Chapter 9

The first triangle given is the right isosceles, showing the angle of forty-five degrees, and formed by bisecting the square with a diagonal line. The child should be given a square of paper and scissors and allowed to discover the new form for himself, letting him experiment until the desired triangle is obtained. He should then study the new form, its edges and angles, and then join his two right-angled triangles into a square, a larger triangle, etc. Then let him observe how many positions these triangles may assume by moving one round the other. He will find them acting according to the law of opposites already familiar to him, and if not comprehended,[64] yet furnishing him with an infallible criterion for his inventive work.

[64] "With this law I give children a guide for creating, and because it is the law according to which they, as creatures of God, have themselves been created, they can easily apply it. It is born with them."--_Reminiscences of Froebel_, page 73.

The equilateral is then taken up, is compared with the half-square, and then studied by itself, its three equal sides and angles (each sixty degrees) being noted as well as the obtuse angles made by all possible combinations of the equilateral.

Next, as we have said, comes the right-angled scalene triangle, with its inequality of sides and angles, which must be studied and compared with the equilateral; and last of all, the obtuse isosceles triangle, which is dealt with in the same way.

Here, again, it should be noted that the two last forms should always be discovered by the child in his play with the equilateral, and that he should cut them himself from paper before he is given the regular pasteboard or wooden triangles for study. If presented for the first time in this latter form, they can never mean as much to him as if he had found them out for himself.

Dictations.

The dictations should invariably be given so that opposites and their intermediates may be readily seen. The different triangles may be studied each in the same way, introducing them one at a time in the order named, afterwards allowing as free a combination as will produce symmetrical figures. It is best always to study one of a new kind, then two, then gradually give larger numbers.

Great possibilities undoubtedly lie in this gift, but it is well to remember that with young children it must not be made the vehicle of too abstract instruction. In order to make the dictations simple, the child must be perfectly familiar with the terms of direction, up, down, right, left, centre; with the simple names of the planes (squares, half-squares, equal-sided, blunt and sharp-angled triangles, etc.); and he must learn to know the longest edge of each triangle, that he may be able to place it according to direction.

The children should be encouraged to invent, to give the dictation exercises to one another, and to copy the simpler forms of the lesson on blackboard or paper. Some duplicate copies in colored papers may be made from their inventions, and the walls of the schoolroom ornamented with them. It will be a pleasure to the little ones themselves, and demonstrate to others how wonderful a gift this is and how charmingly the children use it.

No exercise should be given without previous study, and in the first year's teaching it is wiser to draw or make the figures before giving the dictations. The materials, too, should be prepared beforehand, in such a form that they can be given out readily and quietly by the children at the opening of the exercise. To require a class of a dozen or more pupils to wait while the kindergartner assorts and counts the various colors and shapes of tablets to be used is positively to invite loss of interest on the children's part, and to produce in the teacher a hurry and worry and nervous tension which will infallibly ruin the play.

Life Forms.

The Life forms are no longer absolute representations, but only more or less suggestive images of certain objects, and thus show still more clearly the orderly movement from concrete to abstract.

Hitherto in Life forms the child has produced more or less real objects,--for instance, he built a miniature house, a fountain, a chair, or a sofa. They were not absolutely real, and therefore in one way merely images; but they were bodily images. He could place a little dish on the table, a tiny cup on the edge of the fountain, a doll could sit in the chair, and therefore they were all real for purposes of play, at least.

With the tablets, however, the child can no longer make a chair, though by a certain arrangement of them he can make an image of it.

The child will notice that many of the forms made with squares are flat pictures of those made with the third gift, and with the addition of the right isosceles triangles he can reproduce the façades of many of the elaborate object forms of the fifth. The various triangles differ greatly in their capabilities of producing Life forms, the equilateral and the obtuse isosceles being especially deficient in this regard and requiring to be combined with the other tablets. The fact that both the right isosceles and right scalene triangles produce Life forms in great variety seems to prove that, as Goldammer says, "the right angle predominates in the products of human activity."

Symmetrical Forms.

The symmetrical forms are more varied and innumerable than those of any other gift, and with the addition of the brilliant colors of the pasteboard, or the soft shades of the wooden tablets, make figures which are undeniably beautiful, and which are mosaic-like in their effect.

The whirling figures are interesting and new, and the child with developed eye and growing artistic taste will delight in their oddity, and yet be able to find opposites and their intermediates and make them as correctly as in the more methodical figures, where the exact right and left balanced the upper and lower extremes. Here we note that the equilateral and obtuse isosceles triangles, so ill fitted to produce Life forms, lend themselves to forms of symmetry in great variety. The various sequences of the latter in the third and fifth gifts may of course be faithfully reproduced in surface-extension with the tablets, and thus gain an added charm.

