[Ill.u.s.tration: FIG. 17.--SET OF SIX CIRCLES.]
(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.)
[Ill.u.s.tration: FIG. 18.--SET OF SIX RECTANGLES.]
(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.)
[Ill.u.s.tration: FIG. 19.--SET OF SIX TRIANGLES.]
(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.)
[Ill.u.s.tration: FIG. 20.--SET OF SIX POLYGONS.]
(5) Another drawer contains various figures: an oval, an ellipse, a rhombus, and a trapezoid. (Fig. 21.)
[Ill.u.s.tration: FIG. 21.--SET OF SIX IRREGULAR FIGURES.]
(6) Finally, there are four plain wooden tablets, _i.e._, without any geometrical inset, which should have no b.u.t.ton fixed to them; also two other irregular geometrical figures. (Fig. 22.)
[Ill.u.s.tration: FIG. 22.--SET OF FOUR BLANKS AND TWO IRREGULAR FIGURES.]
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.)
[Ill.u.s.tration: FIG. 23.--FRAME TO HOLD GEOMETRICAL INSETS.]
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 s.p.a.ces 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 b.u.t.tons 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_.
[Ill.u.s.tration: FIG. 24.--CHILD TOUCHING THE INSETS. (MONTESSORI SCHOOL, RUNTON.)]
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 ident.i.ties 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 repet.i.tions 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.
[Ill.u.s.tration: FIG. 25.--SERIES OF CARDS WITH GEOMETRICAL FORMS.]
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 ident.i.ties 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 pa.s.ses 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 a.s.sumes 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 p.r.o.nunciation of new words and in their repet.i.tion. 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 b.u.t.ter.
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 beat.i.tude and pa.s.s 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 pa.s.s 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 _tactile_ sense 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.