curved lines and angles of every degree.

6. The law of mediation of contrasts is no longer illustrated in the
gift itself, but simply governs the use of the material. All lines and
outlines of planes made with a series of dots show its workings, and
the symmetrical figures, as we have noted from the first, owe to it
their very existence.

Meeting-Place of Gifts and Occupations.

When we begin upon a consideration of the tenth gift, the last link in
the chain of objects which Froebel devised to "produce an all-sided
development of the child," we see at once that the meeting-place of
gift and occupation has been reached. The two series are now in fact
so nearly one that the point is much more often used for occupation
work than as a gift. This convergence of the series in regard to their
practical use was first noted in the tablets, and has grown more and
more marked with each succeeding object.

Though the point is in truth the last step which the child takes in
the sequence of gifts as he journeys toward the abstract, yet we are
met at once in practice by the apparently inconsistent fact that it is
one of the first presented in the kindergarten. This can only be
explained by the statement that it is in truth quite as much of an
occupation as a gift, and is used in the former sense among the
child's first work-materials as a preparation for later point-_making_
(perforating), and as an exercise in eye-training and accuracy of
measurement. It is not an occupation, of course, for the reason that
permanent results cannot be produced with it, and because no
transformation of its material is possible.

The Point as a Gift.

Before the child completes his kindergarten course, however, he should
certainly be led to an intellectual perception of the interrelation
of the gifts and their gradual development from solid to point, for
their orderly progression according to law, though it be but dimly
apprehended, will be most useful and strengthening to the mind. To
discern the logical order of a single series of objects is a step
toward the comprehension of world-order in mature life.[78]

[78] "This coming-out of the child from the outer and
superficial and his entrance into the inner view of things,
which, because it is inner, leads to recognition, insight,
and consciousness,--this coming-out of the child from the
house-order to the higher world-order makes the boy a
scholar."--Friedrich Fro