[34] "What must we furnish to the child after the self-contained ball, after the hard sphere, every part of which is similar, and after the single solid cube? It must be something firm which can be easily pulled apart by the child's strength, and just as easily put together again. Therefore it must also be something which is simple, yet multiform; and what should this be, after what we have perceived up to this point, and in view of what the surrounding world affords us, but the cube divided through the centre by three planes perpendicular to one another."—Froebel's Pedagogics.

[35] "Unmaking is as important as making to the child. His destructive energy is as essential to him as his power of construction." (W. T. Harris.)

"The child wishes to discover the inside of the thing, being urged to this by an impulse he has not given to himself,—the impulse which, rightly recognized and rightly guided, seeks to know God in all his works.... Where can the child seek for satisfaction of his impulse to research but from the thing itself?"—Friedrich Froebel, Education of Man.

In the divided cube, however, he can gratify his desires, and at the same time possess the joy of doing right and destroying nothing, for the eight little blocks can be quickly united into their original form, and also into many other pleasing little forms, each one complete in itself, so that every analysis ends as it should, in synthesis.

Froebel calls this gift specifically "the children's delight," and indeed it is, responding so generously to their spontaneous activity, while at the same time it suits their small capabilities, for the possibilities of an object used for form study should not be too varied. "It must be suggestive through its limitations," says Miss Blow, "for the young mind may be as easily crushed by excess as by defect."[36]

[36] "An element which slumbers like a viper under roses is that which is now so frequently provided as a plaything for children; it is, in a word, the already too complex and ornate, too finished toy. The child can begin no new thing with it, cannot produce enough variety by means of it; his power of creative imagination, his power of giving outward form to his own idea, are thus actually deadened."—Froebel's Pedagogics.

Froebel was left motherless at a very early age, and during his first four years of life his father was entirely engrossed with parish duties, and the child had only occasional supervision from a hard-worked servant. Thus it happened that he was frequently alone long hours at a time in a dusky room overshadowed by the neighboring church, and naturally strayed often to the window, from whence he might look down upon the busy world outside. He recalls that he was greatly interested at one time in some workmen who were repairing the church, and that he constantly turned from his post of observation to try and imitate their labors, but his only building material was the furniture of the room, and chairs and tables clumsily resisted his efforts to pile them up into suitable form. He tells us that this strong desire for building and the bitter disappointment of his repeated failures were still keenly remembered when he was a grown man, and thus suggested to him that children ought to be provided with materials for building among their playthings. He often noticed also, in later years, that all children seem to have the building instinct, corresponding to what Dr. Seguin calls "the building mania in the infancy of peoples," and that "to make a house is the universal form of unguided play."[37]

[37] "One of the greatest and most universal delights of children is to construct for themselves a habitation of some sort, either in the garden or indoors, where chairs have generally to serve their purpose. Instinct leads them, as it does all animals, to procure shelter and protection for their persons, individual outward self-existence and independence."—Bertha von Marenholtz-Buelow, Child and Child Nature.

We now understand the meaning of the gift, the reason for its importance in Froebel's plan, and its capabilities as a vehicle for delightful instruction.

Classes of Forms.

There are three different classes of forms for dictation and invention, variously named by kindergartners.

1. Life forms, or upright forms, which are seen in the child's daily life, as a pair of boots, a chair, table, bed, or sofa. Froebel calls them also object forms, or forms of things.

("The child demands that the object constructed stand in connection with himself, his life, or somebody or something in his life."—Froebel.)

2. Mathematical forms, or various combinations of the blocks, upright and supine, for mathematical exercises. They correspond to the forms of knowledge in Logic.

(Also called by Froebel forms of truth, forms of instruction, forms of learning.)

3. Symmetrical forms, or flat designs formed by opposites and their intermediates. These are figures in which four of the blocks generally revolve in order around the other four as a centre.

(Also called by Froebel picture forms, flower forms, star forms, dance forms.)

LIFE FORMS.

Life forms should be given first, as the natural tendency of the young child is to pile things up,[38] and these forms seem simpler for dictation, are more readily grasped by the mind, and more fascinating to the imagination. They are the images of things both dear and familiar to him, and thus are particularly adapted to the beginning since the "starting point of the child's development is the heart and the emotions." It is easier for him to be an architect at first than an artist, though each will be comprehended in the other after a time.[39]

[38] "The building or piling up is with the child, as with the development of the human race, and as with the fixed forms in Nature, the first."—Froebel's Education of Man.

"Towers, pyramids, up, up, connecting themselves with something high, voicing aspiration."

[39] "The representation of facts and circumstances of history, of geography, and especially of every-day life, by means of building, I hold to be in the highest degree important for children, even if these representations are imperfect and fall far short of their originals. The eye is at all events aroused and stimulated to observe with greater precision than before the object that has been represented.... And thus, by means of perhaps a quite imperfect outward representation, the inner perception is made more perfect."—Froebel's Letters, tr. by Michaelis and Moore, page 99.

The dictations should be given very simply, clearly, and slowly, always using one set of terms to express a certain meaning, and having those absolutely correct. We should never give dictations from a book, but from memory, having prepared the lesson beforehand, and should remember that every exercise we give should "incite and develop self-activity." We must guard against mistakes or confusion in our own minds; it is very easy to confuse the child, and he will become inattentive and careless if he is unable to catch our meaning.

Brief stories should occasionally be told, just mere outlines to give color and force to the child's building, and connect it with his experience. If it is an armchair, grandmother may sit in it knitting the baby's stocking. If it is a well, describe the digging of it, the lining with stones or brick, the inflowing of the water, the letting down of the bucket and long chain, the clear, cool water coming up from the deep, dark hole in the ground on a hot summer's day. These, of course, are but the merest suggestions which experience may be trusted to develop.

It is better, perhaps, to give a bit of word-painting to each object constructed than to wait till the end of the series for the day and tell a longer story, as the interest is thus more easily sustained. The children, too, should be encouraged to talk about the forms and tell little stories concerning them. The form created should never be destroyed, but transformed into the next in order by a few simple movements.

SYMMETRICAL FORMS.

"These forms, in spite of their regularity, are called forms of beauty. The mathematical forms which Froebel designates forms of knowledge give only the skeleton from which the beautiful form develops itself.

"Symmetry of the parts which make up these simple figures gives the impression of beauty to the childish eye. He must have the elements of the beautiful before he is in a condition to comprehend it in its whole extent.

"Only what is simple gives light to the child at first. He can only operate with a small number of materials, therefore Froebel gives only eight cubes for this object at this time."

Of course these three classes of forms are not to be kept arbitrarily separate, and the children finish and lay aside one set before attempting another. There are many cases where the three may be united, as indeed they are morally speaking in the life of every human being.

When the distinctions are clear in our own minds, our knowledge and tact will guide us to introduce the gift properly, and carry it on in a natural, orderly, and rational manner, not restricting the child's own productive powers.

If the children have had time to imbibe a love of symmetry and beauty, and have been trained to observe and delight in them, then this second class of forms will attract them as much, after a little, as the first, though more difficult of execution.

Each sequence starts from a definite point, the four outside blocks revolving round the central four, and going through or "dancing through," as Froebel says, all the successive figures before returning in the opposite direction.

All the dictations are most valuable intellectually, but should not be long-continued at one time, as they require great concentration of mind, and are consequently wearisome.

Hints from Ronge's "Guide."

Excellent exercises or suggestions for building can be found in Ronge's "Kindergarten Guide." He mentions one pleasant little play which I will quote. "When each in the class has produced a different form, let the children rise and march round the table to observe the variety." Let them sing in the ascending and descending scales:—

Many pretty forms I see, Which one seems the best to me?

At another time let each child try to build the house he lives in, and while this is being done, let them join in singing some song about home. It is well to encourage singing during the building exercises, as we have so many appropriate selections.[40]

[40] See Kindergarten Chimes (Kate D. Wiggin), Oliver Ditson Publishing Co.: "Building Song," pages 34, 35; "Trade Game," page 70; "The Carpenter," page 92.

Group Work.

With the first of the Building Gifts enters a new variety of group work, which was not adapted for the first and second gifts. The children may now be seated at square tables, one at each side, and build in unison in the centre, the form produced being of course four times as large and fine as any one of the number could have produced alone. All the suggestions or directions for building are necessarily carried out together, and the success of the completed form is obviously dependent on the cooperation of all four children. Forms of Beauty are very easily constructed in this manner, as well as forms of Life, having four uniform sides, and when the little ones are somewhat more expert builders, Life forms having opposite sides alike, or even four different sides, may be constructed.

The other various forms of cooperative work are of course never to be neglected, that a social unity may be produced, in which "the might of each individual may be reinforced by the might of the whole."

MATHEMATICAL FORMS.

A better idea of these may be obtained through a manipulation of the blocks and an arrangement of the geometrical forms in their regular order.

