Dr Montessoris Own Handbook

* * * * * Another interesting piece of material is a little cabinet containing six drawers placed one above another. When they are opened they display six square wooden "frames" in each. (Fig. 16.) [Illustration: FIG. 16.--CABINET WITH DRAWERS TO HOLD GEOMETRICAL INSETS.] Almost all the frames have a large geometrical figure inserted in the center, each colored blue and provided with a small button for a handle. Each drawer is lined with blue paper, and when the geometrical figure is removed, the bottom is seen to reproduce exactly the same form. 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.) [Illustration: 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.) [Illustration: 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.) [Illustration: 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.) [Illustration: FIG. 20.--SET OF SIX POLYGONS.] (5) Another drawer contains various figures: an oval, an ellipse, a rhombus, and a trapezoid. (Fig. 21.) [Illustration: 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 button fixed to them; also two other irregular geometrical figures. (Fig. 22.) [Illustration: 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.) [Illustration: 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 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_. [Illustration: 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 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. * * * * * [Illustration: 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 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.