Period 1. Naming. "This is thick. This is thin."
Period 2. Recognition. "Give me the thick. Give me the thin."
Period 3. The Pronunciation of the Word. "What is this?"
There is a way of helping the child to recognize differences in dimension and to place the objects in correct gradation. After the lesson which I have described, the teacher scatters the brown prisms, for instance, on a carpet, says to the child, "Give me the thickest of all," and lays the object on a table. Then, again, she invites the child to look for the thickest piece among those scattered on the floor, and every time the piece chosen is laid in its order on the table next to the piece previously chosen. In this way the child accustoms himself always to look either for the thickest or the thinnest among the rest, and so has a guide to help him to lay the pieces in gradation.
When there is one dimension only which varies, as in the case of the rods, the objects are said to be "long" and "short," the varying dimension being length. When the varying dimension is height, the objects are said to be "tall" and "short"; when the breadth varies, they are "broad" and "narrow."
Of these three varieties we offer the child as a fundamental lesson only that in which the length varies, and we teach the differences by means of the usual "three periods," and by asking him to select from the pile at one time always the "longest," at another always the "shortest."
The child in this way acquires great accuracy in the use of words. One day the teacher had ruled the blackboard with very fine lines. A child said, "What small lines!" "They are not small," corrected another; "they are thin."
When the names to be taught are those of colors or of forms, so that it is not necessary to emphasize contrast between extremes, the teacher can give more than two names at the same time, as, for instance, "This is red." "This is blue." "This is yellow." Or, again, "This is a square." "This is a triangle." "This is a circle." In the case of a gradation, however, the teacher will select (if she is teaching the colors) the two extremes "dark" and "light," then making choice always of the "darkest" and the "lightest."
Many of the lessons here described can be seen in the cinematograph pictures; lessons on touching the plane insets and the surfaces, in walking on the line, in color memory, in the nomenclature relating to the cubes and the long rods, in the composition of words, reading, writing, etc.
By means of these lessons the child comes to know many words very thoroughly—large, small; thick, thin; long, short; dark, light; rough, smooth; heavy, light; hot, cold; and the names of many colors and geometrical forms. Such words do not relate to any particular object, but to a psychic acquisition on the part of the child. In fact, the name is given after a long exercise, in which the child, concentrating his attention on different qualities of objects, has made comparisons, reasoned, and formed judgments, until he has acquired a power of discrimination which he did not possess before. In a word, he has refined his senses; his observation of things has been thorough and fundamental; he has changed himself.
He finds himself, therefore, facing the world with psychic qualities refined and quickened. His powers of observation and of recognition have greatly increased. Further, the mental images which he has succeeded in establishing are not a confused medley; they are all classified—forms are distinct from dimensions, and dimensions are classed according to the qualities which result from the combinations of varying dimensions.
All these are quite distinct from gradations. Colors are divided according to tint and to richness of tone, silence is distinct from non-silence, noises from sounds, and everything has its own exact and appropriate name. The child then has not only developed in himself special qualities of observation and of judgment, but the objects which he observes may be said to go into their place, according to the order established in his mind, and they are placed under their appropriate name in an exact classification.
Does not the student of the experimental sciences prepare himself in the same way to observe the outside world? He may find himself like the uneducated man in the midst of the most diverse natural objects, but he differs from the uneducated man in that he has special qualities for observation. If he is a worker with the microscope, his eyes are trained to see in the range of the microscope certain minute details which the ordinary man cannot distinguish. If he is an astronomer, he will look through the same telescope as the curious visitor or dilettante, but he will see much more clearly. The same plants surround the botanist and the ordinary wayfarer, but the botanist sees in every plant those qualities which are classified in his mind, and assigns to each plant its own place in the natural orders, giving it its exact name. It is this capacity for recognizing a plant in a complex order of classification which distinguishes the botanist from the ordinary gardener, and it is exact and scientific language which characterizes the trained observer.
Now, the scientist who has developed special qualities of observation and who "possesses" an order in which to classify external objects will be the man to make scientific discoveries. It will never be he who, without preparation and order, wanders dreaming among plants or beneath the starlit sky.
In fact, our little ones have the impression of continually "making discoveries" in the world about them; and in this they find the greatest joy. They take from the world a knowledge which is ordered and inspires them with enthusiasm. Into their minds there enters "the Creation" instead of "the Chaos"; and it seems that their souls find therein a divine exultation.
The success of these results is closely connected with the delicate intervention of the one who guides the children in their development. It is necessary for the teacher to guide the child without letting him feel her presence too much, so that she may be always ready to supply the desired help, but may never be the obstacle between the child and his experience.
A lesson in the ordinary use of the word cools the child's enthusiasm for the knowledge of things, just as it would cool the enthusiasm of adults. To keep alive that enthusiasm is the secret of real guidance, and it will not prove a difficult task, provided that the attitude towards the child's acts be that of respect, calm and waiting, and provided that he be left free in his movements and in his experiences.
Then we shall notice that the child has a personality which he is seeking to expand; he has initiative, he chooses his own work, persists in it, changes it according to his inner needs; he does not shirk effort, he rather goes in search of it, and with great joy overcomes obstacles within his capacity. He is sociable to the extent of wanting to share with every one his successes, his discoveries, and his little triumphs. There is therefore no need of intervention. "Wait while observing." That is the motto for the educator.
