The diagonal line a connection between the horizontal and vertical;
the right angle as a connection between the obtuse angle (largest) and
the acute angle (smallest); in size of parts the half cube standing
between the whole and quarter cubes.
* * * * *
We have thus far been proceeding from unity to variety, from the whole
to its parts, from the simple to the complex, from easily constructed
forms to those more difficult of manipulation and dictation, until we
have arrived at the fifth gift.
Effect of the Study of Froebel's Gifts on the Kindergartner.
How instructive and delightful have we found this orderly procedure;
this development of great from little things; this thoughtful
association of new and practical ideas with all that is familiar to
the child mind and heart. Every year the training teacher feels it
anew herself, and is sure of the growing interest and sympathy of her
pupils.
Many persons who fail to grasp the true meaning of the kindergarten
seem to consider the balls and blocks and sticks with which we work
most insignificant little objects; but we think, on the other hand,
that nothing in the universe is small or insignificant if viewed in
its right connection and undertaken with earnestness and enthusiasm.
Nothing in childhood is too slight for the notice, too trivial for the
sympathy of those on whom the Father of all has bestowed the holy
dignity of motherhood or teacherhood; and to the kindergartner
belongs the added dignity of approaching nearer the former than the
latter, for hers indeed is a sort of vice-motherhood.
We must always be impressed with the knowledge which we ourselves gain
in studying these gifts and preparing the exercises with them. In
concentration of thought; careful, distinct, precise, and expressive
language; logical arrangement of ideas; new love of order, beauty,
symmetry, fitness, and proportion; added ingenuity in adapting
material to various uses, aesthetic and practical,--in all these ways
every practical student of Froebel must constantly feel a decided
advance in ability.
Then, too, the simple rudiments of geometry have been reviewed in a
new light; we have dealt with solid bodies and planes, and studied
them critically so that we might draw the child's attention to all
points of resemblance or difference; we have found some beautifully
simple illustrations of familiar philosophical truths, and, best of
all, have simplified and crystallized our knowledge of the relations
of numbers so that the child's impressions of them may be easily and
clearly gained.
Why we are required to study deeply and to know more than we teach.
We have been required to look at each gift in its broadest aspect, and
to observe it patiently and minutely in all its possibilities, for the
larger the amount of knowledge the kindergartner possesses, the more
free from error will be her practice.
Unless we know more than we expect to teach, we shall find that our
lessons will be stiff, formal affairs, lacking variety, elasticity,
and freshness, and marred continually by lack of illustration and
spontaneity.
Lack of interest in the teacher is as fatal as lack of interest in the
child; in fact, the one follows directly upon the heels of the other.
For this reason, continued study is vitally necessary that new phases
of truth may continually be seen.
Above all other people the teacher should go through life with eyes
and ears open. Unless she is constantly accumulating new information
her mind will not only become like a stagnant pool, but she will find
out that what she possesses is gradually evaporating. There is no
state of equilibrium here; she who does not progress retrogresses.
It should be a comparatively simple matter to gain enough knowledge
for teaching,--the difficult thing is the art of imparting it. Said
Lord Bacon, "The art of well delivering the knowledge we possess to
others is among the secrets left to be discovered by future
generations."
Relation between Gifts, and their Relation to the Child's Mental and
Moral Growth.
These are a few of the technicalities which have been mastered up to
this time by a faithful study of the gifts of Froebel; and yet they
are only technicalities, and do not include the half of what has been
gained in ways more difficult to describe.
"To clearly comprehend the gifts either individually or collectively
we must clearly conceive their relation to and dependence on each
other, for it is only in this intimate connection that they gain
importance or value."
If the kindergartner does not recognize the relationship which exists
between them and their relation to the child's mental and moral
growth, she uses them with no power or intelligence. We conceive
nothing truly so long as we conceive it by itself; the individual
example must be referred to the universal law before we can rightly
apprehend its significance, and for a clear insight into anything
whatsoever we must view it in relation to the class to which it
belongs. We can never really know the part unless we know the whole,
neither can we know the whole unless we know the part.
Pleasure of Child at New Gift.
In the fifth gift, which, it may be said, can commonly only be used
with profit after the child has neared or attained his fifth year, we
find that we have not parted from our good old friend, the cube, that
has taught us so many valuable lessons. We always find contained in
each gift a reminder of the previous one, together with new elements
which may have been implied before, but not realized. So, therefore,
we have again the cube, but greatly enlarged, divided, and
diversified. When the child sees for the first time even the larger
box containing his new plaything, he feels joyful anticipation,
surmising that as he has grown more careful and capable, he has been
entrusted with something of considerable importance. If he has been
allowed to use the third and fourth gifts together frequently, he will
not be embarrassed by the amount of material in the new object.
