The geometrical figures are arranged in the drawers according to analogy of form.

(1) In one drawer there are six circles decreasing in diameter. (Fig. 17.)

(2) In another there is a square, together with five rectangles in which the length is always equal to the side of the square while the breadth gradually decreases. (Fig. 18.)

(3) Another drawer contains six triangles, which vary either according to their sides or according to their angles(the equilateral, isosceles, scalene, right angled, obtuse angled, and acute angled). (Fig. 19.)

(4) In another drawer there are six regular polygons containing from five to ten sides, i.e., the pentagon, hexagon, heptagon, octagon, nonagon, and decagon. (Fig. 20.)

(5) Another drawer contains various figures: an oval, an ellipse, a rhombus, and a trapezoid. (Fig. 21.)

(6) Finally, there are four plain wooden tablets, i.e., without any geometrical inset, which should have no button fixed to them; also two other irregular geometrical figures. (Fig. 22.)

Connected with this material there is a wooden frame furnished with a kind of rack which opens like a lid, and serves, when shut, to keep firmly in place six of the insets which may be arranged on the bottom of the frame itself, entirely covering it. (Fig. 23.)

This frame is used for the preparation of the first presentation to the child of the plane geometrical forms.

The teacher may select according to her own judgment certain forms from among the whole series at her disposal.

At first it is advisable to show the child only a few figures which differ very widely from one another in form. The next step is to present a larger number of figures, and after this to present consecutively figures more and more similar in form.

The first figures to be arranged in the frame will be, for example, the circle and the equilateral triangle, or the circle, the triangle and the square. The spaces which are left should be covered with the tablets of plain wood. Gradually the frame is completely filled with figures; first, with very dissimilar figures, as, for example, a square, a very narrow rectangle, a triangle, a circle, an ellipse and a hexagon, or with other figures in combination.

Afterwards the teacher's object will be to arrange figures similar to one another in the frame, as, for example, the set of six rectangles, six triangles, six circles, varying in size, etc.

This exercise resembles that of the cylinders. The insets are held by the buttons and taken from their places. They are then mixed on the table and the child is invited to put them back in their places. Here also the control of the error is in the material, for the figure cannot be inserted perfectly except when it is put in its own place. Hence a series of "experiments," of "attempts" which end in victory. The child is led to compare the various forms; to realize in a concrete way the differences between them when an inset wrongly placed will not go into the aperture. In this way he educates his eye to the recognition of forms.

The new movement of the hand which the child must coordinate is of particular importance. He is taught to touch the outline of the geometrical figures with the soft tips of the index and middle finger of the right hand, or of the left as well, if one believes in ambidexterity. (Fig. 24.) The child is made to touch the outline, not only of the inset, but also of the corresponding aperture, and, only after having touched them, is he to put back the inset into its place.

The recognition of the form is rendered much easier in this way. Children who evidently do not recognize the identities of form by the eye and who make absurd attempts to place the most diverse figures one within the other, do recognize the forms after having touched their outlines, and arrange them very quickly in their right places.

The child's hand during this exercise of touching the outlines of the geometrical figures has a concrete guide in the object. This is especially true when he touches the frames, for his two fingers have only to follow the edge of the frame, which acts as an obstacle and is a very clear guide. The teacher must always intervene at the start to teach accurately this movement, which will have such an importance in the future. She must, therefore, show the child how to touch, not only by performing the movement herself slowly and clearly, but also by guiding the child's hand itself during his first attempts, so that he is sure to touch all the details--angles and sides. When his hand has learned to perform these movements with precision and accuracy, he will be really capable of following the outline of a geometrical figure, and through many repetitions of the exercise he will come to coordinate the movement necessary for the exact delineation of its form.

This exercise could be called an indirect but very real preparation for drawing. It is certainly the preparation of the hand to trace an enclosed form. The little hand which touches, feels, and knows how to follow a determined outline is preparing itself, without knowing it, for writing.

