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SJ// 9- 
 
 T 
 
 PARADISE OF CHILDHOOD 
 
 A MANUAL FOR SELF-INSTRUCTION IN FRIEDRICH FROEBEL'S 
 EDUCATIONAL PRINCU'LES, 
 
 AXD A ntACTICAL 
 
 Glide to Kinder-Gartners. 
 
 EDWARD WIEBE. 
 
 WITH SEVENTY- FOUR PLATES OF ILLUSTRATIONS. 
 
 c/ 
 
 MILTON BRADLEY & COMPANY, 
 
 SPRINGFIKLD, MASS. 
 
Lbins 
 
 Entered according to Act of Congress, in the year 1869, by 
 MILTON BRADLEY & COMPANY, 
 the Clerk's Office of the District Court of the District of Massachusetts. 
 
 SAMUEL BOWLES AND COMPANY, 
 PRINTERS, ELECTKOTYPERS, AND BINDERS, 
 
 SPRINGFIELD, MASS. 
 
ERRATA. 
 
 PI,ATE XI. Fir.. i6. — Upper row to consist of four whole cubes. 
 
 Fig 19. — In the second row the 2nd and 4th square, on either side should be open, so as to repre- 
 sent windows. 
 Fig. 21.— The remaining whole cube is to be placed upon the center in the first row. 
 PLATE XIII, Fig. 30. — Eight quarter blocks should be connected here with the four outermost whole blocks as 
 
 in figures 28 and 29. 
 PLATE XIV, Fig 51. — Six quarter cubes form star in center as in figure 52. 
 PLATE XVII, Fig. 3. — The blocks forming back wall should stand on those forming foundation. 
 PLATE XIX, Fig. 3. — The four corner pieces are to be like those in figure 2 
 PLATE XX, Fig. 21 in the perspective should extend in front over six squares only. 
 
 Fig. 23. — There should be an open space in the center of two squares, one above the other. 
 PLATE XXII, Fig. 117. — Left upper part should be shaded like the right lower one. 
 PLATE XLVI, Fig. 5. — The two halves of the figure ought to connect as in figure 4. 
 
INTRODUCTION. 
 
 Until a recent period, but little interest has been 
 felt by people in this country, with regard to the 
 Kinder-Garten method of instruction, for the simple 
 reason that a correct knowledge of the system has 
 never been fully promulgated here. However the lec- 
 tures of Miss E. P. Peabody of Cambridge, Mass., 
 have awakened some degree of enthusiasm upon the 
 subject in different localities, and the establishment 
 of a few Kinder-Garten schools has served to call forth 
 a more general inquiry concerning its merits. 
 
 We claim that every one who believes in rational 
 education, will become deeply interested in the pecu- 
 liar features of the work, after having become ac- 
 quainted with Froebel's principles and plan ; and 
 that all that is needed to enlist the popular sentiment 
 in its favor is the establishment of institutions of this 
 kind, in this country, upon the right basis. 
 
 With such an object in view, we propose to present 
 an outline of the Kinder-Garten plan as developed by 
 its originator in Germany, and to a considerable ex- 
 tent by his followers in France and England. 
 
 But as Froebel's is a system which must be carried 
 out faithfully in all its important features, to insure 
 success, we must adopt his plan as a whole and carry 
 it out with such modifications of secondary minutia; 
 only, as the individual case may acquire without vio- 
 lating its fundamental principles. If this cmnot be 
 accomplished, it were better not to attempt the task 
 at all. 
 
 The present work is entitled a Manual for Self- 
 Instruction and a Practical Guide for Kinder-Gartners. 
 Those who design to use it for either of these pur- 
 poses, must not expect to find in it all that they ought to 
 
 know in order to instruct the young successfully ac- 
 cording to Froebel's principles. No book can ever 
 be written which is able to make a perfect Kinder- 
 Gartner ; this requires the training of an able teacher 
 actively engaged in the work at the moment 
 " Kinder-Garten Culture," says Miss Peabody, in the 
 preface to her "Moral Culture of Infancy," "is the 
 adult mind entering into the child's world and ap- 
 preciating nature's intention as displayed in every 
 impulse of spontaneous life, so directing it that the 
 joy of success may be ensured at every step, and 
 artistic things be actually produced, which gives the 
 selfreliance and conscious intelligence that ought to 
 discriminate human power from blind force." 
 
 With this thought constantly present in his mind, 
 the reader will find, in this book, all that is indispens- 
 ably necessary for him to know, from the first estab- 
 lishment of the Kinder-Garten through all its various 
 degrees of development, including the use of the mate- 
 rials and the engagement in such occupations as are 
 peculiar to the system. There is much more, how- 
 ever, that can be learned only by individual obser- 
 vation. The fact, that here and there, persons, pre- 
 suming upon the slight knowledge which they may 
 have gained of Froebel and his educational principles, 
 from books, have established schools called Kinder- 
 Gartens, which in reality had nothing in common with 
 the legitimate Kinder-Garten but the name, has caused 
 distrust and even opposition, in many minds towards 
 everything that pertains to this method of instruc- 
 tion. In discriminating between the spurious and the 
 real, as is the design of this work, the author would 
 mention with special commendation, the Educational 
 
IV 
 
 INTRODUCTION. 
 
 Institute conducted by Mrs. and Miss Kriege in 
 Boston. It connects with the Kinder-Garten proper, 
 a Training School for ladies, and any one who wishes 
 to be instructed in the correct method, will there be 
 able to acquire the desired knowledge. 
 
 Besides the Institute just mentioned, there is one 
 in Springfield, Mass., under the supervision of the 
 writer, designed not only for the instruction of classes 
 of children in accordance with these principles, but 
 also for imparting information to those who are de- 
 sirous to become Kinder-Gartners. From this source, 
 the method has already been acquired in several in- 
 stances, and as one result, it has been introduced into 
 two of the schools connected with the State Institu- 
 tion at Monson, Mass. 
 
 The writer was in early life acquainted with Froebel ; 
 and his subsequent experience as a teacher has only 
 served to confirm the favorable opinion of the system, 
 which he then derived from a personal knowledge of 
 
 its inventor. A desire to promote the interests of true 
 education, has led him to undertake this work of inter- 
 pretation and explanation. 
 
 Withput claiming for it perfection, he believes that, 
 as a guide, it will stand favorably in comparison with 
 any publication upon the subject in the English or the 
 French language. 
 
 The German of Marenholtz, Goldammer, Morgen- 
 stern and Froebel have been made use of in its prep- 
 aration, and though new features have, in rare cases 
 only, been added to the original plan, several changes 
 have been made in minor details, so as to adapt this 
 mode of instruction more readily to the American 
 mind. This has been done, however, without omit- 
 ting aught of that German thoroughness, which char- 
 acterizes so strongly every feature of Froebel's system. 
 
 The plates accompanying this work are reprints 
 from " Goldammer's Kinder-Garten," a book recently 
 published in Germany. 
 
The Paradise of Childhood : 
 A GUIDE TO KINDER-GARTNERS. 
 
 ESTABLISHMENT OF A KINDER-GARTEN. 
 
 The requisites for the establishment of a 
 " Kinder-Garten " are the following : 
 
 1. A house, containing at least one large 
 room, spacious enough to allow the children, 
 not only to engage in all their occupations, 
 both sitting and standing, but also to practice 
 their movement plays, which, during inclem- 
 ent seasons, must be done in-dcors. 
 
 2. Adjoining the large room, one or two- 
 smaller rooms for sundry purposes. 
 
 3. A number of tables, according to the 
 size of the school, each table affording a 
 smooth surface ten feet long and four feet 
 wide, resting on movable frames from eighteen 
 to twenty-four inches high. The table should 
 be divided into ten equal squares, to accom- 
 modate as many pupils ; and each square 
 subdivided into smaller squares of one inch, 
 to guide the children in many of their occu- 
 pations. On either side of the tables should 
 be settees with folding seats, or small chairs 
 ten to fifteen inches high. The tables and 
 settees should not be fastened to the floor, as 
 they will need to be removed at times to 
 make room for occupations in which they are 
 not used. 
 
 4. A piano-forte for gjmnastic and musical 
 exercises — the latter being an important feat- 
 ure of the plan, since all the occupations are 
 interspersed with, and many of them accom- 
 panied by, singing. 
 
 5. Various closets for keeping the apparatus 
 and work of the children — a wardrobe, wash- 
 stand, chairs, teacher's table, &c. 
 
 The house should be pleasantly located, 
 removed from the bustle of a thoroughfare, 
 and its rooms arranged with strict regard to 
 hygienic principles. A garden should sur- 
 round or, at least, adjoin the building, for 
 frequent out door exercises, and for gardening 
 purposes. A .=niall plot is assigned to each 
 child, in which he sows the seeds and culti- 
 vates the plants, receiving, in due time, the 
 flowers or fruits, as the result of his industry 
 and care. 
 
 When a Training School is connected with 
 the'Kinder-Garten, the children of the "Gar-^ 
 ten " are divided into groups of five or ten — 
 each group being assisted in its occupations 
 by one of the lady pupils attending the Train- 
 ing School. 
 
 Should there be a greater number of such 
 assistants than can be conveniently occupied 
 in the Kinder Garten, they may take turns 
 with each other. In a Training School of 
 this kind, under the charge of a competent 
 director, ladies are enabled to acquire a thor- 
 ough and practical knowledge of the system. 
 They should bind themselves, however, to 
 remain connected with the institution a speci- 
 fied time, and to follow out the details of the 
 method patiently, if they aim to fit themselves 
 to conduct a Kinder-Garten with success. 
 
