To many children, however, counting may come through efforts to draw. I have seen a child of four-and-a-half, in drawing a man, make a line for the arm, then lay down her pencil to count her own fingers and then draw five lines for the man’s hand. Froebel says:
“The representation of objects by drawing, and the exact perception conditioned and required by the representation, soon leads the child quickly to recognize the constantly repeated association of certain numbers of different objects—e.g. two eyes and two arms, five fingers, etc. Thus the drawing of the object leads to the discovery of number.… By the development of the capacity for counting, the child’s sphere of knowledge, his world, is again extended.… He was unable to determine relative quantities, but now he knows that he has two large and three small pebbles, four white and five yellow flowers,” etc.—E., p. 80.
Yet another mode of Investigation is that of Experimenting; every normal child is what Froebel calls “a self-teaching scientist.”
“The material must be known not only by its name, but by its qualities and uses.… For this reason the child examines the object on all sides; for this reason he tears and breaks it; for this reason he puts it in his mouth and bites it. We reprove the child for his naughtiness and foolishness; and yet he is wiser than we who reprove him. An instinct which the child did not give himself, the instinct which rightly understood and rightly guided would lead him to know God in his works, drives him to this.”—E., p. 73.
It may well be through his ceaseless experimenting that the little child begins to draw, gains what the late Mr. Ebenezer Cooke called “a language of line,” or as Froebel puts it, notices “linear phenomena, which direct his attention to the linear properties of surrounding objects.”
“A child has found a pebble, a fragment of lime or chalk. In order to determine by experiment its properties, he has rubbed it on a board near by, and has discovered its property of imparting colour. See how he delights in the newly discovered property, how busily he makes use of it! … but soon he begins to find pleasure in the winding, straight, curved, and other forms that appear. These linear phenomena direct his attention to the linear properties of surrounding objects. Now the head becomes a circle, and now the circular line represents the head, the elliptical curve connected with it represents the body; arms and legs appear as straight or broken lines, and these again represent arms and legs; the fingers he sees as straight lines meeting in a common point, and lines so connected are, for the busy child, again hands and fingers; the eyes he sees as dots, and these again represent eyes; and thus a new world opens within and without. For what man tries to represent, that he begins to understand.”—E., p. 75.
I have watched a child go through the process of discovering “linear phenomena,” just as Froebel describes it, no doubt from his own observation. A boy of three, having folded a piece of paper for the roof of a house, was colouring it, by rubbing on red chalk, when he called out, “Oh! I’m making lines.” The other children went on rubbing, but Phil made “lines” till the roof was finished.
But Froebel does not leave unnoticed the fact that the very earliest “drawing” is an outgrowth of the muscular action to which his instinct of activity is urged by the stimulus of contact.
“Would you know how to lead the child in this matter? Watch him, he will teach you what to do. See! he is tracing the table by passing his fingers along its edges and outlines as far as he can reach, he is sketching the object on itself. This is the first and the safest step by which he becomes aware of the outlines and forms of objects. In this way he sketches and so studies the chair, the bench, the window. But soon he advances. He draws lines across the four-cornered bit of board, across the leaf of the table, or the seat of the chair, in the dim anticipation that so he can retain the forms and relations of the surfaces. Now, already he draws the form diminished.
“See! there the child has drawn table, chair and bench on a leaf of the table. Do you not see how he spontaneously trained himself for this? Objects which he could move, which were in sight, he laid on the board, and drew their form on the plane surface, following the boundaries of the objects with his hands. Soon scissors and boxes, and later leaves and twigs, even his own hand and the shadows of objects will thus be copied.