The exercise is obvious; it consists in placing within the compartments a number of objects corresponding to the figure indicated upon the card at the back of the compartment. We give the children various objects in order to vary the lesson, but chiefly make use of large wooden pegs so shaped that they will not roll off the desk. We place a number of these before the child whose part is to arrange them in their places, one peg corresponding to the card marked one, etc. When he has finished he takes his tray to the directress that she may verify his work.
The Lesson on Zero. We wait until the child, pointing to the compartment containing the card marked zero, asks, "And what must I put in here?" We then reply, "Nothing; zero is nothing." But often this is not enough. It is necessary to make the child feel what we mean by nothing. To this end we make use of little games which vastly entertain the children. I stand among them, and turning to one of them who has already used this material, I say, "Come, dear, come to me zero times." The child almost always comes to me, and then runs back to his place. "But, my boy, you came one time, and I told you to come zero times." Then he begins to wonder. "But what must I do, then?" "Nothing; zero is nothing." "But how shall I do nothing?" "Don't do anything. You must sit still. You must not come at all, not any times. Zero times. No times at all." I repeat these exercises until the children understand, and they are then, immensely amused at remaining quiet when I call to them to come to me zero times, or to throw me zero kisses. They themselves often cry out, "Zero is nothing! Zero is nothing!"
EXERCISES FOR THE MEMORY OF NUMBERS
When the children recognise the written figure, and when this figure signifies to them the numerical value, I give them the following exercise:
I cut the figures from old calendars and mount them upon slips of paper which are then folded and dropped into a box. The children draw out the slips, carry them still folded, to their seats, where they look at them and refold them, conserving the secret. Then, one by one, or in groups, these children (who are naturally the oldest ones in the class) go to the large table of the directress where groups of various small objects have been placed. Each one selects the quantity of objects corresponding to the number he has drawn. The number, meanwhile, has been left at the child's place, a slip of paper mysteriously folded. The child, therefore, must remember his number not only during the movements which he makes in coming and going, but while he collects his pieces, counting them one by one. The directress may here make interesting individual observations upon the number memory.
When the child has gathered up his objects he arranges them upon his own table, in columns of two, and if the number is uneven, he places the odd piece at the bottom and between the last two objects. The arrangement of the pieces is therefore as follows:—
The crosses represent the objects, while the circle stands for the folded slip containing the figure. Having arranged his objects, the child awaits the verification. The directress comes, opens the slip, reads the number, and counts the pieces.
When we first played this game it often happened that the children took more objects than were called for upon the card, and this was not always because they did not remember the number, but arose from a mania for the having the greatest number of objects. A little of that instinctive greediness, which is common to primitive and uncultured man. The directress seeks to explain to the children that it is useless to have all those things upon the desk, and that the point of the game lies in taking the exact number of objects called for.