The third quality of the lesson is its objectivity. The lesson must be presented in such a way that the personality of the teacher shall disappear. There shall remain in evidence only the object to which she wishes to call the attention of the child. This brief and simple lesson must be considered by the teacher as an explanation of the object and of the use which the child can make of it.

In the giving of such lessons the fundamental guide must be the method of observation, in which is included and understood the liberty of the child. So the teacher shall observe whether the child interests himself in the object, how he is interested in it, for how long, etc., even noticing the expression of his face. And she must take great care not to offend the principles of liberty. For, if she provokes the child to make an unnatural effort, she will no longer know what is the spontaneous activity of the child. If, therefore, the lesson rigorously prepared in this brevity, simplicity and truth is not understood by the child, is not accepted by him as an explanation of the object,—the teacher must be warned of two things:—first, not to insist by repeating the lesson; and second, not to make the child feel that he has made a mistake, or that he is not understood, because in doing so she will cause him to make an effort to understand, and will thus alter the natural state which must be used by her in making her psychological observation. A few examples may serve to illustrate this point.

Let us suppose, for example, that the teacher wishes to teach to a child the two colours, red and blue. She desires to attract the attention of the child to the object. She says, therefore, "Look at this." Then, in order to teach the colours, she says, showing him the red, "This is red," raising her voice a little and pronouncing the word "red" slowly and clearly; then showing him the other colour, "This is blue." In order to make sure that the child has understood, she says to him, "Give me the red,"—"Give me the blue." Let us suppose that the child in following this last direction makes a mistake. The teacher does not repeat and does not insist; she smiles, gives the child a friendly caress and takes away the colours.

Teachers ordinarily are greatly surprised at such simplicity. They often say, "But everybody knows how to do that!" Indeed, this again is a little like the egg of Christopher Columbus, but the truth is that not everyone knows how to do this simple thing (to give a lesson with such simplicity). To measure one's own activity, to make it conform to these standards of clearness, brevity and truth, is practically a very difficult matter. Especially is this true of teachers prepared by the old-time methods, who have learned to labour to deluge the child with useless, and often, false words. For example, a teacher who had taught in the public schools often reverted to collectivity. Now in giving a collective lesson much importance is necessarily given to the simple thing which is to be taught, and it is necessary to oblige all the children to follow the teacher's explanation, when perhaps not all of them are disposed to give their attention to the particular lesson in hand. The teacher has perhaps commenced her lesson in this way:—"Children, see if you can guess what I have in my hand!" She knows that the children cannot guess, and she therefore attracts their attention by means of a falsehood. Then she probably says,—"Children, look out at the sky. Have you ever looked at it before? Have you never noticed it at night when it is all shining with stars? No! Look at my apron. Do you know what colour it is? Doesn't it seem to you the same colour as the sky? Very well then, look at this colour I have in my hand. It is the same colour as the sky and my apron. It is blue. Now look around you a little and see if you can find something in the room which is blue. And do you know what colour cherries are, and the colour of the burning coals in the fireplace, etc., etc."

Now in the mind of the child after he has made the useless effort of trying to guess there revolves a confused mass of ideas,—the sky, the apron, the cherries, etc. It will be difficult for him to extract from all this confusion the idea which it was the scope of the lesson to make clear to him; namely, the recognition of the two colours, blue and red. Such a work of selection is almost impossible for the mind of a child who is not yet able to follow a long discourse.

I remember being present at an arithmetic lesson where the children were being taught that two and three make five. To this end, the teacher made use of a counting board having coloured beads strung on its thin wires. She arranged, for example, two beads on the top line, then on a lower line three, and at the bottom five beads. I do not remember very clearly the development of this lesson, but I do know that the teacher found it necessary to place beside the two beads on the upper wire a little cardboard dancer with a blue skirt, which she christened on the spot the name of one of the children in the class, saying, "This is Mariettina." And then beside the other three beads she placed a little dancer dressed in a different colour, which she called "Gigina." I do not know exactly how the teacher arrived at the demonstration of the same, but certainly she talked for a long time with these little dancers, moving them about, etc. If I remember the dancers more clearly than I do the arithmetic process, how must it have been with the children? If by such a method they were able to learn that two and three make five, they must have made a tremendous mental effort, and the teacher must have found it necessary to talk with the little dancers for a long time.

