he has built the tower, the child, with a blow of his hand,
knocks it down, so that the cubes are scattered on the carpet, and
then he builds it up again.

[Illustration: FIG. 10.--CHILD PLAYING WITH TOWER. (PHOTO TAKEN AT MR.
HAWKER'S SCHOOL AT RUNTON.)]

[Illustration: FIG. 11.--THE BROAD STAIR.]

[Illustration: FIG. 12.--THE LONG STAIR.]

(2) Ten wooden prisms, colored brown. The length of the prisms is
twenty centimeters, and the square section diminishes from ten
centimeters a side to the smallest, one centimeter a side. (Fig. 11.)

The child scatters the ten pieces over a light-colored carpet, and
then beginning sometimes with the thickest, sometimes with the
thinnest, he places them in their right order of gradation upon a
table.

(3) Ten rods, colored green, or alternately red and blue, all of which
have the same square section of four centimeters a side, but vary by
ten centimeters in length from ten centimeters to one meter. (Fig.
12.)

The child scatters the ten rods on a large carpet and mixes them at
random, and, by comparing rod with rod, he arranges them according to
their order of length, so that they take the form of a set of organ
pipes.

As usual, the teacher, by doing the exercises herself, first shows the
child how the pieces of each set should be arranged, but it will often
happen that the child learns, not directly from her, but by watching
his companions. She will, however, always continue to watch the
children, never losing sight of their efforts, and any correction of
hers will be directed more towards preventing rough or disorderly use
of the material than towards any _error_ which the child may make in
placing the rods in their order of gradation. The reason is that the
mistakes which the child makes, by placing, for example, a small cube
beneath one that is larger, are caused by his own lack of education,
and it is the _repetition of the exercise_ which, by refining his
powers of observation, will lead him sooner or later to _correct_
_himself_. Sometimes it happens that a child working with the long
rods makes the most glaring mistakes. As the aim of the exercise,
however, is _not_ that the rods be arranged in the right order of
gradation, but that the child _should practise by himself_, there is
no need to intervene.

One day the child will arrange all the rods in their right order, and
then, full of joy, he will call the teacher to come and admire them.
The object of the exer