Part 6
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
[Illustration: FIG. 32.--THE MUSICAL STAFF.[A]]
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[A] The single staff is used in the Conservatoire of Milan and utilized in the Perlasca method.
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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.
[Illustration: FIG. 39.--DUMB KEYBOARD.]
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.
[Illustration: FIG. 33.
On the wooden board, round spaces are cut out corresponding to the notes. Inside each of the spaces there is a figure. On one side of each of the discs is written a number and on the other the name of the note. They are fitted by the child into the corresponding places.]
[Illustration: FIG. 34.
The child next arranged the discs in the notes cut out on the staff, but there are no longer numbers written to help him find the places. Instead, he must try to remember the place of the note on the staff. If he is not sure he consults the numbered board (Fig. 33).]
[Illustration: FIG. 35.
The child arranged on the staff the semitones in 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 have the sharp on one side and the flat on the other, e.g., re[sharp]-mi[flat] are written on the opposite sides of the same disc.]
[Illustration: FIG. 36.
The children take a large number of discs and arrange them on the staff, leaving uppermost the side which is blank, i.e., the side on which the name of the note is not written. Then they verify their work by turning the discs over and reading the name.]
[Illustration: FIG. 37.
The double staff is formed by putting the two staves together. The children arrange the notes in the form of a rhombus.]
[Illustration: FIG. 38.
The two boards are then separated and the notes remain arranged according to the treble and bass clefs. The corresponding key signatures are then placed upon the two different staves.]
ARITHMETIC
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.
[Illustration:
===== =====----- =====-----===== 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.
[Illustration: FIG. 41.--COUNTING BOXES.]
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.
[Illustration: FIG. 42.--ARITHMETIC FRAME.]
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.
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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.
MORAL FACTORS
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.
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[B] See the chapters on Discipline in my larger works.
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