Let us wait, and be always ready to share in both the joys and the difficulties which the child experiences. He himself invites our sympathy, and we should respond fully and gladly. Let us have endless patience with his slow progress, and show enthusiasm and gladness at his successes. If we could say: "We are respectful and courteous in our dealings with children, we treat them as we should like to be treated ourselves," we should certainly have mastered a great educational principle and undoubtedly be setting an example of good education.
What we all desire for ourselves, namely, not to be disturbed in our work, not to find hindrances to our efforts, to have good friends ready to help us in times of need, to see them rejoice with us, to be on terms of equality with them, to be able to confide and trust in them—this is what we need for happy companionship. In the same way children are human beings to whom respect is due, superior to us by reason of their "innocence" and of the greater possibilities of their future. What we desire they desire also.
As a rule, however, we do not respect our children. We try to force them to follow us without regard to their special needs. We are overbearing with them, and above all, rude; and then we expect them to be submissive and well-behaved, knowing all the time how strong is their instinct of imitation and how touching their faith in and admiration of us. They will imitate us in any case. Let us treat them, therefore, with all the kindness which we would wish to help to develop in them. And by kindness is not meant caresses. Should we not call anyone who embraced us at the first time of meeting rude, vulgar and ill-bred? Kindness consists in interpreting the wishes of others, in conforming one's self to them, and sacrificing, if need be, one's own desire. This is the kindness which we must show towards children.
To find the interpretation of children's desires we must study them scientifically, for their desires are often unconscious. They are the inner cry of life, which wishes to unfold according to mysterious laws. We know very little of the way in which it unfolds. Certainly the child is growing into a man by force of a divine action similar to that by which from nothing he became a child.
Our intervention in this marvelous process is indirect; we are here to offer to this life, which came into the world by itself, the means necessary for its development, and having done that we must await this development with respect.
Let us leave the life free to develop within the limits of the good, and let us observe this inner life developing. This is the whole of our mission. Perhaps as we watch we shall be reminded of the words of Him who was absolutely good, "Suffer the little children to come unto Me." That is to say, "Do not hinder them from coming, since, if they are left free and unhampered, they will come."
The child who has completed all the exercises above described, and is thus prepared for an advance towards unexpected conquests, is about four years old.
He is not an unknown quantity, as are children who have been left to gain varied and casual experiences by themselves, and who therefore differ in type and intellectual standard, not only according to their "natures," but especially according to the chances and opportunities they have found for their spontaneous inner formation.
Education has determined an environment for the children. Individual differences to be found in them can, therefore, be put down almost exclusively to each one's individual "nature." Owing to their environment which offers means adapted and measured to meet the needs of their psychical development, our children have acquired a fundamental type which is common to all. They have coordinated their movements in various kinds of manual work about the house, and so have acquired a characteristic independence of action, and initiative in the adaptation of their actions to their environment. Out of all this emerges a personality, for the children have become little men, who are self-reliant.
The special attention necessary to handle small fragile objects without breaking them, and to move heavy articles without making a noise, has endowed the movements of the whole body with a lightness and grace which are characteristic of our children. It is a deep feeling of responsibility which has brought them to such a pitch of perfection. For instance, when they carry three or four tumblers at a time, or a tureen of hot soup, they know that they are responsible not only for the objects, but also for the success of the meal which at that moment they are directing. In the same way each child feels the responsibility of the "silence," of the prevention of harsh sounds, and he knows how to cooperate for the general good in keeping the environment, not only orderly, but quiet and calm. Indeed, our children have taken the road which leads them to mastery of themselves.
But their formation is due to a deeper psychological work still, arising from the education of the senses. In addition to ordering their environment and ordering themselves in their outward personalities, they have also ordered the inner world of their minds.
The didactic material, in fact, does not offer to the child the "content" of the mind, but the order for that "content." It causes him to distinguish identities from differences, extreme differences from fine gradations, and to classify, under conceptions of quality and of quantity, the most varying sensations appertaining to surfaces, colors, dimensions, forms and sounds. The mind has formed itself by a special exercise of attention, observing, comparing, and classifying.
The mental attitude acquired by such an exercise leads the child to make ordered observations in his environment, observations which prove as interesting to him as discoveries, and so stimulate him to multiply them indefinitely and to form in his mind a rich "content" of clear ideas.
Language now comes to fix by means of exact words the ideas which the mind has acquired. These words are few in number and have reference, not to separate objects, but rather to the order of the ideas which have been formed in the mind. In this way the children are able to "find themselves," alike in the world of natural things and in the world of objects and of words which surround them, for they have an inner guide which leads them to become active and intelligent explorers instead of wandering wayfarers in an unknown land.
These are the children who, in a short space of time, sometimes in a few days, learn to write and to perform the first operations of arithmetic. It is not a fact that children in general can do it, as many have believed. It is not a case of giving my material for writing to unprepared children and of awaiting the "miracle."
The fact is that the minds and hands of our children are already prepared for writing, and ideas of quantity, of identity, of differences, and of gradation, which form the bases of all calculation, have been maturing for a long time in them.
One might say that all their previous education is a preparation for the first stages of essential culture—writing, reading, and number, and that knowledge comes as an easy, spontaneous, and logical consequence of the preparation—that it is in fact its natural conclusion.