The child, if he were taught as Froebel intended, would make his first acquaintance with numbers in the nursery, beginning in a very small way and progressing slowly. The pupils of the kindergarten are a little older, and having already a slight knowledge of numbers (though not of course in their abstract relations) are able to accomplish greater things.

The child can, with our guidance, make all possible combinations of the parts of the number Eight. The principles of Addition, Subtraction, even Multiplication and Fractions, can also be mastered without one tear of misery or pang of torture. He grasps the whole first, then by simple processes, building with his own hands, he finds out and demonstrates for himself halves, fourths, and eighths, sometimes in different positions, but always having the same contents.

Method and Manner of using the Gift.

Even yet we must not suffer this to become work. The exercises should be repeated again and again, but we must learn to break off when the play is still delightful, and study ways to endow the next one with new life and charm, though it carry with it the same old facts. What we want to secure is, not a formidable number of parrot-like statements, but a firm foundation for future clearness of understanding, depth of feeling, and firmness of purpose. So, at the beginning of the exercise, we should not ask John if he remembers what we talked about last time, and expect him to answer clearly at once. Because he does not answer our formal questions which do not properly belong to babyhood, we need not conclude he has learned nothing, for a child can show to our dull eyes only a very tiny glimpse of his wonderful inner world.

Let our aim be, that the child shall little by little receive impressions so clearly that he will recognize them when they appear again, and that he shall, after a time, know these impressions by their names. It is nothing but play after all, but it is in this childish play that deep meaning lies.

A child is far less interested in that which is given him complete than in that which needs something from him to make it perfect. He loves to employ all his energies in conceiving and constructing forms; the less you do for him the better he enjoys it, if he has been trained to independence.[41]

[41] "Probably the chief wish of children is to do things for themselves, instead of to have things done for them. They would gladly live in a Paradise of the Home-made. For example, when we read how the 'prentices of London used to skate on sharp bones of animals, which they bound about their feet, we also wished, at least, to try that plan, rather than to wear skates bought in shops." (Andrew Lang.)

"Complete toys hinder the activity of children, encourage laziness and thoughtlessness, and do them more harm than can be told. The active tendency in them turns to the distortion of what is complete, and so becomes destructive."

"Any fusing together of lessons, work, and play, is possible only when the objects with which the child plays allow room for independent mental and bodily activity, i. e., when they are not themselves complete in the child's hand. Had man found everything in the world fixed and prepared for use; had all means of culture, of satisfaction for the spiritual and material wants of his nature, been ready to his hand, there would have been no development, no civilization of the human race."

Pedantry and dogmatism must be eliminated from all the dictations; the life must not be shut out of the lessons in order that we may hear a pin drop, nor should they be allowed to degenerate into a tedious formalism and mechanical puppet-show, in which we pull the strings and the poor little dummies move with one accord.

Yet most emphatically a certain order and harmony must prevail, the forms must follow each other in natural sequence, the blocks must, invariably, be taken carefully from the box, so as to present a whole at the first glance, and at the close of the lesson should always be neatly put together again into the original form and returned to the box as a whole.[42]

[42] "In order to furnish to the child at once clearly and definitely the impression of the whole, of the self-contained, the plaything before it is given to the child for his own free use must be opened as follows.... It will thus appear before the observing child as a cube closely united, yet easily separated and again restored."—Froebel's Pedagogics, pages 123, 124.

And now one last word of warning about doing too much for the children in these exercises, and even guiding too much, carrying system and method too far in dictation. We must remember that an excess of systematizing crushes instead of developing originality, and that it is all too easy even in the kindergarten to turn children into machines incapable of acting when the guiding hand is removed.

NOTE.

In opening the boxes, it is well to observe some simple form. It is not irksome, but, on the contrary, rather pleasing to the children, who delight in doing things in concert.

BOXES IN CENTRE OF TABLE.

1. Draw the cover out one half space. 2. Fingers of right hand placed on left-hand side of box. 3. Turn entirely over from left to right. 4. Withdraw lid and place on right-hand upper corner of table. 5. Lift box gently and place on top of cover mouth upwards.

READINGS FOR THE STUDENT.

Reminiscences of Froebel. Von Marenholtz-Buelow. Page 152. Child and Child Nature. Von Marenholtz-Buelow. 145, 146. Education. E. Seguin. 95, 96. Lessons in Form. W. W. Speer. 23. Pedagogics of the Kindergarten. Fr. Froebel. 108-44. Education of Man. Fr. Froebel. Tr. by Josephine Jarvis. 40, 41. Kindergarten at Home. E. Shirreff. 12-14. Kindergarten Culture. W. N. Hailmann. 55-66. Paradise of Childhood. Edward Wiebe. 11-16. Law of Childhood. W. N. Hailmann. 35-38. Kindergarten Guide. J. and B. Ronge. 5-13. Kindergarten Guide. Kraus-Boelte. 27-47. Koehler's Kindergarten Practice. Tr. by Mary Gurney. 20-23. Froebel and Education by Self-Activity. H. Courthope Bowen. 140-42. Kindergarten Toys. Heinrich Hoffmann. 17-26. Conscious Motherhood. E. Marwedel. 165, 166. The Kindergarten. H. Goldammer. 49-70.



FROEBEL'S FOURTH GIFT

"A new gift is demanded—a gift wherein the length, breadth, and thickness of a solid body shall be distinguished from each other by difference of size. Such a gift will open the child's eyes to the three dimensions of space, and will serve also as a means of recognizing and interpreting the manifold forms and structures with which he is constantly brought in contact."

"The inner difference, intimated in the three perpendicular axes of the cube (and the sphere), now becomes externally visible and abiding in each of its building blocks as a difference of size." FR. FROEBEL.

"The fourth gift incites the child to consider things in their relations to space, and to the forces of nature, and in his play with the bricks he is constantly engaged in efforts to adapt himself to the laws of their nature, while rendering them subservient to his ends." W. N. HAILMANN.

1. The fourth gift consists of a cube measuring two inches in each of its dimensions. It is divided once vertically in its height, and three times horizontally in its thickness, giving eight parallelopipeds or bricks, each two inches long, one inch wide, and one half inch thick.

2. Like the third gift in form, size, material, and use, it is unlike it in division. In the third gift the parts were like each other, and like the whole, in the fourth they are like each other, but unlike the whole.

3. The most important characteristics of the gift are:—

a. Approximation to surface in the symmetrical forms.

b. Greater height and greater extension, resulting in a greater possible inclosure of space.

c. The illustration of two philosophical laws, viz., the law of Equilibrium or Balance, and the law of Transmitted Motion or Propagation of Force.

4. Progress is shown in this gift as follows:—

a. In the difficulty of dictation and manipulation arising from the different character of the faces of the bricks, and the many positions which each brick can assume.

b. In the necessity of perfect balance.

c. In a clearer illustration of dimension. In the third gift the parts were equal in height, breadth, and thickness; in the fourth they are unequal, and therefore each dimension is emphasized.

As to progression, the increase of difficulty suits the increase in the child's power of comprehension and receptivity. He is being developed thus far, not by rapid changes in material or greater exercise in number, but by practice with differing forms, each one bringing with it new knowledge and experience. The organs of perception are being constantly made to grow by exercise with intention. We are forming the scientific eye which can detect differences ever after at a glance.

5. The geometrical forms illustrated in this gift are:—

Solids. { Rectangular Parallelopipeds. { Square Prisms.

Planes. { Oblongs. { Squares.

6. The fourth gift presents contrasts of dimension and, as to the area of its faces, contrasts of size and their mediation.

* * * * *

What the Child has gained from Third Gift.

The use of the third gift opened to the child quite a new world of experiences, each one of which was pleasant and instructive, combining all the delights of mental and physical activity, imagination, practical industry, and cooperation.

He has gained an idea, distinct in proportion to the skill with which it has been placed before him, of the cube as a solid body having surfaces, corners, and edges; of a whole and its equal fractional parts; of the power of combining those parts into new wholes; and of the fact that form and size are two separate and distinct characteristics of objects. He has also gained new dexterity.[43] His ten little fingers that seemed "all thumbs" as they arranged so carefully the clumsy little cubes of the Low Wall can now build the Bunker Hill Monument with unerring skill, and can even, with the grave concentration that it demands, drop the last difficult little block cornerwise into the top of the church window.

[43] "A child trained for one year in a kindergarten would acquire a skillful use of his hands and a habit of accurate measurement of the eye which would be his possession through life." (W. T. Harris.)

The child has counted his cubes from one to eight until he knows them like the children of a family, and can divide them into sets of two and four with equal ease.

These are the deeds. As to the new words the little box of blocks has brought him, their number is legion, comprising many terms of direction and position, names of tools and implements, buildings and places.

