Group Work with Sticks.
The sticks are especially serviceable for group work of various kinds, either at the long or square tables. As the children have now an abundance of material they can make all the objects, perhaps, which may be mentioned in a story the kindergartner tells. If it is about the origin of Thanksgiving Day, for instance, Abby, who sits at one end of the line, may make a picture of the Mayflower, and John, her neighbor, make the Speedwell. The next child may construct a cradle for Oceanus, the little Pilgrim baby born on shipboard; the next use his material for the Indian huts the settlers saw after landing; and so on, each child making a different object, which remains upon his table until the close of the story. When this is completed, it will have been fully illustrated by the children with their sticks, and they will be delighted to inspect the different pictures which they will plainly see are much more varied and beautiful than any oneof them could have made alone. Thus the value of coöperation will be plainly shown, without a word from the kindergartner.[71]
Forms of Life.
As to Life forms in general, their number is practically unlimited, though as they are only line-pictures, and heavy lines at that, they are not as real as those made in the Building Gifts. They are easily made, however, and the veriest baby in the kindergarten who handles the sticks as a prelude to his drawing exercises invents with them all sorts of rude forms which he calls by appropriate names.
The question of color as it enters into these forms needs, perhaps, a moment's consideration here. As the gift includes both white and colored sticks, would it not be well to use the former for all dictations in Life forms, reserving the brilliant hues for the forms of symmetry whose charms they would greatly enhance?
Connection of other Objects with Stick Dictations.
We may sometimes connect simple, inexpensive objects with stick dictations, with a view to making them more realistic and delightful. When the little ones are just getting the various positions and correspondingterms into their minds, and when therefore it is advisable to keep them amused and happy with one to three sticks as long as possible,—that is, until the fundamental principles have become very familiar,—these objects are most invaluable.
Innumerable lessons may be practiced with one stick only, calling it at last a whipstock and giving it a bit of curly paper for a lash. Far from being an instrument of punishment, it makes every child laugh with the glee of possession.
With two sticks laid horizontally we may give a little paper horse-car, or when one is vertical and the other runs horizontally across its end, we may call it a candlestick and snip a half-circle of paper into the semblance of a flame. The effect is electrical, though the light be only one candle-power.
And so on,ad infinitum; it is enough to give the hint for the play. We can cut little paper birds for the bird-cages, tumblers for the rude little tables, green leaves for the trees, etc., making the stick exercise, even in its first more difficult details, a time of great satisfaction and gladness.
Complete sets of these card-board objects, one for each child, should always be kept on hand; if well made they will last a year.
Forms of Beauty.
Enough has already been said of the possibilities of the sticks to show that they are most valuable for symmetrical forms. They may becombined with the tablets, and thus very pretty effects be made, and when four children unite their material at the group work tables, the dictations and inventions produced are of course very large, and may be really beautiful if constructed on artistic principles.
Border work may be very fully carried out with the sticks, and another charming feature of the gift is the way in which it lends itself to the making of snow crystals. These are symmetrical combinations and modifications of familiar geometrical forms around the hexagon. Mr. W. N. Hailmann says regarding them: "At first, it is best to give each child only six or twelve sticks, and to dictate the central figure (a hexagon or hexagonal star) verbally or by means of a drawing on the blackboard. They may then receive a number of additional sticks, and let the central figure grow, all obeying the teacher's dictation, or each following his own inventive genius."[72]
In this gift, as well as in the seventh, the child's imitative and inventive powers are obviously more greatly taxed than in the others, and the danger will be, if he is not well trained, that, as he apparently can do anything with the material,he will end by doing nothing. The greater the freedom given to the child, the greater the necessity of teaching him to use that liberty in and through the law, and not to abuse it by failing to reach with its aid the highest ends.
Connection of Sticks with Drawing.