We have already seen that the purpose of the word is to fix ideas and to facilitate the elementary comprehension of things. In the same way writing and arithmetic now fix the complex inner acquisitions of the mind, which proceeds henceforward continually to enrich itself by fresh observations.
* * * * *
Our children have long been preparing the hand for writing. Throughout all the sensory exercises the hand, whilst cooperating with the mind in its attainments and in its work of formation, was preparing its own future. When the hand learned to hold itself lightly suspended over a horizontal surface in order to touch rough and smooth, when it took the cylinders of the solid insets and placed them in their apertures, when with two fingers it touched the outlines of the geometrical forms, it was coordinating movements, and the child is now ready—almost impatient to use them in the fascinating "synthesis" of writing.
The direct preparation for writing also consists in exercises of the movements of the hand. There are two series of exercises, very different from one another. I have analyzed the movements which are connected with writing, and I prepare them separately one from the other. When we write, we perform a movement for the management of the instrument of writing, a movement which generally acquires an individual character, so that a person's handwriting can be recognized, and, in certain medical cases, changes in the nervous system can be traced by the corresponding alterations in the handwriting. In fact, it is from the handwriting that specialists in that subject would interpret the moral character of individuals.
Writing has, besides this, a general character, which has reference to the form of the alphabetical signs.
When a man writes he combines these two parts, but they actually exist as the component parts of a single product and can be prepared apart.
Exercises for the Management of the Instrument of Writing
(THE INDIVIDUAL PART)
In the didactic material there are two sloping wooden boards, on each of which stand five square metal frames, colored pink. In each of these is inserted a blue geometrical figure similar to the geometrical insets and provided with a small button for a handle. With this material we use a box of ten colored pencils and a little book of designs which I have prepared after five years' experience of observing the children. I have chosen and graduated the designs according to the use which the children made of them.
The two sloping boards are set side by side, and on them are placed ten complete "insets," that is to say, the frames with the geometrical figures. (Fig. 28.) The child is given a sheet of white paper and the box of ten colored pencils. He will then choose one of the ten metal insets, which are arranged in an attractive line at a certain distance from him. The child is taught the following process:
He lays the frame of the iron inset on the sheet of paper, and, holding it down firmly with one hand, he follows with a colored pencil the interior outline which describes a geometrical figure. Then he lifts the square frame, and finds drawn upon the paper an enclosed geometrical form, a triangle, a circle, a hexagon, etc. The child has not actually performed a new exercise, because he had already performed all these movements when he touched the wooden plane insets. The only new feature of the exercise is that he follows the outlines no longer directly with his finger, but through the medium of a pencil. That is, he draws, he leaves a trace of his movement.
The child finds this exercise easy and most interesting, and, as soon as he has succeeded in making the first outline, he places above it the piece of blue metal corresponding to it. This is an exercise exactly similar to that which he performed when he placed the wooden geometrical figures upon the cards of the third series, where the figures are only contained by a simple line.
This time, however, when the action of placing the form upon the outline is performed, the child takes another colored pencil and draws the outline of the blue metal figure.
When he raises it, if the drawing is well done, he finds upon the paper a geometrical figure contained by two outlines in colors, and, if the colors have been well chosen, the result is very attractive, and the child, who has already had a considerable education of the chromatic sense is keenly interested in it.
These may seem unnecessary details, but, as a matter of fact, they are all-important. For instance, if, instead of arranging the ten metal insets in a row, the teacher distributes them among the children without thus exhibiting them, the child's exercises are much limited. When, on the other hand, the insets are exhibited before his eyes, he feels the desire to draw them all one after the other, and the number of exercises is increased.
The two colored outlines rouse the desire of the child to see another combination of colors and then to repeat the experience. The variety of the objects and the colors are therefore an inducement to work and hence to final success.
Here the actual preparatory movement for writing begins. When the child has drawn the figure in double outline, he takes hold of a pencil "like a pen for writing," and draws marks up and down until he has completely filled the figure. In this way a definite filled-in figure remains on the paper, similar to the figures on the cards of the first series. This figure can be in any of the ten colors. At first the children fill in the figures very clumsily without regard for the outlines, making very heavy lines and not keeping them parallel. Little by little, however, the drawings improve, in that they keep within the outlines, and the lines increase in number, grow finer, and are parallel to one another.
When the child has begun these exercises, he is seized with a desire to continue them, and he never tires of drawing the outlines of the figures and then filling them in. Each child suddenly becomes the possessor of a considerable number of drawings, and he treasures them up in his own little drawer. In this way he organizes the movement of writing, which brings him to the management of the pen. This movement in ordinary methods is represented by the wearisome pothook connected with the first laborious and tedious attempts at writing.
The organization of this movement, which began from the guidance of a piece of metal, is as yet rough and imperfect, and the child now passes on to the filling in of the prepared designs in the little album. The leaves are taken from the book one by one in the order of progression in which they are arranged, and the child fills in the prepared designs with colored pencils in the same way as before. Here the choice of the colors is another intelligent occupation which encourages the child to multiply the tasks. He chooses the colors by himself and with much taste. The delicacy of the shades which he chooses and the harmony with which he arranges them in these designs show us that the common belief, that children love bright and glaring colors, has been the result of observation of children without education, who have been abandoned to the rough and harsh experiences of an environment unfitted for them.
