Chapter 6

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, æsthetic 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.