Illustration: FIG. 25.--SERIES OF CARDS WITH GEOMETRICAL FORMS.]

Corresponding to every form reproduced in the plane insets there are
three white cards square in shape and of exactly the same size as the
wooden frames of the insets. These cards are kept in three special
cardboard boxes, almost cubic in form. (Fig. 25.)

On the cards are repeated, in three series, the same geometrical forms
as those of the plane insets. The same measurements of the figures
also are exactly reproduced.

In the first series the forms are filled in, _i.e._, they are cut out
in blue paper and gummed on to the card; in the second series there is
only an outline about half a centimeter in width, which is cut out in
the same blue paper and gummed to the card; in the third series,
however, the geometrical figures are instead outlined only in black
ink.

By the use of this second piece of the material, the exercise of the
eye is gradually brought to perfection in the recognition of "plane
forms." In fact, there is no longer the concrete control of error in
the material as there was in the _wooden_ insets, but the child, by
his eye alone, must judge of identities of form when, instead of
_fitting_ the wooden forms into their corresponding apertures, he
simply _rests_ them on the cardboard figure.

Again, the refinement of the eye's power of discrimination increases
every time the child passes from one series of cards to the next, and
by the time that he has reached the third series, he can see the
relation between a wooden object, which he holds in his hand, and an
outline drawing; that is, he can connect the concrete reality with an
_abstraction_. The _line_ now assumes in his eyes a very definite
meaning; and he accustoms himself to recognize, to interpret and to
judge of forms contained by a simple outline.

The exercises are various; the children themselves invent them. Some
love to spread out a number of the figures of the geometric insets
before their eyes, and then, taking a handful of the cards and mixing
them like playing cards, deal them out as quickly as possible,
choosing the figures corresponding to the pieces. Then as a test of
their choice, they place the wooden pieces upon the forms on the
cards. At this exercise they often cover whole tables, putting the
wooden figures above, and beneath each one in a vertical line, the
three corresponding forms of the cardboard series.

Another game invented by the children consists in p