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:—

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.

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.

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]

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.

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.

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]

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.

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.

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.

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.

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."

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.

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 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.

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.

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] 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.

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.