We may make the laying of one-inch sticks in vertical and horizontal positions, in angles and squares, a prelude to the drawing of similar lines; and the copying of stick dictations, either from the table, or from memory, into drawing, is a most excellent exercise, calling into requisition great correctness and good judgment, besides an unusual amount of calculation, since the stick dictation will be on a scale of one inch, and the drawing on a scale of one fourth inch, reducing the original design to one in miniature. The child will almost always begin by attempting to make the picture exactly like his model in size without counting the inches and trying to make it mathematically correct; but after the idea is carefully explained and fully illustrated, he will have no further difficulty excepting, perhaps, with the more complicated figures containing slanting lines.
Ambidexterity.
We should encourage in all possible ways the use of both hands in all the exercises with gifts and occupations, not only that one may be as skillful as the other, but also to avoid a one-sided position of the body which frequently leads to curvature of the spine. The well-knownphysiologist, Professor Brown-Séquard, insists on the equal use of both hands, in order to induce the necessary equal flow of blood to the brain. Through the effect of our irregular and abnormal development, the cause of which is the too persistent use of the right hand, one lobe of our brains and one side of our bodies are in a neglected and weakened condition, and the evils resulting from this weakness are many and widespread. Dr. Daniel Wilson says: "In the majority of cases the defect, though it cannot be wholly overcome, may be in great part cured by early training, which will strengthen at once both the body and mind."[73]
Abuse of Eighth Gift.
No materials of the kindergarten (save the beans, lentils, etc., which serve to represent the point) have been so over-used and so abused as the sticks. When no other work was prepared for the children, when helpers were few, and it was desirable to give something which needed no supervision, when inexperienced students were to take charge of classes, when the kindergartner was weary and wanted a quiet moment to rest, when everybody was in a hurry, when the weather was very cold, or oppressively warm, when there was a torrent of rain, or had been a long drought, the sticks were hastily brought forth from the closet and as hastily thrust upon the children. These small sufferers, being thus provided with work-materials in which it was obvious that superior grown people took no interest, immediately lost interest themselves. In riotous kindergartens the sticks were broken, poked into pockets, and thrown on the floor; in the orderly ones they were gazed at apathetically, no one deeming it worth while to stir a hand to arrange them, save under pressure. Sticks had been presented so often and in so tiresome a manner that they produced a kind of mental atrophy in the child,—they were arresting his development instead of forwarding it.
Such an abuse of material is entirely unnecessary in the kindergarten, where so many ways are provided of presenting the same truths in all sorts of different and charming guises. It is unnecessary and most unfortunate, for it has frequently thrown undeserved contempt on an innocent and attractive gift, which, when properly treated, is one of the most pleasing and useful which Froebel has bequeathed to us.
Paradise of Childhood.Edward Wiebe. Pages 39-45.Kindergarten Guide.J. and B. Ronge. 33-36.Kindergarten Guide.Kraus-Boelte. 239-373.The Kindergarten Principle.Mary J. Lyschinska. 103-20.Law of Childhood.W. N. Hailmann. 39.Kindergarten Culture.W. N. Hailmann. 70-72.The Kindergarten.H. Goldammer. 154-72.Primary Helps.W. N. Hailmann.Industrial Art in Schools.[74]Charles G. Leland.Drawing and Decorative Design.Charles G. Leland.Art and the Formation of Taste.Walter Crane.Manual of Design.Richard Redgrave, R. A.Principles of Decorative Design.Christopher Dresser.Art and Ornament in Dress. Introduction.Charles Blanc.
Paradise of Childhood.Edward Wiebe. Pages 39-45.
Kindergarten Guide.J. and B. Ronge. 33-36.
Kindergarten Guide.Kraus-Boelte. 239-373.
The Kindergarten Principle.Mary J. Lyschinska. 103-20.
Law of Childhood.W. N. Hailmann. 39.
Kindergarten Culture.W. N. Hailmann. 70-72.
The Kindergarten.H. Goldammer. 154-72.
Primary Helps.W. N. Hailmann.
Industrial Art in Schools.[74]Charles G. Leland.
Drawing and Decorative Design.Charles G. Leland.
Art and the Formation of Taste.Walter Crane.
Manual of Design.Richard Redgrave, R. A.
