These are in number and variety almost endless, as we have thirty-nine
pieces of different characters. Edward Wiebe says: "He who is not a
stranger in mathematics knows that the number of combinations and
permutations of thirty-nine different bodies cannot be counted by
hundreds nor expressed by thousands, but that millions hardly suffice
to exhaust all possible combinations."
These forms naturally separate themselves, Froebel says, into two
distinct series, i. e., the series of squares and the series of
triangles, and move from these to the circle as the conclusion of the
whole series of representations. "From these forms approximating to
the circle there is an easy transition to the representation of the
different kinds of cog-wheels, and hence to a crude preliminary idea
of mechanics."
If the movements begin with the exterior part of the figure instead of
the interior, we should make all the changes we wish in that direction
before touching the centre, and _vice versa_.
Each definite beginning conditions a certain process of its own, and
however much liberty in regard to changes may be allowed, they are
always to be introduced within certain limits.[53]
We should leave ample room for the child's own powers of creation, but
never disregard Froebel's principle of connection of opposites; this
alone will furnish him with the "inward guide" which he needs.[54] It
is only by becoming accustomed to a logical mode of action that the
child can use this amount of material to good advantage.
[53] "With these forms of beauty it is above all important
that they be developed one from another. Each form in the
series should be a modification or transformation of its
predecessor. No form should be entirely destroyed. It is also
essential that the series should be developed so that each
step should show either an evolution into greater
manifoldness and variety, or a return to greater
simplicity."--Froebel's _Pedagogics_, page 225.
[54] "This free activity ... is only possible when the law
of free creativeness is known and applied; for that a free
creativeness only can be a lawful one, we are taught by the
smallest blade of grass, whose development takes place only
according to immutable laws."--_Reminiscences of Froebel_,
page 133.
Dangers of Dictation.
The dictations should be made with great care and simplicity. The
child's mind must never be forced if it shows weariness, nor the more
difficult lessons given in too noisy a room, as the nervous strain is
very great under such circumstances. We should remember that great
concentration is needed for a young child to follow these dictations,
and we must be exceedingly careful in enforcing that strict attention
for too long a time. A well-known specialist says that such exercises
should not be allowed at first to take up more than a minute or two at
a time; then, that their duration should gradually extend to five and
ten minutes. The length of time which children closely and voluntarily
attend to an exercise is as follows: Children from five to seven
years, about fifteen minutes; from seven to ten years, twenty minutes;
from twelve to eighteen years, thirty minutes. A magnetic teacher can
obtain attention somewhat longer, but it will always be at the expense
of the succeeding lesson. "By teachers of high pretensions, lessons
are often carried on greatly and grievously in excess of the proper
limits; but when the results are examined they show that after a
certain time has been exceeded, everything forced upon the brain only
tends to drive out or to confuse what has been previously stored in
it."
We find, of course, that the mind can sustain more labor for a longer
time when all the faculties are employed than when a single faculty is
exerted, but the ambitious teacher needs to remind herself every day
that no error is more fatal than to overwork the brain of a young
child. Other errors may perhaps be corrected, but the effects of this
end only with life. To force upon him knowledge which is too advanced
for his present comprehension, or to demand from him greater
concentration, and for a longer period than he is physically fitted to
give, is to produce arrested development.[55]
[55] "Whoever sacrifices health to wisdom has generally
sacrificed wisdom, too." (Jean Paul.)