” “mes moues.” We can add “maman” and make sentences like “mimi ment à ma maman” or “un mot, un mais” “même,” m’aime,” “homme, “ are also possible at this level. ”maman est émue:”

This enormous set is not always needed to reach mastery of one consonant; but since we can thus practice the vowels and practice the act of reading, it certainly recommends itself. Clearly, with a smaller number of vowels we can provide a surer way of getting retention. Teachers will make the selections that suit them and their students best. With a second consonant: n, we can form n’a, nu, ni, ne (neu), noeud, nous, nez, nait, (no), nos, n’en, nom, nain, une, noix. With this consonant alone “ni nu ni nain,” “ne nait” “nos noms” “nos noix n’ ont ni un noeud ni un nez” “nos nez n’en ont” “une naine et un nain” “un ananas,” can be made. With both consonants the choice is much wider: “mane,” “mine,” “mène,” “n’aime,” “anime,” “amène,” “m’amène,” “nomme,” “nîmes,” “emmena,” and “un homme emmena maman à nîmes,” “mimi anima 6


1 Teaching Reading And Writing To The Blind: A Reformed Braille

nos nains et nos naines” “mimi emmena nos nains à une mine” “un moine aime moins animer en un mois un ananas.” Likewise, we introduce after that one consonant at a time, form words of one or more syllables as per example with r, alone, rat, rue, rit, roue, re, ret, rot, or, rare, rire, and “mur, mer, mere, mort, rein, rien, marin, murmure, romarin, romain, riant, rient, rhum, rame, mare, rime, rhume” with two consonants, and “nord, ruine, ranime, ramene, etc.” with three. This allows us to offer sentences such as: “rome est au nord,” “mimi ramèna mon romarin au romain,” “maman a un rhume,” “anne murmura,” “mare et art riment,” ‘‘mort en mer,” “rémus a remis une rame à marie” and so on with all the consonants. These examples show how it will be progressively possible for blind students to be able to read any combinations of the 37 signs we have devised to trigger all the sounds of French i.e. all the words of the French language and hence all possible statements in that language. When we take age and experience into account, and select statements that are utterances that the students can understand, we have reached the optimal point for reading with comprehension. Beyond this, the use of reading for instruction through language will follow in all fields of human endeavor in the way it is done for the sighted. As to writing, we can consider, that since blind people will never write with Braille except for themselves and for other blind people, we do not have to be concerned with spelling for a while. This will become a need if a typewriter is introduced and the blind are invited to widen the range of people they wish to reach in writing by achieving what is expected of sighted people. The usual way of teaching writing in Braille clearly must be adapted to our 37 sign system. Now that the written language systematically reflects the spoken language the practice of feeling each sign as its

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A New Braille And Other Topics

mirror image moving from right to left, can be begun at a stage when the students indicate readiness to act on the dynamic tactile images we presented to them instead of visual ones we present sighted people. We could for instance, teach writing with the puncher by dictating one vowel at a time, get the sign made, turn the page and let the student notice whether what he now has under his fingers is what he thought he punched, giving him criteria for reversing the design needed for reading to produce the one required for writing. Step by step, by writing a number of the sentences above, the skill will become second nature. The meaning of calligraphy here would be: correct evocation of the dot configuration and correct pressure on the puncher so that relief and not a hole appears. Here we leave out numerals and punctuation although they are part of traditional Braille. © Caleb Gattegno, 1980

An NSF Award On September 11th, we received a letter starting with the following words “The National Science Foundation hereby awards a grant of $52, 000 to Educational Solutions, Inc. for support of the project described in the proposal referenced above. This project, under your direction is entitled: “Microcomputer Courseware to Develop Insights into Arithmetic using Perceivable Algorithms.”

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2 Seminar On “Energy And Energies”

The long seminar on “Energy and Energies” in France, last July, lasted from the 11th to the 21st, seven hours of work a day. It involved 50 participants who were mostly French but included Americans, Italians, Swiss, a Brazilian, a Canadian and a German. The place for the seminar was a three or four hundred year old French chateau in the country away from even small villages and requiring cars to go shopping for anything. There were 30 vegetarians among the 46 who took their meals regularly in the dining room, the rest camped out 4 miles away. The people conscious of their food provided a session on the energy transactions that feeding represents, when the time came for it in the study of energy and its forms. The study of energy was woven session after session, and led gradually to a vision of its presence everywhere and in everything. *** Starting with cosmic energy changing itself into atoms in the cosmic laboratories that the stars are, it became clear that since all the studies of the sky are run from earth by earthians, conscious of their experiences on earth, our view of the content of our universe is what physicists, chemists, astronomers, cosmologists find it is and tell us about. With their help we can conclude that cosmic energy, when changing itself into matter, has selected to tie nuclear particles with the

