Nora Archibald Smith

"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:—

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.

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.

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."

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.

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.

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.

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.

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.

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.

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]

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

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]

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.

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]

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] 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]

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.

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."

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.

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]

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]

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.

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.