lustration: FIG. 21.--SET OF SIX IRREGULAR FIGURES.]

(6) Finally, there are four plain wooden tablets, _i.e._, without any
geometrical inset, which should have no button fixed to them; also two
other irregular geometrical figures. (Fig. 22.)

[Illustration: FIG. 22.--SET OF FOUR BLANKS AND TWO IRREGULAR FIGURES.]

Connected with this material there is a wooden frame furnished with a
kind of rack which opens like a lid, and serves, when shut, to keep
firmly in place six of the insets which may be arranged on the bottom
of the frame itself, entirely covering it. (Fig. 23.)

[Illustration: FIG. 23.--FRAME TO HOLD GEOMETRICAL INSETS.]

This frame is used for the preparation of the _first presentation_ to
the child of the plane geometrical forms.

The teacher may select according to her own judgment certain forms
from among the whole series at her disposal.

At first it is advisable to show the child only a few figures which
differ very widely from one another in form. The next step is to
present a larger number of figures, and after this to present
consecutively figures more and more similar in form.

The first figures to be arranged in the frame will be, for example,
the circle and the equilateral triangle, or the circle, the triangle
and the square. The spaces which are left should be covered with the
tablets of plain wood. Gradually the frame is completely filled with
figures; first, with very dissimilar figures, as, for example, a
square, a very narrow rectangle, a triangle, a circle, an ellipse and
a hexagon, or with other figures in combination.

Afterwards the teacher's object will be to arrange figures similar to
one another in the frame, as, for example, the set of six rectangles,
six triangles, six circles, varying in size, etc.

This exercise resembles that of the cylinders. The insets are held by
the buttons and taken from their places. They are then mixed on the
table and the child is invited to put them back in their places. Here
also the control of the error is in the _material_, for the figure
cannot be inserted perfectly except when it is put in its own place.
Hence a series of "experiments," of "attempts" which end in victory.
The child is led to compare the various forms; to realize in a
concrete way the differences between them when an inset wrongly placed
will not go into the aperture. In this way he educates his eye to the
_recognition of forms_.

[Illustration: FIG. 24.--CHILD TOUCHING TH