The exercises with this material not only are exercises of composition with the pieces of an inset or of the substitution of them into their relative metal plates; they are also exercises in drawing which, because of the labor they require, allow the child to take cognizance of every detail and to meditate upon it.
The designing done with these geometric insets, as will be explained, is of two kinds: geometric and artistic (mechanical and decorative). And the union of the two kinds of drawings gives new ways of applying the material.
The geometric design consists in reproducing the figure outlined by the corresponding insets. In this way the child learns to use the different instruments of drawing—the square, the ruler, the compass, and the protractor. In these exercises he acquires, with the aid of the special portfolio which comes with the material, actual and real cognitions in geometry.
Artistic designs are made by combining the small pieces of the various geometric insets. The resulting figures are then outlined and filled in with colored pencils or watercolors. Such combinations on the part of the child are real esthetic creations. The insets are of such reciprocal proportions that their combination results in an artistic harmony which facilitates the development of the child's esthetic sense. With our insets we were able to reproduce some of the classic decorations found in our masterpieces of art, such as decorations by Giotto.
A combination of geometric design and artistic design is formed by decorating the different parts of the geometric figure—as the center, the sides, the angles, the circumference, etc.; or by elaborating with free-hand details the decorations which have resulted from the combination of the insets. But a far better concept of all this will be gained as we pass on to explain our didactic material.
II
THE DIDACTIC MATERIAL USED FOR GEOMETRY