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A New Braille And Other Topics

strong force to produce more and more complex atoms. After a certain stage these particles could not manage to hold together and produced atoms that decayed spontaneously, yielding some of the existing atoms that were stable, as well as radiation whose energy could be evaluated. Radioactive elements and the fact that atoms of higher atomic number than 92 — although they can be produced in earthian laboratories but only last for a very short time — do not exist, allow us to speak of the first impasse of energy. Cosmic energy found one way of working in producing all the matter of the universe but found that that way cannot be continued indefinitely to produce an endless set of different atoms. A second way of working of cosmic energy is in the formation of molecules using electric charges associated with the particles in the nuclei. This weak force that links the atoms, produces stable and also less stable molecules. Even the stable ones can be broken into their constituent parts using electric currents or temperatures which are not too high as compared to those on stars. Molecules generally contain from two to a few atoms except when Carbon or Silicon are among them. Then, molecules can contain many atoms sometimes thousands — as is the case in DNA. Large molecules although microscopic, are systems whose structures can be determined by physical means. Complexity then becomes a notion about which we can speak with precision. We can say that cosmic energy tried another way of working using the products of its first way (the atoms) to explore what can be done with lesser amounts of itself. In particular, all possible crystals or arrangements of atoms that form the minerals we find on earth, have been produced, showing us what a thorough job cosmic energy can do. But in the field of carbon compounds the process of complexation can go that far and no more. The largest molecules are not stable, as soon as they are made they break down. An impasse has again been reached and cosmic energy does not know how to go on producing new molecules as far as we can see. As soon as one is attempted it breaks down into two existing molecules; though some of those pieces at once attempt again to find a way of becoming larger they find out that they cannot do it. Growth and breakdown follow each other at once. Such a process looks very much like reproduction but it is better described as we just said.

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2 Seminar On “Energy And Energies”

On earth, where we do all our studies, the largest molecules that can be made, utilize bricks that may themselves be large molecules (or some that are not so large) and use some molecules or atoms to expedite the chemical reactions concerned. These are called catalysts and have been studied thoroughly. Their presence between atoms or molecules make possible in the circumstances, what could not happen, without them. As the earth cooled down and more and more molecules were formed using energies that were found on earth; gravity, sun radiation, radiation from radio active decays, cosmic radiation, heat from exothermic reactions, it was possible for a combination of a large number of molecules to come together in a small space and remain together. Such masses of matter exerting attraction upon each other would also develop a surface tension that helped keep that matter together. A new complexity was born of cosmic energy and its forms, in which the contents of “molecular cells” kept as they were, could go on becoming new chemical laboratories in which what was happening was new and, not only of one description, since the original molecules that came together did not need to be the same. At that stage, proximity and the processing of the environmental energy will offer opportunities for new kinds of constellations of molecules to present themselves. The microscopic entities will allow energy within the cell to try to organize in space the large molecules in forms that may be stable architecturally while developing dynamics resembling the growth and breakdown borrowed from the molecular realm. In the small “molecular cell” there is enough energy and enough chemical experience to lead to stabilization of processes so that the presence of certain catalysts would facilitate the formation of the same molecules whose electric and magnetic properties end up providing “directional” dynamics within the cell. On earth our studies of the living have changed with the progress of the technology of the microscope. We find in the smallest living units — which are cells that can live by processing molecules and energy taken from the environment — capabilities that will obtain as we move from one cell to aggregates of cells as big as sequoias and elephants. These capabilities are the new ways of working of cosmic energy within a

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A New Braille And Other Topics

form of energy we call vital which represents a radically new trial at creating a realm. How the molecular cell becomes a vital cell is not yet clear, but once it does become one it is possible to give vital energy the means of producing on earth two realms: the vegetable and the animal. The vegetable is the trial of all the forms that the sets of molecules which are in the cells can produce with each other, not only chemically but geometrically. The vegetable kingdom attempts with more variety but also more risks, what happened in the mineral field where all the forms possible have been achieved. Looking at the set of bacteria will show us the many forms taken by the vegetables made of one cell. We can see that if the content of the cells is made of molecules (large molecules with many carbon atoms) what makes the cells must be another entity than the structure of the molecules within. Hence our proposal that the vegetable kingdom represents the domain of this cosmic energy concerned with architectural form. As soon as forms are viable and capable of making many copies of themselves by the same processes, a new trial is undertaken taking further that kind of working of energy. Only when too many of these entities have to process the molecules needed for their constitution do we come across the Darwinian concepts of struggle for survival and natural selection. It happens again that an impasse of form is reached when the stability of the edifices that the plants are, cannot be maintained in the cosmic conditions of the earth. They cannot grow indefinitely above the ground and underground, they can only expand in search of substance and of the mechanical equilibrium between the part exposed to the atmospheric conditions with that which is in the soil. The animal kingdom is the domain of another form of energy which from the protozoa to the dinosaurs will show its way of working: letting instinct give itself the form most adequate for its expression. The working of vital energy in animals can borrow from the plants how to make the forms adapted to the various spectra of behaviors and their compatible combinations. The energy of any instinct needs only to be as large as is required by a “user” of the vital and cosmic energies that go to make the form taken by that instinct. We can call it the “quantum” representing each individual in a species. Representing a species, an instinct is the energy which is needed to objectify the set of behaviors characteristic of the species and related to specific somas and utilizing energies found in the environment. The domain of the 12