Principles of Decorative Design.Christopher Dresser.
Art and Ornament in Dress. Introduction.Charles Blanc.
"Art developed in the same way. The Egyptian temples show us only straight-lined figures, which consequently show mathematical relations. Only in later times appeared the lines of beauty, that is, the arched or circular lines. I carry the child on in the same way."Friedrich Froebel."The curve bears with it in its unity and variety, its rich symbolism to everything which lives and moves, the most intimate relation to that which the child sees, feels, and loves."Emma Marwedel."It might be said that to produce useful objects is the result of the struggle for life; but the tendency to create that which is simply artistic results from no such urgent need, yet it is found wherever the former exists."Charles G. Leland."Thou canst not wave thy staff in air,Or dip thy paddle in the lake,But it carves the bow of beauty there,And the ripples in rhymes the oar forsake."Emerson.
"Art developed in the same way. The Egyptian temples show us only straight-lined figures, which consequently show mathematical relations. Only in later times appeared the lines of beauty, that is, the arched or circular lines. I carry the child on in the same way."
Friedrich Froebel.
"The curve bears with it in its unity and variety, its rich symbolism to everything which lives and moves, the most intimate relation to that which the child sees, feels, and loves."
Emma Marwedel.
"It might be said that to produce useful objects is the result of the struggle for life; but the tendency to create that which is simply artistic results from no such urgent need, yet it is found wherever the former exists."
Charles G. Leland.
"Thou canst not wave thy staff in air,Or dip thy paddle in the lake,But it carves the bow of beauty there,And the ripples in rhymes the oar forsake."
Emerson.
1. The rings of the ninth gift are made of silvered wire, either soldered or unsoldered, and are whole circles three inches, two inches, and one inch in diameter, with their respective halves and quarters.
2. As the first six gifts emphasized solids and divided solids, the seventh, the plane, and theeighth, the straight line, so the ninth, the ring, embodies the curve, and illustrates the circumference of the sphere and the edge of the cylinder.
3. All the objects hitherto used have, with the exception of the ball and cylinder, dealt with straight lines and the figures formed by those lines. We now begin a series of exercises with the curve, and the variety of symmetrical figures that can be constructed is immensely increased.
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 passes 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 illustrated in this gift are:—
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 hehastens 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 thesame 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]
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 performedby 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 aswere 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.
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 æsthetic 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 æsthetic 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 whennecessary 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 thekindergarten 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.
Paradise of Childhood.Edward Wiebe. Pages 45, 46.Kindergarten Guide.Kraus-Boelte. 373-417.The Kindergarten.H. Goldammer. 173-78.The Kindergarten. Principles of Froebel's System.Emily Shirreff. 17-20.Industrial Art in Schools.[77]Charles G. Leland.Childhood's Poetry and Studies. With Diagrams.Emma Marwedel.The Grammar of Ornament.Owen Jones.Art.Sir John Lubbock.How to Judge a Picture.Van Dyke.
Paradise of Childhood.Edward Wiebe. Pages 45, 46.
Kindergarten Guide.Kraus-Boelte. 373-417.
The Kindergarten.H. Goldammer. 173-78.
The Kindergarten. Principles of Froebel's System.Emily Shirreff. 17-20.
Industrial Art in Schools.[77]Charles G. Leland.
Childhood's Poetry and Studies. With Diagrams.Emma Marwedel.
The Grammar of Ornament.Owen Jones.
Art.Sir John Lubbock.
How to Judge a Picture.Van Dyke.
"The awakening mind of the child ... is led from the material body and its regular division to the contemplation of the surface, from this to the contemplation of the line and to the point made visible."Friedrich Froebel."And it is precisely thus that the first artistic work of primeval man occurs; he begins by the forming of simple rows, as strings of beads, or of shells, for instance."H. Poesche."For the last step in this analysis the child receives small lentil seeds or pebbles—concrete points, so to speak—with which he constructs the most wonderful pictures."W. N. Hailmann.
