simply glance at the
sequence of figures even without a thorough explanation, for they
contain demonstratively the larger number of those axioms in
elementary geometry which relate to the conditions of the plane in
regular figures."

As the tablets are used in the kindergarten, they are intended only
"to increase the sum of general experience in regard to the qualities
of things," but they may be made the medium of really advanced
instruction in mathematics, such as would be suitable for a
connecting-class or a primary school. All this training, too, may be
given in the concrete, and so lay the foundation for future
mathematical work on the rock of practical observation.

The kindergarten child is expected only to know the different kinds of
triangles from each other, and to be familiar with their simple names,
to recognize the standard angles, and to know practically that all
right angles are equally large, obtuse angles greater, and acute less
than right angles. All this he will learn by means of play with the
tablets, by dictations and inventions, and by constant comparison and
use of the various forms.

How and when Tablets should be introduced.

As to the introduction of the tablets, the square is first of all of
course given to the child. A small cube of the third gift may be taken
and surrounded on all its faces by square tablets, and then each one
"peeled off," disclosing, as it were, the hidden solid. We may also
mould cubes of clay and have the children slice off one of the square
faces, as both processes show conclusively the relation the square
plane bears to the cube whose faces are squares. If the first tablets
introduced are of pasteboard, as probably will be the case, the new
material should be noted and some idea given of the manufacture of
paper.

There is a vast difference in opinion concerning the introduction of
this seventh gift, and it is used by the child in the various
kindergartens at all times, from the beginning of his ball plays up to
his laying aside of the fifth gift. It seems very clear, however, that
he should not use the square plane until after he has received some
impression of the three dimensions as they are shown in solid bodies,
and this Mr. Hailmann tells us he has no proper means of gaining, save
through the fourth gift.[63]

[63] "The perception of the difference between a
surface-extension and an extension in three dimensions begins
late and is establish