2 Seminar On “Energy And Energies”

animal kingdom is obtained by the capacity of the individual guanta to adapt to the varying circumstances and conditions in the environment and the subsequent discovery that that quantum can generate behaviors which do not quite belong to the species. The way of working of animal energy consists in developing a new instinct out of an existing one by the individual finding that it is not bound 100% by the species behaviors. The vital part of the instinct can affect the molecules in the cells and in particular those in the DNA and give a new animal the chance to explore a new set of behaviors as far as the available energy permits. Not all new forms are viable, particularly because animals do not go to the cosmos to find all their energy, they use organisms to provide them their supply and in so doing become dependent on the content of the vegetable and animal kingdoms, which is finite. The evolution of the animal kingdom represents the successful trials of animal energy to objectify itself in instincts that can not only command the vital and cosmic energies to give itself forms but to find the extent of variation compatible with every form and set of behaviors. Hence its apex will be reached when some individuals will recognize that their quantum does not need to identify with the form it gave itself. This means that the characteristics of will, awareness, intelligence etc. which belong to the animal’s instinct — are also independent of it. Man comes into being when a quantum acknowledges this freedom as its essential attribute. Man can be seen as possessing a new form of energy — which we can call spiritual — that in its working can integrate behaviors, forms, molecules and atoms, to produce species of a single individual forcing variation rather than heredity to become his characteristic. Hence, by definition, man has no instinct, but his spiritual energy will begin its work on the forms which are virtual rather than objectified, generating the history of mankind. In fact from the huge amounts of energy needed to produce the atoms to the minute amounts needed for example, to hypothesize on anything the evolution of energy is seen by an on Earth as leading to a human planet on which awareness of all the forms of energy or all the energies, leads to a new beginning. Thus much more is possible because we have known that very small amounts of energy working at the local level can

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A New Braille And Other Topics

use selectively and discriminately, the large amounts found in the cosmos to achieve ends that can be beneficial to mankind. The era of the “nothings� is upon us in the perspective of energy and energies. *** During that seminar the proposal on the Reformed Braille emerged and a two-hour session was used to teach all the sighted people to use it and to get feedback from a blind educator present (cf. article # 1 of this Newsletter).

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3 Notes On The Use Of The English Video Series In France

It has been almost 2 years since we began an English course in Lyon using The Silent Way video cassettes. Even though there have not been a large number of participants, it can certainly be said that there has been variety in: •

the age of the students: from 10-57 years,

the number of students per course: from 1 to 8,

the frequency and duration of courses: 3 times a week, l

or 2 hours,

2 times a week, 2 or 3 hours, 1 day every 2 weeks, 6 to 7 hours, 1 weekend a month, 12 to 14 hours, 4 days in a row, 8 hours a day, 8 days in a row, 6 hours a day.

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A New Braille And Other Topics

Up to now, (March ‘80) 16 people have taken the whole course and expressed their satisfaction. Some have only watched a portion of the course, but hope to continue. To our knowledge, only one person was disappointed with the approach and he dropped out halfway through without giving any explanation. It should be noted that the number of participants in a class affects their rate of learning: if there is only one person watching, the session is much less lively and the possibilities of expressing oneself during the supplementary exercises are obviously limited since there is no one to talk to or about. And, of course, the questions are less varied since in a class, each student experiences different problems. Although it is true that a student watching alone feels less stimulated than he would in a group, there is nothing keeping him from establishing his own rhythm or from spending as much time as he needs to work through each of his difficulties. In a class with others, the same student might not have classmates who would put up with his pace, whether too fast or too slow. It seems to me that the most productive courses are those which have regular and frequent sessions. As far as the one day or weekend courses go, progress is quickly noticed: the ears and voices get a good workout which leads to a better pronunciation, to a smooth flow of speech and to a more accurate melody. Only 2 of our students, up to now, were actual beginners in English, the others, being “faux debutants,” had mainly to struggle with their formerly acquired pronunciation, with their lack of attention to the colors, with the desire to translate. These “faux débutants’’ do seem on the other hand, to know how to involve themselves in the things that are new to them, that is, they approach the work on individual sounds and on the melody, the progression of structures presented… and when they offer help to the “vrai débutants” our work with them is very rewarding.

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3 Notes On The Use Of The English Video Series In France

As far as the cassettes go, we have observed that, although each one runs 30 minutes, our perception of the length of any particular one depends on its content and on who happens to be present at its showing. The student viewers have a tendency to want to move on right away when they think they “have it.� If a student in the video class is spending time on elements which the viewers think they have, they get impatient and therefore miss the opportunity to practice to themselves in order to improve their pronunciation and assure retention. However, when we give our students challenges as demanding as those given by the video teacher, they realize that they have not actually mastered the things that they were quick to be over with. Our students begin right away to identify with the video students and even choose one as a model with whom they empathize. As Dr. Gattegno himself said during a Silent Way seminar which he conducted in Lyon on November 8th & 9th, 1979, each half hour lesson is like a magnifying glass which allows us to see all the details of one element to be learned. One situation (several rods of several different colors, set up in a certain way, for example) is studied: from different points of view; the situation can be described in a static way or in a dynamic way, in time and according to the person who is describing it. What each person is required to say changes, according to his or her placement relative to the rods and to members of the class whom they address. In its various aspects; the rods can be considered as one set or made up of several subsets. Once an introductory sentence has been pointed out and one student utters it correctly, no more elements are introduced before each student has a chance to describe the situation from his point of view, modifying the original utterance when necessary.