Truly if the kindergartner has been wise and faithful, the child has gained wonders from this simple unassuming toy, one which is almost too plain and rude to fix the momentary attention of a modern spoiled child, though even he will grow to appreciate its treasures if rightly guided.

Differences between Third and Fourth Gifts.

And now we approach another cubical box, containing the fourth gift, and, on opening it, see that it presents resemblances between and differences when compared with that just left behind.

We notice at once the new method of division, and in separating it find that the parts, evidently in number the same as before, are entirely novel in form, though the whole was familiar in its aspect. If the child is old enough to understand the process of comparison, he will see that the parts of the two gifts have each six surfaces, eight corners, and twelve edges; but that while edges and corners are alike, the faces differ greatly on the new block, which he will probably call the "brick," as it is a familiar form and name to him. This process of comparison will be greatly facilitated if he models the two cubes in clay, and divides them with string or wire, the one into inch cubes, the other into bricks.

Dr. Seguin's Objections to the Cube as the Primary Figure in the Kindergarten.

Dr. E. Seguin, in his celebrated "Report on Education," says, in regard to the use of the cube as the primary block or figure in the kindergarten: "Had the kindergartners chosen it with their senses, as it must speak to the senses of the child, instead of with their mind, they would certainly never have selected the cube, a form in which similarity is everywhere, difference nowhere, a barren type incapable by itself of instigating the child to active comparison. Had they, on the contrary, from infantile reminiscences, or from more philosophical indications, selected a block of brick-form, the child would soon have discovered and made use of the similarity of the straight lines, and of the difference of the three dimensions. For example: Put a cube on your desk and let a pupil put one on his; you change the position of yours, he, accordingly, of his. If you renew these moves till both of you are tired, they will not make any perceptible change in the aspect of the object. The movement has been barren of any modification perceptible to the senses and appreciable to the mind. There has been no lesson unless you have, by words speaking to the mind, succeeded in making the child comprehend the idea of a cube derived from its intrinsic properties; a body with six equal sides and eight equal angles."

Answers to these Objections.

With all deference to Dr. Seguin, whose opinions and deductions are generally indisputable, we cannot regard as unwise the choice of the cube as the primary figure in the gifts.

In the first place, Froebel, having a sequence of forms in his mind, undoubtedly wished to introduce, early in that sequence, the one which would best serve him as a foundation for further division and subdivision. This need is, beyond question, better met in the cube than in the brick, which would lend itself awkwardly to regular division.

Secondly, although there is in the cube "similarity everywhere, difference nowhere," and therefore it might be called in truth a "barren type, incapable by itself of instigating the child to comparison and action," we do not introduce it, by itself, but in contrast with the sphere and cylinder.

Then, when it appears again in the building gifts, "as the simplest and most easily handled form element," the kindergartner has every opportunity to use it so that it may lead the child to comparison and action, and to develop the slowly dawning sense of difference and agreement without which she well knows "knowledge has not yet made the first step." But, if the cube is a form speaking little to the senses of a child, and requiring description by words spoken to the mind, it is evident that we should use great care in dealing with the second gift, lest we run needlessly into abstractions, and strive to give the child ideas of which he can have no comprehension.

Value of the Brick Form.

The "brick" is a form rich in impressions, for we find that every position in which it is placed gives the child a new perception, and the union of these perceptions furnishes him with a complete idea of the object, and of its possible uses in relation to its form.

Dr. Seguin does not rate it too highly when he says: "What a spring of effective movements, of perceptions and of ideas in the exercises with this form, where analogy and difference, incessantly noted by the touch and the view, challenge the mind to comparison and judgment!"

Dimension.

The fourth gift contains all that the three former gifts showed, and introduces differences of dimension and equilibrium only hinted at before. It also, as Froebel says, "throws into relief the perception of size by showing similarity of size with dissimilarity of dimension and position."

As to dimension, the child built the Shot-tower with the third gift, and knew that it was high, the Platform and that it was broad, the Well and that it was deep, the Wall and saw that it was thick, etc., so that he has a conception of height, length, breadth; but in the fourth gift he is shown these dimensions in a single block. He is thus led from the known to the unknown.[44] They are united and contrasted in one object, and therefore emphasized.

[44] "The three principal dimensions of space, which in the cube only make themselves known as differences of position, in the fourth gift become more prominent and manifest themselves as differences of size. These three relations of size are in the fourth gift as abiding and changeless as the position of the three principal directions was before and still is."—Froebel's Pedagogics, page 189.

Equilibrium.

As to the law of equilibrium, it is very forcibly brought to the child's attention every time his forms fall to the table when constructed without due regard to its principles.

He soon sees its practical significance, takes care to follow its manifest expression, and to observe with more care the centre of gravity. Great liberties could be taken with the stolid little cubes and they seldom showed any resentment; they quietly settled down into their places and resisted sturdily all the earthquake shocks which are apt to visit a kindergarten table during the building hour. The bricks on the other hand have to be humored and treated with deference. The moment one is placed upon another, end to end, the struggle begins, and in any of the high Life forms, the utmost delicacy of touch is necessary as well as sure aim and steady hand.

Here comes in, too, a necessity of calculation not before required. The cubes could be placed on any side and always occupy the same space, but the building with the bricks will vary according as they are placed on the broad, the narrow, or the short face. They must also fit together and bear a certain relation to each other.

In the dictations it will be perceived that we now have to specify the position which the brick must take as well as the place which it is to occupy. We designate the three faces of the brick as the broad face, the narrow face, and the short face or end.

Fourth Gift Building.

The symmetrical forms are much more interesting than before and decidedly more artistic when viewed in comparison with the somewhat thick and clumsy designs made with the cubes. The fourth gift forms cover more space, approach nearer the surface, and the bricks slide gracefully from one position to another, and slip in and out of the different figures with a movement which seems like a swan's, compared with the goose-step of the stubby little cubes.

It is a noteworthy fact that "the buds," as Froebel calls them, of all the fourth gift Beauty forms were contained in those of the third gift, and have here opened into fuller bloom.

The Life forms are much more artistic now, and begin to imitate a little more nearly the objects they are intended to represent. We can make more extensive buildings also since we have an additional height or length of eight inches over that of the third gift, and thus can cover double the amount of surface and inclose a much greater space. In the first play with the gift, the children's eyes, so keen in seeing play possibilities, quickly discover the value of the bricks in furniture-making, and set to work at once on tables and chairs, or bureaus and sofas and bedsteads.

They engage too in a lively contest with the law of equilibrium, and experiment long and patiently until they comprehend its practical workings.

When they understand the fourth gift fairly well, know the different faces and can handle the bricks with some dexterity, the third gift should be added and the two used together. They complement each other admirably, and give variety and strength to the building, whether forms of Life, Beauty, or Knowledge are constructed.

Froebel, however, is most emphatic in directing that each set of blocks should be given to the child in its own box, opened so as to present a whole at the first glance, and carefully rebuilt and packed away when the play is over. The cubes and bricks should never be left jumbled together at the close of the exercise, nor should they be kept in and returned to a common receptacle.

"Unimportant as these little rules may appear," he says, "they are essential to the clear and definite development of the child, to his orderly apprehension of external objects, and to the logical unfolding of his own concepts and judgments."

"The box of building blocks should be regarded by the child," he concludes, "as a worthy, an appreciated, and a loved comrade."

The mathematical forms are constructed and applied in precisely the same manner as before. The fourth gift, however, offers a far greater number of these than its predecessor, while it is particularly adapted to show that objects identical in form and size may be produced in quite different ways.

Throughout all these guided plays, it should be remembered that time is always to be allowed the child for free invention, that the kindergartner should talk to him about what he has produced so that his thought may be discovered to himself,[45] and that in all possible ways Group work should be encouraged in order that his own strength and attainments may be multiplied by that of his playfellows and swell the common stock of power. Froebel, the great advocate of the "Together" principle says, "Isolation and exclusion destroy life; union and participation create life."[46]

[45] "The child is allowed the greatest possible freedom of invention; the experience of the adult only accompanies and explains."—Froebel's Pedagogics, page 130.

[46] Pedagogics, page 180.

It is perhaps needless to say that the philosophical laws which govern the outward manifestations of a moving force, as equilibrium or self-propagating activity, are for personal study, and are never to be spoken of abstractly to the child, but merely to be illustrated with simple explanations.

Transmitted Motion.

To show simply the law of transmitted motion, for instance, let the child place his eight bricks on end, in a row, one half inch apart, with their broad faces toward each other. Then ask him to give the one at the right a very gentle push towards the others and see what will happen; the result is probably as great a delight as you could reasonably wish to put within his reach.

When he asks, "What makes them do so?" as every thoughtful child is apt to do, let us ask the class the same question and set them thinking about it. "Which brick did it?" we may say familiarly, and they will see it all in a moment,—where the force originated, how it gave itself to the next brick in order, that one in turn doing the same, and so on.

