{ Sphere.
{ Cube.
Solids. { Cylinder.
{ Double Cone. } Seen in motion.
{ Conoid. }
Planes. { Circles.
{ Squares.
6. The sphere and cube are sharply contrasting forms, and the cylinder
illustrates the connecting link between the two, possessing
characteristics of both.
"The cylinder is the first example Froebel gives of the intermediate
transition--forms connecting opposites, which he explains as the very
ground plan of Nature, and on which his fundamental law of contrasts
and connection of contrasts, the law of all harmonious development and
creative industry, is based."[20]
[20] E. Shirreff.
* * * * *
Points to be noted in each New Gift.
"That which follows is always conditioned upon that which goes
before,"[21] says Froebel, and he makes this apparent to children
through his educational processes; the gifts show this idea in
concrete form.
[21] "We cannot evolve what has not first been involved."
In entering upon a consideration of the second gift one thing cannot
fail to impress us, and that is the continuous development in each new
set of objects placed before the child; together with an increase of
difficulty or complexity which is never without a corresponding
forethought, careful arrangement, and attention to logical sequence;
thus the newly introduced objects can never seem unnatural to him.
We shall find that in every new gift or occupation there is always a
suggestion of the last, enough to make it a pleasant reminder of
knowledge gained and difficulties surmounted, and so the child sees
not everything painfully strange, but something which at least recalls
to his mind his former friend and familiar playfellow.[22]
[22] "Nothing charms us more than the recognition of the old
in the new. The man who hurries through a foreign city,
indifferent and inattentive to the passing crowd, feels a
quick thrill of pleasure when in the midst of all the
strangers he recognizes a familiar face." (E. Minhinnick.)
Method of Attack in First Exercise.
In the first lesson with the second gift the child will quickly see
the similarities between his former worsted ball and his new
companion, the wooden sphere. Let him take these two balls together,
and find out the similarities and dissimilarities, remembering that
before he compares objects _consciously_, experiences should
invariably be given him.
We should always draw attention to the universal properties of things
first and then proceed to the specific. The qualities common to all
objects are the universal ones: Form, Size, Color, Material, etc. The
invariable rule should be: simple before complex, concrete before
abstract, unity before variety, universal qualities before special
ones.
If we are in doubt as to whether we shall first direct attention to
the similarities or to the dissimilarities between the ball and
sphere, we may recall the educational maxim, "The child's eye always
at first seizes the analogous, the point of union, the whole
connection of things, and only after that begins to discern
differences and opposition."[23]
[23] "The infant mind is transparent to resemblance, but
opaque to difference."--Susan E. Blow, _Symbolic Education_,
page 83.
Ball and Sphere.
In comparing the ball and the sphere the child will observe, in the
first place that they are both round and both roll equally well, but
that one has color, one being without; one is soft, the other hard;
one quiet, one noisy; one a little rough to the touch, the other
velvet smooth. He should find for and by himself, aided by our
suggestive questioning, the reasons for these evident differences.
It is absolutely necessary that each child should have one of the
boxes containing the solids, or at least the three forms of the gift
without the box, rods, and standards, and examine them thoroughly and
often as he will be glad to do.
If the solids as ordinarily manufactured are too costly for a
kindergartner of limited means, she can substitute large marbles,
blocks, and linen thread spools; the material does not matter so long
as each child has the objects to handle.
Value of the Discriminative Power; Method by which it may be developed.
We need not be distressed if the lessons are a little noisy when the
children are making the acquaintance of these wonderful new friends.
To be sure they will pound the wooden forms heartily up and down on
the table (if they are three-year old babies, they certainly would and
should do so); but within bounds what does it matter? If it can be
arranged so that other classes shall not be disturbed, and each child
can have the same opportunity for experimenting as his neighbor, there
will be no great harm done.
We are endeavoring to rouse all the latent energies of the child by
the presentation of these objects to his observation, and he must have
full liberty to make the various experiments which suggest themselves
to him. His desire to hear the sound of the objects is so manifest
that it would be folly to try and thwart it. It is far better to use
the desire for educational purposes and divert it into the channel of
systematized noise. Let us suppose that we are carpenters today and
pound the wooden objects on the floor in exact time with a building
song; let us play we are drummer boys and tap with our drumsticks for
the soldiers to march; or shall we make believe that the sphere is a
woodpecker and let it tap on the trees while we recite some simple
little rhyme?[24]
[24] For second gift songs, see _Kindergarten Chimes_ (Kate D.
Wiggin), pages 32, 33, Oliver Ditson Publishing Co.
"This craving of young children for information," says Bernard Perez,
"is an emotional and intellectual absorbing power, as dominant as the
appetite for nutrition, and equally needing to be watched over and
regulated."
