THE TEACHING OF NUMERATION 331 to the number drawn on the vertical plane. A variety of small objects are given to the child to make a change in the exercise. I use small spindles which I have made on purpose, FroebePs. cubes, and the discs which are used in the game of draughts. A group of objects having been placed beside the child, he has to put them in position; for example, one disc corresponding to 1,. two discs to 2, etc. When he thinks he has finished it correctly he asks the teacher to come and verify it. LESSONS ON ZERO Let us wait till the time comes when the child, pointing to the Zero compartments, asks: "What must I put in here?*' and then answer, " Nothing, zero is nothing ". But that is not enough; they must/^7 what nothing is. For this purpose we employ exercises which amuse the children immensely. I place myself in the midst of them as they sit around in their little chairs; I turn to one who has already performed the counting exercise and say to him: " Come, dear, come to me zero times." The child almost always runs to me and then returns to his plape. " But, my child, you have come once, and I said zero times." He begins to wonder. " But what ought I to do then? " " Nothing, zero is nothing." " But how do I do nothing? " w Do nothing; you must stay where you are, you must not move, you must not come any times; zero means no times." We repeat the exercise. " You, dear, throw me zero kisses with your finger-tips." "The baby gives himself little shake,, laughs and stays where he is. " Have you understood," I repeat in an almost passionate tone of voice. " Send me zero kisses, zero kisses." A pause. General laughter. I make my voice harsh as if I were angry about their laughter, and I ask one very severely, "You come here zero times, come here zero times at once, do you understand? I am saying to you 'Come here zero times'." He does not move. The laughter grows more bois- terous, excited all the more by my change of manner, first of begging,.