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A New Braille And Other Topics

If a student simply repeats what one of his classmates has said, the teacher points either to the word which must be dropped or to the one that should replace the inappropriate one. Where an utterance is correct as far as structure and choice of words go, the teacher might demand that the student work on achieving: •

a more accurate pronunciation of particular sounds which he indicates by pointing to the triggers of the sounds in question on the Fidel or Word Charts,

a more fluid utterance which he indicates by waving the pointer or by grouping his fingers,

a more English melody which he represents by drawing a curve in space with the pointer, putting in the accents with a downward movement.

Thus each student works at his own level. The teaching is individualized. Every situation becomes an exhaustive study of the new elements to be integrated with the already acquired language. The learners prove that they have assimilated the new elements by trying them out in increasingly complex sentences. New concepts are presented at just the right moment. They are introduced without explanation or prefacing. The teacher makes sure, however, by giving as many exercises as are required (without proposing repetitious drills) that the new concept is understood, accepted and that, little by little, it becomes a part of the learner’s linguistic baggage. Thus, “step by step and point by point, they become independent, autonomous and responsible.” If the teacher hears, when a student speaks, that he has misunderstood a recently introduced concept which is being further studied, he has the student work on that point. This individualized work gives the other students the chance either to realize that they too had misunderstood or to feel more at home with it by allowing them time to make up their own sentences. 18


3 Notes On The Use Of The English Video Series In France

Let us mention the exercises in which the words in color on the charts are read in groups according to: meaning, pronunciation and spelling. Hence systematically proposed on two occasions: 1

before their meanings have been studied — through specific situations,

2 after they have been used — in order to give a different type of practice on pronunciation and comprehension these words are assimilated. By alternating these reading exercises, hidden-word games, writing exercises (visual dictation), oral sentences that described a situation, with questions that demand a response, with commands, the teacher ensures that the lessons are never predictable or boring. The video students seem to be always active and learning even when they aren’t speaking. We see a real class emerging on the screen: when one of the students hesitates, the others whisper to him; when someone makes mistakes the others make fun; the ones who are having difficulty with something are helped out by those who have already mastered it. Dan, for example, shows Barbara that she has left something out in writing a number on her paper. Odile works with Dan on how to pronounce “the” by showing him where to put the end of his tongue. Batuman, whose frequent mistakes lead to plenty of laughs and multiple pronunciation exercises, helps Carlos who mixes up the final sounds in “wish” and “which,” by referring him to “she.” The fact that at the beginning these people have no common language of communication is not even noticeable. The class is calm and very alert. And this concentration persists even during the most difficult exercises which may require a long time to understand and then say correctly what is appropriate. Each student finds something to work on, be it meaning, pronunciation, rhythm or melody. Sometimes, it is possible to see confusion or frustration in the faces of the students, but there is never the look of indifference.

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A New Braille And Other Topics

They are always involved. Why? Personal motivation, the attraction and mystery of the teaching tools and their use, the intensive climate of work, all play a part in the deep involvement of the students. Sometimes, and I don’t know why, an error is ignored and passed over. But in those cases, I do know what needs to be done to correct it when a viewer picks up on it either by making the same error or by drawing attention to the fact that it is an error. As I carefully watch the unfolding of each lesson, I have learned to: •

introduce new elements separately and unambiguously,

welcome errors and work with them,

vary the exercises,

give each student the jobs that their capabilities allow them, without underestimating them,

allow for “wasting time” on working with one student because it is obvious that all can benefit,

not presume that only amount of time should be spent on any particular structure: to work with the students from where they are, giving them confidence in themselves and welcoming their initiatives — work with individuals and with the whole group.

My work as a monitor consists of trying to make the supplementary exercises yield as much as possible. Of course the manual and exercise book have been very helpful in giving the content of each cassette and in suggesting preparatory and follow-up activities. Finally, in trying to answer the question, “What is the function of the monitor?” I would say that it seems to me more important to discover how to work effectively with the students than it is to know English. It also seems to me that in a group of students, if there is one who “catches on” right away and who, thus, has the time to observe what the teacher on the screen is doing, he or she can certainly become a guide during the supplementary classroom exercises.

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3 Notes On The Use Of The English Video Series In France

Adapted from the French original of Anne Marie Clair by Sarah Benesch.