The children make a special point of touching the outlines of the plane insets with accuracy. They themselves have invented the exercise of blindfolding their eyes so as to recognize the forms by touch only, taking out and putting back the insets without seeing them.

Corresponding to every form reproduced in the plane insets there are three white cards square in shape and of exactly the same size as the wooden frames of the insets. These cards are kept in three special cardboard boxes, almost cubic in form. (Fig. 25.)

On the cards are repeated, in three series, the same geometrical forms as those of the plane insets. The same measurements of the figures also are exactly reproduced.

In the first series the forms are filled in, i.e., they are cut out in blue paper and gummed on to the card; in the second series there is only an outline about half a centimeter in width, which is cut out in the same blue paper and gummed to the card; in the third series, however, the geometrical figures are instead outlined only in black ink.

By the use of this second piece of the material, the exercise of the eye is gradually brought to perfection in the recognition of "plane forms." In fact, there is no longer the concrete control of error in the material as there was in the wooden insets, but the child, by his eye alone, must judge of identities of form when, instead of fitting the wooden forms into their corresponding apertures, he simply rests them on the cardboard figure.

Again, the refinement of the eye's power of discrimination increases every time the child passes from one series of cards to the next, and by the time that he has reached the third series, he can see the relation between a wooden object, which he holds in his hand, and an outline drawing; that is, he can connect the concrete reality with an abstraction. The line now assumes in his eyes a very definite meaning; and he accustoms himself to recognize, to interpret and to judge of forms contained by a simple outline.

The exercises are various; the children themselves invent them. Some love to spread out a number of the figures of the geometric insets before their eyes, and then, taking a handful of the cards and mixing them like playing cards, deal them out as quickly as possible, choosing the figures corresponding to the pieces. Then as a test of their choice, they place the wooden pieces upon the forms on the cards. At this exercise they often cover whole tables, putting the wooden figures above, and beneath each one in a vertical line, the three corresponding forms of the cardboard series.

Another game invented by the children consists in putting out and mixing all the cards of the three series on two or three adjoining tables. The child then takes a wooden geometrical form and places it, as quickly as possible, on the corresponding cards which he has recognized at a glance among all the rest.

Four or five children play this game together, and as soon as one of them has found, for example, the filled-in figure corresponding to the wooden piece, and has placed the piece carefully and precisely upon it, another child takes away the piece in order to place it on the same form in outline. The game is somewhat suggestive of chess.

Many children, without any suggestion from any one, touch with the finger the outline of the figures in the three series of cards, doing it with seriousness of purpose, interest and perseverance.

We teach the children to name all the forms of the plane insets.

At first I had intended to limit my teaching to the most important names, such as square, rectangle, circle. But the children wanted to know all the names, taking pleasure in learning even the most difficult, such as trapezium, and decagon. They also show great pleasure in listening to the exact pronunciation of new words and in their repetition. Early childhood is, in fact, the age in which language is formed, and in which the sounds of a foreign language can be perfectly learned.

When the child has had long practise with the plane insets, he begins to make "discoveries" in his environment, recognizing forms, colors, and qualities already known to him--a result which, in general, follows after all the sensory exercises. Then it is that a great enthusiasm is aroused in him, and the world becomes for him a source of pleasure. A little boy, walking one day alone on the roof terrace, repeated to himself with a thoughtful expression on his face, "The sky is blue! the sky is blue!" Once a cardinal, an admirer of the children of the school in Via Guisti, wished himself to bring them some biscuits and to enjoy the sight of a little greediness among the children. When he had finished his distribution, instead of seeing the children put the food hastily into their mouths, to his great surprise he heard them call out, "A triangle! a circle! a rectangle!" In fact, these biscuits were made in geometrical shapes.

In one of the people's dwellings at Milan, a mother, preparing the dinner in the kitchen, took from a packet a slice of bread and butter. Her little four-year-old boy who was with her said, "Rectangle." The woman going on with her work cut off a large corner of the slice of bread, and the child cried out, "Triangle." She put this bit into the saucepan, and the child, looking at the piece that was left, called out more loudly than before, "And now it is a trapezium."