It is not alone the noise of the sphere which delights the child,[25]
though this is always pleasing,--it is the knowledge he is gaining,
the new ideas that dawn upon him for the first time in recognizable
form. It is, in fact, a knowledge of cause and effect. He has often
dropped the woolen ball and pounded it on the table, and it produced
no sound. He does the same with the sphere and recognizes the
difference. He will begin to experiment with other objects, by and by
to classify his knowledge, and finally, he will see and remember that
like causes produce like effects, and in progressing thus far will
have made a tremendous stride. The child will see all the more
clearly, in comparing the woolen ball and wooden sphere, the
difference between soft and hard, rough and smooth, light and heavy,
if he is allowed to perform his own experiments.
[25] "The sound is a yet higher sign of life to the child,
as he then, and also later, likes to lend speech to all dumb
things; therefore he also desires to hear sound and speech
from everything."--Froebel's _Pedagogics_, page 72.
The Cube.
We will now turn to the investigation of the cube and open a new world
of information to the child, and here we seem to deviate a little from
the famous educational maxim, "Proceed from the known to the unknown,"
and almost to make a leap into the dark. However, we very soon give
the cylinder, and thus connect the opposites. Here he meets a dazzling
quantity of new appearances; the square sides or faces, and the many
edges and corners, all of which must be viewed in comparison with the
sphere. We can give him an experience of the faces of the cube without
conscious analysis, by letting the ball roll against them.
Mediation of Contrasts.
Of course we shall see the underlying idea of the gift to be the
connection of opposites. Not too much can be said of this law, so
all-important and significant in Froebel's system.[26] We should bear
it constantly in mind, and bring it in connection with every new phase
of our work. Froebel cannot be understood clearly unless this deep
principle, which lies at the very root of his system, is appreciated
and comprehended. At the same time it is, when formulated, an abstract
and metaphysical statement, which one cannot grasp at once, but to
which one must grow.
[26] "But each thing is recognized only when it is connected
with the opposite of its kind, and when the union, accord,
similitude with this object are found; and the connection
with the opposite, and the discovery of the uniting, renders
the recognition so much the more complete."--Froebel's
_Education of Man_, page 26.
It may be said that comparatively few kindergartners know its value;
nevertheless knowledge of this kind can never be useless or fruitless
to the person who is forming the mind of the child, and who should be
a perfect mistress of her science and her art.
Value of Contrasts.
These contrasts of the second gift, and all contrasts, arouse the mind
to attention. We can have no judgment without comparison. We should
have no idea of heat or darkness if we had not a conception of cold
and light; the quality of sweetness would have no meaning if its
opposite did not serve to stimulate comparison.
The sphere is sharply contrasted with the cube, so that there may be a
ready perception of the striking qualities of both. The more abrupt
the contrast the more readily noticed and described; for it takes a
more developed eye to discern the difference between a sphere and a
spheroid, for instance, than between a sphere and a cube.
The contrasts of the first gift were contrasts of color, mediations of
them being shown also, and contrasts of direction and position or
situation. Another point less readily seen in the first gift perhaps
was Froebel's thought that the ball, in its perfect simplicity and
unity, when first given to the young child, is regarded by him as
another contrasted individuality, almost as capable of life in its
varied movements as he is himself.
Mobility of Sphere.
The sphere is the symbol of motion, the cube the embodiment of rest,
and the fact should be illustrated in divers ways. We may, for
instance, place the sphere near the rim of a plate, and by inclining
the latter a little, the sphere will roll rapidly round its own axis
and round the rim. A few simple little rhymes may be taught, which the
children may say or sing together while the sphere is journeying
rapidly round and round the plate, for, as Froebel says, the thought
always grows clearer to the child when word and motion go hand in
hand.
Sphere and Cube.
The cube can only be moved, on the contrary, when force is exerted,
and then it merely slides, to stop when the force is removed. The
children will soon see why the cube is so lazily inclined, and why the
sphere is ever rolling, rolling about, scarcely to be kept still, for
by various experiments we may show that the sphere stands only on a
little part of its face, the cube on the whole.
The sphere is always the same in whatever way regarded, and to
whatever tests subjected. It is always an emblem of unity, and cannot
be robbed of its simplicity, its unity, its freedom from all that is
puzzling.
The cube, on the contrary, being made to revolve on any one of its
axes, constantly shows a different aspect, so that the child views it
as a very extraordinary little block, full of fascinating surprises
and whimsical apparitions.
It is put upon the string, and, when whirled rapidly, mysteriously
loses its identity, and appears to the little one's laughing gaze as
an entirely different object; and yet as the motion grows more sedate,
the new form fades away and the cube reappears so quickly as to make
him rub his eyes and wonder if he has been dreaming.
Counting Faces.