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Book Review

“Chinese Medicine� by Dr. John H. F. Shen We were lucky to be selected by Dr. Shen as the publishers of his first book about a field he has dwelled in for forty-five years. Essentially it is a text attempting to educate both medical professionals and the lay public outside China about Chinese medical thought. This thought stretches over five thousand years and includes the work of hundreds of generations of critics, investigators, and innovators. Eminently readable, the book avoids jargon that would obscure the subject. It helps readers understand the main notions and the empirical basis of the Chinese quest for health and what makes health break down. The central role of energy is made evident as well as the need for restoring its balance, boosting its depressions, and displacing its accumulations towards needy regions. Dr. Shen, is a teacher of medicine who challenges the western mind, and proves himself very competent at that. His sensitivity, needed so much in his diagnoses, has helped him discuss subtle matters and select what is required by readers in order to understand new perspectives on old preoccupations. Those who have struggled for years with the literature on Chinese medicine will appreciate most how the author has gone directly to the key notions that generate light. Written by a practitioner who has an extraordinary capacity to retain individual states and to recall unrecorded diagnoses months after they were made, it is a very practical book. It provides in a detailed and

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A New Braille And Other Topics

enjoyable way, the methods needed to practice Chinese medicine. Part one is a compendium that catches the essential and the necessary. Part two, concerning thirty-six case studies, gives readers a chance to meet patients of all sorts and kinds and to follow the reasoning behind the treatment suggested by this very humane doctor who always uses the common arsenal of Chinese medical tradition. Chinese Medicine is a book that can be read several times without generating a sense of dĂŠjĂ vu; it is a profound study of a very important field and a needed companion for those who want to understand better the mysteries of life and the impacts of different civilizations on the same set of human preoccupations. This text will have a special place in the collection of books valued by its readers. Once again, we are very happy to be the organization that published Chinese Medicine in 1980. (See letter enclosed about purchase of this book.)

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News Items

1 International Congress on Mathematical Education Educational Solutions has taken part in the recent International Congress on Mathematical Education (ICME) in Berkeley, California — through our films and through the participation of two staff members, Arthur Powell and Steve Shuller. One of our new Animated Geometry films, Epi and Hypocycloids, was selected as exemplary by the ICME Films Committee and shown in a session attended by about 250 congress participants from all over the world. During four days of the congress, several of our films were available on request for viewing at the ICMR Drop-in Film Library. Included were the other six films in the Animated Geometry series, the five Folklore of Mathematics segments on Trigonometry, and the new computeranimated Foundations of Geometry film. Many congress participants availed themselves of the opportunity to view these films. Among those who watched Foundations of Geometry were Georges and Frédérique Papy and Jean Dieudonné. The afternoon following the large film session at which Epi and Hypocycloids was shown, Steve Shuller conducted an informal workshop on this film. The participants worked as students and observers of the 25


A New Braille And Other Topics

teaching-learning process for about two and a half hours. All who attended found the session stimulating and expressed their appreciation of the film as a powerful tool for the teaching of geometry. Steve Shuller also presented a poster-session paper, “Developing insight into Mathematics with Microcomputers: An Alternative to Drill” based on a proposal from Educational Solutions recently funded by the National Science Foundation (see ref. page 6). The approach we advocate appears timely, as more and more mathematics educators share Seymour Papert’s ICME plenary address concerning that rotelearning uses of computers are rapidly closing off possibilities for this new technology to provide a genuine breakthrough in learning. Dr. Gattegno’s impact on mathematical education was evident in several of the ICME sessions. Professor A. J. (Sandy) Dawson of Simon Fraser University, Burnaby, B.C., discussed “the implications of the work of Lakatos and Gattegno for focusing mathematical learning on student hypothesizing and refuting strategies.” To illustrate Dr. Gattegno’s insight into the use of the students’ imagery in teaching mathematics, Professor Dawson engaged the hundred or so members of the audience in evoking the imagery of a point in uniform circular motion, leading to a visual definition of the sine and cosine functions (see Newsletter IX, Issue 3, page 4, for the words he used to trigger the imagery). Speakers at sessions on Mathematization and on Alternative Approaches to Beginning the Teaching of Calculus also made reference to Dr. Gattegno’s work. At the former, Professor David Wheeler cited this work explicitly, and its influence on the development of mathematization as a teaching approach could be seen in other presentations as well. The planners of the conference assigned to the mathematization session a rather small auditorium, which was filled to overflowing. The large turnout, both in absolute numbers and in comparison with what the conference planners predicted, was one of several indications that the climate in mathematics education is changing towards one more receptive towards our work. 26


