{ Circles.
{ Semicircles.
Planes. { Quadrants.
{ Sectors.
{ Segments.
By the union of straight and curved lines (sticks and rings) the
entire geometry of the circle may be illustrated, and the child
may thus become acquainted with the appearance of the
Diameter.
Radius.
Circumference.
Chord.
Arc.
6. The law of mediation of contrasts is shown as follows: the
semicircles, when placed on the table with ends towards right or left,
connect points of opposite direction up and down, and when placed with
ends pointing upward or downward they connect the right with the left
side.
The circle is of course an unending line traced from a given point
back to itself, according to certain laws, but it is also a union of
two semicircles curving outward in opposite directions. "It is a
representation of the general law, since the periphery and centre
stand in contrast to each other, and are connected by the
radii."--(Froebel.)
* * * * *
The New Gift and its Charms.
Having already analyzed straight lines in the sticks, we will pass
directly to the consideration of the ninth in the series of Froebel's
gifts, the rings, which are whole, half, and quarter circles of bright
silvered wire.
If the sticks were fascinating to the child as the embodied straight
edge or line, and perfect treasure-houses of new possibilities to the
kindergartner, the rings are just a bit more delightful as, with their
glittering surface and curved lines, and their wonderful property of
having neither beginning nor end, they are quite different in
appearance from anything which precedes or follows them. Of course the
child sees at once that here is an entirely new field for invention,
and he hastens to possess it, fully conscious of his power of
combining the new elements.
Introduction of the Ring.
We must first discuss the new form with the children so as to be
certain that they fully understand its relation to the other gifts.
Perhaps in a previous exercise with the eighth gift we have allowed
the children to experiment with a stick, and to break it partially in
a number of places so as to produce a measurably correct curved line,
afterwards promising them that they should soon have perfect curves to
play with. This exercise has its value because it illustrates
practically that a curved line is one which changes its direction at
every point.
Let us see when to-day's play begins if the children can think of any
way to make such curves, save by the stick already used. Some
quick-witted little one will remember at once the surface of the ball
and his repeated experiments in dividing it, and will suggest in
sufficiently plain words that a curved line might be made from a clay
sphere. His neighbor thinks a clay cylinder would make one more
easily, and both experiments are tried by all the children with a
resultant of quite perfect clay rings. Then some one wants to make
paper rings, and some one else cloth rings, and the wise kindergartner
encourages all this experimenting, knowing that "the power of memory
increases in the same ratio as delight, animation, and joy are
connected with free mental activity."
Material of the Rings.
When the wire rings are at last given, some conversation about their
material will be pleasant and timely, as it is of a kind we have not
had before in the gifts, and shall not have again. The children will
see that it is akin to the substance of which their sewing and weaving
needles and their scissors are made, and possibly some one may know
that both are products of iron. At this juncture it may be well to
show a piece of iron, to let the children handle it and note its
various properties, and while this is being done, to tell them of the
many parts of the world in which it is found, of its great strength
and usefulness, and that its value is greater than that of the shining
yellow gold. A description of iron mines will easily follow, and the
children will delight to hear of the great shafts sunk deep in the
earth, of the baskets in which the miners travel up and down, of the
darkness underground where they toil all day with pick and shovel, of
the safety lamps they carry in their caps, of the mules that drag the
loads of iron ore to and fro, and--startling fact, at which round eyes
are invariably opened--that some of these mules have their stables
down in the ground below, and never come up where the sun shines and
the flowers bloom. If there is a foundry in the vicinity of the
kindergarten, and we can take the little ones to see the huge
furnaces, the intense fires, the molten iron, and the various
roasting, melting, and moulding processes necessary in refining the
ore, they will gain an ineffaceable idea of the value of the metal in
human labor, and of the endless chain of hands, clasped each in the
other, through which the slender wire rings have passed to reach them.
First Exercises.
In the first dictation exercise several whole circles of the same size
may be given, and their equality shown by laying one on top of the
other. Then we may lay them side by side in actual contact, and the
important fact will be discovered by the children that circles can
touch each other at one point only. Subsequent exercises take up rings
of different sizes, when concentric circles are of course made,
showing one thing completely inclosed in another, and next follow the
half and quarter rings, which the children must be led, as heretofore,
to discover and make for themselves.
With the semicircles, which offer still richer suggestions for
invention than the whole rings, another property of the curved line is
seen. Two blocks, two tablets, two sticks could not touch each other
without forming new angles, nor could they be so placed as to produce
a complete figure. Two semicircles, on the other hand, form no new
angles when they touch, and they may be joined completely and leave no
opening.
In his work with the sticks the child became well versed in handling a
comparatively large amount of material, so that now he can deal
successfully from the first exercise with a fair number of whole,
half, and quarter rings. We must be careful, however, not to give him
too many of these in the beginning, lest he be overwhelmed with the
riches at his command.[75]
[75] "The number of rings should only gradually be augmented.