 In any establishment of more than twenty 
 children, a nurse should be in constant at- 
 tendance. It should be her duty also to 
 preserve order and cleanliness in the rooms, 
 and to act as janitrix to the institution. 
 
MEANS AND WAYS OF OCCUPATION 
 
 IN THE KINDER-GARTEN. 
 
 Before entering into a description of the 
 various means of occupation in tlie Kinder- 
 Garten, it will be proper to state that Fried- 
 rich Froebel, the inventor of this system of 
 education, calls all ocaipations in the Kinder- 
 Garten '■^ plays" and the materials for occupa- 
 tion '■^ gifts." In these systematically-arranged 
 plays, Froebel starts from the fundamental 
 idea that all education should begin with a 
 development of the desire for activity innate 
 in the child; and he has been, as is universally 
 acknowledged, eminently successful in this 
 part of his important work. Each step in 
 the course of training is a logical sequence 
 of the preceding one ; and the various means 
 of occupation are developed, one from another, 
 in a perfectly natural order, beginning with the 
 simplest and concluding with the most difficult 
 features in all the varieties of occupation. To- 
 gether, they satisfy all the demands of the child's 
 nature in respect both to mental and physical 
 culture, and lay the surest foundation for all 
 subsequent education in school and in life. 
 
 Th& time of occupation in the Kinder-Garten 
 is three or four hours on each week day, usually 
 from 9 to 1 2 or I o'clock ; and the time allot- 
 ted to each separate occupation, including the 
 changes from one to another, is from twenty to 
 thirty minutes. Movement plays, so-called, in 
 which the children imitate the flying of birds, 
 swimming of fish, the motions of sowing, mow- 
 wing, threshing, &c., in connection with light 
 gymnastics and vocal exercises, alternate with 
 the plays performed in a sitting posture. All 
 occupations that can be engaged in out of 
 doors, are carried on in the garden whenever 
 the season and weather permit. 
 
 For the reason that the various occupations, 
 as previously stated, are so intimately con- 
 nected, growing, as it were, out of each other, 
 they are introduced very gradually, so as to 
 afford each child ample time to become suffi- 
 ciently prepared for the next step, without 
 interfering, however, with the rapid progress 
 of such as are of a more advanced age, or 
 endowed with stronger or better developed 
 faculties. 
 
 The following is a list of the gifts or ma- 
 "terial and means of occupation in the Kinder- 
 Garten, each of which will be specified and 
 described separately hereafter. 
 
 There are altogether twenty gifts, according 
 to Froebel's general definition of the term, al- 
 though the first six only are usually designated 
 by this name. We choose to follow the classi- 
 fication and nomenclature of the great inventor 
 of the system. 
 
 LIST OF FROEBEL'S GIFTS. 
 
 1. Six rubber balls, covered with a net-work 
 of twine or worsted of various colors. 
 
 2 . Sphere, cube, and cylinder, made of wood. 
 
 3. Large cube, consisting of eight small 
 cubes. 
 
 4. Large cube, consisting of eight oblong 
 parts. 
 
 5. Large cube, consisting of whole, half, 
 and quarter tubes. 
 
 6. Large cube, consisting of doubly divided 
 oblongs. 
 
 [The third, fourth, fifth and sixth gifts serve 
 for building purposes.] 
 
 7. Square and triangular tablets for laying 
 of figures. 
 
GUIDE TO KINDER- GARTNERS. 
 
 8. Staffs for laying of figures. 
 
 9. Whole and half rings for laying of 
 figures. 
 
 10. Material for drawing. 
 
 11. Material for perforating. 
 
 12. Material for embroidering. 
 
 13. Material for cutting of paper and com- 
 bining pieces. 
 
 14. Material for braiding. 
 
 15. Slats for interlacing. 
 
 16. The slat with many links. 
 
 17. Material for intertwining. 
 
 18. Material for paper folding. 
 
 19. Material for peas-work. 
 
 20. Material for modeling. 
 
 THE FIRST GIFT. 
 
 The First Gift, which consists of sLx rubber 
 balls, over-wrought with worsted, for the pur- 
 pose of representing the three fundamental 
 and three mLxed colors, is introduced in this 
 manner: 
 
 The children are made to stand in one or 
 two rows, with heads erect, and feet upon a 
 given line, or spots marked on tlie floor. 
 The teacher then gives directions like the 
 following : 
 
 " Lift up your right hands as high as you 
 can raise them." 
 
 " Take them down." 
 
 " Lift up your left hands." " Down." 
 
 " Lift up both your hands." " Down." 
 
 " Stretch forward your right hands, that I 
 may give each of you something tliat I have 
 in my box." 
 
 The teacher then places a ball in the hand 
 of each child, and asks — 
 
 " Who can tell me the -name of what you 
 have received ? " Questions may follow about 
 the color, material, shape, and other qualities 
 of the ball, which will call forth the replies, 
 blue, yellow, rubber, round, light, soft, &c. 
 
 The children are then required to repeat 
 sentences pronounced by the teacher, as — 
 "The ball is round;" ^' My ball is green;" 
 "All these balls are made of rubber," &c. 
 They are then required to return all, except 
 the blue balls, those who give up theirs being 
 allowed to select from the box a blue ball in 
 
 exchange ; so that in the end each child has 
 a ball of that color. The teacher then says : 
 " Each of you has now a blue, rubber ball, 
 which is round, soft,znd light; and these balls 
 will be your balls to play with. I will give 
 you another ball to-morrow, and the next day 
 another, and so on, until you have quite a 
 number of balls, all of which will be of rub- 
 ber, but no two of the same color." 
 
 The six differently colored balls are to be 
 used, one on each day of the week, which 
 assists the children in recollecting the days of 
 the week, and the colors. After distributing 
 the balls, the same questions may be asked as 
 at the beginning, and the children taught to 
 raise and drop their hands with the balls in 
 them ; and if there is time, they may make a 
 few attempts to Uirow and catch the balls. 
 This is enough for the first lesson ; and it will 
 be sure to awaken enthusiasm and delight in 
 die children. 
 
 The object of the first occupation is to teach 
 the children to distinguish between the right 
 and the left hand, and to name the various 
 colors. It may serve also to develop their 
 vocal organs, and instaict them in the rules 
 of politeness. How the latter may be accom- 
 plished, even with such simple occupation as 
 playing with balls, may be seen from the fol- 
 lowing : 
 
 In presenting the balls, pains should be 
 taken to make each child extend the right 
 
GUIDE TO KINDER-GARTNERS. 
 
 hand, and do it gracefully. The teacher, in 
 putting the ball into the little outstretched 
 hand, says : 
 
 " Charles, I place this red (green, yellow, 
 &c.,) ball into your right hand." The child 
 is taught to reply — 
 
 " I thank you, sir." 
 After the play is over, and the balls are to 
 be replaced, each one says, in returning his 
 ball— 
 
 " I place this red (green, yellow, &c.,) ball, 
 with my right hand, into the box." 
 
 When the children have acquired some 
 knowledge of the different colors, they may 
 be asked at the commencement : 
 
 " With which ball would you like to play 
 this morning — the green,, red, or blue one ? " 
 The child will reply : 
 
 " With the blue one, if you please ; " or one 
 of such other color as may be preferred. 
 
 It may appear rather monotonous to some 
 to have each child repeat the same phrase ; 
 but it is only by constant repetition and 
 patient drill that anything can be learned 
 accurately ; and it is certainly important that 
 these youthful minds, in their formative state, 
 should be taught at once the beauty of order 
 and the necessity of rules. So the left hand 
 should never be employed when tlie right 
 hand is required; and all mistakes should 
 be carefully noticed and corrected by the 
 teacher. One important feature of this sys- 
 tem is the inculcation of habits of precision. 
 
 The children's knowledge of color may be 
 improved by asking them what other things 
 are similar to the different balls, in respect to 
 color. After naming several objects, they 
 may be made to repeat sentences like the fol- 
 lowing : 
 
 " My ball is green, like a leaf" " My ball 
 is yellow, like a lemon." " And mine is red, 
 like blood," &c. 
 
 Whatever is pronounced in these conversa- 
 tional lessons should be articulated very dis- 
 tinctly and accurately, so as to develop the 
 organs of speech, and to correct any defect 
 of utterance, whether constitutional or the 
 
 result of neglect. Opportunities for phonetic 
 and elocutionary practice are here afforded. 
 Let no one consider the infant period as too 
 early for such exercises. If children learn to 
 speak well before they learn to read, they 
 never need special instruction in the art of 
 reading with expression. 
 
 For a second play with the balls, the class 
 forms a circle, after the children have received 
 the balls in the usual manner. They need to 
 stand far enough apart, so that each, -with 
 arms extended, can just touch his neighbor's 
 hand. Standing in this position, and having 
 the balls in their right hands, the children 
 pass them into the left hands of their neigh- 
 bors. In this way, each one gives and re- 
 ceives a ball at the same time, and the left 
 hands should, therefore, be held in such a 
 manner that the balls can be readily placed 
 in them. The arms are then raised over the 
 head, and the balls passed from, the left into 
 the right hand, and the arms again extended 
 into the first position. This process is re- 
 peated until the balls make the complete 
 circuit, and return into the right hands of the 
 original owners. The balls are then passed 
 to the left in the same way, everything being 
 done in an opposite direction. This exercise 
 should be continued until it can be 3one 
 rapidly and, at the same time, gracefully. 
 