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As the first speaker at the Calculus session, Georges Papy, Professor at the Free University of Brussels, prefaced his remarks with the acknowledgment that his proposals are based on the “pedagogy of Gattegno.” He then spoke about the importance in teaching of generating insight into the relationships crucial for the particular chapter of mathematics under consideration before formalizing definitions. He ended his talk with the observation that definitions are the truly creative moments in mathematics, a notion central to Dr. Gattegno’s work. One of four project presentations by Great Britain’s Open University was subtitled, “The awareness of awareness in problem solving,” Although the subtitle was in part an attempt to appeal to those at the Mathematization session in the interest of enlarging John Mason’s audience, his presentation was clearly in the spirit of Dr. Gattegno’s work. Mason is exploring the fundamental role of energy in education; in particular, he is studying the place of affectivity in working on mathematical problem solving. In the session, Mason shared some techniques for mobilizing the students’ affectivity and helping them become more aware of the role of their own affectivity in their learning. Another project presentation from Great Britain contained applications to television of aspects of Dr. Gattegno’s number array, the use of finger games to teach complementarity, and complements and transformations as the basis of an approach to addition and subtraction. Leapfrog, which appears weekly on British television, is shown in many classrooms and has been well received by children and teachers alike. The informal interactions of Arthur Powell and Steve Shuller with other congress participants let us know that mathematics educators throughout the world are acquainted with Dr. Gattegno’s work, and are interested in knowing more about current developments. Moreover, there seems to be a growing conviction in the mathematics education community that the influence of behaviorism in teaching and research must be curbed. Many are beginning to see that we must learn how to 27


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study learning directly and to subordinate our teaching to the learning of our students. As mathematics educators are increasingly prepared to change, a new openness is emerging, creating a climate in which new ideas and those which have not received a fair hearing until now, have a chance to make an impact on mathematical education throughout the world. As a result, Educational Solutions faces a new challenge — that of responding to those who are prepared to work with us in ways that will improve mathematical education dramatically. The next few years will tell how successful we can be. S.S.

2 More Comments On The ICME Conference Overall the ICME Conference in Berkeley, California was a bit disappointing. There were too many sessions per hour and per day. The schedule of the conference, from the time it began until it ended, was chuck full of activities, presentations, lectures, etc. Thus, there was little time left for meeting new individuals, discussing with a presenter questions which arose during her/ his talk, or to make a significant contribution in any session one attended. In short, these are the disadvantages of a non-working conference, such as the type that the Canadian Mathematics Education Study Group organizes and in which I took part in June at Laval University in Quebec City. There were, however, a number of benefits that I gained as a result of my participation in ICME. For attending as many sessions as I did I became exposed to the range of investigations, and projects presently active in the field of mathematics education. Given the international character of the Congress, though predominately Western, I was also acquainted with problems of pedagogy, methodological research, utilization of advanced technology and the lack of access to it. For me, this was quite valuable, since almost my entire exposure to and study of the pedagogy of mathematics has been the work of Dr. Gattegno and my own mathematics educational experience.

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In regard to this last point, the Congress gave me a more profound appreciation of the work of Dr. Gattegno in the field of mathematics education. For example, after listening to Dr. Hermina Sinclair’s lecture on young children’s acquisition of language and understanding of mathematics and problems which arise in this context, I left the auditorium feeling that her conclusions were trivial. So, I got together with Marty Hoffman and Sandy Dawson to discuss with them the content of the talk. I was feeling that perhaps I was not quite attentive or that her talk was outside my area of understanding. As Sandy explained, however, I realized that the questions which Dr. Sinclair had considered and presented were questions which Dr. Gattegno had entertained decades ago. It became apparent to me that many of the questions which Dr. Gattegno has considered are only now being taken up by the general mathematics education community. For example, Hans Freudenthal challenged the Congress participants to begin to work towards the education of intuition and spatial awareness of geometry students. Seymour Papert of MIT spoke against the use of micro-computers in the classroom for drill and practice and placing bad teaching on the color TV screen. Georges Papy of the Universite Libre de Bruxelles prefaced his lecture on alternative approaches to beginning the teaching of calculus by stating that what he has done is “based on the pedagogy of Dr. Caleb Gattegno.” And in another session I attended, besides D. Wheeler, J. Trivett and A. Dawson’s on Mathematization, the concept of “awareness of awareness” was discussed in connection with children’s play on the micro-computer. As a result of this experience at ICME, I have become aware of areas of research which I am stimulated to pursue and the need for those of us who are closest to the work of Dr. Gattegno to operate in the social field. For this task I am now sure—though I was not before—is not the area in which we can be most effective as opposed to Dr. Gattegno himself. Additionally, I made contact with members of a recently formed African organization, The African Mathematics Union. Within this structure there is a committee of individuals concerned with mathematics pedagogy. At a meeting of theirs during the conference, I made a brief presentation on the highlights of the subordination of

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teaching to learning. Some, in particular Dr. George Eshiwani of Kenya, were aware of Dr. Gattegno’s work and had been including aspects of it in their teacher training courses. A. P.

3 Among Mathematics And Math Education Professors At Laval University As an addendum to a News Item of the June ‘80 issue of our Newsletter, we can report one more instance of the renewed attention to Dr. Gattegno’s work in the teaching of math. As a guest speaker to the annual meeting of the Canadian Study Group on Math Education, Dr. Gattegno spent 2 days at the meetings of the group in Quebec City, that included an opening two hour lecture, one hour for its discussion, a 2½ hour presentation of the math films and an aggregate of 5½ hours in participation in three study groups: 3 hours with those who looked into the teaching of the calculus, and a little more than one hour each with those looking into Geometry and those looking into remediation. The many hours of informal contacts during meals, at breaks and other sessions, between meals amounted to an intense feeling of a timely encounter between some people needing solutions they did not suspect and someone who had had some of them available for a number of years. Laval University had invited Dr. Gattegno in 1960 to give a summer course for math teachers, specially in understanding how the Algebricks (called Cuisenaire rods at the time) could make a difference in elementary school math education. Three of the professors at the 1980 meeting had been young participants at that 1960 workshop and said they were still exploiting in their research-work some of the suggestions they gleaned at that time. Among the others, many had never heard of Dr. Gattegno although they had been exposed to some of his findings through speakers who had worked with him in the last 25 years.