The father, a working man, who was present, was much impressed with the incident. He went straight to look for the teacher and asked for an explanation. Much moved, he said, "If I had been educated in that way I should not be now just an ordinary workman."

It was he who later on arranged for a demonstration to induce all the workmen of the dwellings to take an interest in the school. They ended by presenting the teacher with a parchment they had painted themselves, and on it, between the pictures of little children, they had introduced every kind of geometrical form.

As regards the touching of objects for the realization of their form, there is an infinite field of discovery open to the child in his environment. Children have been seen to stand opposite a beautiful pillar or a statue and, after having admired it, to close their eyes in a state of beatitude and pass their hands many times over the forms. One of our teachers met one day in a church two little brothers from the school in Via Guisti. They were standing looking at the small columns supporting the altar. Little by little the elder boy edged nearer the columns and began to touch them, then, as if he desired his little brother to share his pleasure, he drew him nearer and, taking his hand very gently, made him pass it round the smooth and beautiful shape of the column. But a sacristan came up at that moment and sent away "those tiresome children who were touching everything."

The great pleasure which the children derive from the recognition of objects by touching their form corresponds in itself to a sensory exercise.

Many psychologists have spoken of the stereognostic sense, that is, the capacity of recognizing forms by the movement of the muscles of the hand as it follows the outlines of solid objects. This sense does not consist only of the sense of touch, because the tactile sensation is only that by which we perceive the differences in quality of surfaces, rough or smooth. Perception of form comes from the combination of two sensations, tactile and muscular, muscular sensations being sensations of movement. What we call in the blind the tactilesense is in reality more often the stereognostic sense. That is, they perceive by means of their hands the form of bodies.

It is the special muscular sensibility of the child from three to six years of age who is forming his own muscular activity which stimulates him to use the stereognostic sense. When the child spontaneously blindfolds his eyes in order to recognize various objects, such as the plane and solid insets, he is exercising this sense.

There are many exercises which he can do to enable him to recognize with closed eyes objects of well defined shapes, as, for example, the little bricks and cubes of Froebel, marbles, coins, beans, peas, etc. From a selection of different objects mixed together he can pick out those that are alike, and arrange them in separate heaps.

In the didactic material there are also geometrical solids--pale blue in color--a sphere, a prism, a pyramid, a cone, a cylinder. The most attractive way of teaching a child to recognize these forms is for him to touch them with closed eyes and guess their names, the latter learned in a way which I will describe later. After an exercise of this kind the child when his eyes are open observes the forms with a much more lively interest. Another way of interesting him in the solid geometrical forms is to make them move. The sphere rolls in every direction; the cylinder rolls in one direction only; the cone rolls round itself; the prism and the pyramid, however, stand still, but the prism falls over more easily than the pyramid.

Little more remains of the didactic material for the education of the senses. There is, however, a series of six cardboard cylinders, either closed entirely or with wooden covers. (Fig. 26.)

When these cases are shaken they produce sounds varying in intensity from loud to almost imperceptible sounds, according to the nature of the objects inside the cylinder.

There is a double act of these, and the exercise consists, first, in the recognition of sounds of equal intensity, arranging the cylinders in pairs. The next exercise consists in the comparison of one sound with another; that is, the child arranges the six cylinders in a series according to the loudness of sound which they produce. The exercise is analogous to that with the color spools, which also are paired and then arranged in gradation. In this case also the child performs the exercise seated comfortably at a table. After a preliminary explanation from the teacher he repeats the exercise by himself, his eyes being blindfolded that he may better concentrate his attention.

We may conclude with a general rule for the direction of the education of the senses. The order of procedure should be:

(1) Recognition of identities (the pairing of similar objects and the insertion of solid forms into places which fit them).

(2) Recognition of contrasts (the presentation of the extremes of a series of objects).

(3) Discrimination between objects very similar to one another.