 Simple as this performance may appear to 
 those who have never tried it, it is, neverthe- 
 less, not easily done by very young children 
 without frequent mistakes and interruptions. 
 It is better that the children should not turn 
 their heads, so as to watch their hands during 
 the changes, but be guided solely by the sense ' 
 of touch ; and to accomplish this with more 
 certainty, they may be required to close their 
 eyes. It is advisable not to introduce this 
 play or any of the following, until expertness 
 is acquired in the first and simpler form. 
 
 In the third play, the children forrii in two 
 rows fronting each other. Those of one row 
 only receive balls. These they toss to the 
 opposite row : first, one by one ; then two by 
 two; finally, the whole row at once, always 
 
GUIDE TO KINDER-GARTNERS. 
 
 to the counting of the teacher — "one, two, 
 throw." 
 
 Again, forming four rows, the children in 
 the first row toss up and catch", tlien throw to. 
 the second row, then to the third, then to the 
 fourth, accompanying the exercise with count- 
 ing as before, or with singing, as soon as this 
 can be done. 
 
 For a further variety, the balls are thrown 
 upon the floor, and caught, as they rebound, 
 with the rig/tt hand or the ic/t hand, or witli 
 the hand inverted, or they may be sent back 
 to the floor several times before catching. 
 
 Throwing the balls against the wall, tossing 
 them into the air, and many other exercises 
 
 may be introduced whenever the balls are 
 used, and will always serv-e to interest the 
 children. Care should be taken to have every 
 movement performed in perfect order, and that 
 every child take part in all the exercises in its 
 turn. 
 
 At the close of every ball play, the children 
 occupy their original places marked on the 
 floor, the balls are collected by one or two of 
 the older pupils, and after this has been done, 
 each child takes the hand of its opposite 
 neighbor, and bowing, says, " good morning," 
 when they march by twos, accompanied by 
 music, once or twice through the hall, and 
 then to their seats for other occupation. 
 
 THE SECOND GIFT. 
 
 The Second Gift consists of a sphere, a 
 cube, and a cylinder. These the teacher places 
 upon the table, together with a rubber ball, 
 and asks : 
 
 " Which of these three objects looks most 
 like theball?" 
 
 The children will certainly point out the 
 sphere, but, of course, without giving its name. 
 
 " Of what is it made ?•" the teacher asks, 
 placing it in the hand of some pupil, or rolling 
 it across the table. 
 
 The answer will doubtless be, " Of wood." 
 " So we might call the object a wooden ball. 
 But we will give it another name. We will 
 call it a sphere." 
 
 Each child must here be taught to pro- 
 nounce the word, enunciating each sound very 
 distinctly. The ball and sphere are then fur- 
 ther compared with each other, as to material, 
 color, weight, &c., to find their similarities 
 and dissimilarities. Both are round; both 
 roll. The ball is soft; the sphere is hard. 
 The ball is light; the sphere is heaiiy. The 
 sphere makes a louder noise when it falls from 
 
 the table than the ball. The ball rebounds 
 when it is thrown upon the floor ; the sphere 
 does not. All these answers are drawn out 
 from the pupils by suitable experiments and 
 questions, and every one is required to repeat 
 each sentence when fully explained. 
 
 The children then form a circle, and the 
 teacher rolls the sphere to one of them, ask- 
 ing the child to stop it with both his feet. 
 This child then takes his place in the center, 
 and rolls the sphere to another one, who again 
 stops it with his feet, and so on, until all the 
 children have in turn taken their place in the 
 center of the circle. At another time, the 
 children may sit in two rows upon the floor, 
 facing each other. A white and a black 
 sphere are then given to the heads of the 
 rows, who exchange by rolling them across to 
 each other. Then the spheres are rolled 
 across obliquely to the second individuals in 
 the rows. These exchange as before, and 
 then roll the spheres to those who sit third, 
 and so on, until they have passed throughout 
 the lines and back again to the head. Both 
 
GUIDE TO KINDER-GARTNERS. 
 
 spheres should be rolling at the same instant, 
 which can be effected only by counting or 
 when time is kept to accompanying music. 
 
 Another variety of play in the use of this 
 gift consists in placing the rubber ball at a 
 distance on the floor, and letting each child, 
 in turn, attempt to hit it with the sphere. 
 
 For the purpose of further instruction, the 
 sphere, cube, and cylinder are again placed 
 upon the table, and the children are asked 
 to discover and designate the points of re- 
 semblance and difference in the first two. 
 They will find, on examination, that both are 
 made of wood, and of the same color ; but 
 the sphere can roll, while the cube cannot.. 
 Inquire the cause for this difference, and the 
 answer will, most likely, be either, " the sphere 
 is round," or "the cube has corners." 
 
 " How many corners has the cube ? " The 
 children count them, and reply, " Eight." 
 
 " If I put my finger on one of these comers, 
 and let it glide down to the corner below it, 
 (thus,) my finger has passed along an edge 
 of the cube. How many such edges can we 
 count on this cube? I will let my finger 
 glide over the edges, one after the other, and 
 you may count." 
 
 "One, two, three, 12." 
 
 "Our cube, then, has eight corners, and 
 twelve edges. I will now show you four cor- 
 ners and four edges, and say that this part 
 of the cube, which is contained between these 
 four corners and four edges, is called a side 
 of the cube. Count how many sides the cube 
 has." 
 
 " One two, three, four, five, si.x." 
 
 " Are these sides all alike, or is one small 
 and another large ? " " They are all alike." 
 
 " Then we may say that our cube has six 
 sides, all alike, and that each side has four 
 edges, all alike. Each of these sides of the 
 cube is called a square.^' 
 
 To explain the cylinder, a conversation like 
 the following may take place. It will be ob- 
 served that instruction is here given mainly 
 by comparison, which is, in fact, tlie only 
 philosophical method. 
 
 The sphere, cube, and cylinder are placed 
 together as before, in the presence of the 
 children. They readily recognize and name 
 the first two, but are in doubt about the third, 
 whether it is a barrel or a wheel. They may 
 be suffered to indulge their fancy for awhile 
 in finding a name for it, but are, at last, told 
 that it is a cyHnda; and are taught to pro- 
 nounce the word distinctly and accurately. 
 
 " What do you see on the cylinder which 
 you also see on the cube ? " " The cylinder 
 has two"sides." " Are the sides square, like 
 those of the cube?" " They are not." 
 
 But the cylinder can stand on these sides 
 just as the cube can. Let us see if it cannot 
 roll, too, as the sphere does. Yes ! it rolls ; 
 but not like the- sphere, for it can roll only 
 _in two ways, while the sphere can roll any 
 way. So, you see, the sphere, cube, and 
 cylinder are alike in some respects, and differ- 
 ent in others. Can you tell me in what re- 
 spects they are just alike?" 
 
 " They are made of wood ; are smooth ; 
 are of the same color; are heavy; make a 
 loud noise when they fall on the floor." 
 
 These answers must be drawn out by ex- 
 periments with the objects, and by questions, 
 logically put, so as to lead to these results as 
 natural conclusions. The e.xercise may be 
 continued, if desirable, by asking the children 
 to name objects which look like the sphere, 
 cube, or cylinder. The edge of a cube may 
 also be explained as representing a straight 
 line. The point where two or three lines or 
 edges meet is called a corner; the inner 
 point of a corner is an angle, of which each 
 side, or square, of the cube has four. To 
 sum up what has already been taught : The 
 cube has six sides, or squares, all alike ; eight 
 corners, and twelve edges ; and each side of 
 the cube has four edges, all alike ; four cor- 
 ners, and four angles. 
 
 The sphere, cube, and cylinder, when sus- 
 pended by a double thread, can be made to 
 rotate around themselves, for the purpose of 
 showing that the sphere appears the same in 
 form in whatever manner we look at it ; that 
 
GUIDE TO KINDER-GARTNERS. 
 
 the cube, when rotating, (suspended at the 
 center of one of its sides,) shows the form 
 of the cyhnder ; and that the cylinder, when 
 rotating, (suspended at the center of its round 
 side,) presents the appearance of a sphere. 
 
 Thus, there is, as it were, an inner triunity 
 in these three objects — sphere contained in 
 cyhnder, and cylinder in cube, the cylinder 
 forming the mediation between the two others, 
 or the transition from one to the other. Al- 
 
 though the child may not be told, the teacher 
 may think, in this connection, of the natural 
 law, according to which the fruit is contained 
 in the flower, the flower is hidden in the bud. 
 Suspended at other points, cylinder and 
 cube present other forms, all of which are 
 interesting for the children to look at, and can 
 be made instructive to their young minds, if 
 accompanied by apt conversation on the part 
 of the teacher. 
 
 THE THIRD GIFT. 
 
 This consists of a cube, divided into eight 
 smaller one-inch cubes. 
 
 A prominent desire in the mind of ever)' 
 child is to divide things, in order to examine 
 the parts of which they consist. This natural 
 instinct is observable at a very early period. 
 The little one tries to change its toy by break- 
 ing it, desirous of looking at its inside, and is 
 sadly disappointed in finding itself incapable 
 of reconstructing the fragments. Froebel's 
 Third Gift is founded on this observation. 
 In it the child receives a whole, whose parts 
 he can easily separate, and put together again 
 at pleasure. Thus he is able to do that which 
 he could not in the case of the toys — restore 
 to its original form that which was broken — 
 making a perfect whole. And not only this — 
 he can use the parts also for the construction 
 of other wholes. 
 