This law of transmitted motion, when so simply illustrated in the fourth gift, easily suggests to the children the force of example, and indeed every physical law seems to have its correlate in the moral world. We may make the children see it very clearly through the seven poor, weak little bricks that fell down because they were touched by the first one. They really could not help it; now, how about seven little boys or girls? They can help doing things, can they not?

By such simple exercises and appropriate comments the children may be made to realize their moral free agency.

READINGS FOR THE STUDENT.

Kindergarten at Home. Emily Shirreff. Pages 58-61. Kindergarten Culture. W. N. Hailmann. 66. Koehler's Kindergarten Practice. Tr. by Mary Gurney. 23, 24. Kindergarten Guide. J. and B. Ronge. 13-24. Pedagogics of the Kindergarten. Fr. Froebel. 166-95. Paradise of Childhood. Edward Wiebe. 17-19. Kindergarten Guide. Kraus-Boelte. 47-81. Froebel and Education by Self-Activity. H. Courthope Bowen. 141, 142. Kindergarten Toys. H. Hoffmann. 27-30.



FROEBEL'S FIFTH GIFT

"The material for making forms increases by degrees, progressing according to law, as Nature prescribes. The simple wild rose existed before the double one was formed by careful culture. Children are too often overwhelmed with quantity and variety of material that makes formation impossible to them."

"The demand of the new gift, therefore, is that the oblique line, hitherto only transiently indicated, shall become an abiding feature of its material."

"In the forms made with the fifth gift there rules a living spirit of unity. Even members and directions which are apparently isolated are discovered to be related by significant connecting members and links, and the whole shows itself in all its parts as one and living,—therefore, also, as a life-rousing, life-nurturing, and life-developing totality." FR. FROEBEL.

1. The fifth gift is a three-inch cube, which, being divided equally twice in each dimension, produces twenty-seven one-inch cubes. Three of these are divided into halves by one diagonal cut, and three others into quarters by two diagonal cuts crossing each other, making in all thirty-nine pieces, twenty-one of which are whole cubes, the same size as those of the third gift.

2. The fifth gift seems to be an extension of the third, from which it differs in the following points:—

The third gift is a two-inch cube, the fifth a three-inch cube; the third is divided once in each dimension, the fifth twice. In the third all the parts are like each other and like the whole; in the fourth, they are like each other but unlike the whole; and in the fifth they are not only for the most part unlike each other, but eighteen of them are unlike the whole.

The third gift emphasized vertical and horizontal divisions producing entirely rectangular solids; the fifth, by introduction of the slanting line and triangular prism, extends the element of form. In the third gift, the slanting direction was merely implied in a transitory way by the position of the blocks; in the fifth it is definitely realized by their diagonal division.

In number, the third gift emphasized two and multiples of two; the fifth is related to the fourth in its advance in complexity of form and mathematical relations.

3. The most important characteristics of the gift are: introduction of diagonal line and triangular form; division into thirds, ninths, and twenty-sevenths; illustration of the inclined plane and cube-root. As a result of these combined characteristics, it is specially adapted to the production of symmetrical forms.

It includes not only multiplicity, but, for the first time, diversity of material.

4. The fifth gift realizes a higher unity through a greater variety than has been illustrated previously. It corresponds with the child's increasing power of analysis; it offers increased complexity to satisfy his growing powers of creation, and less definitely suggestive material in order to keep pace with his developing individuality.

5. The geometrical forms illustrated in this gift are:—

{ Cube. { Rectangular Parallelopiped. { Square Prism. { Triangular Prism. Solids. { Rhomboidal Prism. { Trapezoidal Prism. { Pentagonal Prism. { Hexagonal Prism. { Heptagonal Prism. { Octagonal Prism.

{ Square. { Oblong. { Right Isosceles Triangle. { Rhomboid. Planes. { Trapezium. { Trapezoid. { Pentagon. { Hexagon. { Heptagon. { Octagon.

6. The fifth gift shows the following contrasts and mediations:—

The diagonal line a connection between the horizontal and vertical; the right angle as a connection between the obtuse angle (largest) and the acute angle (smallest); in size of parts the half cube standing between the whole and quarter cubes.

* * * * *

We have thus far been proceeding from unity to variety, from the whole to its parts, from the simple to the complex, from easily constructed forms to those more difficult of manipulation and dictation, until we have arrived at the fifth gift.

Effect of the Study of Froebel's Gifts on the Kindergartner.

How instructive and delightful have we found this orderly procedure; this development of great from little things; this thoughtful association of new and practical ideas with all that is familiar to the child mind and heart. Every year the training teacher feels it anew herself, and is sure of the growing interest and sympathy of her pupils.

Many persons who fail to grasp the true meaning of the kindergarten seem to consider the balls and blocks and sticks with which we work most insignificant little objects; but we think, on the other hand, that nothing in the universe is small or insignificant if viewed in its right connection and undertaken with earnestness and enthusiasm. Nothing in childhood is too slight for the notice, too trivial for the sympathy of those on whom the Father of all has bestowed the holy dignity of motherhood or teacherhood; and to the kindergartner belongs the added dignity of approaching nearer the former than the latter, for hers indeed is a sort of vice-motherhood.

We must always be impressed with the knowledge which we ourselves gain in studying these gifts and preparing the exercises with them. In concentration of thought; careful, distinct, precise, and expressive language; logical arrangement of ideas; new love of order, beauty, symmetry, fitness, and proportion; added ingenuity in adapting material to various uses, aesthetic and practical,—in all these ways every practical student of Froebel must constantly feel a decided advance in ability.

Then, too, the simple rudiments of geometry have been reviewed in a new light; we have dealt with solid bodies and planes, and studied them critically so that we might draw the child's attention to all points of resemblance or difference; we have found some beautifully simple illustrations of familiar philosophical truths, and, best of all, have simplified and crystallized our knowledge of the relations of numbers so that the child's impressions of them may be easily and clearly gained.

Why we are required to study deeply and to know more than we teach.

We have been required to look at each gift in its broadest aspect, and to observe it patiently and minutely in all its possibilities, for the larger the amount of knowledge the kindergartner possesses, the more free from error will be her practice.

Unless we know more than we expect to teach, we shall find that our lessons will be stiff, formal affairs, lacking variety, elasticity, and freshness, and marred continually by lack of illustration and spontaneity.

Lack of interest in the teacher is as fatal as lack of interest in the child; in fact, the one follows directly upon the heels of the other. For this reason, continued study is vitally necessary that new phases of truth may continually be seen.

Above all other people the teacher should go through life with eyes and ears open. Unless she is constantly accumulating new information her mind will not only become like a stagnant pool, but she will find out that what she possesses is gradually evaporating. There is no state of equilibrium here; she who does not progress retrogresses.

It should be a comparatively simple matter to gain enough knowledge for teaching,—the difficult thing is the art of imparting it. Said Lord Bacon, "The art of well delivering the knowledge we possess to others is among the secrets left to be discovered by future generations."

Relation between Gifts, and their Relation to the Child's Mental and Moral Growth.

These are a few of the technicalities which have been mastered up to this time by a faithful study of the gifts of Froebel; and yet they are only technicalities, and do not include the half of what has been gained in ways more difficult to describe.

"To clearly comprehend the gifts either individually or collectively we must clearly conceive their relation to and dependence on each other, for it is only in this intimate connection that they gain importance or value."

If the kindergartner does not recognize the relationship which exists between them and their relation to the child's mental and moral growth, she uses them with no power or intelligence. We conceive nothing truly so long as we conceive it by itself; the individual example must be referred to the universal law before we can rightly apprehend its significance, and for a clear insight into anything whatsoever we must view it in relation to the class to which it belongs. We can never really know the part unless we know the whole, neither can we know the whole unless we know the part.

Pleasure of Child at New Gift.

In the fifth gift, which, it may be said, can commonly only be used with profit after the child has neared or attained his fifth year, we find that we have not parted from our good old friend, the cube, that has taught us so many valuable lessons. We always find contained in each gift a reminder of the previous one, together with new elements which may have been implied before, but not realized. So, therefore, we have again the cube, but greatly enlarged, divided, and diversified. When the child sees for the first time even the larger box containing his new plaything, he feels joyful anticipation, surmising that as he has grown more careful and capable, he has been entrusted with something of considerable importance. If he has been allowed to use the third and fourth gifts together frequently, he will not be embarrassed by the amount of material in the new object.

Lest he be overwhelmed, however, by its variety as much as by its quantity, it might be well before presenting the new material as a whole to allow the child to play with a third gift in which one cube cut in halves and one in quarters have been substituted for two whole cubes. He will joyfully discover the new forms, study them carefully, and find out their distinctive peculiarities and their value in building. When he has used them successfully once or twice, and has learned how to place the triangular prisms to form the cube, then the mass of new material as a whole can have no terrors for him.

