4. Much new knowledge can be conveyed by means of this fresh material, a complete set of new figures may be produced, and the imitation of objects pa.s.ses from that of things constructed by man, which are mostly rectilinear, to those of nature in which curved lines in every possible variety prevail.
5. The geometrical forms ill.u.s.trated in this gift are:--
{ 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 ill.u.s.trated, and the child may thus become acquainted with the appearance of the
Diameter.
Radius.
Circ.u.mference.
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 a.n.a.lyzed straight lines in the sticks, we will pa.s.s 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 ill.u.s.trates 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 pa.s.sed 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 pa.s.sed 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, ill.u.s.trate 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 ill.u.s.trate 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 s.p.a.ces 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.