ing that the number of faces shall be learned and
recited. Every teacher of experience will corroborate Mr. W. N.
Hailmann when he says: "If the kindergartner sets the cube before the
child and counts the faces, edges, and corners, so that he may 'know
all about it,' the child's interest, if born at all, will soon die."

If the faces are counted, as they are all so exactly alike, the
children may sometimes be puzzled as to the number, by enumerating the
same one more than once. This difficulty may be obviated by pasting a
paper square of a different color on each face, and then submitting it
to examination, giving each child an opportunity to count, since
independent self-activity is to be more and more encouraged.

If the faces, edges, and corners be made the integral point of an
interesting story or play, the child will have little difficulty in
recalling their number and character, but we must remember that
"lively interest and steady progress come only from following and
feeding the child's purposes."

Cylinder.

We now proceed to the cylinder, the reconciliation of the two
opposites; an object which having qualities possessed by both occupies
a middle ground in which each has something in common.

Froebel originally took the doll[27] as the intermediate form "uniting
in itself the opposites of the sphere and cube," and thus showed that
he understood child nature well, for no toy follows the ball with
greater certainty than the doll.

[27] "But now as man both unites the single, which finds its
limits in itself, and the manifold, which is constantly
developing, and reconciles them within himself as opposites,
there results also to the child from both, from _sphere_ and
_cube_ outwardly united, the expression of the animate and
active, especially as embodied in the _doll_."--Froebel's
_Pedagogics_, page 106.

The cylinder, however, was subsequently selected, as being more in
line with the other geometrical forms shown in the sequence of gifts.
It is as easily moved as the sphere, upon one side; as prone to rest
as the cube, when placed upon the other; it has the curved surface of
the sphere and the flat faces of the cube; it has no corners but two
curved edges; more edges than the sphere, fewer than the cube; less
unity than the sphere, more than the cube.

Its importance as a mediation, or connecting link, is further shown by
suspending the cube on a string, by which it may be