How great is his pleasure when he withdraws the cover and finds indeed something full of immense possibilities; he feels, too, a command of his faculties which leads him to regard the new materials, not with doubt or misgiving, but with a conscious power of comprehension.

Its New Features.

At the first glance the most striking characteristics are its greater size and greater number of divisions, into thirds, ninths, and twenty-sevenths, instead of halves, quarters, and eighths.

These divisions open a new field in number lessons, while the introduction of the slanting line and triangular prism makes a decided advance in form and architectural possibilities.

Importance of Triangular Form.

The triangle, by the way, is a valuable addition in building exercises, for as a fundamental form in architecture it occurs very frequently in the formation of all familiar objects. Indeed, the new form and its various uses in building constitute the most striking and valuable feature of the gift.

We find it an interesting fact that all the grand divisions of the earth's surface have a triangular form, and that the larger islands assume this shape more or less.

The operation of dividing the earth's surface into greater and lesser triangles is used in making a trigonometrical survey and in ascertaining the length of a degree of latitude or longitude. The triangle is also of great use in the various departments of mechanical work, as will be noted hereafter in connection with the seventh gift.

Difficulties of the Fifth Gift.

The difficulties of the fifth gift are only apparent, for the well-trained child of the kindergarten sees more than any other, and he will grasp the small complexities with wonderful ease, smoothing out a path for himself while we are wondering how we shall make it plain to him.

Effect of Good Training.

But here let us note that we can only succeed in attaining satisfactory results in kindergarten work by beginning intelligently and never discontinuing our patient watchfulness, self-command, and firmness of purpose,—firmness, remember, not stubbornness, for it is a rare gift to be able to yield rightly and at the proper time.

If we help the little one too much in his first simple lessons or dictations; if we supply the word he ought to give; if, to save time and produce a symmetrical effect, we move a block here and there in weariness at some child's apparent stupidity, we shall never fail to reap the natural results. The effect of a rational conscientious and consistent behavior to the child in all our dealings with him is very great, and every little slip from the loving yet firm and straightforward course brings its immediate fruit.

The perfectly developed child welcomes each new difficulty and invites it; the imperfectly trained pupil shrinks in half-terror and helplessness, feeling no hope of becoming master of these strange new impressions.

Arrangement of Pieces.

To return to the specific consideration of the gift, there must be a plan of arranging the various pieces which go to make up the whole cube.

We have now for the first time the slanting line, the mediation of the two opposites, vertical and horizontal, and by this three of the small cubes are divided into halves and three into quarters. It is advisable, when building the cube, to place nine whole cubes in each of the two lower layers, keeping all the divided cubes in the upper or third layer, halves in the middle row, quarters at the back. Then we may slide the box gently over the cube as in the third and fourth gifts, which enables us to have the blocks separated properly when taken out again, and forms the only expedient way of handling the pieces.[47]

[47] "This procedure is by no means intended merely to make the withdrawal of the box easy for the child, but, on the contrary, brings to him much inner profit. It is well for him to receive his playthings in an orderly manner—not to have them tossed to him as fodder is tossed to animals. It is good for the child to begin his play with the perception of a whole, a simple self-contained unit, and from this unity to develop his representations. Finally, it is essential that the playing child should receive his material so arranged that its various elements are discernible, and that by seeing them his mind may unconsciously form plans for using them. Receiving his material thus arranged, the child will use it with ever-recurrent and increasing satisfaction, and his play will produce far more abiding results than the play of one whose material lies before him like a heap of cobblestones."—Froebel's Pedagogics, page 205.

The exercises with this gift are like those which have preceded it.

Exercises of the Gift

1. Informal questions by the kindergartner and answers by the children, on its introduction, that it may be well understood. This should be made entirely conversational, familiar, and playful, but a logical plan of development should be kept in mind. A consideration of the various pieces of the gift may occupy a part of each building or number lesson.

2. Dictation, building by suggestion, and cooperative plays in the various forms. With all except advanced children the Life forms are most useful and desirable.[48]

[48] "The child, in a word, follows the same path as the man, and advances from use to beauty and from beauty to truth."—Froebel's Pedagogics, page 219.

3. Free invention with each lesson.

4. Number and form lessons. In number there will of course be some repetition of what has been done before, but a sufficient amount of new presentation to awaken interest. It is only by constant review and repetition that we can assist children to remember these things and to receive them among their natural experiences, and fortunately the habit of repetition in childhood is a natural one, and therefore seldom irksome.

Errors in Form Teaching.

As to the form lessons, we must remember that our method has nothing to do with scientific geometry, but is based entirely on inspection and practice. It lays the foundation of instruction in drawing, and forms an admirable preparation for different trades, as carpentry, cabinet-making, masonry, lock-smithing, pattern-making, etc. Even in the primary schools, and how much more in the kindergarten, the form or geometrical work should be essentially practical and given by inspection. Even there all scientific demonstration should be prohibited, and the teacher should be sparing in definitions.

It is enough if the children recognize the forms by their special characteristics and by perceiving their relations, and can reproduce the solids in modeling, and the planes and outlines in tablets, sticks, rings, slats, drawing, and sewing.[49]

[49] "The Conference recommends that the child's geometrical education should begin as early as possible; in the kindergarten, if he attends a kindergarten, or if not, in the primary school. He should at first gain familiarity through the senses with simple geometrical figures and forms, plane and solid; should handle, draw, measure, and model them; and should gradually learn some of their simpler properties and relations."—Report of Committee of Ten, page 110.

LIFE FORMS.

We can now be quite methodical and workman-like in our building, and can learn to use all the parts economically and according to principle. We can discuss ground plans, cellars, foundations, basements, roofs, eaves, chimneys, entrances, and windows, and thus can make almost habitable dwellings and miniature models of larger objects.[50]

[50] "The child's life moves from the house and its living-rooms, through kitchen and cellar, through yard and garden, to the wider space and activity of street and market, and this expansion of life is clearly reflected in the order and development of his productions."—Froebel's Pedagogics, page 221.

The child is a real carpenter now, and innocently happy in his labor. Who can doubt that in these cheerful daily avocations he becomes in love with industry and perseverance, and as character is nothing but crystallized habit, he gets a decided bias in these directions which affects him for many a year afterward.[51]

[51] "In some German kindergartens large building-logs are supplied in one corner of the play garden. These logs are a foot or more in length, three inches wide, and one inch thick. Several hundred of these are kept neatly piled against the fence, and the children are expected to leave them in good order. This bit of voluntary discipline has its good uses on the playground, and the free building allowed with this larger material gives rise to individual effort, and tests the power of the children in a way which makes the later, more organized work at the tables far more full of meaning."—Kindergarten Magazine, November, 1894.

Objects which he meets in his daily walks are to be constructed, and also objects with which he is not so familiar,[52] so that by pleasant conversation the realm of his knowledge may be extended, and the sphere of his affections and fancies enlarged; for these exercises when properly conducted address equally head, heart, and hand.

[52] "As these building gifts afford a means of clearing the perceptions of the child, they give occasion for extending these perceptions, and for representing in their essential parts objects of which the child has only heard."—Froebel's Pedagogics, page 222.

Froebel says of all this building, "It is essential to proceed from the cube as a whole. In this way the conception of the whole, of uniting, stamps itself upon the child's mind, and the evolution of the particular, partial, and manifold from unity is illustrated."

Group Work.

Our opportunities for group work, or united building, are greatly extended, and none of them should be neglected, as it is essential to inculcate thus early the value of cooperation. We have material enough to call into being many different things on the children's tables; the house where they live, the church they see on Sunday, the factory where their fathers or brothers work, the schoolhouse, the City Hall, the public fountain, the stable, and the shops. Thus we may create an entire village with united effort, and systematic, harmonious action. Each object may be brought into intimate relation with the others by telling a story in which every form is introduced. This always increases the interest of the class, and the story itself seems to be more distinctly remembered by the child when brought into connection with what he has himself constructed.

The third gift may be used with the fifth if we wish to increase the number of blocks for cooperative work, and is particularly adapted to the laying of foundations for large buildings in the sand-table. A large fifth gift, constructed on the scale of a foot instead of an inch, is very useful for united building. One child or the kindergartner may be the architect of the monument or other large form which is to be erected in the centre of the circle. The various children then bring the whole cubes, the halves, and quarters, and lay them in their appropriate places, and the erection when complete is the work of every member of the community.

SYMMETRICAL FORMS.

These are in number and variety almost endless, as we have thirty-nine pieces of different characters. Edward Wiebe says: "He who is not a stranger in mathematics knows that the number of combinations and permutations of thirty-nine different bodies cannot be counted by hundreds nor expressed by thousands, but that millions hardly suffice to exhaust all possible combinations."

These forms naturally separate themselves, Froebel says, into two distinct series, i. e., the series of squares and the series of triangles, and move from these to the circle as the conclusion of the whole series of representations. "From these forms approximating to the circle there is an easy transition to the representation of the different kinds of cog-wheels, and hence to a crude preliminary idea of mechanics."