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The lecture lasted only a few minutes and led to a seminar type of encounter. A topic had been singled out by Dr. Gattegno to polarize the discussion around a promising point. But it was too new to the audience that needed more time to get better acquainted with it. Dr. Gattegno insisted that to be of our present time meant to be aware of “nothings” which would meet most of the needs of students at the various levels of education. “Nothings” as a word was used to refer to the awareness — that we could all have — that to think requires no energy (at least none that our present instruments can isolate and measure). The word “effort” is descriptive of another component of our human condition, mainly at the emotional level. Most people do not take the trouble to distinguish in their mental functionings where much energy is being used and where none is required. The participants who believed effort was helpful, had not come across “nothings” and neither could they understand their sudden appearance in their midst, nor believe they could be helped by them. During the following sessions of work numerous occasions occurred to illustrate the occurrence of a solution to a difficult problem in terms of the working of “nothings.” They made “nothings” slightly less strange and perhaps even attractive as an instrument for recognizing what a true educational solution is. As example of the power of “nothings” the insertion of one line in the array of numerals (which we present to teach people to read and write numeration in any language) yields an entry into any basis of numeration. This struck home for some. For others, the “nothings” represented by the dots that follow 1, 2, 3 to suggest infinity, and the “nothing” which is the thought of identifying potential infinity which actual infinity, were the critical ones. Still more were touched when the mathematics films — made with computer graphic animation so that infinite classes are considered all the time about any property that we wish to single out and illustrate — were looked at. “Nothings” were selected from among many topics that could be studied because they can serve to focus attention of a diverse group, and indeed they managed to do just that. But in actuality, the discussion in the subgroups were specialized and oriented towards

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making a contribution towards solving specific problems. As a temporary member in 3 of the 4 groups, Dr. Gattegno could only intervene within the terms raised by the leaders in the written notes distributed, or in an oral invitation to participate. As a result the interventions were only effective if the other people present encouraged them or even, as it happened, indicated their keen interest in making room for this odd participant. Taking advantage of this readiness to give him time, Dr. Gattegno was able to bring to the fore his work in the three areas of concern and he noted that it was being found helpful. Most of all in the field of remediation, in which more than 1/3 of the whole group was registered. The CMESG is one of the few groups in the world made of teachers at the postsecondary level, working individually and collectively on the improvement of teaching at that level. Since no one requires professors to be good teachers and since there are no institutions preparing them for that side of their lives, it is fortunate for Canada that so many can be so deeply involved in looking seriously at what can be done and educating themselves by working on the problems. Educational Solutions has something to contribute to the field and can now expect that some people here and there, will look into that contribution.

4 The Practicum — For Improving Language Teaching As in the past two years, this summer Steve Shuller arranged for a fiftyhour practicum course to take place at Educational Solutions. Teachers interested in improving their teaching of English as a second language participated in the practicum. Because Steve has been involved in the development of Educational Solutions’ latest project — the Math Mini Tests — he could not take

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upon himself the supervision of the practicum. Shakti Gattegno replaced him. It was possible this time to have forty students divided into four groups: one at the beginner level, two at the intermediate level, and one at the advanced level. Eight teachers registered to take part in the practicum. They worked in pairs in each class. (One of the teachers discontinued taking the course after the first twelve hours). Under this arrangement, the teachers had the opportunity to observe each other’s teaching as well as the learning processes of their students. During the last week they arranged among themselves their teaching schedule in such a manner that they could be present as observers in the classrooms other than their own. Time spent in various classes was helpful in improving their observational skills and their teaching. The teachers and the students worked for two hours, three evenings a week, for four weeks, and for ten hours over the concluding weekend. Each time after teaching, the teachers met with their supervisor for an hour, a meeting which usually got extended to an hour and a half. During these feedback sessions the teachers shared their observations and discussed new ways of presenting linguistic challenges to their students. The discussions were of a factual nature, pertaining to what had taken place in different classes. Besides examining their actual teaching, the teachers looked into effective ways of involving students in taking initiative as learners — that is, how to put the “right” challenges to students. The teachers investigated and learned to integrate in their teaching the ways of responding to students’ learning processes which can enhance their learning. About a third of the way into the practicum an important question emerged: “What is the nature of teacher-preparation for teaching languages?” The question was discussed at an empirical level. Possible answers can be stated as follows: 1

