Here, also, we face a widespread prejudice; namely, the belief that the child left to himself gives absolute repose to his mind. If this were so he would remain a stranger to the world, and, instead, we see him, little by little, spontaneously conquer various ideas and words. He is a traveller through life, who observes the new things among which he journeys, and who tries to understand the unknown tongue spoken by those about him. Indeed, he makes a great and voluntary effort to understand and to imitate. The instruction given to little children should be so directed as to lessen this expenditure of poorly directed effort, converting it instead into the enjoyment of conquest made easy and infinitely broadened. We are the guides of these travellers just entering the great world of human thought. We should see to it that we are intelligent and cultured guides, not losing ourselves in vain discourse, but illustrating briefly and concisely the work of art in which the traveller shows himself interested, and we should then respectfully allow him to observe it as long as he wishes to. It is our privilege to lead him to observe the most important and the most beautiful things of life in such a way that he does not lose energy and time in useless things, but shall find pleasure and satisfaction throughout his pilgrimage.
I have already referred to the prejudice that it is more suitable to present the geometric forms to the child in the solid rather than in the plane, giving him, for example, the cube, the sphere, the prism. Let us put aside the physiological side of the question showing that the visual recognition of the solid figure is more complex than that of the plane, and let us view the question only from the more purely pedagogical standpoint of practical life.
The greater number of objects which we look upon every day present more nearly the aspect of our plane geometric insets. In fact, doors, window-frames, framed pictures, the wooden or marble top of a table, are indeed solid objects, but with one of the dimensions greatly reduced, and with the two dimensions determining the form of the plane surface made most evident.
When the plane form prevails, we say that the window is rectangular, the picture frame oval, this table square, etc. Solids having a determined form prevailing in the plane surface are almost the only ones which come to our notice. And such solids are clearly represented by our plane geometric insets.
The child will very often recognise in his environment forms which he has learned in this way, but he will rarely recognise the solid geometric forms.
That the table leg is a prism, or a truncated cone, or an elongated cylinder, will come to his knowledge long after he has observed that the top of the table upon which he places things is rectangular. We do not, therefore, speak of the fact of recognising that a house is a prism or a cube. Indeed, the pure solid geometric forms never exist in the ordinary objects about us; these present, instead, a combination of forms. So, putting aside the difficulty of taking in at a glance the complex form of a house, the child recognises in it, not an identity of form, but an analogy.
He will, however, see the plane geometric forms perfectly represented in windows and doors, and in the faces of many solid objects in use at home. Thus the knowledge of the forms given him in the plane geometric insets will be for him a species of magic key, opening the external world, and making him feel that he knows its secrets.
I was walking one day upon the Pincian Hill with a boy from the elementary school. He had studied geometric design and understood the analysis of plane geometric figures. As we reached the highest terrace from which we could see the Piazza del Popolo with the city stretching away behind it, I stretched out my hand saying, "Look, all the works of man are a great mass of geometric figures;" and, indeed, rectangles, ovals, triangles, and semicircles, perforated, or ornamented, in a hundred different ways the grey rectangular façades of the various buildings. Such uniformity in such an expanse of buildings seemed to prove the limitation of human intelligence, while in an adjoining garden plot the shrubs and flowers spoke eloquently of the infinite variety of forms in nature.
The boy had never made these observations; he had studied the angles, the sides and the construction of outlined geometric figures, but without thinking beyond this, and feeling only annoyance at this arid work. At first he laughed at the idea of man's massing geometric figures together, then he became interested, looked long at the buildings before him, and an expression of lively and thoughtful interest came into his face. To the right of the Ponte Margherita was a factory building in the process of construction, and its steel framework delineated a series of rectangles. "What tedious work!" said the boy, alluding to the workmen. And, then, as we drew near the garden, and stood for a moment in silence admiring the grass and the flowers which sprang so freely from the earth, "It is beautiful!" he said. But that word "beautiful" referred to the inner awakening of his own soul.
This experience made me think that in the observation of the plane geometric forms, and in that of the plants which they saw growing in their own little gardens, there existed for the children precious sources of spiritual as well as intellectual education. For this reason, I have wished to make my work broad, leading the child, not only to observe the forms about him, but to distinguish the work of man from that of nature, and to appreciate the fruits of human labour.