Chapter 7

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 coöperation. 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 coöperative 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.