Chapter 8

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

Difficulties of the New Gift.

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

Forms of Life.

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

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

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

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

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

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

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

Forms of Symmetry.

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

Forms of Knowledge.

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

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

Coöperative Work.

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

The Gifts and their Treatment by the Kindergartner.

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

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

Underlying Idea of Froebel's Gifts.

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

Education _vs._ Cramming.

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

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

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

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

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

Suggestions as to Method.

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

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

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

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

READINGS FOR THE STUDENT.

Paradise of Childhood. _Edward Wiebe_. Pages 27-29. Kindergarten Guide. _J._ and _B. Ronge_. 20-31. Kindergarten Guide. _Kraus-Boelte_. 113-145. Koehler's Kindergarten Practice. Tr. by _Mary Gurney_. 31, 32. The Kindergarten. _H. Goldammer_. 105-110. Stones of Venice. _John Ruskin_. Architecture, Mysticism, and Myth. _W. K. Lethaby_. The Sources of Architectural Types. _Spencer's Essays_, vol. ii. page 375. The Two Paths. _John Ruskin_. (Chapter on Influence of Imagination in Architecture.) Discourses on Architecture. _E. E. Viollet-le-Duc_. Tr. by _Henry Van Brunt_. (First and Second Discourses.)

FROEBEL'S SEVENTH GIFT

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

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

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

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

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

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

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

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

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

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

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

Squares.

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

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

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

* * * * *

Step from Solid to Plane.

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

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

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

Systematic Relation between the Tablets.

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

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

[62] _Pamphlet on the Seventh Gift_. (Milton Bradley Co.)

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

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

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

Possibilities of the Gift in Mathematical Instruction.

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

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

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

How and when Tablets should be introduced.

As to the introduction of the tablets, the square is first of all of course given to the child. A small cube of the third gift may be taken and surrounded on all its faces by square tablets, and then each one "peeled off," disclosing, as it were, the hidden solid. We may also mould cubes of clay and have the children slice off one of the square faces, as both processes show conclusively the relation the square plane bears to the cube whose faces are squares. If the first tablets introduced are of pasteboard, as probably will be the case, the new material should be noted and some idea given of the manufacture of paper.

There is a vast difference in opinion concerning the introduction of this seventh gift, and it is used by the child in the various kindergartens at all times, from the beginning of his ball plays up to his laying aside of the fifth gift. It seems very clear, however, that he should not use the square plane until after he has received some impression of the three dimensions as they are shown in solid bodies, and this Mr. Hailmann tells us he has no proper means of gaining, save through the fourth gift.[63]

[63] "The perception of the difference between a surface-extension and an extension in three dimensions begins late and is established slowly."--W. Preyer, _The Mind of the Child_, page 180.

As to the triangular tablets, it is evident enough they should not be dealt with until after the child has seen the triangular plane on the solid forms of the fifth gift. Mr. Hailmann says that a clear idea of the extension of solids in three dimensions can only come from a familiarity with the bricks, and again that the abstractions of the tablet should not be obtruded on the child's notice until he has that clear idea.

Though the six tablets which surround the cube may be given to the child at the first exercise, it is better to dictate simple positions of one or two squares first, and let him use the six in dictation and many more in invention.

Order of introducing Triangles.