The education of the chromatic sense becomes at this point of a child's development the lever which enables him to become possessed of a firm, bold and beautiful handwriting.
The drawings lend themselves to limiting, in very many ways, the length of the strokes with which they are filled in. The child will have to fill in geometrical figures, both large and small, of a pavement design, or flowers and leaves, or the various details of an animal or of a landscape. In this way the hand accustoms itself, not only to perform the general action, but also to confine the movement within all kinds of limits.
Hence the child is preparing himself to write in a handwriting either large or small. Indeed, later on he will write as well between the wide lines on a blackboard as between the narrow, closely ruled lines of an exercise book, generally used by much older children.
The number of exercises which the child performs with the drawings is practically unlimited. He will often take another colored pencil and draw over again the outlines of the figure already filled in with color. A help to the continuation of the exercise is to be found in the further education of the chromatic sense, which the child acquires by painting the same designs in water-colors. Later he mixes colors for himself until he can imitate the colors of nature, or create the delicate tints which his own imagination desires. It is not possible, however, to speak of all this in detail within the limits of this small work.
Exercises for the Writing of Alphabetical Signs
In the didactic material there are series of boxes which contain the alphabetical signs. At this point we take those cards which are covered with very smooth paper, to which is gummed a letter of the alphabet cut out in sandpaper. (Fig. 29.) There are also large cards on which are gummed several letters, grouped together according to analogy of form. (Fig. 30.)
The children "have to touch over the alphabetical signs as though they were writing." They touch them with the tips of the index and middle fingers in the same way as when they touched the wooden insets, and with the hand raised as when they lightly touched the rough and smooth surfaces. The teacher herself touches the letters to show the child how the movement should be performed, and the child, if he has had much practise in touching the wooden insets, imitates her with ease and pleasure. Without the previous practise, however, the child's hand does not follow the letter with accuracy, and it is most interesting to make close observations of the children in order to understand the importance of a remote motor preparation for writing, and also to realize the immense strain which we impose upon the children when we set them to write directly without a previous motor education of the hand.
The child finds great pleasure in touching the sandpaper letters. It is an exercise by which he applies to a new attainment the power he has already acquired through exercising the sense of touch. Whilst the child touches a letter, the teacher pronounces its sound, and she uses for the lesson the usual three periods. Thus, for example, presenting the two vowels i, o, she will have the child touch them slowly and accurately, and repeat their relative sounds one after the other as the child touches them, "i, i, i! o, o, o!" Then she will say to the child: "Give me i!" "Give me o!" Finally, she will ask the question: "What is this?" To which the child replies, "i, o." She proceeds in the same way through all the other letters, giving, in the case of the consonants, not the name, but only the sound. The child then touches the letters by himself over and over again, either on the separate cards or on the large cards on which several letters are gummed, and in this way he establishes the movements necessary for tracing the alphabetical signs. At the same time he retains the visual image of the letter. This process forms the first preparation, not only for writing, but also for reading, because it is evident that when the child touches the letters he performs the movement corresponding to the writing of them, and, at the same time, when he recognizes them by sight he is reading the alphabet.
The child has thus prepared, in effect, all the necessary movements for writing; therefore he can write. This important conquest is the result of a long period of inner formation of which the child is not clearly aware. But a day will come—very soon—when he will write, and that will be a day of great surprise for him—the wonderful harvest of an unknown sowing.
* * * * *
The alphabet of movable letters cut out in pink and blue cardboard, and kept in a special box with compartments, serves "for the composition of words." (Fig. 31.)
In a phonetic language, like Italian, it is enough to pronounce clearly the different component sounds of a word (as, for example, m-a-n-o), so that the child whose ear is already educated may recognize one by one the component sounds. Then he looks in the movable alphabet for the signs corresponding to each separate sound, and lays them one beside the other, thus composing the word (for instance, mano). Gradually he will become able to do the same thing with words of which he thinks himself; he succeeds in breaking them up into their component sounds, and in translating them into a row of signs.
When the child has composed the words in this way, he knows how to read them. In this method, therefore, all the processes leading to writing include reading as well.
If the language is not phonetic, the teacher can compose separate words with the movable alphabet, and then pronounce them, letting the child repeat by himself the exercise of arranging and rereading them.
In the material there are two movable alphabets. One of them consists of larger letters, and is divided into two boxes, each of which contains the vowels. This is used for the first exercises, in which the child needs very large objects in order to recognize the letters. When he is acquainted with one half of the consonants he can begin to compose words, even though he is dealing with one part only of the alphabet.
The other movable alphabet has smaller letters and is contained in a single box. It is given to children who have made their first attempts at composition with words, and already know the complete alphabet.
It is after these exercises with the movable alphabet that the child is able to write entire words. This phenomenon generally occurs unexpectedly, and then a child who has never yet traced a stroke or a letter on paper writes several words in succession. From that moment he continues to write, always gradually perfecting himself. This spontaneous writing takes on the characteristics of a natural phenomenon, and the child who has begun to write the "first word" will continue to write in the same way as he spoke after pronouncing the first word, and as he walked after having taken the first step. The same course of inner formation through which the phenomenon of writing appeared is the course of his future progress, of his growth to perfection. The child prepared in this way has entered upon a course of development through which he will pass as surely as the growth of the body and the development of the natural functions have passed through their course of development when life has once been established.