If the movements begin with the exterior part of the figure instead of the interior, we should make all the changes we wish in that direction before touching the centre, and vice versa.

Each definite beginning conditions a certain process of its own, and however much liberty in regard to changes may be allowed, they are always to be introduced within certain limits.[53]

We should leave ample room for the child's own powers of creation, but never disregard Froebel's principle of connection of opposites; this alone will furnish him with the "inward guide" which he needs.[54] It is only by becoming accustomed to a logical mode of action that the child can use this amount of material to good advantage.

[53] "With these forms of beauty it is above all important that they be developed one from another. Each form in the series should be a modification or transformation of its predecessor. No form should be entirely destroyed. It is also essential that the series should be developed so that each step should show either an evolution into greater manifoldness and variety, or a return to greater simplicity."—Froebel's Pedagogics, page 225.

[54] "This free activity ... is only possible when the law of free creativeness is known and applied; for that a free creativeness only can be a lawful one, we are taught by the smallest blade of grass, whose development takes place only according to immutable laws."—Reminiscences of Froebel, page 133.

Dangers of Dictation.

The dictations should be made with great care and simplicity. The child's mind must never be forced if it shows weariness, nor the more difficult lessons given in too noisy a room, as the nervous strain is very great under such circumstances. We should remember that great concentration is needed for a young child to follow these dictations, and we must be exceedingly careful in enforcing that strict attention for too long a time. A well-known specialist says that such exercises should not be allowed at first to take up more than a minute or two at a time; then, that their duration should gradually extend to five and ten minutes. The length of time which children closely and voluntarily attend to an exercise is as follows: Children from five to seven years, about fifteen minutes; from seven to ten years, twenty minutes; from twelve to eighteen years, thirty minutes. A magnetic teacher can obtain attention somewhat longer, but it will always be at the expense of the succeeding lesson. "By teachers of high pretensions, lessons are often carried on greatly and grievously in excess of the proper limits; but when the results are examined they show that after a certain time has been exceeded, everything forced upon the brain only tends to drive out or to confuse what has been previously stored in it."

We find, of course, that the mind can sustain more labor for a longer time when all the faculties are employed than when a single faculty is exerted, but the ambitious teacher needs to remind herself every day that no error is more fatal than to overwork the brain of a young child. Other errors may perhaps be corrected, but the effects of this end only with life. To force upon him knowledge which is too advanced for his present comprehension, or to demand from him greater concentration, and for a longer period than he is physically fitted to give, is to produce arrested development.[55]

[55] "Whoever sacrifices health to wisdom has generally sacrificed wisdom, too." (Jean Paul.)

MATHEMATICAL FORMS.

We must beware of abstractions in these forms of knowledge, and let the child see and build for himself, then lead him to express in numbers what he has seen and built. He will not call it Arithmetic, nor be troubled with any visions of mathematics as an abstract science.[56]

[56] "Perceptions and recognitions which are with difficulty gained from words are easily gained from facts and deeds. Through actual experience the child gains in a trice a total concept, whereas the same concept expressed in words would be only grasped in a partial manner. The rare merit, the vivifying influence of this play-material is that, through the representations it makes possible, concepts are recognized at once in their wholeness and unity, whereas such an idea of a whole can only very gradually be gained from its verbal expression. It must, however, be added that later, through words, the concept can be brought into higher and clearer consciousness."—Froebel's Pedagogics, page 206.

The cube may be divided into thirds, ninths, and twenty-sevenths, and the fact thus practically shown that whether the thirds are in one form or another, in long lines or squares, upright or flat, the contents remain the same. We may also illustrate by building, that like forms may be produced which shall have different contents, or different forms having the same contents.

Halves and quarters may be discussed and fully illustrated, and addition, subtraction, multiplication, and division may be continued as fully as the comprehension of the child will allow.

During the practice with the forms of knowledge we should frequently illustrate the lawful evolution of one form from another, as in the series moving from the parallelopiped to the hexagonal prism.

It should not be forgotten that whenever the cube is separated and divided, recombination should follow, and that the gift plays should always close with synthetic processes.

Some of the mathematical truths shown in the fifth gift were also seen in the third, but "repeated experiences," as Froebel says, "are of great profit to the child."[57]

We should allow no memorizing in any of these exercises or meaningless and sing-song repetitions of words. We must always talk enough to make the lesson a living one, but not too much, lest the child be deprived of the use of his own thoughts and abilities.

[57] "It is through frequent return to a subject and intense activity upon it for short periods, that it 'soaks in' and becomes influential in the building of character. Especially is this true if the principles of apperception and concentration are not forgotten by the teacher in working upon the disciplinary subjects." (Geo. P. Brown.)

THE FIFTH GIFT B.

There is a supplemental box of blocks called in Germany the fifth gift B, which may be regarded as a combination of the second and fifth gifts, and whose place in the regular line of material is between the fifth and sixth. It was brought out in Berlin more than thirteen years ago, but has not so far been used to any extent in this country.

It is a three-inch wooden cube divided into twelve one-inch cubes, eight additional cubes from each of which one corner is removed and which correspond in size to a quarter of a cylinder, six one-inch cylinders divided in halves, and three one-inch cubes divided diagonally into quarters like those of the fifth gift.

Hermann Goldammer argues its necessity in his book "The Gifts of the Kindergarten" (Berlin, 1882), when he says that the curved line has been kept too much in the background by kindergartners, and that the new blocks will enable children to construct forms derived from the sphere and cylinder, as well as from the cube.

Goldammer's remark in regard to the curved line is undoubtedly true, but it would seem that he himself indicates that the place of the new blocks (or of some gift containing curved lines) should be supplemental to the third, rather than the fifth, as they would there carry out more strictly the logical order of development and amplify the suggestions of the sphere, cube, and cylinder.

It is possible that we need a third gift B and a fourth gift B, as well as some modifications of the one already existing, all of which should include forms dealing with the curve.

Goldammer says further: "In Froebel's building boxes there are two series of development intended to render a child by his own researches and personal activity familiar with the general properties of solid bodies and the special properties of the cube and forms derived from it. These two series hitherto had the sixth gift as their last stage, although Froebel himself wished to see them continued by two new boxes. He never constructed them, however, nor are the indications which he has left us with regard to those intended additions sufficiently clear to be followed by others."

The curved forms of the fifth gift B are, of course, of marked advantage in building, especially in constructing entrances, wells, vestibules, rose-windows, covered bridges, railroad stations, viaducts, steam and horse cars, house-boats, fountains, lighthouses, as well as familiar household furniture, such as pianos, tall clocks, bookshelves, cradles, etc.

Though one may perhaps consider the fifth gift B as not entirely well placed in point of sequence, and needing some modification of its present form, yet no one can fail to enjoy its practical use, or to recognize the validity of the arguments for its introduction.

READINGS FOR THE STUDENT.

Paradise of Childhood. Edward Wiebe. Pages 21-27. Kindergarten Guide. J. and B. Ronge. 24-29. Kindergarten Guide. Kraus-Boelte. 81-113. Koehler's Kindergarten Practice. Tr. by Mary Gurney. 25-31. Froebel and Education by Self-Activity. H. Courthope Bowen. 142, 143. Pedagogics of the Kindergarten. Fr. Froebel. 201-236. Art and the Formation of Taste. Walter Crane. 152, 197-242. Seven Lamps of Architecture. John Ruskin. The Kindergarten. H. Goldammer. 85-104, 111-116. Kindergarten Toys. H. Hoffmann. 31-36.



FROEBEL'S SIXTH GIFT

"The artistically cultivated senses of the new generation will again restore pure, holy art." FRIEDRICH FROEBEL.

"Life brings to each his task, and whatever art you select, algebra, planting, architecture, poems, commerce, politics,—all are attainable, even to the miraculous triumphs, on the same terms, of selecting that for which you are apt; begin at the beginning, proceed in order, step by step." R. W. EMERSON.

"The sixth gift reveals the value of axial contrasts." W. N. HAILMANN.

1. The sixth gift is a three-inch cube divided by various cuts into thirty-six pieces, eighteen of which are rectangular parallelopipeds, or bricks, the same size as those of the fourth gift, two inches long, one inch wide, and one half inch thick. Twelve additional pieces are formed by cutting six of these parallelopipeds or units of measure in halves breadthwise, giving blocks with two square and four oblong faces. The remaining six pieces are formed by cutting three parallelopipeds or units of measure in halves, lengthwise, giving square prisms, columns, or pillars.

2. The sixth is the last of the solid gifts, and is an extension of the fourth, from which it differs in size and number of parts. It deals with multiples of the number two and three also; with halves rather than with quarters or thirds, the "half" being treated in a new manner, i. e., by dividing the unit of measure both in its length and breadth, giving two solids, different in form but alike in cubical contents.

