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,.