Chapter III: Part 3

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.