ent. _Owen Jones_.
Art. _Sir John Lubbock_.
How to Judge a Picture. _Van Dyke_.

[77] Circulars of Information of the Bureau of Education,
No. 4, 1882.

FROEBEL'S TENTH GIFT

THE POINT

"The awakening mind of the child ... is led from the material
body and its regular division to the contemplation of the
surface, from this to the contemplation of the line and to
the point made visible." FRIEDRICH FROEBEL.

"And it is precisely thus that the first artistic work of
primeval man occurs; he begins by the forming of simple rows,
as strings of beads, or of shells, for instance."
H. POESCHE.

"For the last step in this analysis the child receives small
lentil seeds or pebbles--concrete points, so to speak--with
which he constructs the most wonderful pictures."
W. N. HAILMANN.

1. The point made concrete, which forms the tenth and last of
Froebel's gifts, is represented by many natural objects, by beans,
lentils, pebbles, shells, leaves, and buds of flowers, by seeds of
various kinds, as well as by tiny spheres of clay and bits of wood
and cork.

2. We have been moving by gradual analysis from the solid through
the divided solid, the plane and the line, and thus have reached in
logical sequence the point, into a series of which the line may be
resolved.

3. The point which was visible in the preceding gifts, but inseparable
from them, now in the tenth gift has an existence of its own.
Although it is an imaginary quantity having neither length, breadth,
nor thickness, yet it is here illustrated by tangible objects which
the child can handle. By its very lack of individuality, it lends
itself to many charming plays and transformations.

4. By the use of the point the child learns practically the
composition of the line, that its direction is determined by two
points, that the shortest distance between two points is a straight
line, and that a curved line is one which changes its direction at
every point. The gift closes the series of objects obtained by
analysis from the solid, and prepares for the occupations which are
developed by synthesis from the point.

5. The outlines of all geometrical plane figures both rectilinear and
curvilinear may be illustrated with the point as well as straight and