330 THE DISCOVERY OF THE CHILD
Now to the sense exercises of recognizing the longer and
shorter pieces, there are added those of numeration. The pieces
having been placed on the ground or mixed up on a table, the
teacher simply shows one of them to the child and counts its
segments, e.g. five. Then she says to the child: " Give me a
longer one." The child chooses by sight, and the teacher verifies-
if he has guessed rather than judged by comparing the lengths
and counting the sections. Such exercises may be repeated many
times. Every piece in the set is now given a name of its own by
which it will be known henceforth: the piece of one, of two, of
three, of four, etc.; finally, for shortness, they are spoken of as-
they are being handled as " the one, the two, the three, the
four", etc.
NUMBERS AND THE WRITTEN SYMBOLS WHICH
REPRESENT THEM
At this point, if the child can write already, he is presented
with the sandpaper numbers, which are used in the same way as
all the other objects presented, that is, in the well-known stages:
"This is one;" "This is two;" "Give me one;" "Give me
two; '* " Which number is this? " The numbers have to be traced
in the same way as the letters.
EXERCISES ON NUMBERS; ASSOCIATION OF THE WRITTEN
SIGN WITH THE QUANTITY
I have made two cases for counting. Each includes a
horizontal tray, divided into five parts by small upright partitions,,
within each of which compartments small objects may be deposited;
a second, a vertical board is attached to the first at right angles-
and is also divided into five parts by lines drawn vertically, a figure
being placed within each space. In the first case are the figures
0, 1, 2, 3, 4; and in the second 5, 6, 7, 8, 9. :
The exercise is obvious. It consists in placing within the en-
closure of the horizontal plane a number of objects corresponding