To concentrate the attention of the child upon the sensory stimulus which is acting upon him at a particular moment, it is well, as far as possible, to isolate the sense; for instance, to obtain silence in the room for all the exercises and to blindfold the eyes for those particular exercises which do not relate to the education of the sense of sight.

The cinematograph pictures give a general idea of all the sense exercises which the children can do with the material, and any one who has been initiated into the theory on which these are based will be able gradually to recognize them as they are seen practically carried out.

It is very advisable for those who wish to guide the children in these sensory exercises to begin themselves by working with the didactic material. The experience will give them some idea of what the children must feel, of the difficulties which they must overcome, etc., and, up to a certain point, it will give them some conception of the interest which these exercises can arouse in them. Whoever makes such experiments himself will be most struck by the fact that, when blindfolded, he finds that all the sensations of touch and hearing really appear more acute and more easily recognized. On account of this alone no small interest will be aroused in the experimenter.

For the beginning of the education of the musical sense, we use in Rome a material which does not form part of the didactic apparatus as it is sold at present. It consists of a double series of bells forming an octave with tones and semitones. These metal bells, which stand upon a wooden rectangular base, are all alike in appearance, but, when struck with a little wooden hammer, give out sounds corresponding to the notes doh, re, mi, fah, soh, lah, ti, doh, doh ♯, re ♯, fah ♯, soh ♯, lah ♯.

One series of bells is arranged in chromatic order upon a long board, upon which are painted rectangular spaces which are black and white and of the same size as the bases which support the bells. As on a pianoforte keyboard, the white spaces correspond to the tones, and the black to the semitones. (Fig. 27.)

At first the only bells to be arranged upon the board are those which correspond to the tones; these are set upon the white spaces in the order of the musical notes, doh, re, mi, fah, soh, lah, ti, doh.

To perform the first exercise the child strikes with a small hammer the first note of the series already arranged (doh). Then among a second series of corresponding bells which, arranged without the semitones, are mixed together upon the table, he tries, by striking the bells one after the other, to find the sound which is the same as the first one he has struck (doh). When he has succeeded in finding the corresponding sound, he puts the bell thus chosen opposite the first one (doh) upon the board. Then he strikes the second bell, re, once or twice; then from among the mixed group of bells he makes experiments until he recognizes re, which he places opposite the second bell of the series already arranged. He continues in the same way right to the end, looking for the identity of the sounds and performing an exercise of pairing similar to that already done in the case of the sound-boxes, the colors, etc.

Later, he learns in order the sounds of the musical scale, striking in rapid succession the bells arranged in order, and also accompanying his action with his voice--doh, re, mi, fah, soh, lah, ti, doh. When he is able to recognize and remember the series of sounds, the child takes the eight bells and, after mixing them up, he tries by striking them with the hammer, to find doh, then re, etc. Every time that he takes a new note, he strikes from the beginning all the bells already 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 bells in the order of the scale, guided only by his ear, and having succeeded, he strikes all the notes one after the other up and down the scale. This exercise fascinates children from five years old upwards.

If the objects which have been described constitute the didactic material for the beginnings of a methodical education of the auditory sense, I have no desire to limit to them an educational process which is so important and already so complex in its practise, whether in the long established methods of treatment for the deaf, or in modern physiological musical education. In fact, I also use resonant metal tubes, small bars of wood which emit musical notes, and strings (little harps), upon which the children seek to recognize the tones they have already learned with the exercise of the bells. The pianoforte may also be used for the same purpose. In this way the difference in timbre comes to be perceived together with the differences in tone. At the same time various exercises, already mentioned, such as the marches played on the piano for rhythmic exercises, and the simple songs sung by the children themselves, offer extensive means for the development of the musical sense.

To quicken the child's attention in special relation to sounds there is a most important exercise which, contrary to all attempts made up to this time in the practise of education, consists not in producing but in eliminating, as far as possible, all sounds from the environment. My "lesson of silence" has been very widely applied, even in schools where the rest of my method has not found its way, for the sake of its practical effect upon the discipline of the children.

