feel the little buttons and
finds that some cylinders have too much room. He thinks that perhaps
they are out of their right place and tries to place them correctly.
He repeats the process again and again, and finally he succeeds. Then
it is that he breaks into a smile of triumph. The exercise arouses the
intelligence of the child; he wants to repeat it right from the
beginning and, having learned by experience, he makes another attempt.
Little children from three to three and a half years old have repeated
the exercise up to _forty_ times without losing their interest in it.

If the second set of cylinders and then the third are presented, the
_change_ of shape strikes the child and reawakens his interest.

The material which I have described serves to _educate the eye_ to
distinguish _difference in dimension_, for the child ends by being
able to recognize at a glance the larger or the smaller hole which
exactly fits the cylinder which he holds in his hand. The educative
process is based on this: that the control of the error lies in _the
material itself_, and the child has concrete evidence of it.

The desire of the child to attain an end which he knows, leads him to
correct himself. It is not a teacher who makes him notice his mistake
and shows him how to correct it, but it is a complex work of the
child's own intelligence which leads to such a result.

Hence at this point there begins the process of auto-education.

The aim is not an external one, that is to say, it is _not_ the object
that the child should learn how to place the cylinders, and _that he
should know how to perform an exercise_.

The aim is an inner one, namely, that the child train himself to
observe; that he be led to make comparisons between objects, to form
judgments, to reason and to decide; and it is in the indefinite
repetition of this exercise of attention and of intelligence that a
real development ensues.

* * * * *

[Illustration: FIG. 9.--THE TOWER.]

The series of objects to follow after the cylinders consists of three
sets of geometrical solid forms:

(1) Ten wooden cubes colored pink. The sides of the cubes diminish
from ten centimeters to one centimeter. (Fig. 9.)

With these cubes the child builds a tower, first laying on the ground
(upon a carpet) the largest cube, and then placing on the top of it
all the others in their order of size to the very smallest. (Fig. 10.)
As soon as