 The child's first plaything, or means of 
 occupation, was the ball. Next came the 
 sphere, similar to, yet so diflerent from, the 
 ball. Then followed cube and cylinder, both, 
 in some points, resembling the sphere, yet 
 each having its own peculiaritiqg, which dis- 
 tinguish it from the sphere and ball. The 
 pupil, in receiving the cube, divisible into 
 eight smaller cubes, meets with friends, and is 
 delighted at the multiplicity of the gift. Each 
 
 of the eight parts is precisely like the whole, 
 except in point of size, and the child is im- 
 mediately struck with this quality of his first 
 toy for building purposes. By simply looking 
 at this gift, the pupil receives the ideas of 
 whole a.nd part — of form and cmnparative size ; 
 and by dividing the cube, is impressed with 
 the relation of one part to another in regard 
 to position rfnd order of movements, thus 
 learning readily to comprehend the use of 
 such terms as above, below, before, behind, right, 
 left, &c., &c. 
 
 With this and all the following gifts, we 
 produce what Froebel zaW^ forms of life, forms 
 of knotuledge, and forms of beauty. 
 
 The first are representations of objects which 
 actually exist, and which come under our com- 
 mon observation, as the works of human skill 
 and art. The second are such as afford in- 
 struction relative to number, order, proportion, 
 &c. The third are figures representing only 
 ideal forms, yet so regularly constructed as to 
 present perfect models of symmetry and order 
 in the arrangement of the parts. Thus in the 
 occupations connected with the use of these 
 simple building blocks, the child is led into 
 the living world — there first to take notice of 
 objects by comparison ; then to learn some- 
 thing of their properties by induction, and 
 
GUIDE TO KINDER-GARTNERS. 
 
 lastly, to gather into his soul a love and desire 
 for the beautiful by the contemplation of those 
 forms which are regular and symmetrical. 
 
 THE PRESENTATION OF THE THIRD GIFT. 
 
 The children having taken their usual seats, 
 the teacher addresses them as follows : 
 
 " To-day, we have something new to play 
 with." 
 
 Opening the package and displaying the 
 box, he does not at once gratify their curiosity 
 by showing them what it contains, but com- 
 mences by asking the question — 
 
 " Which one of the three objects we played 
 with yesterday does this box look like?" 
 
 They answer readily, " The cube." 
 
 " Describe the box as the cube has been 
 described, with regard to its sides, edges, 
 corners, &c." 
 
 If this is satisfactorily done, the cover may 
 then be removed, and the box placed inverted 
 upon the table. If the box is made of wood, 
 it is placed upon its cover, wliich, when drawn 
 out will allow the cubes to stand on the table. 
 Lifting it up carefully, so that the contents may 
 remain entire, the teacher asks : 
 
 " What do you see now?" 
 
 The answer is as before, " A cube." 
 
 One of the scholars is told to push it across 
 the table. In so doing, the parts will be likely 
 to become separated, and that which was pre- 
 viously whole will lie before them in fragments. 
 The children are permitted to examine the 
 small cubes ; and after each one of them has 
 had one in his hand, the eight cubes are re- 
 turned to the teacher, who remarks : 
 
 " Children, as we have broken the thing, we 
 must try to mend it. Let us see if we can put 
 it together as it was before." 
 
 This having been done, the boxes are then 
 distributed among the children, and they are 
 practiced in removing the covers, and taking 
 out the cube without destroying its unity. 
 They will find it difficult at first, and there 
 will be many failures. But let them continue 
 to try until some, at least, have succeeded, 
 and then proceed to another occupation. 
 
 PREPARATION FOR CONSTRUCTING 
 FORMS. 
 
 The surface of the tables is covered with a 
 net-work of lines, forming squares of One inch. 
 The spaces allotted to the pupils are separated 
 from each other by heavy dark lines, and the 
 centers are marked by some different color. 
 In these first conversational lessons, the chil- 
 dren must be taught to point out the right 
 upper corner of their table space, the left 
 upper, the right and left lower, the upper and 
 lower edges, the right and left edges, and the 
 center. With little staffs, or sticks cut at con- 
 venient lengths, they may indicate direction, 
 e. g., by laying them upon the table in a line 
 from left to right, covering the center of the 
 space, or extending them from the right upper 
 to the left lower corner covering the center ; 
 then from the middle of the upper edge to the 
 middle of the lower edge, and so on. The 
 teacher must be careful to use terms that can 
 be easily comprehended, and avoid changing 
 them in such a way as to produce any ambigu- 
 ity in the mind of the child. 
 
 Here, as in the more advanced exercises, 
 everj'thing should be done with a great deal 
 of precision. The children must understand 
 that order and regularity in all the perform- 
 ances are of the utmost importance. The 
 following will serve as an illustration of the 
 method : The children having received the 
 boxes, they are required to place them exactly 
 in the center of their spaces, so as to cover 
 four squares. They then take hold of the box 
 with the left hand, and remove the cover with 
 the right, placing it by the right upper corner 
 of the net-work on the table. They next 
 place the left hand upon the open box, and 
 reverse it with the right hand, so that the left 
 is on the table. Drawing it carefully from 
 beneath, they let the inverted box rest on the 
 squares in the center. The right hand is used 
 to raise the bpx carefully from its place, and, 
 if successful, eight small cubes will stand in 
 the center of the space, forming one large 
 cube. Lastly, the box is placed in the cover 
 at the right Upper corner, and care should 
 
GUIDE TO KINDER-GARTNERS. 
 
 be taken that all are arranged in exact posi- 
 tion. 
 
 (If the cubes are enclosed in wooden boxes 
 with covers to be drawn out at the side, these 
 manipulations are to be changed accordingly.) 
 
 At the close of any play, when the ma- 
 terials are to be returned to the teacher, the 
 same minuteness of detail must be observed. 
 
 Replacing the box over the cubes, placing 
 the left hand beneath, and lifting the box with 
 the right, reversing it, and placing it again 
 upon the center of the table, then covering 
 it — these are processes which must be re- 
 peated many times before the scholar can 
 acquire such expertness as shall render it 
 desirable to proceed to the real building occu- 
 pation. 
 
 FORMS OF LIFE. 
 
 The boxes being opened as directed, and 
 the cubes upon the center squares — in each 
 space — the question is asked : 
 
 " How many little cubes are there ? " 
 " Eight." 
 
 " Count them, placing them in a row from 
 left to right," (or from right to left.) 
 
 " What is that.' " " A row of cubes." 
 
 It may bear any appropriate name which 
 the children give it — as "a train of cars," "a- 
 company of soldiers," " a fence," &c. 
 
 " Now count your cubes once more, placing 
 them one upon another. What have you 
 there ? " 
 
 " An upright row of eight cubes." 
 
 "Have you ever seen anything standing 
 like this upright row of cubes ? " 
 
 " A chimney." " A steeple." 
 
 " Take down your cubes, and build two 
 upright rows of them — one square apart. 
 What have you now ? " 
 
 " Two little steeples," or " two chimneys." 
 Thus, with these eight cubes, many forms of 
 life can be built under the guidance of the 
 teacher. It is an important rule in this occu- 
 pation, that nothing should be rudely destroyed 
 which has been constructed, but each new form 
 is to be produced by slight change of the pre- 
 ceding one. 
 
 On Plates I. and II., a number of these are 
 given. They are designated by Froebel as 
 follows : 
 
 1. Cube, or Kitchen Table. 
 
 2. Fire-Place. 
 
 3. Grandpa's Chair. 
 
 4. Grandpa's and Grandma's Chairs. 
 
 5. A Castle, with two towers. 
 
 6. A Stronghold. 
 
 7. A Wall. 
 
 8. A High Wall. 
 
 9. Two Columns. 
 
 10. A Large Column, with two memorial 
 stones. 
 
 11. Sign-Post. 
 
 12. Cross. 
 
 13. Two Crosses. 
 
 14. Cross, with pedestal. 
 
 15. Monument. 
 
 16. Sentry-Box. 
 
 17. A Well. 
 
 18. City Gate. 
 
 19. Triumphal Arch. 
 
 20. City Gate, with Tower. 
 
 21. Church. 
 
 22. City Hall. 
 
 23. Castle. 
 
 24. A Locomotive. 
 
 25. A Ruin. 
 
 26. Bridge, with Keeper's House. 
 
 27. Two Rows of Trees. 
 
 28. Two Long Logs of Wood. 
 
 29. A Bole. 
 
 30. Two Small Logs of Wood. 
 
 31. Four Garden Benches. 
 
 32. Stairs. 
 
 33. Double Ladder. 
 
 34. Two Columns on Pedestals. 
 
 35. Well-Trough. 
 
 36. Bath. 
 
 37. A Tunnel. 
 
 38. Easy Chair. 
 
 39. Bench, with back. 
 
 40. Cube. 
 
 Several of the names in this list represent 
 objects which, being more specifically German, 
 will not be recognized by the children. Ruins, 
 
14 
 
 GUIDE TO KINDER-GARTNERS. 
 
 castles, sentry-boxes, sign-posts, perhaps they 
 have never aeen ; but it is easy to tell them 
 something about these objects which will in- 
 terest them. They will listen with pleasure 
 to short stories, narrated by way of explana- 
 tion, and thus associating the story with the 
 form, be able, at another time, to reconstruct 
 the latter while they repeat the former in their 
 own words. It is not to be expected, how- 
 ever, that teachers in this country should 
 adhere closely to the list of Froebel. They 
 may, with advantage, vary the forms, and, if 
 they choose, affix other names to those given 
 upon the plates. It is well sometimes to 
 adopt such designations as are suggested by 
 the children themselves. They will be found 
 to be quite apt in tracing resemblances be- 
 tween their structures and the objects with 
 which they are familiar. 
 