The square faces of the cube, in comparison with the one curved,
unbroken surface of the sphere, must now be noted, and may be counted
if we are using the gift as a means of instruction.
We must beware, however, of making this counting exercise into a
lesson, or requiring 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 twisted rapidly
and caused to revolve; in this motion a cylinder being readily seen.
When the cylinder is spun in like manner a sphere suddenly appears,
and so the wonderful and subtle bond of union is complete.[28]
[28] "On revolving the cylinder on an axis parallel to the
circular faces, we find that it incloses a solid, opaque
sphere; teaching us the lesson, not only that each member of
the second gift contains each and all of the others, but that
whatever is in the universe is in every individual part of
it; that even the meanest holds the elements of the noblest;
that the highest life is even in what in short-sighted
conceit we call death."--W. N. Hailmann, _Law of Childhood_,
page 35.
Hints as to Manner and Method.
Let the children call the cylinder a "roller" or "barrel" if they
choose, and tell them the right name when it is needful. Each gift
must be thoroughly understood before we pass to the next, or there
will be no orderly development; but as the impressions have all been
made through the senses of the child, we must not expect him to voice
these impressions in logical phrases all at once, so beware of making
the lesson irksome or wearisome to him through a formal questioning
that does not properly belong to childhood.
When the keen appetite for knowledge disappears we may well despair.
If several children in our class express dislike of a certain exercise
or lesson, and seem to dread its appearance, we may be well assured
that the fault lies in our method of putting it before them, and
strive in all humility for a better understanding of them, of
ourselves, and of the subject.
We must not, however, be too hard in our self-judgments and lose
courage. We are not responsible for a child who is "born tired," and
who seems to have no interest in anything, either in heaven above or
in the earth beneath, until, by ingenuity and perseverance, we are
able to open the eyes and ears which see and hear not.
It will be remembered that in discussing the first play or lesson with
the second gift great freedom was advised; but let us note the
difference between liberty and lawlessness, between spontaneity and
the confusion of self-assertion which is sometimes mistaken for it.
No lesson or play amounts to anything unless conducted with order and
harmony, unless at its close, no matter how merry and hearty the
enjoyment, some quiet and lasting impression has been made on the
mind. Many teachers miss the happy medium, and in trying with the best
intentions to allow the individuality of the child proper development,
only succeed in gaining excitement and disorder.
Dangers of Object Lessons.
The second gift is, more than any other, too much used for mere object
lessons, and these are invariably dangerous because there is apt to be
too much impressing of the teacher's own ideas upon the mind, and too
little actual handling, perceiving, observing, comparing, judging,
concluding, on the child's part, and that is the only logical way in
which he is able to form a clearly crystallized idea.
We can have no higher authority than Dr. Alexander Bain, who says that
the object lesson more than anything else demands a careful handling;
there being "great danger lest an admirable device should settle down
into a plausible but vicious formality."
How to deal successfully with Second Gift.
It is not uncommon to hear students in kindergarten training classes
(and even some full-fledged kindergartners) express a distaste for the
second gift, and it is, unfortunately, even more common to find the
children dealing with it either sunk in deepest apathy, or mercifully
oblivious of the matter in hand and chatting with their neighbors. The
fact is that we have too commonly made the exercises dull, dreary
affairs; we have doled out the forms to the children and asked a
series of formal questions about them, giving no experiments, no
concerted work, and no opportunity for action. The children have been
intensely bored, therefore either stupid or wandering, and the
kindergartner has attributed her want of success to the gift, and not
to her method of dealing with it.
Let the light of imagination shine on the scene, and note the
answering sparkle in the children's eyes. Who cares for the names of
all the faces on a stupid block; but who doesn't care when it's a
house and Johnnie can't find his mother, though he looks in the front
door and the back door, the right-hand door, the left-hand door, the
cellar-door, and finally the trap-door leading to the roof? Nobody
knows, or wants to know, when questioned if the cylinder rolls better
on its flat circular face, or on its rounding face; but when it's a
log of wood in the forest, and must be taken home for winter fires,
then it is worth while to experiment and see how it may be moved most
easily.
The second gift, too, is delightful for groupwork in the sand table,
where the objects may be treated symbolically, and likened to a
hundred different things. With the second gift beads, which in the
natural wood color are admirable supplements to the larger forms, the
children are always charmed, assorting and stringing them according to
fancy or dictation, and with the addition of sticks making them into
rows of soldiers, trees in flowerpots, kitchen utensils, churns,
stoves, lamps, and divers other household objects.
The kindergartner may give many a lesson in the simple principles of
mechanics with the second gift and its rods and standards, allowing
the children to experiment freely as well as to follow her
suggestions. The pulley, the steelyard, the capstan, the pump, the
mechanical churn, the wheelbarrow, etc., may all be made, adding the
beads where necessary, and thus the child gain a real working
knowledge of simple machinery.