For the interesting and very complex phenomena relating to the development of writing and then of reading, see my larger works.
THE READING OF MUSIC
[A] The single staff is used in the Conservatoire of Milan and utilized in the Perlasca method.
When the child knows how to read, he can make a first application of this knowledge to the reading of the names of musical notes.
In connection with the material for sensory education, consisting of the series of bells, we use a didactic material, which serves as an introduction to musical reading. For this purpose we have, in the first place, a wooden board, not very long, and painted pale green. On this board the staff is cut out in black, and in every line and space are cut round holes, inside each of which is written the name of the note in its reference to the treble clef.
There is also a series of little white discs which can be fitted into the holes. On one side of each disc is written the name of the note (doh, re, mi, fah, soh, lah, ti, doh).
The child, guided by the name written on the discs, puts them, with the name uppermost, in their right places on the board and then reads the names of the notes. This exercise he can do by himself, and he learns the position of each note on the staff. Another exercise which the child can do at the same time is to place the disc bearing the name of the note on the rectangular base of the corresponding bell, whose sound he has already learned to recognize by ear in the sensorial exercise described above.
Following this exercise there is another staff made on a board of green wood, which is longer than the other and has neither indentures nor signs. A considerable number of discs, on one side of which are written the names of the notes, is at the disposal of the child. He takes up a disc at random, reads its name and places it on the staff, with the name underneath, so that the white face of the disc shows on the top. By the repetition of this exercise the child is enabled to arrange many discs on the same line or in the same space. When he has finished, he turns them all over so that the names are outside, and so finds out if he has made mistakes. After learning the treble clef the child passes on to learn the bass with great ease.
To the staff described above can be added another similar to it, arranged as is shown in the figure. (Fig. 32.) The child beginning with doh, lays the discs on the board in ascending order in their right position until the octave is reached: doh, re, mi, fah, soh, lah, ti, doh. Then he descends the scale in the same way, returning to doh, but continuing to place the discs always to the right: soh, fah, mi, re, doh. In this way he forms an angle. At this point he descends again to the lower staff, ti, lah, soh, fah, mi, re, doh, then he ascends again on the other side: re, mi, fah, soh, lah, ti, and by forming with his two lines of discs another angle in the bass, he has completed a rhombus, "the rhombus of the notes."
After the discs have been arranged in this way, the upper staff is separated from the lower. In the lower the notes are arranged according to the bass clef. In this way the first elements of musical reading are presented to the child, reading which corresponds to sounds with which the child's ear is already acquainted.
For a first practical application of this knowledge we have used in our schools a miniature pianoforte keyboard, which reproduces the essentials of this instrument, although in a simplified form, and so that they are visible. Two octaves only are reproduced, and the keys, which are small, are proportioned to the hand of a little child of four or five years, as the keys of the common piano are proportioned to those of the adult. All the mechanism of the key is visible. (Fig. 39.) On striking a key one sees the hammer rise, on which is written the name of the note. The hammers are black and white, like the notes.
With this instrument it is very easy for the child to practise alone, finding the notes on the keyboard corresponding to some bar of written music, and following the movements of the fingers made in playing the piano.
The keyboard in itself is mute, but a series of resonant tubes, resembling a set of organ-pipes, can be applied to the upper surface, so that the hammers striking these produce musical notes corresponding to the keys struck. The child can then pursue his exercises with the control of the musical sounds.
DIDACTIC MATERIAL FOR MUSICAL READING.
-mi[flat] are written on the opposite sides of the same disc.]
The children possess all the instinctive knowledge necessary as a preparation for clear ideas on numeration. The idea of quantity was inherent in all the material for the education of the senses: longer, shorter, darker, lighter. The conception of identity and of difference formed part of the actual technique of the education of the senses, which began with the recognition of identical objects, and continued with the arrangement in gradation of similar objects. I will make a special illustration of the first exercise with the solid insets, which can be done even by a child of two and a half. When he makes a mistake by putting a cylinder in a hole too large for it, and so leaves one cylinder without a place, he instinctively absorbs the idea of the absence of one from a continuous series. The child's mind is not prepared for number "by certain preliminary ideas," given in haste by the teacher, but has been prepared for it by a process of formation, by a slow building up of itself.
To enter directly upon the teaching of arithmetic, we must turn to the same didactic material used for the education of the senses.
Let us look at the three sets of material which are presented after the exercises with the solid insets, i.e., the material for teaching size (the pink cubes), thickness (the brown prisms), and length (the green rods). There is a definite relation between the ten pieces of each series. In the material for length the shortest piece is a unit of measurement for all the rest; the second piece is double the first, the third is three times the first, etc., and, whilst the scale of length increases by ten centimeters for each piece, the other dimensions remain constant (i.e., the rods all have the same section).
The pieces then stand in the same relation to one another as the natural series of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
In the second series, namely, that which shows thickness, whilst the length remains constant, the square section of the prisms varies. The result is that the sides of the square sections vary according to the series of natural numbers, i.e., in the first prism, the square of the section has sides of one centimeter, in the second of two centimeters, in the third of three centimeters, etc., and so on until the tenth, in which the square of the section has sides of ten centimeters. The prisms therefore are in the same proportion to one another as the numbers of the series of squares (1, 4, 9, etc.), for it would take four prisms of the first size to make the second, nine to make the third, etc. The pieces which make up the series for teaching thickness are therefore in the following proportion: 1 : 4 : 9 : 16 : 25 : 36 : 49 : 64 : 81 : 100.