 In order to make the occupation still more 
 useful, they should be required also to point 
 out the dissimilarities existing between the 
 form and that which it represents. 
 
 It is proper to allow the child, at times, to 
 invent forms, the teacher assisting the fantasy 
 of the little builder in the work of construct- 
 ing, and in assigning names to the structure. 
 When a figure has been found, and named, 
 the child should be required to take the blocks 
 apart, and build the same several times in suc- 
 cession. Older and more advanced scholars 
 suggest to younger and less abler ones, and 
 the latter will be found to appreciate such 
 help. 
 
 It is a common observation, that the younger 
 children in a family develop more rapidly than 
 the older ones, since the former are assisted 
 in their mental growth by companionship with 
 the latter. This benefit of association is seen 
 more fully in the Kinder-Garten, under the 
 judicious guidance of a teacher who knows 
 how to encourage what is right, and check 
 what is wrong, in the disposition of the chil- 
 dren. 
 
 It should be remarked, in connection with 
 these directions, that in the use of this and 
 the succeeding gift it is essential that all the 
 
 blocks should be used in the building of each 
 figure, in order to accustom the child to look 
 upon things as mutually related. There is 
 nothing which has not its appointed place, 
 and each part is needed to constitute the 
 whole. For example, the well-trough (35) 
 may be built of six cubes, but the remaining 
 two should represent two pails with which the 
 water is conveyed to the trough. 
 
 FORMS OF KNOWLEDGE. 
 
 These do not represent objects, either real 
 or ideal. They instruct the pupil concerning 
 the properties and relations of numbers, by 
 a particular arranging and grouping of the 
 blocks. Strictly speaking, the first effort to 
 count, by laying them on the table one after 
 another, is to be classed under this head. . 
 The form thus produced, though varied at 
 each trial, is one of the forms of knowledge, 
 and by it the child receives its first lesson in 
 arithmetic. 
 
 Proceeding further, he is taught to add, 
 always by using the cubes to illustrate the 
 successive steps. Thus, having placed two 
 of the blocks at a little distance from each 
 other on the table, he is caused to repeat, 
 " One and one are two." Then placing 
 another upon the table, he repeats, " One 
 and two are three," and so on, until all the 
 blocks are added. 
 
 Subtraction is taught in a similar manner. 
 Having placed all the cubes upon the table, 
 the scholar commences taking them off, one 
 at a time, repeating, as he does this, " One 
 from eight leaves seven; "One from seven 
 leaves six," and so on. 
 
 According to circumstances, of which the 
 Kinder-Gartner, of course, will be the best 
 judge, these exercises may be continued fur- 
 ther, by adding and subtracting two, three, 
 and so on ; but care should always be taken 
 that no new step be made until all that has 
 j gone before is perfectly understood. 
 
 With the more advanced classes, exercises 
 in multiplication and division may be tried, 
 by grouping the blocks. 
 
GUIDE TO KINDER-GARTNERS. 
 
 15 
 
 The division of the large cube, to illustrate 
 the principles of proportion, is an interesting 
 and instructive occupation ; and we will here 
 proceed to give the method in detail. 
 
 The children have their cube of eight be- 
 fore them on the table. The teacher is also 
 furnished with one, and lifting the upper half 
 in the manner shown on Plate III., No. 4, 
 asks: 
 
 " Did I take the whole of my cube in my 
 hand, or did I leave some of it on the table ? " 
 
 " Yoii left some on the table." 
 
 " Do I hold in my hand more of my cube 
 than I left on the table, or are both parts 
 alike .' " 
 
 " Both are alike." 
 
 " If things are alike, we call them equal. 
 So I divided my cube into two equal parts, 
 and each of these equal parts I call a half. 
 Where are the two halves of my cube ? " 
 
 " One is in your hand ; the other is on the 
 table." 
 
 " So I have two half cubes. I will now 
 place the half which I have in my hand upon 
 the half standing on the table. What have I 
 now ? " 
 
 " A whole cube." 
 
 The teaclier, then separating the cube again 
 into halves, by drawing four of the smaller 
 cubes to the right and four to the left, as is 
 indicated on Plate III., No. 2, asks : 
 
 " What have I now before me ? " 
 
 " Two half cubes." 
 
 " Before, I had an upper and a lower half. 
 Now, I have a right and a left half. Uniting 
 the halves again I have once more a whole." 
 
 The scholars are taught to repeat as fol- 
 lows while the teacher divides and unites the 
 cubes in both ways, and also as represented 
 by Form No. 3 : 
 
 " One whole — two halves." 
 
 "Two halves — one whole." 
 
 Again, each half is divided, as shown in 
 Forms No. 5, 6, and 7. and the children are 
 required to repeat during these occupations : 
 
 " One whole — two halves." 
 
 "One half — two quarters (or fourths.)" 
 
 "Two quarters — one half." 
 
 "Two halves — one whole." 
 
 After these processes are fully explained, 
 and the principles well understood by the 
 scholars, they are to try their hand at divid- 
 ing of the cube — first, individually, then all 
 together. If they succeed, they may then be 
 taught to separate it into eighths. It is not 
 advisable, in all cases, to proceed thus far. 
 
 Children under four years of age should be 
 restricted, for the most part, to the use of the 
 cubes for practical building purposes, and for 
 simpler forms of knowledge. 
 
 FORMS OF BEAUTY. 
 
 Starting with a few simple arrangements, 
 or positions, of the blocks, we are able to 
 develop the forms contained in this class by 
 means of a fixed law, viz., that every change 
 of position is to be accompanied by a cor- 
 responding movement on the opposite side. 
 In this way symmetrical figures are construct- 
 ed in infinite variety, representing no real 
 objects, yet, by their regularity of outline, 
 adapted to please the eye, and minister to a 
 correct artistic taste. The love of the beau- 
 tiful cannot fail to be awakened in the youth- 
 ful mind by such an occupation as this, and 
 with this emotion will be associated, to some 
 extent, the love of the good, for they are in- 
 separable. 
 
 The works of God are characterized by 
 perfect order and symmetry, and his good- 
 ness is commensurate with the beauty mani- 
 fest everj-where in the fruits of his creative 
 power. The construction of forms of beauty 
 with the building blocks will prepare the child 
 to appreciate, by and by, the order that rules 
 the universe. 
 
 By Plates IV. and V. it will be seen that 
 these forms are of only one block's height, 
 and, consequently, represent outlines of sur- 
 faces. It is necessarj' that the children should 
 be guided, in their construction, by an easily 
 recognizable center. Around this visible point 
 all the separate parts of the form to be created 
 must be arranged, just as in working out the 
 
i6 
 
 GUIDE TO KINDER-GARTNERS. 
 
 highest destiny of man, all his thoughts and 
 acts need to be regulated by an invisible cen- 
 ter, around which he is to construct a har- 
 monious and beautiful whole. 
 
 In order to produce the varied forms of 
 beauty with the simple material placed in the 
 hands of the scholar, he must first learn in' 
 what ways two cubes may be brought in con- 
 tact with each other. Four positions are 
 shown on Plate IV. The blocks may be ar- 
 ranged either — side by side, as in Fig. i ; edge 
 to edge, as in Fig. 2 ; or edge to side, and side 
 to edge, as in Nos. 3 and 4. Nos. i and 3 are 
 the opposites to 2 and 4. Other changes of 
 position may be made. For example, in Fig. i 
 the block marked a may be placed above or to 
 the right or to the left of the block marked b. 
 The cubes may also be placed in certain rela- 
 tions to each other on the table, without being 
 in actual contact. These positions should be 
 practiced perseveringly at the outset, so as to 
 furnish a foundation for the processes of con- 
 struction which are to follow. It is one of the 
 important features of Froebel's system, that it 
 enables the child readily to discover, and 
 critically to observe, all relations which ob- 
 jects sustain to one another. Thoroughness, 
 therefore, is required in all the details of these 
 occupations. 
 
 We start from any fundamental form that 
 may present itself to our mind. Take, for 
 illustration, Form No. 5. Four cubes are 
 here united side to side, constituting a square 
 surface, and the outline is completed by plac- 
 ing the four remaining cubes severally side to 
 side with this middle square. In 6, edge 
 touches edge ; in 7, side touches edge, and in 
 
 8, edge touches side midway. Another mode 
 of development is shown in Forms 9 — 15. 
 
 The four outside cubes move toward the 
 right by a half cube's length, until the original 
 form reappears in No. 15. 
 
 Now, the four outside cubes occupy the 
 opposite position. Fig. 16, edges touch sides. 
 They are moved as before, by a half cube's 
 length, until, in Form No. 22, the one with 
 which we started, is regained. 
 
 We now extract the inside cubes (^), Fig. 
 23, and each of them travels around its neigh- 
 bor cube (a), until a standing, hollow square 
 is developed, as in Fig. 29. 
 
 Now cube a again is set in motion. It 
 assumes a slanting direction to the remain- 
 ing cubes. Fig. 30, and, pursuing its course 
 around them, the Form, No. 29, reappears 
 in No. 36. 
 
 Next, b is drawn out. Fig. 37, and a pushed 
 in, until a standing cross is formed. Fig. 38, 
 b, constantly traveling on by a half cube's 
 length, until. Fig. 43, all cubes are united in a 
 large square, and b again begins traveling, by 
 a cube's length, turning side to side and edge 
 to edge. In Fig. 48, b performs as a has 
 done. 
 