3. The most important characteristics of the gift are:—

a. Irregularity of division.

b. Introduction of column.

c. Extent of surface covered by symmetrical forms.

d. Greater inclosure of space in symmetrical forms.

e. Introduction of distinct style of architecture.

f. Greater height of Life forms.

g. Severe simplicity of Life forms produced by the rectangular solids.

4. The sixth gift has no great increase of difficulty, and though new forms are presented there is little complexity in dictation. The building needs a somewhat more careful handling, inasmuch as the Life forms rise to considerable height and need the most exact balance.

The child sees solids whose faces are all either squares or oblongs, but of different sizes, viz., oblongs of three sizes, squares of two sizes.

This is the last of the Building Gifts; the child having received sufficient knowledge to be introduced step by step into the domain of the abstract, the first step being the planes of the seventh gift.

5. The geometrical forms illustrated in this gift are:—

{ Rectangular parallelopipeds. Solids. { Square prisms. { Cubes.

Planes. { Squares. { Oblongs.

6. The brick of the sixth gift is identical with that of the fourth, therefore it presents the same contrasts and mediations.

In number the different classes of blocks stand to each other as 6:12:18.

We may add that the brick is the foundation form of the gift, and that we gain the remaining two forms, the square block and pillar, by dividing it in exactly opposite directions.

* * * * *

Introduction of the Gift.

The sixth gift is so evidently an enlarged and diversified fourth gift, that it is well to compare it on its introduction with the fourth, as well as with its immediate predecessor in the series. When the fourth is placed beside it, and the contents of the two boxes brought to view, it is evident at once to the child that a higher round in the ladder of evolution has been reached, and a new and highly specialized form developed. He is fired at once with creative activity, and his eager hands so quiver with impatience to investigate the possibilities of the new blocks that the wise kindergartner does not detain him long with comparisons, only assuring herself that he notes the relation of the new gift to the former ones, that he compares the two new solids to the brick, or unit of measure, and to each other, and discovers how each has been produced.

Difficulties of the New Gift.

The difficulties of the new gift are very slight, as has been said, consisting neither in dictation, in mass of material, nor in new forms, lines, or angles. Equilibrium alone presents novel problems, but this law the child now understands fairly well in its practical workings, while he has gained so much dexterity in his use of the other blocks that the height and delicate poise of the new forms are added attractions rather than obstacles.

Forms of Life.

The sixth gift far surpasses all the other building blocks in its decided adaptation to the purely architectural forms. The bricks of the fourth gift may be used as a foundation for the construction of large and ambitious structures, and with this additional material, the sixth gift may excel in producing elegant and graceful forms.

The bricks of course admit of a much greater superficial extension and the inclosure of a more extensive space than has heretofore been possible.

The children will unaided construct familiar objects, such as household furniture and implements, churches, fences, walled inclosures, and towers, with the new blocks, and seize with delight upon the possibilities of the column, which is really the distinctive feature of the gift.

So far, the building of object forms will closely resemble those of the previous gifts, but a step in advance may be made by the children if the kindergartner is complete mistress of the new forms and knows their capabilities. The gift may serve as a primer of architecture if its materials are thoroughly exploited, and may lead later on to a healthy discontent with incorrect outline, with vulgar ornamentation, and with crudity of form.[58]

[58] "The sense of beauty must be awakened in the soul in childhood if in later life he is to create the beautiful."—Reminiscences of Froebel, page 158.

Froebel himself, who had made exhaustive studies in architecture, and obtained the training necessary to enable him to take it up as a profession, has left us many examples of sixth gift building, which are to be found in all the German "Guides." The structures are no longer rude representations, but have a marked grace and symmetry, and in their simplicity, clearness of outline, and fine proportion, strongly resemble early Greek architecture. Colonnades, commemorative columns, facades of palaces, belvederes, temples, arches, city gates, monuments, fountains, portals, fonts, observatories,—all can be constructed in miniature with due regard to law, fitness, and proportion, and as the soft, creamy-white structures rise on the various tables, we see borne out Froebel's saying that the order of his Building Gifts was such that the child might be led in their use through the world's great architectural epochs from Egypt to Rome.[59]

[59] "As the gifts proceed from the first to the sixth, observation is demanded with increasing strictness, relativity more and more appreciated, and the opportunity afforded for endless manifestations of the constructive faculty, while all the time impressions are forming in the mind which in due time will bear rich fruits of mathematical and practical knowledge as well as aesthetic culture, for the dawning sense of the beautiful as well as of the true is gaining consistency and power." (Karl Froebel.)

Forms of Symmetry.

Although with this gift we cannot produce symmetrical forms in as great diversity as with the fifth, yet the materials are productive to the inventive mind, and when the pieces are arranged with care and taste, beautiful figures may always be developed, those having a triangular centre being novel and especially pleasing. Although not as diversified, however, they have the added advantage of approaching nearer the plane; and that this progression may be more clearly shown, it seems evident that the symmetrical forms should only be produced by laying the columns, "square-faced blocks" and bricks, flat upon the table, and that the practice, advised by some authorities, of changing the figures by placing the blocks erect, or half erect, should be discouraged.

Forms of Knowledge.

In the forms of knowledge we find again much less diversity than in the fifth gift,—the rectilinear solids and consequent absence of oblique angles limiting us in the construction of geometrical forms. The blocks, however, offer excellent means for general arithmetical instruction, for working out problems as to areas, for further illustration of dimension, and for building many varieties of parallelopipeds, square prisms, and cubes, and studying the parallelograms which bound them. The elements of this knowledge, it is true, were gained with the fourth gift, but we must remember that interest in any subject is not necessarily decreased by repetition, and that the value of review depends upon whether or not it is mechanical.[60]

[60] "What makes Froebel's gifts particularly instructive is, indeed, the fact that the most varied materials constantly lead to the same observations, but always under different conditions, so that we obtain the necessary repetitions without the dryness, the tiresomeness, the fatigue inseparable from constant unvaried iteration. But they also accustom the child to discover similarity in things that appear to differ, to find resemblance in contrasts, unity in diversity, connection in what appears unconnected."—H. Goldammer's The Kindergarten, page 109.

cooperative Work.

The group work at the square tables is now especially beautiful, both when forms of symmetry or object forms are constructed. The fourth gift may be used, as has been said, if more material is needed, and of course combines perfectly with the sixth gift blocks. A large sixth gift made as was suggested for the fifth, on the scale of a foot instead of an inch, is most useful for cooperative exercises in the centre of the ring, and the slender, graceful columns, for instance, which may thus be built in unison to commemorate some historic birthday, are so many concrete evidences to the child's eyes of the value of united effort.

The Gifts and their Treatment by the Kindergartner.

Every gift and occupation and exercise of the kindergarten has been developed with infinite love and forethought to meet the child's wishes and capabilities; every one of them has been so delicately adjusted to meet the demands of the case, and so gently drawn into the natural and legitimate channel of childlike play, that they never fail to meet with an enthusiastic reception from the child, nor to awaken the strongest interest in him.

The kindergartner should be careful that he never builds hastily or lawlessly, and above all she should guide him to those forms which he will be able to construct with perfection and accuracy. She should always follow him in his work, answering his questions and suggesting new ideas, letting him feel in every way that she is in sympathy with him, and that none of his plans or experiments, however small they may be, are indifferent to her. It is always a delight to the child if his productions are understood by grown-up people, for he often feels somewhat doubtful of the value of his work until the seal of approval has been set upon it by a superior mind.

Underlying Idea of Froebel's Gifts.

If we have grasped the underlying idea which welds the mass of material which forms the kindergarten gifts into a harmoniously connected whole; if we have developed the analytical faculty sufficiently to perceive their relation to the child, the child's relation to them, and the reasons for their selection as mediums of education; if we see clearly why each object is given, what connection it has with the child's development, and what natural laws should govern it in play, then we comprehend Froebel's own idea of their use.

Education vs. Cramming.

Certainly the ignorant and unsympathetic kindergartner may err in dealing with them, and introduce the cramming process into her field of labor as easily as the public school teacher, for it is as easy to cram with objects as with books, and should this occur there is cause for grave uneasiness, since the opportunity for injuring the brain of the child is greater during these first years than at any other time.

If we force the child, or make the lesson seem work to him, his faculties will rebel, he will be dull, inattentive, or restless, according to his temperament or physical state; he will not be interested in what we teach him, and therefore it will make no impression on him.

The child has memory enough; he remembers the picnic in the woods, the glorious sail across the bay, the white foam in the wake of the boat, the very tint of the flowers that he gathered,—in fact, he remembers everything in which he is interested. If we would have him remember our teachings forever, we must make them worthy of being remembered forever. And to this end it is essential that only the best teachers be provided for little children. The ideal teacher should know her subject thoroughly, but should be able to boil it down, to condense it, so that the concentrated extract alone will remain, and this be presented to her pupils.[61]

[61] "If you would be pungent, be brief; for it is with words as with sunbeams,—the more they are condensed the deeper they burn."