The amount of material given to the child is now a matter for the decision of the kindergartner, and is dependent only on the ability of the child to use it to advantage. This increase of material presents a further difficulty, and it is time for us to add still another, that is, to expect more of the child, and to require that he produce not only something original, but something which shall, though simple, be really beautiful.

Inventions in borders are a new and charming feature of this gift, and the circular and oblong tablets as well as the squares and various triangles are well adapted to produce them. The various borders laid horizontally across the tablets may be divided by lines of sticks, and thus make an effect altogether different from anything we have had before.

Mathematical Forms.

The work with forms of knowledge, as has been fully shown, will be in geometry than in arithmetic, to which indeed the gift is not especially well adapted. In addition to the study and comparison of the various forms, their lines and angles, we have a great variety of figures to be produced by combination. We can make the nine regular forms already mentioned in the introduction in a variety of ways, and thus give new charm to the old truths. We must allow the child to experiment by himself very frequently, and interpret to him his discoveries when he makes them.

The Seventh Gift in Weaving.

The square tablets afford a valuable aid to the occupation of weaving, as all the simple patterns can be formed with them, the child laying them upon his table until he has mastered the numerical principle upon which they are constructed. We can easily see how these same patterns may be further utilized as designs for inlaid tiles, or parquetry floors. Thus the seventh gift may introduce children to subsequent practical life, and serve as a useful preparation for various branches of art-work.

Seventh Gift Parquetry.

It is easy to see when we begin the practical use of the tablets that the essential characteristics of the gifts in their progress from solid to point are now becoming less marked, and that they begin to merge into the occupations, which develop from point to solid. The meeting-place of the two series is close at hand, and, like drops of water fallen near each other, they tremble with impatience to rush into one.

The inventions which the child makes with tablets he now very commonly expresses a desire to give away, or to take home with him,--a thought which he seldom had with the gifts, wishing rather to show them in their place upon the tables. As this is a natural and legitimate desire, a supplement to the seventh gift has been devised, consisting of paper substitutes for the various forms, of the same size and appropriate coloring, and to be had either plain or gummed on the back. After the inventions have been made, they are easily transferred to paper with parquetry, and so can be bestowed according to the will of the inventor.

Group Work.

The parquetry of the seventh gift lends an added grace to coöperative work, for the children can now combine all their material in one form to decorate the room, or perhaps to send as a gift to an absent playmate. They may make an inlaid floor for the doll's house, a brightly colored windowpane for the sun to stream through, and with larger forms may even design an effective border for the wainscoting of the schoolroom.[65]

[65] "The utility of this united action is not to be overlooked. The children all proceed according to one and the same law, they all work to produce one and the same result, the same purpose unites them all; in short, we see here in the children's play all that forms the base of every human society, all that renders it possible for men to act together in organized communities, such as are the family, the state, and the church. And to prepare for the future, to be mindful even amidst play of that which a child will afterwards require in order worthily to fill his place in the world, ought surely not to be among the least important ends of an education claiming to be in conformity with nature and reason."--H. Goldammer, _The Kindergarten_, page 135.

The group work at the square tables is also carried on very fully with the tablets, the symmetrical figures when the colors are well combined being quite dazzling in beauty.

Color with Seventh Gift.

In this connection, a danger may be noted in the treatment of the gifts, both by kindergartner and children. Color appears again here in almost bewildering profusion after its long absence in the series, and is another straw to prove that the wind is blowing strongly toward the occupations. Many of the pasteboard tablets are of different colors on the opposite sides, and though this is of great use in Beauty forms, when properly treated, it is quite often unfortunate in forms of life, unless careful attention is given to arranging the material beforehand. The effect of a barn, for instance, with its front view checkered with violet, red, and yellow squares, may be imagined, or of a pigeon-house with a parti-colored green and blue roof, an orange standard, and red supports. Yet these are no fancy pictures I have painted, and if the child places the tablets in this fashion, they are often allowed so to remain without criticism from the purblind kindergartner. She even sometimes dictates, herself, extravagant and vulgar combinations of color, such as a violet centre-piece with green corners and an orange border.