 But with more developed children we may 
 proceed on other principles, Fig. 49, intro- 
 ducing changes only on two instead of four 
 sides, and thus arriving successively at Forms 
 50 — 60. 
 
 After each occupation, the scholars should 
 replace their cubes in the boxes, as heretofore 
 described, and the material should be re- 
 turned to the closet where it is kept before 
 commencing any other play. 
 
THE FOURTH GIFT. 
 
 The preceding gift consisted of cubical 
 blocks, all of their three dimensions being the 
 same. In the Fourth Gift, we have greater 
 variety for purposes of construction, since each 
 of the parts of the large cube is an oblong, 
 whose length is twice its width, and four times 
 its thickness. The dimensions bear the same 
 proportion to each other as those of an or- 
 dinary brick ; and hence these blocks are 
 sometimes called bricks. . They are useful in 
 teaching the child difference in regard to 
 length, breadth, and height. This difference 
 enables them to construct a greater variety 
 of forms than he could by means of the third 
 gift. By these he is made to understand, 
 more distinctl)', the meaning of the terms per- 
 pendicular and horizontal. And if the teacher 
 sees fit to pursue the course of experiment 
 sufficiently far, many philosophical truths will 
 be developed ; as. for instance, the law of 
 equilibrium, shown by laying one block across 
 another, or the phenomenon of continuous 
 motion, exhibited in the movement of a row 
 of the blocks, set on end, and gently pushed 
 from one direction. 
 
 PREPARATION FOR CONSTRUCTING 
 FORMS. 
 
 This gift is introduced to the children in a 
 manner similar to the presentation of the third 
 gift. The cover is removed, and the box is 
 reversed upon the table. Lifting the box 
 carefully, the cube remains entire. The chil- 
 dren are made to observe that, when whole, 
 its size is the same as that of the previous one. 
 Its parts, however, are very different in form, 
 though their number is the same. There are 
 still eight blocks. Let the scholars compare 
 one of the small cubes of the third gift with 
 one of the oblongs in this gift ; note the simi- 
 3 
 
 larities and the differences ; then, if they can 
 comprehend that notwithstanding they are so 
 unlike m /arm. their solid contents is the same, 
 since it takes just eight of each to make the 
 same sized cube, an important lesson will 
 have been learned. If told to name objects 
 that resemble the oblong, they will readily 
 designate a brkk^ table, piano, closet, &c., and 
 if allowed to invent forms of life, will, doubt- 
 less, construct boxes, benches, &c. 
 
 The same precision should be observed in 
 all the details of opening and closing the 
 plays with this gift as in those previously de- 
 scribed. 
 
 FORMS OF LIFE. 
 
 The following is a list of Froebel's forms, 
 which are represented on Plates VI. and VII. 
 If the names do not appear quite striking, or 
 to the point, the teacher may try to substitute 
 better ones : 
 
 1. The Cube. 
 
 2. Part of a Floor, or Top of a Table. 
 
 3. Two Large Boards. 
 
 4. Four Small Boards. 
 
 5. Eight Building Blocks. 
 
 6. A Long Garden Wall. 
 
 7. A City Gate. 
 
 8. Another City Gate. 
 
 9. A Bee Stand. 
 
 10. A Colonnade. 
 
 11. A Passage. 
 
 12. Bell Tower. 
 
 13. Open Garden House. 
 
 14. Garden House, with Doors. 
 
 15. Shaft. 
 
 16. Shaft. 
 
 17. A Well, with Cover. 
 
 18. Fountain. 
 
 19. Closed Garden Wall. 
 
18 
 
 GUIDE TO KINDER-GARTNERS. 
 
 20. An Open Garden. 
 
 21. An Open Garden. 
 
 22. Watering-Trough. 
 
 23. Shooting-Stand. 
 
 24. Village. 
 
 25. Triumphal Arch. 
 
 26. Caroussel. 
 
 27. Writing Desk. 
 
 28. Double Settee. 
 
 29. Sofa. 
 
 30. Large Garden Settee. 
 
 31. Two Chairs. 
 
 32. Garden Table Chairs. 
 
 33. Children's Table. 
 
 34. Tombstone. 
 
 35. Tombstone. 
 
 36. Tombstone. 
 
 37. Monument. 
 
 38. Monument. 
 
 39. Winding Stairs. 
 
 40. Broader Stairs. 
 
 41. Stalls. 
 
 42. A Cross Road. 
 
 43. Tunnel. 
 
 44. Pyramid. 
 
 45. Shooting-Stand. 
 
 46. Front of a House. 
 
 47. Chair, with Footstool. 
 
 48. A Throne. 
 
 49. f Illustration of 
 
 50. \ Continuous Motion. 
 
 Here, as in the use of tlie previous gift, 
 one form is produced from another by slight 
 changes, accompanied by explanations on the 
 part of the teacher. Thus, Form 30 is easily 
 changed to 31, 32, and ^3, and Form 34 may 
 be changed to 35, 36, and 37. In every case, 
 all the blocks are to be employed in con- 
 structing a figure. 
 
 FORMS OF KNOWLEDGE. 
 This gift, like the preceding, is used to 
 communicate ideas of divisibility. Here, how- 
 ever, on account of the particular form of 
 the parts, the processes are adapted rather to 
 illustrate the division of a surface, than of a 
 solid body. 
 
 The cube is first arranged so that one per- 
 pendicular and three horizontal cuts appear, 
 aiid a child is then requested to separate it into 
 halves, these halves into quarters, and these 
 quarters into eighths. Each of the latter will 
 be found to be one of the oblong blocks, and 
 this for the time, may be made the subject of 
 conversation. 
 
 " Of what material is this block made ? " 
 
 "What is the color?"- 
 
 "What objects resemble it in form?" 
 
 " How many sides has it?" 
 
 " Which is the largest side ? " 
 
 "Which is the smallest side?" 
 
 " Is there a side larger than the smallest 
 and smaller than the largest?" 
 
 In this way, the scholars learn that there 
 are three kinds of sides, symmetrically arrang- 
 ed in pairs. The upper and lower, the right 
 and left, the front and back, are respectively 
 equal to and like each other. 
 
 By questions, or by direct explanation, facts 
 like the following, may be made apparent to 
 the minds of children. "The upper and low- 
 er sides of the block are twice as large as the 
 two long sides, or the front and back, as they 
 may be called. Again, the front and back are 
 twice as large as the right and left, or the two 
 short sides of the block. Consequently, the 
 two largest sides are four times as large as 
 the two smallest sides." This can be demon- 
 strated in a very interesting way, by placing 
 several of the blocks side by side, in a varie- 
 ty of positions, and in all these operations 
 the children should be allowed to experiment 
 for themselves. The small cubes of the pre- 
 ceding gift may also with propriety be brought 
 in comparison with the oblongs of this gift, and 
 the differences observed. 
 
 When the single block has been employed 
 to advantage, through several lessons, the 
 whole cube may then be made use of, for the 
 representation of forms of knowledge. 
 
 Construct a tablet or plane as in Plate VIII. 
 a. In order to show the relations of dimen- 
 sion, divide this plane into halves, either by a 
 perpendicular or horizontal cut (b and c). 
 
GUIDE TO KINDER-GARTNERS. 
 
 19 
 
 These two forms will give rise to instruct- 
 ive observations and remarks by asking : 
 
 " What was the form of the original tablet?" 
 
 "What is the form of its halves? " 
 
 " How many times larger is their breadth 
 than their height ? " 
 
 So with regard to the position of the oblong 
 halves ; the one at b may be said to be lying 
 while that at c is statiding. 
 
 " Change a lying to a standing oblong." In 
 order to do this, the child will move the first 
 so as to describe a quarter of a circle to the 
 right or left. 
 
 "Unite two oblongs by joining their small 
 sides. You then have a large lying oblong "(f). 
 
 "Separate again (/) and divide each part 
 into halves, (;'). You have now four parts 
 called quarters, and these are squares, in their 
 surface form." 
 
 Each of these quarters may be subdivided, 
 and the children taught the method of division 
 by two. Other material may also be used in 
 connection with the blocks, such as apples, or 
 any small objects which serve to illustrate the 
 properties of number. It is evident that these 
 operations should be conducted in the most 
 natural way, and never begun at too early a 
 stage of development of the little ones. In 
 figures e, g, h and k on Plate VIII. another 
 mode is indicated, for the purpose of illus- 
 trating further the conditions of form connect- 
 ed with this gift. Figs, i— 16 Plate VIII. 
 show the manner in which exercises in addition 
 and subtraction may be introduced, as has al- 
 ready been alluded to in the description of the 
 Third Gift. 
 
 FORMS OF BEAUTY. 
 We first ascertain, as in the case of the 
 cubes, the various modes in which the oblongs 
 can be brought in relation to each other. 
 These are much more numerous than in the 
 Third Gift, because of the greater variety in 
 
 the dimensions of the parts. Plate IX. shows 
 a number of forms of beauty derivable from 
 the original form, I. Each two blocks form 
 a separate group, which four groups touching 
 in the center, form a large square. The out- 
 side blocks (a) move in Figs, i — 9, around the 
 stationary middle. 
 
 The inside blocks {b) are now drawn out 
 (Fig. 10), then the blocks (a) united to form 
 a hollow square (Fig. 11), around which b 
 moves gradually (Figs. 12 and 13). 
 
 Now b is combined into a cross with open 
 center, a goes out (Fig. 14) and moves in an 
 opposite direction until Fig. 17 appears. 
 