The children are taught "not to move"; to inhibit all those motor impulses which may arise from any cause whatsoever, and in order to induce in them real "immobility," it is necessary to initiate them in the control of all their movements. The teacher, then, does not limit herself to saying, "Sit still," but she gives them the example herself, showing them how to sit absolutely still; that is, with feet still, body still, arms still, head still. The respiratory movements should also be performed in such a way as to produce no sound.

The children must be taught how to succeed in this exercise. The fundamental condition is that of finding a comfortable position, i.e., a position of equilibrium. As they are seated for this exercise, they must therefore make themselves comfortable either in their little chairs or on the ground. When immobility is obtained, the room is half-darkened, or else the children close their eyes, or cover them with their hands.

It is quite plain to see that the children take a great interest in the "Silence"; they seem to give themselves up to a kind of spell: they might be said to be wrapped in meditation. Little by little, as each child, watching himself, becomes more and more still, the silence deepens till it becomes absolute and can be felt, just as the twilight gradually deepens whilst the sun is setting.

Then it is that slight sounds, unnoticed before, are heard; the ticking of the clock, the chirp of a sparrow in the garden, the flight of a butterfly. The world becomes full of imperceptible sounds which invade that deep silence without disturbing it, just as the stars shine out in the dark sky without banishing the darkness of the night. It is almost the discovery of a new world where there is rest. It is, as it were, the twilight of the world of loud noises and of the uproar that oppresses the spirit. At such a time the spirit is set free and opens out like the corolla of the convolvulus.

And leaving metaphor for the reality of facts, can we not all recall feelings that have possessed us at sunset, when all the vivid impressions of the day, the brightness and clamor, are silenced? It is not that we miss the day, but that our spirit expands. It becomes more sensitive to the inner play of emotions, strong and persistent, or changeful and serene.

"It was that hour when mariners feel longing,
And hearts grow tender."

(Dante, trans. Longfellow.)

The lesson of silence ends with a general calling of the children's names. The teacher, or one of the children, takes her place behind the class or in an adjoining room, and "calls" the motionless children, one by one, by name; the call is made in a whisper, that is, without vocal sound. This demands a close attention on the part of the child, if he is to hear his name. When his name is called he must rise and find his way to the voice which called him; his movements must be light and vigilant, and so controlled as to make no noise.

When the children have become acquainted with silence, their hearing is in a manner refined for the perception of sounds. Those sounds which are too loud become gradually displeasing to the ear of one who has known the pleasure of silence, and has discovered the world of delicate sounds. From this point the children gradually go on to perfect themselves; they walk lightly, take care not to knock against the furniture, move their chairs without noise, and place things upon the table with great care. The result of this is seen in the grace of carriage and of movement, which is especially delightful on account of the way in which it has been brought about. It is not a grace taught externally for the sake of beauty or regard for the world, but one which is born of the pleasure felt by the spirit in immobility and silence. The soul of the child wishes to free itself from the irksomeness of sounds that are too loud, from obstacles to its peace during work. These children, with the grace of pages to a noble lord, are serving their spirits.

This exercise develops very definitely the social spirit. No other lesson, no other "situation," could do the same. A profound silence can be obtained even when more than fifty children are crowded together in a small space, provided that all the children know how to keep still and want to do it; but one disturber is enough to take away the charm.

Here is demonstration of the cooperation of all the members of a community to achieve a common end. The children gradually show increased power of inhibition; many of them, rather than disturb the silence, refrain from brushing a fly off the nose, or suppress a cough or sneeze. The same exhibition of collective action is seen in the care with which the children move to avoid making a noise during their work. The lightness with which they run on tiptoe, the grace with which they shut a cupboard, or lay an object on the table, these are qualities that must be acquired by all, if the environment is to become tranquil and free from disturbance. One rebel is sufficient to mar this achievement; one noisy child, walking on his heels or banging the door, can disturb the peaceful atmosphere of the small community.