There needs no reasoning to prove that such a person is radically unfit to handle the subject of color-teaching, and is sure to corrupt the children under her charge; for in general, if ordinarily well trained, they should now be far beyond the stage in which they would be satisfied with such crudity of combination. They have had their season of "playing with brightness," as Mr. Hailmann calls it, and should now begin to have really good ideas as to harmonious arrangement of hues. If they have not, if they really seem to prefer the pigeon-house or barn above mentioned, then they are viciously ill-taught, or altogether deficient in color sense.

It has been noted that the older children often choose the light and dark wooden tablets, for invention, rather than the gay pasteboard forms; but this may be on account of the high polish of the wood, and its novelty in this guise, rather than because, as has been suggested, they have been surfeited with brightness.

READINGS FOR THE STUDENT.

Paradise of Childhood. _Edward Wiebe_. Pages 30-38. Law of Childhood. _W. N. Hailmann_. 38, 39. Kindergarten Guide. _Kraus-Boelte_. 145-237. Koehler's Kindergarten Practice. Tr. by _Mary Gurney_. 6-9. The Kindergarten. _H. Goldammer_. 116-54. Kindergarten Culture. _W. N. Hailmann_. 68-70. Kindergarten and Child-Culture. _Henry Barnard_. 210, 255, 257. Prang Primary Course in Art Education. Part I. _Mary D. Hicks_, _Josephine C. Locke_. Color in the School-Room. _Milton Bradley_. Elementary Color. _Milton Bradley_. Color Teaching in Public Schools. _Louis Prang_, _J. S. Clark_, _Mary D. Hicks_. Color, an Elementary Manual for Students. _A. H. Church_. The Principles of Harmony and Contrasts of Colors. _M. E. Chevreul_. Students' Text-Book of Color. _O. N. Rood_. Suggestions with Regard to the Use of Color. _Prang Ed. Co._

FROEBEL'S EIGHTH GIFT

THE STRAIGHT LINE.

_The Single and Jointed Slats and Staff or Stick._

"The knowledge of the linear lies at the foundation of the knowledge of each form; the forms are viewed and recognized by the intermediation of the straight-lined." FRIEDRICH FROEBEL.

"Froebel's laths, wherewith the child can form letters, correspond to the beech-staves (_buchenen Stäbchen_, now contracted to _Buchstaben_, i. e., letters of the alphabet), whereon were carved the runes and magic symbols of our primitive ancestors." HERMANN POESCHE.

"It will be readily seen how useful stick-laying may become in perspective drawing, in the study of planes and solids, in crystallography; how, while it insures an enjoyable familiarity with geometrical forms and secures ever-increasing manual skill and delicacy of touch, it develops at the same time the artistic sense of the children in a high degree." W. N. HAILMANN.

1. The wooden staffs of the eighth gift (sometimes called the tenth) are of various lengths, but have for their uniform thickness the tenth of an inch.

They present, as now made, flat sides and square ends, are sometimes uncolored and sometimes dyed in the six primary colors.

2. The previous gifts dealt with solids and plane surfaces, wholes or divided wholes, while this one illustrates the edge or line.

The previous gifts more definitely suggested their uses by their prominent characteristics; this depends for its value largely upon the ingenuity of the teacher.

We have contrasts of size in the preceding gifts, both in the units themselves and in the component parts of which the divided units are made; but in this gift the dimension _length_ is alone emphasized.

3. The most important characteristic of the gift is the representation of the line. The relations of position and form enter as essential elements of usefulness.

4. The laying of sticks may be used as an occupation very early in the kindergarten course, and thus serve as a preparation for the first drawing exercises, but there should be no attempt at this time to give them their legitimate connection with the cube as the edge of the solid and with the tablet as a portion of the surface.

Later they may be introduced in their proper place in the sequence of gifts, and thus assume their true relation in the child's mind. This relation is made more evident as we can and should reproduce the lessons with the solids in outline with the sticks. When the child is more advanced, the connection of the sticks with the preceding objects will be more clearly explained and intelligently comprehended, and then they may be used in connection with softened peas or tiny corks, which serve to illustrate the points of contact of the sides of surfaces and edges of solids whose skeletons the child can then construct with these materials.

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

Angles of every degree. Triangles, quadrilaterals, and additional polygons. Skeletons of solids by means of corks or peas.

6. The law of the mediation of contrasts is shown in the fact that every line is a connection between opposite points. As in the other gifts, the law governs the use of the line in the formation of all outlines of objects and all symmetrical designs.

* * * * *

As we have already noted, the gifts of Froebel are thus far solids, divided solids, planes and divided planes.

Relation of the Single and Jointed Slats to the other Gifts. How both are used.