Treatment of Previous Gifts when passed over.
The preceding gift need not entirely disappear, but be used
occasionally for a pleasing review as a bond of friendly intercourse
between older and younger pupils.[29] This will convey an indirect
hint, perhaps, to the little ones that it is not well to neglect old
friends for new ones, but that they should still love and value the
playthings and playmates of former days.
[29] "The giving of a new play by no means precludes the
further use of the preceding and earlier plays. But, on the
contrary, the use of the preceding play for some time longer
with the new play, and alternating with it, makes the
application of the new play so much the easier and more
widely significant."--Froebel's _Pedagogics_, page 145.
Second Gift Forms in Architecture and Cube in Ancient Times.
These three objects, the sphere, cylinder, and cube, constitute a
triad of forms united in architecture and sculpture producing the
column, which is made up of the pedestal or base (the cube), the shaft
(the cylinder), and the capital (the sphere).
In a book on Egyptian antiquities we find that, in the beginning of
the culture of that country, the three Graces, or goddesses of beauty,
were represented by three cubes leaning upon each other. The Egyptians
did not, of course, know that it was the first regular form of solid
bodies in nature or crystallization; but the significant fact again
brings us to the thought expressed in the first lecture: "It would
seem, indeed, as though Froebel, in selecting his gifts, looked far
back into the past of humanity, and there sought the thread which from
the beginning connects all times and leads to the farthest future."
Froebel's Monument.
And here we leave the second gift, that trinity of forms which,
wrought in marble, marks the place dear and sacred to all
kindergartners, the grave of Froebel,--a simple monument to one so
great, yet so connected with our study and the child's experience that
with all its simplicity it is strangely effective. A still more
enduring monument he has in the millions of happy children who have
found their way to knowledge through the door which he opened to them;
indeed, if half the children he has benefited could build a tower of
these tiny blocks to commemorate his life and death, its point would
reach higher than St. Peter's dome and draw the thoughts of men to
heaven.
Suggestions of the Gift.
This gift can hardly be studied but that an inner unity, born of these
reconciled contrasts, suggests itself to the imagination.
The cube seems to stand as the symbol of the inorganic, the mineral
kingdom, with its wonderful crystals; the cylinder as the type of
vegetable life, suggesting the roots, stems, and branches, with their
rounded sides, and forming a beautiful connection between the cube,
that emblem of "things in the earth beneath," and the sphere which
completes the trinity and speaks to us of a never-ending and perfect
whole having "Unity for its centre, Diversity for its circumference."
The cube seems to suggest rest, immobility; the cylinder, in this
connection, growth; and the sphere, perfection, completeness,--so
delicately poised it is,--only kept in its proper place by the most
exquisite adjustment. And so to us, sometimes, the things that are
visible become luminous with suggestions of greater realities which
are yet unseen; and in the least we discern a faint radiance of the
greatest.
Things that are small mirror things that are mighty. The tiny sphere
is an emblem of the "big round world" and the planetary systems. The
cube recalls the wonderful crystals, and shows the form that men
reflect in architecture and sculpture. As for the cylinder it is
Nature's special form, and God has taught man through Nature to use it
in a thousand ways, and indeed has himself fashioned man more or less
in its shape.
Mr. Hailmann says: "The second gift presents types of the principal
phases of human development; from the easy mobility of infancy and
childhood,--the ball,--we pass through the half-steady stages of
boyhood and girlhood, represented in the cylinder, to the firm
character of manhood and womanhood for which the cube furnishes the
formula."
Bishop Brooks, speaking from the words, "The length and the breadth of
it are equal," in his sermon on Symmetry of Life, uses the cube as a
symbol of perfect character: The personal push of a life forward, its
outreach laterally or the going out in sympathy to others, the upward
reach toward God,--these he considers the three life dimensions. But
such building must be done without nervous haste; the foundation must
hint solidly of the threefold purpose; length, breadth, and thickness
must be kept in proportion, if the perfect cube of life is ever to be
found.
NOTE ON SECOND GIFT. [30] "The second gift, even in the nursery, calls
for modifications from the form in which it comes to us from Froebel.
It is incomparable in its rich symbolism for illustrating Froebel's
thought to mature minds, and answers quite a useful purpose in the
nursery, where it may help mamma tell her stories. But in the
kindergarten the child wants to build with blocks. Hence, the third,
fourth, fifth, and sixth gifts are indicated; the second gift, as
such, is, to say the least, an anachronism. Only in the form of the
beads, or some similar expedient which gives many of these things for
control, will it satisfy the kindergarten child. When he is expected
to _study_ the cube, as an object lesson, to count the squares and
corners and tell where they are, it is wholly unpalatable to him and
entirely foreign to his plans."
[30] W. N. Hailmann.