Lest he be overwhelmed, however, by its variety as much as by its
quantity, it might be well before presenting the new material as a
whole to allow the child to play with a third gift in which one cube
cut in halves and one in quarters have been substituted for two whole
cubes. He will joyfully discover the new forms, study them carefully,
and find out their distinctive peculiarities and their value in
building. When he has used them successfully once or twice, and has
learned how to place the triangular prisms to form the cube, then the
mass of new material as a whole can have no terrors for him.
How great is his pleasure when he withdraws the cover and finds indeed
something full of immense possibilities; he feels, too, a command of
his faculties which leads him to regard the new materials, not with
doubt or misgiving, but with a conscious power of comprehension.
Its New Features.
At the first glance the most striking characteristics are its greater
size and greater number of divisions, into thirds, ninths, and
twenty-sevenths, instead of halves, quarters, and eighths.
These divisions open a new field in number lessons, while the
introduction of the slanting line and triangular prism makes a decided
advance in form and architectural possibilities.
Importance of Triangular Form.
The triangle, by the way, is a valuable addition in building
exercises, for as a fundamental form in architecture it occurs very
frequently in the formation of all familiar objects. Indeed, the new
form and its various uses in building constitute the most striking and
valuable feature of the gift.
We find it an interesting fact that all the grand divisions of the
earth's surface have a triangular form, and that the larger islands
assume this shape more or less.
The operation of dividing the earth's surface into greater and lesser
triangles is used in making a trigonometrical survey and in
ascertaining the length of a degree of latitude or longitude. The
triangle is also of great use in the various departments of mechanical
work, as will be noted hereafter in connection with the seventh gift.
Difficulties of the Fifth Gift.
The difficulties of the fifth gift are only apparent, for the
well-trained child of the kindergarten sees more than any other, and
he will grasp the small complexities with wonderful ease, smoothing
out a path for himself while we are wondering how we shall make it
plain to him.
Effect of Good Training.
But here let us note that we can only succeed in attaining
satisfactory results in kindergarten work by beginning intelligently
and never discontinuing our patient watchfulness, self-command, and
firmness of purpose,--firmness, remember, not stubbornness, for it is
a rare gift to be able to yield rightly and at the proper time.
If we help the little one too much in his first simple lessons or
dictations; if we supply the word he ought to give; if, to save time
and produce a symmetrical effect, we move a block here and there in
weariness at some child's apparent stupidity, we shall never fail to
reap the natural results. The effect of a rational conscientious and
consistent behavior to the child in all our dealings with him is very
great, and every little slip from the loving yet firm and
straightforward course brings its immediate fruit.
The perfectly developed child welcomes each new difficulty and invites
it; the imperfectly trained pupil shrinks in half-terror and
helplessness, feeling no hope of becoming master of these strange new
impressions.
Arrangement of Pieces.
To return to the specific consideration of the gift, there must be a
plan of arranging the various pieces which go to make up the whole
cube.
We have now for the first time the slanting line, the mediation of the
two opposites, vertical and horizontal, and by this three of the
small cubes are divided into halves and three into quarters. It is
advisable, when building the cube, to place nine whole cubes in each
of the two lower layers, keeping all the divided cubes in the upper or
third layer, halves in the middle row, quarters at the back. Then we
may slide the box gently over the cube as in the third and fourth
gifts, which enables us to have the blocks separated properly when
taken out again, and forms the only expedient way of handling the
pieces.[47]
[47] "This procedure is by no means intended merely to make
the withdrawal of the box easy for the child, but, on the
contrary, brings to him much inner profit. It is well for him
to receive his playthings in an orderly manner--not to have
them tossed to him as fodder is tossed to animals. It is good
for the child to begin his play with the perception of a
whole, a simple self-contained unit, and from this unity to
develop his representations. Finally, it is essential that
the playing child should receive his material so arranged
that its various elements are discernible, and that by seeing
them his mind may unconsciously form plans for using them.
Receiving his material thus arranged, the child will use it
with ever-recurrent and increasing satisfaction, and his play
will produce far more abiding results than the play of one
whose material lies before him like a heap of
cobblestones."--Froebel's _Pedagogics_, page 205.
The exercises with this gift are like those which have preceded it.