Satiety destroys every impulse of creation."--Emma Marwedel,
_Childhood's Poetry and Studies_, page 15.
When the Rings should be introduced.
The rings should not be used freely until the child is familiar with
vertical, horizontal, and slanting lines, and not only familiar in the
sense of being able to receive and obey dictations intelligently, but
in constantly making correct and artistic use of them in his
creations. The practice with them, however, is often deferred entirely
too long, and the intense pleasure and profit which the child gains
from the beautiful and satisfying curved line are not given him until
very late in the kindergarten course. This is manifestly unnecessary,
for although, if we introduce Froebel's gifts and occupations in
orderly sequence, we make greater use of the straight line after the
first and second gifts are passed than we do of the curve, yet we
should not end with it, nor accept it as a finality; neither should
we keep the child tied down altogether to the contemplation of such
lines.
There is no need of exhausting all the possibilities of the straight
line before beginning work with the curve, for sufficient difficulties
could be devised with the former to last an indefinite length of time.
If the child understands the relation of the edge to the solid, and of
the outline to the body; if he is skilled in the use of six to a dozen
sticks laid in various positions, he can appreciate perfectly the
relation of the curved edge or line to the spherical and circular
objects which he has seen in the kindergarten. He remembers the faces
of the cylinder, the conversation about spherical and flat rounding
objects in his plays with the ball, and he has seen the circular as
well as square paper-folding.
He will be accustomed in that to the appearance of the semicircle,
segment, quadrant, and sector, and will take great delight in cutting
and drawing rings and crescents if we open the way for him.
How we may keep the Curve before the Child's Eye.
Although the gifts, from third to ninth, illustrate straight lines,
angles, and rectilinear figures, yet the occupations present many
facilities for keeping the curve before the eye of the child. In
sewing, we introduce curving outlines during the study of the ball,
and work out a series of objects in the vegetable and animal world in
order to vary the mathematical precision of the making of lines,
angles, and geometrical figures, as well as to illustrate more fully
the spherical form.
We may also use the circular paper-folding in some simple sequence as
early as the child's development will permit, and we have, of course,
at the very outset, the occupation of modeling, which is one of the
most valuable of aids in this matter, and the stringing of wooden
spheres and beads.
The thread game enters here also, and makes a useful supplement to the
rings, as the wet thread may be pushed while it lies on the surface of
the table or slate into numberless different forms, all of which may
be included under curving outlines.
In linear drawing we give the child lines running in various
directions at the earliest possible time, so that he may not grow into
a strained and unnatural position of the hand, for this constant
drawing of the vertical line, which is necessary to its execution with
perfect precision by the young child, limits the freedom of the wrist
and muscles, and instead of preparing him to write a good hand, does
absolutely the reverse. The various exercises, on the other hand, in
drawing the curves of circle and oval and their combinations are quite
perfect preparations for clear, graceful penmanship.
We also have, in drawing, Miss Emma Marwedel's circular system, and
the outline work performed by means of pasteboard patterns, most of
which are of the curving outlines of leaves, flowers, fruits, and
vegetables. When the children can draw quite well from these patterns
we always encourage the drawing without them, merely looking at the
object to be copied.
These exercises are of the greatest value as connected with modeling
when the subjects chosen for invention are comprehended under the
sphere, prolate and oblate spheroid, ovoid, cone, etc., the cube with
its straight lines coming last of all.
In this way, while keeping up the regular sequence of lessons and
occupations with the straight line, we do not debar the child from the
contemplation of the line of beauty.
Uniting the Straight and Curved Lines.
After this, he takes great pleasure in uniting the straight and curved
lines in his inventions with the sticks and rings given him together,
and is quite able to use them separately or unitedly in his creative
work. About this time the fruit of these exercises will begin to
appear in his drawing. He will attempt to unite his straight lines by
curves, and even essay large designs in curves which will be far from
perfect, but nevertheless will not be without their value.
Copying Inventions.
The first trials of this kind may be in copying the inventions in
rings which he has made on his table, exactly as he previously
transferred his stick inventions to the slate. The spaces should be
just as carefully counted, and accuracy expected in preserving the
numerical proportions. But this needs much tact and patience on the
part of the kindergartner, as well as skill in teaching; for the
principles of drawing the curve are much less obvious to the child and
much more difficult for him to comprehend than the measurement and
calculation of straight lines with their various lengths and
inclinations.
These inventions with rings, which are often wonderfully
beautiful,--so beautiful, in fact, that the uninstructed person is
sometimes skeptical as to their production by the children,--may also
be preserved in permanent form by parquetry. It is furnished in
various colors for this gift, as for the seventh and eighth, and is
greatly enjoyed by the children.