In the case of the pink cubes the edge increases according to the numerical series, i.e., the first cube has an edge of one centimeter, the second of two centimeters, the third of three centimeters, and so on, to the tenth cube, which has an edge of ten centimeters. Hence the relation in volume between them is that of the cubes of the series of numbers from one to ten, i.e., 1 : 8: 27 : 64: 125 : 216 : 343 : 512 : 729 : 1000. In fact, to make up the volume of the second pink cube, eight of the first little cubes would be required; to make up the volume of the third, twenty-seven would be required, and so on.
===== =====——- ====——-==== A ====——-====——- B ====——-====——-===== =====——-====——-====——- ====——-====——-====——-==== ====——-====——-====——-====——- ====——-====——-====——-====——-===== =====——-====——-====——-====——-====——- 1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10
FIG. 40.—DIAGRAM ILLUSTRATING USE OF NUMERICAL RODS.]
The children have an intuitive knowledge of this difference, for they realize that the exercise with the pink cubes is the easiest of all three and that with the rods the most difficult. When we begin the direct teaching of number, we choose the long rods, modifying them, however, by dividing them into ten spaces, each ten centimeters in length, colored alternately red and blue. For example, the rod which is four times as long as the first is clearly seen to be composed of four equal lengths, red and blue; and similarly with all the rest.
When the rods have been placed in order of gradation, we teach the child the numbers: one, two, three, etc., by touching the rods in succession, from the first up to ten. Then, to help him to gain a clear idea of number, we proceed to the recognition of separate rods by means of the customary lesson in three periods.
We lay the three first rods in front of the child, and pointing to them or taking them in the hand in turn, in order to show them to him we say: "This is one." "This is two." "This is three." We point out with the finger the divisions in each rod, counting them so as to make sure, "One, two: this is two." "One, two, three: this is three." Then we say to the child: "Give me two." "Give me one." "Give me three." Finally, pointing to a rod, we say, "What is this?" The child answers, "Three," and we count together: "One, two, three."
In the same way we teach all the other rods in their order, adding always one or two more according to the responsiveness of the child.
The importance of this didactic material is that it gives a clear idea of number. For when a number is named it exists as an object, a unity in itself. When we say that a man possesses a million, we mean that he has a fortune which is worth so many units of measure of values, and these units all belong to one person.
So, if we add 7 to 8 (7 + 8), we add a number to a number, and these numbers for a definite reason represent in themselves groups of homogeneous units.
Again, when the child shows us the 9, he is handling a rod which is inflexible—an object complete in itself, yet composed of nine equal parts which can be counted. And when he comes to add 8 to 2, he will place next to one another, two rods, two objects, one of which has eight equal lengths and the other two. When, on the other hand, in ordinary schools, to make the calculation easier, they present the child with different objects to count, such as beans, marbles, etc., and when, to take the case I have quoted (8 + 2), he takes a group of eight marbles and adds two more marbles to it, the natural impression in his mind is not that he has added 8 to 2, but that he has added 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 to 1 + 1. The result is not so clear, and the child is required to make the effort of holding in his mind the idea of a group of eight objects as one united whole, corresponding to a single number, 8.
This effort often puts the child back, and delays his understanding of number by months or even years.
The addition and subtraction of numbers under ten are made very much simpler by the use of the didactic material for teaching lengths. Let the child be presented with the attractive problem of arranging the pieces in such a way as to have a set of rods, all as long as the longest. He first arranges the rods in their right order (the long stair); he then takes the last rod (1) and lays it next to the 9. Similarly, he takes the last rod but one (2) and lays it next to the 8, and so on up to the 5.
This very simple game represents the addition of numbers within the ten: 9 + 1, 8 + 2, 7 + 3, 6 + 4. Then, when he puts the rods back in their places, he must first take away the 4 and put it back under the 5, and then take away in their turn the 3, the 2, the 1. By this action he has put the rods back again in their right gradation, but he has also performed a series of arithmetical subtractions, 10 - 4, 10 - 3, 10 - 2, 10 - 1.
The teaching of the actual figures marks an advance from the rods to the process of counting with separate units. When the figures are known, they will serve the very purpose in the abstract which the rods serve in the concrete; that is, they will stand for the uniting into one whole of a certain number of separate units.
The synthetic function of language and the wide field of work which it opens out for the intelligence is demonstrated, we might say, by the function of the figure, which now can be substituted for the concrete rods.
The use of the actual rods only would limit arithmetic to the small operations within the ten or numbers a little higher, and, in the construction of the mind, these operations would advance very little farther than the limits of the first simple and elementary education of the senses.
The figure, which is a word, a graphic sign, will permit of that unlimited progress which the mathematical mind of man has been able to make in the course of its evolution.
In the material there is a box containing smooth cards, on which are gummed the figures from one to nine, cut out in sandpaper. These are analogous to the cards on which are gummed the sandpaper letters of the alphabet. The method of teaching is always the same. The child is made to touch the figures in the direction in which they are written, and to name them at the same time.