"The awakening mind of the child ... is led from the material body and its regular division to the contemplation of the surface, from this to the contemplation of the line and to the point made visible."
Friedrich Froebel.
"And it is precisely thus that the first artistic work of primeval man occurs; he begins by the forming of simple rows, as strings of beads, or of shells, for instance."
H. Poesche.
"For the last step in this analysis the child receives small lentil seeds or pebbles—concrete points, so to speak—with which he constructs the most wonderful pictures."
W. N. Hailmann.
1. The point made concrete, which forms the tenth and last of Froebel's gifts, is represented by many natural objects, by beans, lentils, pebbles, shells, leaves, and buds of flowers, by seeds of various kinds, as well as by tiny spheres of clay and bits of wood and cork.
2. We have been moving by gradual analysis from the solid through the divided solid, the plane and the line, and thus have reached in logical sequence the point, into a series of which the line may be resolved.
3. The point which was visible in the preceding gifts, but inseparable from them, now in thetenth gift has an existence of its own. Although it is an imaginary quantity having neither length, breadth, nor thickness, yet it is here illustrated by tangible objects which the child can handle. By its very lack of individuality, it lends itself to many charming plays and transformations.
4. By the use of the point the child learns practically the composition of the line, that its direction is determined by two points, that the shortest distance between two points is a straight line, and that a curved line is one which changes its direction at every point. The gift closes the series of objects obtained by analysis from the solid, and prepares for the occupations which are developed by synthesis from the point.
5. The outlines of all geometrical plane figures both rectilinear and curvilinear may be illustrated with the point as well as straight and curved lines and angles of every degree.
6. The law of mediation of contrasts is no longer illustrated in the gift itself, but simply governs the use of the material. All lines and outlines of planes made with a series of dots show its workings, and the symmetrical figures, as we have noted from the first, owe to it their very existence.
Meeting-Place of Gifts and Occupations.
When we begin upon a consideration of the tenth gift, the last link in the chain of objects which Froebel devised to "produce an all-sided development of the child," we see at once that the meeting-place of gift and occupation has been reached. The two series are now in fact so nearly one that the point is much more often used for occupation work than as a gift. This convergence of the series in regard to their practical use was first noted in the tablets, and has grown more and more marked with each succeeding object.
Though the point is in truth the last step which the child takes in the sequence of gifts as he journeys toward the abstract, yet we are met at once in practice by the apparently inconsistent fact that it is one of the first presented in the kindergarten. This can only be explained by the statement that it is in truth quite as much of an occupation as a gift, and is used in the former sense among the child's first work-materials as a preparation for later point-making(perforating), and as an exercise in eye-training and accuracy of measurement. It is not an occupation, of course, for the reason that permanent results cannot be produced with it, and because no transformation of its material is possible.
The Point as a Gift.
Before the child completes his kindergarten course, however, he should certainly be led to an intellectual perception of the interrelationof the gifts and their gradual development from solid to point, for their orderly progression according to law, though it be but dimly apprehended, will be most useful and strengthening to the mind. To discern the logical order of a single series of objects is a step toward the comprehension of world-order in mature life.[78]
The mind in later childhood should be what Froebel describes his own to have been. "I often felt," he says, "as if my mind were a smooth, still pool scarce a handbreadth over, or even a single water-drop, in which surrounding things were clearly mirrored, while the blue vault of the sky was seen as well, reaching far away and above."
When the derivation of plane and of straight and curved line and their place in the gifts are clearly understood by the child, there will be no difficulty in gaining an equally clear apprehension of the point and its position in the series. This may be done somewhat as follows. When the children are playing with blocks on some occasion, we may direct the conversation to the essential characteristics of the cube, its faces, edges, and corners. Do they remember whichone of their playthings is like the face of the cube; do they remember cutting clay tablets from the clay blocks?
It is most unlikely that this experiment will have been forgotten, but if it has been, it may be easily repeated. Speak next of the edges of the cube, and let the children recall the derivation of the stick. That portion of the cube not yet discussed will now be seized upon by the children, and they will ask if any of their playthings are like the cube's corners. Can they think of anything; shall we not try to make something?