 By extricating b the eight-rayed star (Fig. 
 18) is formed. In Fig. 19 a revolves, b is 
 drawn out until edge touches edge, and thus 
 the form of a flower appears (Fig. 20). 
 
 Now b is turned (Fig. 21), and in Fig. 22, 
 a wreath is shown. In Fig. 22, the inside 
 edges touch each other; in Fig. 23, inside 
 and outside ; in Fig. 24, edges with sides, and 
 b is united to a large hollow square, around 
 which a commences a regular moving. In 
 Fig. 29, a is finally united to a lying cross, and 
 thereby another starting-point gained for a 
 new series of developments. 
 
 Each of these figures can be subjected to 
 a variety of changes by simply placing the 
 blocks on their long or short sides, or as the 
 children will say, by letting them stand up or 
 lie down. The net-work of lines on the 
 table is to be the constant guide, in the con- 
 struction of forms. In inventing a new series, 
 place a block above, below, at the right or 
 left of the center ; and a second opposite and 
 equidistant. A third and a fourth are placed 
 at the right and left of these, but in the same 
 position relative to the center. The remain- 
 ing four are placed symmetrically about those 
 first laid. By moving the a's or Vf, regularly 
 in either direction, a variety of figures may 
 be formed. 
 
THE FIFTH GIFT. 
 
 CUBE, TWICE DIVIDED IN EACH DIRECTION. 
 
 (plates X. .TO XVI.) 
 
 All gifts used as occupation material in the 
 Kinder-Garten develop, as previously stated, 
 one from another. The Fifth Gift, like that 
 of the Third and Fourth Gifts, consists of a 
 cube again, although larger than the previous 
 ones. The cube of the Third Gift was divided 
 mice in all directions. The natural progress 
 from I is to 2 ; hence the cube of the Fifth 
 Gift is divided twict in all directions ; conse- 
 quently, in three equal parts, each consisting 
 of 7iine smaller cubes of equal size. But as 
 this division would only have multiplied, not 
 diversified, the occupation material, it was 
 necessary to introduce a new element, by 
 subdividing some of the cubes in a slanting 
 direction. 
 
 We have heretofore introduced only perpen- 
 dicular and horizontal lines. These opposites, 
 however, require their mediate element, and 
 this mediation was already indicated in the 
 forms of life and of beauty of the Third and 
 Fourth Gifts, when side and edge, or edge 
 and side, were brought to touch each other. 
 The slanting direction appearing there trans- 
 itionally — occasionally — here, becomes per- 
 manent by introducing the slanting line, sepa- 
 rated by the division of the body, as a bodily 
 reality. 
 
 Three of the part cubes of the Fifth Gift 
 are divided into half cubes, three others into 
 quarter cubes, so that there are left twenty- 
 one whole cubes of the twenty-seven, produced 
 by the division of the cube mentioned before, 
 and the whole Gift consists of thirty-nine sin- 
 gle pieces. 
 
 4 
 
 It is most convenient to pack them in the 
 box, so as to have all half and quarter cubes 
 and three whole cubes in the bottom row, (see 
 Plate XV., 1%) which only admits of separating 
 the whole cube in the various ways required 
 hereafter, as it will also assist in placing the 
 cube upon the table, which is done in the 
 same manner as described with the previous 
 Gifts. 
 
 The first practice with this Gift is like that 
 with others introduced thus far. Led by the 
 question of the teacher, the pupils state that 
 this cube is larger than their other cubes; 
 and the manner in which it is divided will 
 next attract their attention. They state how 
 many times the cube is divided in each "direc- 
 tion, how many parts we have if we separate 
 it according to these various divisions, and 
 carrying out what we say, gives them the 
 necessary assistance for answering these ques- 
 tions correcdy. In No. 3, Plate XV., the three 
 parts of the cube have been laid side by side 
 of each other. 
 
 These three squares we can again divide 
 in three parts, and these latter again in three, 
 so that then we shall have twenty-seven parts, 
 which teaches the pupil that 3X3=9-3X9 
 = 27. 
 
 To some, the repetition of the apparently 
 simple e-xercises may appear superfluous ; but 
 repetition alone, in this simple manner, will 
 assist children to remember, and it is always 
 interesting, as they have not to deal with ab- 
 stractions, but have real things to look at for 
 the formation of their conclusions. 
 
GUIDE TO KINDER-GARTNERS. 
 
 But, again I say, do not continue these 
 occupations any longer than you can com- 
 mand the attention of your pupils by them. 
 As soon as signs of fatigue or lackof interest 
 become manifest, drop the subject at once, 
 and leave the Gift to the pupils for their own 
 amusement. If you act according to this ad- 
 vice, your pupils never will over-e.xert them- 
 selves, and will always come with enlivened 
 interest to the same occupation whenever it 
 is again taken up. 
 
 After the children have become acquainted 
 with the manner of division of their new 
 large cube, and have exercised with it in the 
 above-mentioned way, their attention is drawn 
 to the shape of the divided half and quarter 
 cubes. 
 
 They are divided by means of slanting lines, 
 which should be made particularly prominent, 
 and the pupils are then asked to point out, 
 on the whole cubes, in what manner they 
 were divided in order to form half and quar- 
 ter cubes. The pupils also point out hori- 
 zontal, perpendicular and slanting lines which 
 they observe in things in the room or other 
 near objects. 
 
 Take the two halves of your cube apart, 
 and say, " How many corners and angles you 
 can count on the upper and lower sides of 
 these two half cubes?" "Three." Three 
 corners and three angles, which latter, you 
 recollect, are the insides of corners. We call, 
 therefore, the upper and lower side of the 
 half cube a triangle, which simply means a 
 side or plane with three angles. The child 
 has now enriched its knowledge of lines by 
 the introduction of the oblique or slanting 
 line, in addition to the horizontal and perpen- 
 dicular lines, and of sides or planes by the 
 introduction of the triangle, in addition to 
 the square and oblong previously introduced. 
 With the introduction of the triangle, a great 
 treasure for the development of forms is 
 added, on account of its frequent occurrence 
 as elementary forms in all the many forma- 
 tions of Tegular objects. 
 
 The child is expected to know this Gift now 
 
 sufficiently to employ it for the production 
 of the various forms of life and beauty now 
 to be introduced. 
 
 FORMS OF LIFE. 
 (plates X. AND XI.) 
 
 The main condition here, as always, is 
 that for each representation the whole of 
 the occupation material be employed; not 
 that only one object should always be built, 
 but in such manner that remaining pieces 
 be always used to represent accessory parts, 
 although apart from, yet in a certain rela- 
 tion to the main figure. The child should, 
 again and again, be reminded that nothing 
 belonging to a whole is, or could be, allowed 
 to be superfluous, but that each individual 
 part is destined to fill its position actively 
 and effectively in its relation to some greater 
 whole. 
 
 Nor should it be forgotten that nothing 
 should be destroyed, but everything produced 
 by re-building. It is advisable always to start 
 with the figure of the cube. 
 
 There are only the few following models on 
 our Plates lo and ii : 
 
 1. Cube. 
 
 2. Flower-Stand. 
 
 3. Large Chair. 
 
 4. Easy Chair, with Foot Bench. 
 
 5. A Bed. Lowesfrow, fifteen whole cubes ; 
 second row, six whole and six half cubes, com- 
 posed of twelve quarter cubes; third row, six 
 half cubes. 
 
 6. Sofa. First row, sixteen whole and two 
 half cubes ; 6°, ground plan. 
 
 7. A Well. 7°, ground plan. 
 
 8. House, with Yard. 8% ground plan ; 
 twelve wTiole cubes, ground ; nine whole and 
 six half cubes, second row ; roof, twelve quar- 
 ter cubes. 
 
 9. A Peasant's House. First row, ten 
 whole cubes ; second row, eight whole and 
 two half cubes; roof, eight cubes, three 
 halves and two halves, and eight quarters 
 and two halves and four quarters ; 9°, ground 
 plan. 
 
GUIDE TO KINDER-GARTNERS. 
 
 23 
 
 10. School-House. Third row, three whole 
 and six half cubes; fourth row, one whole 
 and four quarter cubes ; 10°, ground plan. 
 
 11. Church. Building itself. eighteen whole 
 cubes ; roof, twelve quarter cubes ; steeple, 
 four whole cubes and one half cube ; vestry, 
 one whole and one half cube ; 1 1°, ground 
 plan of Church. 
 
 12. Church, with Two Steeples. Building 
 itself, twelve whole cubes ; roof, twelve quar- 
 ter cubes ; steeples, twice five whole cubes 
 and one half cube ; between steeples, one 
 whole cube ; 12", ground plan. 
 
 13. Factory, with Chimney and Boiler- 
 house. Factory, sixteen whole cubes; roof, 
 six half and four quarter cubes ; chimney, five 
 whole and two quarter cubes ; boiler-house, 
 four quarter cubes ; roof, two quarter cubes ; 
 13", ground plan. 
 
 14. Chapel, with Hermitage. 
 
 15. Two Garden Houses, with Rows of 
 Trees. 
 
 16. A Castle. 16", ground plan. 
 
 17. Cloister in Ruins. 17°, ground plan. 
 
 18. City Gate, with Three Entrances. 18°, 
 ground plan. 
 
 19. Arsenal. 19°, ground plan. 
 
 20. City Gate, with Two Guard-Houses. 
 20°, ground plan. 
 
 21. A Monument. 21°, ground plan; first 
 row, nine whole and four half cubes ; second 
 to fourth row, each, four whole cubes ; on 
 either side, two quarter cubes, united to a 
 square column, and to unite the four columns, 
 four quarter cubes. 
 