Teachers who think of language mainly in terms of knowledge, and of their students as devoid of that knowledge, will prepare themselves to teach in the traditional manner. Their teaching will consist of imparting knowledge to those who do not have it. Their 33


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emphasis will be on the curriculum and on covering the curriculum. 2 Teachers who see language primarily as a social means of communication, and consider students as people in need of the means, will prepare themselves to bring into circulation topical, conversational, and “survival” language. They will have their students focus on translation, repeating after the model and memorization as the ways to acquire the target language. Their teaching will emphasize those aspects of the language which are required in social situations for social exchange. 3 But teachers who understand a language to be an evolved and an evolving human phenomenon — which, through its behavior, represents the sensitivities, the intelligence, and the mode of thought of a people — and, who know students of a language as people equipped to learn a second language because they have learned their first one, will prepare themselves differently. Their teaching will be neither traditional nor overtaken by social concerns. Their preparation will include a study of the reality of the language and its essential components. They will equip themselves with efficient ways of presenting aspects of this reality to the students. They will be prepared to let the students meet the reality of the new language through their own sensitivities and their own intelligence, through their own perceptive powers and their own thinking. The teaching of these teachers will help students become independent learners and users of all that they learn. It will enable students to transfer their learning to social situations in which they find themselves. The emphasis, in this case, will be on the learners and their learning. During the practicum it also became clear that in order for teaching to serve learning, teachers must learn how to respond adequately to the actual learning processes that individual students go through. With this ability, teachers can help everyone transform his/her time into learning experiences at all stages. The study of some new ideas and the self-examination that the participating teachers underwent day after day, affected their teaching in many ways. They became more and more conscious of the linguistic

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needs as well as of the dynamic mental powers of their students. Three visitors observed the classes on different occasions. They were impressed by the pace of learning and by the joy which characterized the teaching-learning interaction going on. One of the visitors remarked that those were highly motivated students. That the students had become self-motivated learners in the course of the practicum, was obvious to the supervisors and the participating teachers. The latter had been learning to apply specific techniques which assisted the students in mobilizing their mental dynamics and thus helped them become better learners. Halfway through the practicum, teachers began to see that their students were able to enter into many different areas as users of English. They also gave evidence that they were preparing themselves to explore the richness of the language on their own. The teachers were asked to write 150 to 300 words about the most important thing that they had learned from their teaching, observing, and group discussions. Their writings contained important and honest observations about themselves and their teaching. Their papers included thoughtful reflections on several issues raised during the feedback sessions. The teachers proposed to themselves, in their papers, certain new tasks and specific changes to look for in their teaching. The transformation of their reflections into actions became evident the next day, it being obvious that they were learning how to become better teachers. As for the students, the ones in the advanced group soon identified for themselves the area(s) in which they were very much beginners in spite of their good command of vocabulary. They requested more and more help with their pronunciation. They had realized that the “means of communication� they had previously acquired needed repairing. The students in the beginner class were happy to have had a chance to prepare themselves to become users of English in an intelligent manner. They did this by discovering how to use themselves well as learners, not by having to imitate the teacher.

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The students in the two classes at the intermediate level would have been very happy to go on learning in the way they were being taught. On the last day one of them expressed his thoughts: “I have attended many English classes. Teachers tell all the time. They teach, teach, teach and you don’t learn much. Here I can say I learned because the teacher did not tell. He let me find out.” S. G.

5 The Math Mini Tests The good reception enjoyed nationwide by our Reading Mini Test project in the last five years, encouraged us to revive one we conceived at the same time eight or nine years ago, concerning mathematics. Since last spring, six of us, at Educational Solutions, work together to give shape to a program which we shall offer in stages to the public beginning around the end of this year and complete by next spring. It is a big project, complex and thorough, molded on what made the reading project popular. Teachers will find in the pages of its “starters” the approaches which can put almost every one of their students on top of the subject matter being tested. We know, from our long experience with students who “missed the boat” at school, that it is now possible to help everyone to make sense of the “mysteries of mathematics” and therefore to let test-takers raise themselves to the level considered in the tests as proper for certain age groups of students. Our idea of a good preparation for the test is that we must offer students insights that make them equal to the challenges they must face in that subject and are gathered in the tests. After awareness, sufficient practice completes the preparation. Interested people can inquire from our Mini Test Division, directed by Dorothea E. Hinman, Ed. D.

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6 Introduction Of The Silent Way In The Netherlands In the Fall of 1979, The Silent Way was tried out in short intensive French courses with adults at Nijmegen University in the Netherlands. This first experiment was videotaped and the tape was shown at Educational Solutions in April, 1980. These results encouraged us to continue to experiment on a larger scale. During the second semester of the academic year 1980-1981, five teachers will teach French in courses of 40 hours each, over ten weeks. The course participants will be adults of both low and intermediate levels of proficiency in French. These five teachers got their training in The Silent Way in a 3-day workshop. Extracted from a message from Professor Wil Knibbeler, Ph.D. Institute of Applied Linguistics University of Nijmegen The Netherlands                

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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

A New Braille and Other Topics  

Newsletter vol. X no. 1 September 1980

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