Now the clay appears, cubes are quickly fashioned, and each child is allowed to cut off the eight corners of his block. He has no sooner done this than he sees the nearest approach we can make to a point, and proceeds to make a design from them while he recalls the beans, shells, lentils, etc., he has used before in a similar way.
It is well here to suggest making the bits of clay into tiny oblate spheroids, and laying them away to dry so that we may make a group work invention of them to-morrow. Better still, however, is the instant introduction of sticks or wires to connect with the clay points, and thus form at once the skeleton of the solid, which will give an ineffaceable impression of the relation of point and line to each other.
Pleasure of Child in Point-laying and Stringing.
The pleasure the child finds in point-laying is not confined to the kindergarten, for playing with beads and pin-heads is an ordinary nursery occupation in all countries, and which of us cannot recall long happy hours on the seashore, or by the brookside, when we gathered and sorted shells and smooth glistening pebbles, and laid them in rows and patterns? The mere handling of a great store of these gave a Midas-like delight, and what primitive artistic pleasure we felt as we arranged them according to the principle of repetition to border our garden-beds or to inclose our miniature parks and playgrounds.
The same joy is felt in plucking, arranging, and stringing rose-hips, the seeds of the ailantus, the nasturtium, the pumpkin, or the "cheeses" of the mallow and wild geranium.
Miscellaneous Materials.
It will commonly be found that the child enjoys tenfold more the objects for point-work which he finds himself than the more perfect school-materials. Imagine the joy, for instance, of a bevy of kindergarten children set free on Pescadero Beach (California), and allowed to ramble up and down its shining sands to pick up the wonderful Pescadero pebbles. What colors of dull red and amber, of pink and palest green, what opaline lights, and smooth, glimmering surfaces! "Busy work" with such materials would be worth while indeed,—yeteasy to obtain as they are, they are almost never seen in use.
Smooth, white pebbles, washed entirely clean and sorted according to size, are not uncommonly seen in the kindergartens, however, and are especially useful in the sand-table, and if these and the shining cream-colored shells could be found by the children themselves, their pleasure in them would be immensely increased. That this is true is proved by the experience of many teachers with seed-work. One of our own brood of kindergartners once had a birthday melon party for one of her children. The melons were brought to the kindergarten room and there divided, the small host serving his guests himself. Great interest was immediately shown in the jet-black seeds of the water-melon in contrast with the smaller light-colored seeds of the musk-melon, and unanimous appeals were made to the kindergartner that they might be saved and used for inventions. This was done, and they were always called for afterwards in point-work, rather than the beans, or vegetable and wooden lentils.
In those kindergartens where the seeds of all fruits are saved by the children at lunch hour, it is also noted that the collection thus made is always the object of universal interest and preference.
Use of the Gift.
One of the first uses of the point may be in following the outline of some form of life whichthe kindergartner has drawn in white or colored chalk on the child's table. This is much more fascinating work than the placing of seeds one space apart, three in a row, etc., for the latter belongs to the "knowledge-acquiring side of the game," which, as Froebel says, is the "quickly tiring side, only to be given quite casually at first, and as chance may provide suitable openings for it."
The forms drawn in chalk may very well be of curving outlines of vegetables, fruits, leaves, and flowers to connect with the study of the first gift, and may include any other simple appropriate object which the kindergartner is capable of drawing.
The more advanced child can of course make his own Life forms without the aid of drawing, and if he is given different sizes and kinds of shells, seeds, or pebbles, often arranges them with great ability to imitate the shading of the object.
The beginning of the forms of knowledge is in placing the points in regular order on the squared tables at the intersection of vertical and horizontal lines. Next, the child lays one space vertical lines, three points in a line, then two space lines with five points, then horizontal lines, angles, parallelograms, borders, etc., following out the school of linear drawing, and in this way progresses in an orderly manner to the designing of symmetrical forms. Curved lines of course are quite aseasily represented as the straight, and really beautiful designs are often made by the children with them.