With the single and jointed slats we shall not deal separately, merely stating that they form a transition between the surface and the line, having more breadth and relation to the surface itself than to the edge, but manifestly tending towards the embodied line of which the little stick given by Froebel is the realization.

The jointed slats, generally ruled in half and quarter inches for measuring, may be used to show how one form is developed from another,--for instance, the rhombus from the square, the rhomboid from the oblong, and they are very useful also for explaining and illustrating the different kinds of angles, as the opening between the joints may be made narrower or wider at pleasure.

The disconnected slats are used for the occasional play or exercise of interlacing, forming a variety of figures, geometrical and artistic, which hold together when carefully treated.[66]

[66] "The slats form, in some sort, the transition from the surface-pictures of the laying-tablets to the lineal representations of the laying-sticks, but have this advantage over both tablets and sticks, that the forms constructed with them are not bound down to the surface of the table, but possess sufficient solidity to bear being removed from it."--H. Goldammer, _The Kindergarten_, page 155.

Materials of Froebel's Gifts.

As to the unpretentious little sticks themselves, the use of these bits of waste wood is entirely unique and characteristic. No one else would have deemed them worthy of a place in school apparatus or among educational appliances; but Froebel had the eye and mind of a true philosopher, ever seeing the great in the small,--ever bringing out of the commonplace material, which lies unused on every hand, all its inherent possibilities and capabilities of usefulness. Froebel was no destructive reformer, but the most conservative of philosophers.

How the Stick is to be regarded.

The stick of course is to be regarded in its relation to what comes before and after it,--as the embodied edge of the cube, as the tablet was its embodied face. The child should at last identify his stick, the embodiment of the straight line, with the axis of the sphere, the edge of the cube, and the side of the square.[67] The sticks and rings are, properly speaking, one gift, contrasting the curved and straight lines.

[67] "Just as we obtained the tablets from the cubes, of which they are the embodied faces, so now we obtain also the laying-sticks from the cube, whose edges they represent. But they are contained also in the laying-tablets, for one may regard the surface as produced by the progressive movement of a line, and this may be made clear to the child by slicing a square tablet into a number of sticks."--H. Goldammer, _The Kindergarten_, page 161.

Method and Manner of Lessons.

Although the stick exercises should make their appearance at least once every week after their introduction, they may always be varied by stories, and when occasionally connected with other objects, cut from paper to illustrate some point, are among the pleasantest and most fruitful exercises of the kindergarten.

The sticks may be used for teaching number and elementary geometry, both in the kindergarten and school, or for reviewing and fixing knowledge already gained in these directions, for practice in the elements of designing, for giving a correct idea of outlines of familiar objects, and should constantly serve as an introduction to drawing and sewing lessons, to which they are the natural prelude.

They should be used strictly after the manner of the other gifts, beginning with careful dictations, in which the various positions of one stick should be exhausted before proceeding to a greater number, with coöperative work, and with free invention. These exercises and original designs may be put into permanent form in parquetry, which is furnished for this gift in the various colored papers, as well as for the tablets. The inventions may also be transferred to paper by drawing, and to card-board by sewing.

The exercises may continue from the various simple positions which one stick may assume to really complex dictations requiring from fifteen to twenty-five sticks, and introducing many difficult positions and outlines of new geometrical figures.

Forms of Knowledge and Number Work.

When we consider that the length of the sticks varies from one to six inches, and that the number given to the child is limited only by his capacity for using them successfully, we can see that the outlines of all the rectilinear plane figures can easily be made by their use. Of course in these exercises there must be a great deal of incidental arithmetic, but the gift may also be used for definite number work, and is far better adapted to this purpose than any other in the series, since it presents a number of separate units which may be grouped or combined to suit any simple arithmetical process. Representing the line as it does, it has less bodily substance than any previous gift, and hence comes nearest to the numerical symbols, as the next step to using a line would obviously be making one. It also offers very much the same materials for calculation as were used by the race in its childhood, and hence fits in with the inherited instincts of the undeveloped human being.[68]

[68] "Each following generation and each following individual man is to pass through the whole earlier development and cultivation of the human race,--and he does pass it; otherwise he would not understand the world past and present,--but not by the dead way of imitation, of copying, but by the living way of individual, free, active development and cultivation."--Friedrich Froebel, _Education of Man_, page 11.

Who has not seen him arranging twigs and branches in his play, counting them over and over or simulating the process, and delighting to divide them into groups? So the cave-dweller used them, doubtless, not in play, but in serious earnest, for some such purpose as keeping tally of the wild beasts he had killed, or the number of his enemies vanquished.