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.
Educationvs.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 beinterested 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]
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.
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.
Paradise of Childhood.Edward Wiebe. Pages 27-29.Kindergarten Guide.J.andB. Ronge. 20-31.Kindergarten Guide.Kraus-Boelte. 113-145.Koehler's Kindergarten Practice. Tr. byMary 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. byHenry Van Brunt. (First and Second Discourses.)
Paradise of Childhood.Edward Wiebe. Pages 27-29.
Kindergarten Guide.J.andB. Ronge. 20-31.
Kindergarten Guide.Kraus-Boelte. 113-145.
Koehler's Kindergarten Practice. Tr. byMary 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. byHenry Van Brunt. (First and Second Discourses.)
"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.
"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 childdivided 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.
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-materialmight 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]
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 equilateralhas 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 ofgeneral 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 newmaterial 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.
Order of introducing Triangles.
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.
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, andto 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 inone 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. Themeeting-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]
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 ifthe 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.
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. byMary 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.
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. byMary 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.
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 toBuchstaben, 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.
"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 toBuchstaben, 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 andplane 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 dimensionlengthis 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 andintelligently 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]
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.
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, andshould 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 anyother 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]
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.
"With a few packets of Froebel's sticks," as has been very well said, "the child is provided with an excellent calculating machine." The use of this machine in the primary school in word making as well as in number work is practicallyunlimited; but in the kindergarten it may very well give a clear, practical understanding of the first four rules of arithmetic,—an understanding which will be based on personal activity and experience.[69]
Evolution of the Kindergarten Stick.
It is well by way of prelude to the first few lessons to draw from the children the origin and history of the tiny bit of wood given them for their play, and they will henceforth regard it in a new light and treat it with greater respect and care.
Let us trace it carefully from its baby beginnings in the seed, its germination and growth, the influences which surround and foster it from day to day, its steady increase in size and strength, its downward grasp and its upward reach, the hardening of the tender stem and slender cylindrical trunk into the massive oak or pine, the growth of its tough, strong garment of bark, its winter times of rest and spring times of renewal, until from the tender green twig so frail and pliant it has become too large to clasp with the arms, and high enough to swing its dry leaves into the church tower.
Then let us follow out its usefulness; for instance, we might first paint a glowing word-picture of the logging-camp, the chopping and hewing and felling, the life of the busy woodcutter in the leafy woods in autumn, or in the dense forests in winter time, when the snow, cold and white and dazzling, covers the ground with its fleecy carpet. Again, let us depict the road and the busy teamsters driving their yokes of strong oxen with their heavy loads of logs to the towns and cities where they are to be sold. A scene, a perfect word-picture, should be painted of everything concerning the trip,—the crunching of the oxen's hoofs on the pressed snow, the creaking of the heavy truck as its runners slip along the smooth surface, the breath of the men and animals rising like steam into the clear, cold air. All these things rise in image before the child's eye and are not soon forgotten, you may be sure. The work and life of the river-drivers might also be described, and their manner of floating the logs down river in springtime when the water is high and the current strong. Then perhaps the children will help to tell us about the mill of which they doubtless know something,—where the sawmills are built, how the water helps in turning the great wheel, the buzzing and hissing of the big saws, and the way in which they quickly make boards of the long, strong logs. This and much more may be said, and if it is well said, nochild can ever look at the tiny stick afterwards and entirely forget the charm which once surrounded it.[70]