In this case he does more than when he learned the letters; he is shown how to place each figure upon the corresponding rod. When all the figures have been learned in this way, one of the first exercises will be to place the number cards upon the rods arranged in gradation. So arranged, they form a succession of steps on which it is a pleasure to place the cards, and the children remain for a long time repeating this intelligent game.
After this exercise comes what we may call the "emancipation" of the child. He carried his own figures with him, and now using them he will know how to group units together.
For this purpose we have in the didactic material a series of wooden pegs, but in addition to these we give the children all sorts of small objects—sticks, tiny cubes, counters, etc.
The exercise will consist in placing opposite a figure the number of objects that it indicates. The child for this purpose can use the box which is included in the material. (Fig. 41.) This box is divided into compartments, above each of which is printed a figure and the child places in the compartment the corresponding number of pegs.
Another exercise is to lay all the figures on the table and place below them the corresponding number of cubes, counters, etc.
This is only the first step, and it would be impossible here to speak of the succeeding lessons in zero, in tens and in other arithmetical processes—for the development of which my larger works must be consulted. The didactic material itself, however, can give some idea. In the box containing the pegs there is one compartment over which the 0 is printed. Inside this compartment "nothing must be put," and then we begin with one.
Zero is nothing, but it is placed next to one to enable us to count when we pass beyond 9—thus, 10.
If, instead of the piece 1, we were to take pieces as long as the rod 10, we could count 10, 20, 30, 40, 50, 60, 70, 80, 90. In the didactic material there are frames containing cards on which are printed such numbers from 10 to 90. These numbers are fixed into a frame in such a way that the figures 1 to 9 can be slipped in covering the zero. If the zero of 10 is covered by 1 the result is 11, if with 2 it becomes 12, and so on, until the last 9. Then we pass to the twenties (the second ten), and so on, from ten to ten. (Fig. 42.)
For the beginning of this exercise with the cards marking the tens we can use the rods. As we begin with the first ten (10) in the frame, we take the rod 10. We then place the small rod 1 next to rod 10, and at the same time slip in the number 1, covering the zero of the 10. Then we take rod 1 and figure 1 away from the frame, and put in their place rod 2 next to rod 10, and figure 2 over the zero in the frame, and so on, up to 9. To advance farther we should need to use two rods of 10 to make 20.
The children show much enthusiasm when learning these exercises, which demand from them two sets of activities, and give them in their work clearness of idea.
* * * * *
In writing and arithmetic we have gathered the fruits of a laborious education which consisted in coordinating the movements and gaining a first knowledge of the world. This culture comes as a natural consequence of man's first efforts to put himself into intelligent communication with the world.
All those early acquisitions which have brought order into the child's mind, would be wasted were they not firmly established by means of written language and of figures. Thus established, however, these experiences open up an unlimited field for future education. What we have done, therefore, is to introduce the child to a higher level—the level of culture—and he will now be able to pass on to a school, but not the school we know to-day, where, irrationally, we try to give culture to minds not yet prepared or educated to receive it.
To preserve the health of their minds, which have been exercised and not fatigued by the order of the work, our children must have a new kind of school for the acquisition of culture. My experiments in the continuation of this method for older children are already far advanced.
A brief description such as this, of the means which are used in the "Children's House," may perhaps give the reader the impression of a logical and convincing system of education. But the importance of my method does not lie in the organization itself, but in the effects which it produces on the child. It is the child who proves the value of this method by his spontaneous manifestations, which seem to reveal the laws of man's inner development.[B] Psychology will perhaps find in the "Children's Houses" a laboratory which will bring more truths to light than thus hitherto recognized; for the essential factor in psychological research, especially in the field of psychogenesis, the origin and development of the mind, must be the establishment of normal conditions for the free development of thought.
[B] See the chapters on Discipline in my larger works.
As is well known, we leave the children free in their work, and in all actions which are not of a disturbing kind. That is, we eliminate disorder, which is "bad," but allow to that which is orderly and "good" the most complete liberty of manifestation.
The results obtained are surprising, for the children have shown a love of work which no one suspected to be in them, and a calm and an orderliness in their movements which, surpassing the limits of correctness have entered into those of "grace." The spontaneous discipline, and the obedience which is seen in the whole class, constitute the most striking result of our method.
The ancient philosophical discussion as to whether man is born good or evil is often brought forward in connection with my method, and many who have supported it have done so on the ground that it provides a demonstration of man's natural goodness. Very many others, on the contrary, have opposed it, considering that to leave children free is a dangerous mistake, since they have in them innate tendencies to evil.
I should like to put the question upon a more positive plane.
In the words "good" and "evil" we include the most varying ideas, and we confuse them especially in our practical dealings with little children.
The tendencies which we stigmatize as evil in little children of three to six years of age are often merely those which cause annoyance to us adults when, not understanding their needs, we try to prevent their every movement, their every attempt to gain experience for themselves in the world (by touching everything, etc.). The child, however, through this natural tendency, is led to coordinate his movements and to collect impressions, especially sensations of touch, so that when prevented he rebels, and this rebellion forms almost the whole of his "naughtiness."
What wonder is it that the evil disappears when, if we give the right means for development and leave full liberty to use them, rebellion has no more reason for existence?