If any should fear that the long contemplation of rectangular solids,
planes, and straight lines in Froebel's gifts should tend towards too
great rigidity and barrenness of imagination in inventive work, it is
obviously within our power, as has been shown, to vary this
mathematical exactness, which is no doubt less agreeable to the child
than the graceful image of his own fancy (could he attain it), by
introducing the curve freely into many of the occupations and
exercises with the kindergarten material in general.
Forms of Life, Beauty, and Knowledge.
The rings are of course not as well adapted to the production of
objects constructed by man as were the sticks, but, nevertheless, the
material is not without value in this direction. Various fruits,
flowers, and leaves may be made, as well as such objects as bowls,
goblets, hour-glasses, baskets, and vases. When connected with sticks,
the number of Life forms is obviously much increased on account of the
union of straight and curved lines thus made possible. Tablets may
also be added and contribute a new element to the possibilities for
invention.
For symmetrical forms, however, the gift is admirably adapted, since
the child can hardly put two rings together without producing
something pleasing.[76] Borders enter here in great variety, tablets
and sticks being added when desirable, and the group work forms,
combining the seventh, eighth, and ninth gifts, give full play to the
creative impulses of the child, while calling constantly upon those
principles of design which he has learned empirically.
[76] "It is true that the child produces forms of beauty with
other material also, but it is the curved line which offers
the strongest inducements to attempt such forms, since even
the simplest combinations of a small number of semicircles
and circles yield figures bearing the stamp of beauty."--H.
Goldammer's _The Kindergarten_, page 177.
The forms of knowledge which can be made with the ninth gift are
necessarily few. It is not especially well fitted for number work, and
development of geometrical form is limited to the planes and lines of
the circle.
Wooden Rings.
Miss Emma Marwedel introduced a supplement to the ninth gift in the
form of wooden circles and half-circles in many colors. These are much
heavier than the metal rings, therefore somewhat easier to handle and
give, as she claims, "the child's creative powers a much larger field
for aesthetic development." Of course, this larger field is to be
found in color blending, not in beauty of design, as the form elements
remain the same. The bright hues are undoubtedly a great attraction,
however, and perhaps are in line with that return to color which was
noted in the seventh gift, when the architectural forms were laid
aside. If we adopt the wooden rings we need not on that account lay
aside the metal ones, for the two materials may be combined to great
advantage.
Difficulties of the Gift.
The gift presents little difficulty, the dictations requiring less
concentration than heretofore as the positions in which the rings may
be placed are few and simple. Froebel's purpose evidently was that the
child should now concentrate his activity entirely upon design, and
that he should use the material by itself, and in connection with
sticks and tablets to give out in visible form whatever aesthetic
impressions he had received through the preceding gifts. The office of
the kindergartner is hardly now more than to suggest, merely to watch
the child in his creative work, and to advise when necessary as to
the most artistic disposition of the simple material. She may here, if
she adopts this attitude, have the experience of seeing the direct
result of her teachings, for the child's work will be a mirror in
which she can see reflected her successes or her failures.
Froebel's Idea.
The idea of Froebel in devising all these gifts was not, it seems
hardly necessary to say, to instruct the child in abstractions, which
do not properly belong to childhood, but to lead him early in life to
the practical knowledge of things about him; to inculcate the love of
industry, helpfulness, independence of thought and action, neatness,
accuracy, economy, beauty, harmony, truth, and order.
The gifts and occupations are only means to a great end, and if used
in this sense will attain their highest usefulness.
No dictation with any of the kindergarten materials, no study of
lines, angles, oblongs, triangles, and pentagons, no work with numbers
either concrete or abstract are fit employments for little children,
if not connected in every possible way with their home pleasures and
the natural objects of their love. Only when thus connected do they
produce real interest, only thus can agreement with the child's inner
wants be secured.
Actual experiences in the child's life are its most natural and potent
teachers. We need constantly to remember that the prime value of the
kindergarten lies in its personal influence upon individuals, and seek
to develop each separate member of our class according to his
possibilities.
An Objection answered.
The objection has been made that the study and practice with straight
lines, angles, geometrical forms, cubes, and other rectangular solids
would fit the child for later work in the exact and mathematical
sciences more than for other branches of study. But yet it is
difficult to see how, when the child's powers of observation are so
carefully trained in every way; when he is constantly led to notice
objects in nature and reproduce them with clay, pencil, chalk, or
needle; when these objects are so frequently presented for his
critical inspection and comparison; when he is led to see in the
flowers, plants, rocks, and stars, the unity which holds together
everything in the universe; when beauty and harmony, mingled freely,
constitute the atmosphere of the ideal kindergarten,--it is difficult
indeed to see how he can receive anything but benefit from the gift
plays, which present at first mainly the straight line, seemingly
deferring the curve to a later period when it can be managed more
successfully.