In leaving these first six gifts, we need finally to remember these things:—

Suggestions as to Method.

First, that we must not be too anxious to resolve these plays into the routine of lessons; with our younger pupils especially this is not admissible, and we must guard against it in all exercises with the kindergarten materials.

Second, we may assure ourselves, in all modesty, that it is a difficult matter, indeed, to direct these plays properly; that is, to have system and method enough to guard the children from all lawlessness, idleness, and disorder, and yet to keep from falling into a mechanical drill which will never produce the wished-for results. Play is the natural, the appropriate business and occupation of the child left to his own resources, and we must strive to turn our lessons into that channel,—only thus shall we reach the highest measure of true success.

Third, we must strive by constant study and thought, by entering into the innermost chambers of the child-nature, and estimating its cravings and necessities, to penetrate the secret, the soul of the Froebel gifts, then we shall never more be satisfied with their external appearances and superficial uses.

NOTE. In arranging the blocks of the sixth gift, place the eighteen bricks erect, in three rows, with their broad faces together. On top of these place nine of the square-faced blocks, thus forming a second layer. The third layer is formed by placing the remaining three blocks of this class on the back row, and filling in the space in front with the six pillars, placed side by side.

READINGS FOR THE STUDENT.

Paradise of Childhood. Edward Wiebe. Pages 27-29. Kindergarten Guide. J. and B. Ronge. 20-31. Kindergarten Guide. Kraus-Boelte. 113-145. Koehler's Kindergarten Practice. Tr. by Mary Gurney. 31, 32. The Kindergarten. H. Goldammer. 105-110. Stones of Venice. John Ruskin. Architecture, Mysticism, and Myth. W. K. Lethaby. The Sources of Architectural Types. Spencer's Essays, vol. ii. page 375. The Two Paths. John Ruskin. (Chapter on Influence of Imagination in Architecture.) Discourses on Architecture. E. E. Viollet-le-Duc. Tr. by Henry Van Brunt. (First and Second Discourses.)



FROEBEL'S SEVENTH GIFT

"The properties of number, form, and size, the knowledge of space, the nature of powers, the effects of material, begin to disclose themselves to him. Color, rhythm, tone, and figure come forward at the budding-point and in their individual value. The child begins already to distinguish with precision nature and the world of art, and looks with certainty upon the outer world as separate from himself." FRIEDRICH FROEBEL.

"Froebel's thin colored planes correspond with the mosaic wood or stone work of early man." H. POESCHE.

"There is nothing in the whole present system of education more deserving of serious consideration than the sudden and violent transition from the material to the abstract which our children have to go through on quitting the parental house to enter a school. Froebel therefore made it a point to bridge over this transition by a whole series of play-material, and in this series it is the laying-tablets which occupy the first place." H. GOLDAMMER.

1. The seventh gift consists of variously colored square and triangular tablets made of wood or pasteboard, the sides of the pieces being about one inch in length. Circular and oblong pasteboard tablets have lately been introduced, as well as whole and half circles in polished woods.

2. The first six gifts illustrated solids, while the seventh, moving from the concrete towards the abstract, makes the transition to the surface.

The Building Gifts presented to the child divided units, from which he constructed new wholes. Through these he became familiar with the idea of a whole and parts, and was prepared for the seventh gift, which offers him not an object to transform, but independent elements to be combined into varied forms. These divided solids also offered the child a certain fixed amount of material for his use; after the introduction of the seventh gift, the amount to be used is optional with the kindergartner.

3. The child up to this time has seen the surface in connection with solids. He now receives the embodied surface separated from the solid, and gradually abstracts the general idea of "surface," learning to regard it not only as a part, but as an individual whole.

This gift also emphasizes color and the various triangular forms, besides imparting the idea of pictorial representation, or the representation of objects by means of plane surfaces.

4. The gift leads the child from the object itself towards the representation of the object, thus sharpening the observation and preparing the way for drawing.

It is also less definitely suggestive than previous gifts, and demands more creative power for its proper use. It appeals to the sense of form, sense of place, sense of color, and sense of number.

5. The geometrical forms illustrated in this gift are:—

Squares.

{ Right isosceles. { Obtuse isosceles. Triangles. { Equilateral. { Right-angled scalene.

{ Oblong. { Rhombus. { Rhomboid. { Trapezoid. In combination. { Trapezium. { Pentagon. { Hexagon. { Heptagon. { Octagon.

6. The law of Mediation of Contrasts is shown in the forms of the gift. We have in the triangles, for instance, two lines running in opposite directions, connected by a third, which serves as the mediation. Contrasts and their mediations are also shown in the squares and in the forms made by combination. This gift, representing the plane, is a link between the divided solid and the line.

* * * * *

Step from Solid to Plane.

We have now left the solid and are approaching abstraction when we begin the study of planes. All mental development has ever begun and must begin with the concrete, and progress by successive stages toward the abstract, and it was Froebel's idea that his play-material might be used to form a series of steps up which the child might climb in his journey toward the abstract.

Beginning with the ball, a perfect type of wholeness and unity, we are led through diversity, as shown in the three solids of the second gift, toward divisibility in the Building Gifts, and approximation to surface in the sixth gift. The next move in advance is the partial abstraction of surface, shown in the tablets of the seventh gift.

The tablets show two dimensions, length and breadth, the thickness being so trifling relatively that it need not be considered, as it does not mar the child's perception and idea of the plane. They are intended to represent surfaces, and should be made as thin as is consistent with durability.

Systematic Relation between the Tablets.

The various tablets as first introduced in Germany and in this country were commonly quite different in size and degrees of angles in the different kindergartens, as they were either cut out hastily by the teachers themselves, or made by manufacturers who knew very little of the subject. The former practice of dividing an oblong from corner to corner to produce the right-angled scalene triangle was much to be condemned, as it entirely set aside the law of systematic relation between the tablets and rendered it impossible to produce the standard angles, which are so valuable a feature of the gift.

"One of the principal advantages of the kindergarten system is that it lays the foundation for a systematic, scientific education which will help the masses to become expert and artistic workmen in whatever occupation they may be engaged."[62]

[62] Pamphlet on the Seventh Gift. (Milton Bradley Co.)

In this direction the seventh gift has doubtless immense capabilities, but much of its force and value has been lost, much of the work thrown away which it has accomplished, for want of proper and systematic relation between the tablets. The order in which these are now derived and introduced is as follows:—

The square tablet is, of course, the type of quadrilaterals, and when it is divided from corner to corner a three-sided figure is seen,—the half square or right isosceles triangle; but one which is not the type of three-sided figures. The typical and simplest triangle, the equilateral, is next presented, and if this be divided by a line bisecting one angle, the result will be two triangles of still different shape, the right-angled scalene. If these two are placed with shortest sides together, we have another form, the obtuse-angled triangle, and this gives us all the five forms of the seventh gift.

The square educates the eye to judge correctly of a right angle, and the division of the square gives the angle of 45 deg., or the mitre. The equilateral has three angles of 60 deg. each; the divided equilateral or right-angled scalene has one angle of 90 deg., one of 60 deg., and one of 30 deg., while the obtuse isosceles has one angle of 120 deg., and the remaining two each 30 deg. These are the standard angles (90 deg., 45 deg., 60 deg., and 30 deg.) used by carpenter, joiner, cabinet-maker, blacksmith,—in fact, in all the trades and many of the professions, and the child's eye should become as familiar with them as with the size of the squares on his table.

Possibilities of the Gift in Mathematical Instruction.

Edward Wiebe says in regard to the relation of the seventh gift to geometry and general mathematical instruction: "Who can doubt that the contemplation of these figures and the occupations with them must tend to facilitate the understanding of geometrical axioms in the future, and who can doubt that all mathematical instruction by means of Froebel's system must needs be facilitated and better results obtained? That such instruction will be rendered fruitful in practical life is a fact which will be obvious to all who simply glance at the sequence of figures even without a thorough explanation, for they contain demonstratively the larger number of those axioms in elementary geometry which relate to the conditions of the plane in regular figures."

As the tablets are used in the kindergarten, they are intended only "to increase the sum of general experience in regard to the qualities of things," but they may be made the medium of really advanced instruction in mathematics, such as would be suitable for a connecting-class or a primary school. All this training, too, may be given in the concrete, and so lay the foundation for future mathematical work on the rock of practical observation.

The kindergarten child is expected only to know the different kinds of triangles from each other, and to be familiar with their simple names, to recognize the standard angles, and to know practically that all right angles are equally large, obtuse angles greater, and acute less than right angles. All this he will learn by means of play with the tablets, by dictations and inventions, and by constant comparison and use of the various forms.