Further, by the substitution of a series of outbursts of joy for the old series of outbursts of rage, the moral physiognomy of the child comes to assume a calm and gentleness which make him appear a different being.
It is we who provoked the children to the violent manifestations of a real struggle for existence. In order to exist according to the needs of their psychic development they were often obliged to snatch from us the things which seemed necessary to them for the purpose. They had to move contrary to our laws, or sometimes to struggle with other children to wrest from them the objects of their desire.
On the other hand, if we give children the means of existence, the struggle for it disappears, and a vigorous expansion of life takes its place. This question involves a hygienic principle connected with the nervous system during the difficult period when the brain is still rapidly growing, and should be of great interest to specialists in children's diseases and nervous derangements. The inner life of man and the beginnings of his intellect are controlled by special laws and vital necessities which cannot be forgotten if we are aiming at health for mankind.
For this reason, an educational method, which cultivates and protects the inner activities of the child, is not a question which concerns merely the school or the teachers; it is a universal question which concerns the family, and is of vital interest to mothers.
To go more deeply into a question is often the only means of answering it rightly. If, for instance, we were to see men fighting over a piece of bread, we might say: "How bad men are!" If, on the other hand, we entered a well-warmed eating-house, and saw them quietly finding a place and choosing their meal without any envy of one another, we might say: "How good men are!" Evidently, the question of absolute good and evil, intuitive ideas of which guide us in our superficial judgment, goes beyond such limitations as these. We can, for instance, provide excellent eating-houses for an entire people without directly affecting the question of their morals. One might say, indeed, that to judge by appearances, a well-fed people are better, quieter, and commit less crime than a nation that is ill-nourished; but whoever draws from that the conclusion that to make men good it is enough to feed them, will be making an obvious mistake.
It cannot be denied, however, that nourishment will be an essential factor in obtaining goodness, in the sense that it will eliminate all the evil acts, and the bitterness caused by lack of bread.
Now, in our case, we are dealing with a far deeper need—the nourishment of man's inner life, and of his higher functions. The bread that we are dealing with is the bread of the spirit, and we are entering into the difficult subject of the satisfaction of man's psychic needs.
We have already obtained a most interesting result, in that we have found it possible to present new means of enabling children to reach a higher level of calm and goodness, and we have been able to establish these means by experience. The whole foundation of our results rests upon these means which we have discovered, and which may be divided under two heads—the organization of work, and liberty.
It is the perfect organization of work, permitting the possibility of self-development and giving outlet for the energies, which procures for each child the beneficial and calming satisfaction. And it is under such conditions of work that liberty leads to a perfecting of the activities, and to the attainment of a fine discipline which is in itself the result of that new quality of calmness that has been developed in the child.
Freedom without organization of work would be useless. The child left free without means of work would go to waste, just as a new-born baby, if left free without nourishment, would die of starvation. The organization of the work, therefore, is the corner-stone of this new structure of goodness; but even that organization would be in vain without the liberty to make use of it, and without freedom for the expansion of all those energies which spring from the satisfaction of the child's highest activities.
Has not a similar phenomenon occurred also in the history of man? The history of civilization is a history of successful attempts to organize work and to obtain liberty. On the whole, man's goodness has also increased, as is shown by his progress from barbarism to civilization, and it may be said that crime, the various forms of wickedness, cruelty and violence have been gradually decreasing during this passage of time.
The criminality of our times, as a matter of fact, has been compared to a form of barbarism surviving in the midst of civilized peoples. It is, therefore, through the better organization of work that society will probably attain to a further purification, and in the meanwhile it seems unconsciously to be seeking the overthrow of the last barriers between itself and liberty.
If this is what we learn from society, how great should be the results among little children from three to six years of age if the organization of their work is complete, and their freedom absolute? It is for this reason that to us they seem so good, like heralds of hope and of redemption.
If men, walking as yet so painfully and imperfectly along the road of work and of freedom, have become better, why should we fear that the same road will prove disastrous to the children?
Yet, on the other hand, I would not say that the goodness of our little ones in their freedom will solve the problem of the absolute goodness or wickedness of man. We can only say that we have made a contribution to the cause of goodness by removing obstacles which were the cause of violence and of rebellion.
Let us "render, therefore, unto Caesar the things that are Caesar's, and unto God the things that are God's."
Illustrations have been moved closer to their relevant paragraphs.
The page numbers in the List of Illustrations do not reflect the new placement of the illustrations, but are as in the original.
The list of "didactic material for the education of the senses" on pages 18-19 is missing item (j) as in the original.
Author's archaic and variable spelling is preserved.
Author's punctuation style is preserved.
Passages in italics indicated by underscores.
Passages in bold indicated by equal signs.
Typographical problems have been changed and are listed below.
Page vii: Was 'marvellous' [In fact, Helen Keller is a marvelous example of the phenomenon common to all human beings]
Page 46: Was 'anvles' [which vary either according to their sides or according to their angles (the equilateral, isosceles, scalene, right angled, obtuse angled, and acute)]
Page 63: Added commas [recognized and arranged in order—doh, re, doh, re, mi; doh, re, mi, fah; doh, re, mi, fah, soh, etc. In this way he succeeds in arranging all the]
Fig. 35 caption: Was 'si' [the spaces which remain where the discs are far apart: do-re, re-mi, fah-soh, soh-la, la-ti. The discs for the semitones]