In another lesson a teacher wished to demonstrate to the children the difference between noise and sound. She began by telling a long story to the children. Then suddenly someone in league with her knocked noisily at the door. The teacher stopped and cried out—"What is it! What's happened! What is the matter! Children, do you know what this person at the door has done? I can no longer go on with my story, I cannot remember it any more. I will have to leave it unfinished. Do you know what has happened? Did you hear! Have you understood? That was a noise, that is a noise. Oh! I would much rather play with this little baby (taking up a mandolin which she had dressed up in a table cover). Yes, dear baby, I had rather play with you. Do you see this baby that I am holding in my arms?" Several children replied, "It isn't a baby." Others said, "It's a mandolin." The teacher went on—"No, no, it is a baby, really a baby. I love this little baby. Do you want me to show you that it is a baby? Keep very, very quiet then. It seems to me that the baby is crying. Or, perhaps it is talking, or perhaps it is going to say papa or mamma." Putting her hand under the cover, she touched the strings of the mandolin. "There! did you hear the baby cry! Did you hear it call out?" The children cried out—"It's a mandolin, you touched the strings, you made it play." The teacher then replied, "Be quiet, be quiet, children. Listen to what I am going to do." Then she uncovered the mandolin and began to play on it, saying, "This is sound."

To suppose that the child from such a lesson as this shall come to understand the difference between noise and sound is ridiculous. The child will probably get the impression that the teacher wished to play a joke, and that she is rather foolish, because she lost the thread of her discourse when she was interrupted by noise, and because she mistook a mandolin for a baby. Most certainly, it is the figure of the teacher herself that is impressed upon the child's mind through such a lesson, and not the object for which the lesson was given.

To obtain a simple lesson from a teacher who has been prepared according to the ordinary methods, is a very difficult task. I remember that, after having explained the material fully and in detail, I called upon one of my teachers to teach, by means of the geometric insets, the difference between a square and a triangle. The task of the teacher was simply to fit a square and a triangle of wood into the empty spaces made to receive them. She should then have shown the child how to follow with his finger the contours of the wooden pieces and of the frames into which they fit, saying, meanwhile, "This is a square—this is a triangle." The teacher whom I had called upon began by having the child touch the square, saying, "This is a line,—another,—another,—and another. There are four lines: count them with your little finger and tell me how many there are. And the corners,—count the corners, feel them with your little finger. See, there are four corners too. Look at this piece well. It is a square." I corrected the teacher, telling her that in this way she was not teaching the child to recognise a form, but was giving him an idea of sides, of angles, of number, and that this was a very different thing from that which she was to teach in this lesson. "But," she said, trying to justify herself, "it is the same thing." It is not, however, the same thing. It is the geometric analysis and the mathematics of the thing. It would be possible to have an idea of the form of the quadrilateral without knowing how to count to four, and, therefore, without appreciating the number of sides and angles. The sides and the angles are abstractions which in themselves do not exist; that which does exist is this piece of wood of a determined form. The elaborate explanations of the teacher not only confused the child's mind, but bridged over the distance that lies between the concrete and the abstract, between the form of an object and the mathematics of the form.

Let as suppose, I said to the teacher, that an architect shows you a dome, the form of which interests you. He can follow one of two methods in showing you his work: he can call attention to the beauty of line, the harmony of the proportions, and may then take you inside the building and up into the cupola itself, in order that you may appreciate the relative proportion of the parts in such a way that your impression of the cupola as a whole shall be founded on general knowledge of its parts, or he can have you count the windows, the wide or narrow cornices, and can, in fact, make you a design showing the construction; he can illustrate for you the static laws and write out the algebraic formulæ necessary in the calculation of such laws. In the first place, you will be able to retain in your mind the form of the cupola; in the second, you will have understood nothing, and will come away with the impression that the architect fancied himself speaking to a fellow engineer, instead of to a traveller whose object was to become familiar with the beautiful things about him. Very much the same thing happens if we, instead of saying to the child, "This is a square," and by simply having him touch the contour establish materially the idea of the form, proceed rather to a geometrical analysis of the contour.