338
THE DISCOVERY OF THE CHILD
the staircase up to the nine, there being no more figures, there still
remains this kst section which we again begin to mark with 1. But
it is a 1 placed higher, and in order to distinguish it from the
other we put near it a sign which has no value—the zero. Thus
we have 10. Covering the zero with the separate rectangular
numbers, in the order of their succession, there are formed:
11, 12, 13, 14, 15, 16, 17, 18, 19. These numbers are made up
with the rods, putting in succession on the piece of ten that of one,
and then again that of two; then three as a substitute until there is
reached the piece of nine added to that of ten, in doing which we
obtain a very long rod. Counting the alternate blue and red
segments, nineteen is arrived at.
The teacher may then direct the movements of the system of
length showing the cards of the ten and of the figure placed over
the zero, e.g. 16; the child adds to the piece of ten that of six.
The teacher takes from the ten card the 6, and places over the
zero the rectangle which bears e.g. the number eight, giving 18;
the child takes away the rod of the six and places that of the 8.
Every one of such exercises can
then be written out, e.g. 10+6=16;
10+8=18, etc. The procedure would be
the same for subtraction.
When the number itself begins to
have a clear meaning for the child, the
combinations are made with the cards
alone, placing in various ways the rect-
angles which bear the nine figures on
the two columns of numerals, which are
drawn on long cards, as in the figures
A and B.
In card A there is placed over the
zero of the second 10 the rectangle with
1; and underneath, that with 2, etc.;
whilst in the left column there remains
10
10
10
11
10
12
10
13
10
A
14
15
10
16
10
17
10
18
10
19