 22. A Monument. 22°, ground plan; first 
 row, nine whole and four quarter cubes ; sec- 
 ond row, five whole and four half cubes ; third 
 row, four whole cubes ; fourth row, four half 
 cubes. 
 
 23. A Large Cross. 23°, ground plan ; first 
 row, nine whole and four times three quarter 
 cubes ; second row, four whole cubes ; third 
 row, four half cubes. 
 
 Tables, chairs, sofas, beds, arc the first 
 objects the child builds. They are the ob- 
 jects with which it is most familiar. Then 
 
 the child builds a house, in which it lives, 
 speaking of kitchen, sleeping-room, parlor, 
 and eating-room, when representing it. Soon 
 the realm of its ideas widens. It roves into 
 garden, street, &c. It builds the church, the 
 school-house, where the older brothers and 
 sisters are instructed ; the factory, arsenal, 
 from which, at nooii and after the day's work 
 is over, so many laborers walk out to their 
 homes, to eat their dinner and supper, to 
 rest from their work, and to play with their 
 little children. The ideas which the children 
 receive of all these objects by this occupa- 
 tion, grow more correct by studying them in 
 their details, where they meet with them in 
 reality. In all this they are, as a matter 
 of course, to be assisted by the instructive 
 conversation of the teacher. It is not to be 
 forgotten that the teacher may influence the 
 minds of the children veiy favorably, by re- 
 lating short stories about things and persons 
 in connection with the object represented. 
 Not their minds alone are to be -disciplined ; 
 their hearts are to be developed, and each 
 beautiful and noble feeling encouraged and 
 strengthened. 
 
 Be it remembered again that it is not neces- 
 sary that the teacher should always follow the 
 course of development shown in the pictures 
 on our plates. Every course is acceptable, 
 if only destruction is prevented and re-build- 
 ing adhered to. Some of the pictures may 
 not be familiar to some of the children. The 
 one- has never seen a castle or a city gate, 
 a well or a monument. Short descriptive 
 stories about such objects will introduce the 
 child into a new sphere of ideas, and stimu- 
 late the desire to see and hear more and 
 more, thus adding, daily and hourly, to the 
 stock of knowledge of which he is already 
 possessed. Thus, these plays will not only 
 cultivate the manutil dexterity of the child, 
 develop his eye, excite his fantasy, strengthen 
 his power of invention, but the accompanying 
 oral illustrations will also instruct him, and 
 create in him a love for the good, the noble, 
 the beautiful. 
 
24 
 
 GUIDE TO KINDER-GARTNERS. 
 
 The Fifth Gift is used with children from 
 five to six years old, who are expected to be 
 in their third year in the Kinder-Garten. 
 
 A box, with its contents, stands on the 
 table before each child. They empty the 
 box, as heretofore described, so that the bot- 
 tom row of the cube, containing the half and 
 quarter cubes, is made the top row. 
 
 " What have you now ? " 
 
 " A cube." 
 
 " We will build a church. Take off all 
 quarter and half cubes, and place them on 
 the table before you in good order. Move 
 the three whole cubes of the upper row 
 together, so that they are all to the left of 
 the other cubes. Take three more whole 
 cubes from the right side, and put them be- 
 side the three cubes which were left of the 
 upper row. Take the three remaining cubes, 
 which were on the right side, and add them 
 to the quarter and half cubes. What have 
 you now ? " 
 
 " A house without roof, three cubes high, 
 three cubes long, and two cubes broad." 
 
 " We will now make the roof Place on 
 each of the six upper cubes a quarter cube 
 with its largest side. Fill up the space be- 
 tween each two quarter cubes with another 
 quarter cube, and place another quarter cube 
 on top of it. What have you now ? " 
 
 " A house with roof." 
 
 " How many cubes are yet remaining .? " 
 
 " Three whole and six half cubes." 
 
 " Take the whole cubes, and place them, 
 one on top of the other, before the house. 
 Add another cube, made of two half cubes, 
 and cover the top with half a cube for a roof. 
 What have you now .'' " 
 
 " A steeple." 
 
 '• We will employ the remaining three half 
 cubes to build the entrance. Take two of the 
 half cubes, form a whole cube of them, and 
 place it on the other side of the house, op- 
 posite the steeple, and lay upon it the last 
 half cube as a roof. What have we built 
 now ? " 
 
 " A cliurch, with steeple and entrance." 
 
 FORMS OF BEAUTY. 
 
 If we consider that the Fifth Gift is put 
 into the hands of pupils when they have 
 reached the fifth year, with whom, conse- 
 quently, if they have been treated rationally, 
 the external organs, the limbs, as well as the 
 senses, and the bodily mediators of all men- 
 tal activity, the nerves, and their central organ, 
 the brain, have reached a higher degree of 
 development, and their physical powers have 
 kept pace with such development, we may 
 well expect a somewhat more extensive activ- 
 ity of the pupils so prepared, and be justified 
 in presenting to them work requiring more 
 skill and ingenuity than that of the previous 
 Gifts. 
 
 And, in fact, the progress with these forms 
 is apparently much greater than with the 
 forms of life ; because here the importance 
 of each of the thirty-nine parts of the cube 
 can be made more prominent. He who is 
 not a stranger in mathematics knows that the 
 number of combinations and permutations of 
 thirty-nine different bodies does not count by 
 hundreds, nor can be expressed by thousands; 
 but that millions hardly suffice to exhaust all 
 possible combinations. 
 
 Limitations are, therefore, necessary here ; 
 and these limitations are presented to us in 
 tiie laws of beauty, according to which the 
 whole structure is not only to be formed har- 
 moniously in itself, but each main part of it 
 mast also answer the claims of symmetry. 
 In order to comply with these conditions, it 
 is sometimes necessary, during the process 
 of building a Form of Beauty, to perform 
 certain movements with various parts simul- 
 taneously. In such cases it appears advis- 
 able to divide the activity in its single parts, 
 and allow the child's eye to rest on these 
 transition figures, that it may become perfectly 
 conscious of all changes and phases during 
 the process of development of the form in 
 question. This will render more intelligible 
 to the young mind, that real beauty can only 
 be produced when one opposite balances 
 another, if the proportions of all parts are 
 
GUIDE TO KINDER-GARTNERS. 
 
 25 
 
 equally regulated by uniting them with one 
 common center. 
 
 Another limitation we find in the fact, that 
 each fundamental form from which we start 
 is divided in two main parts — the internal 
 and the external— and that if we begin the 
 changes or mutations with one of these oppo- 
 sites, they are to be continued with it until a 
 certain aim be reached. By this process cer- 
 tain small series of building steps are created, 
 which enable the child — and, still more, the 
 teacher — to control the method according to 
 which the perfect form is reached. 
 
 " Each definite beginning conditions a cer- 
 tain process of its own, and however much 
 liberty in regard to changes may be allowed, 
 they are always to be introduced within cer- 
 tain limils only." 
 
 Thus, tlie fundamental form conditions all 
 the changes of the whole following series. 
 All fundamental forms are distinct from each 
 other by their different centers, which may be 
 a square, (Plate XII., Fig. 9,) a triangle, 
 (Plate XIV., Fig. 37,) a he.xagon, octagon, or 
 circle. 
 
 Before the real formation of figures com- 
 mences, the child should become acquainted 
 with the combinations in which the new forms 
 of the divided cubes can be brought with 
 each other. It takes two half cubes, forms 
 of them a whole, and, being guided by the 
 law of opposites, arrives at the forms repre- 
 sented on Plate XII. — i to 8, and perhaps at 
 others of less significance. 
 
 The scries of figures on Plates XIIL, XIV., 
 XV., arc all developed, one from another, as 
 the careful observer will easily detect. As it 
 would lead too far to show the gradual grow- 
 ing of one from another, and all from a com- 
 mon fundamental form, we will show only the 
 course of development of Figures 9 to 14, on 
 Plate XII. 
 
 The fundamental form (Fig. 9) is a stand- 
 ing square, formed of nine cubes, and sur- 
 rounded by four equilateral triangles. 
 
 The course of development starts from the 
 center part. The four cubes a move exter- 
 
 nally, (Fig. 10,) the four cubes li do the same, 
 (Fig. II,) cubes a move farther to the corner 
 of the triangles, (Fig. 12,) cubes i move to 
 the places where cubes a were previously, 
 (Fig. 13.) If all eight cubes continue their 
 way in the same manner, we ne.xt obtain a 
 form in which a and l> remain with their cor- 
 ners on the half of the catheti ; then follows 
 a figure like 13, different only in so far as a 
 and -i^ have exchanged positions; then, in 
 like manner, follow 12, 11, 10, and 9. 
 
 We, therefore, discontinue the course. The 
 internal cubes so far occupied positions that 
 l> and iT turned corners, a and c sides towards 
 each other. In Fig. 14, the opposite appears, 
 /> and t: show each other sides, a and £ cor- 
 ners. Thus, in Fig. 15, we reach a new 
 fundamental form. Here, not the cubes of 
 the internal, but those of the external tri- 
 angles furnish the material for changing the 
 form. 
 
 It is not necessaiy that the teacher, by 
 strictly adhering to the law of development, 
 return to the adopted fundamental form. She 
 may interrupt the course, as we have done, 
 and continue according to new conditions. 
 But however useful it may be to leave free 
 scope to the child's own fantasy, we should 
 never lose sight of Froebel's principle, to lead 
 to Imnful action, to accustom to following a 
 definite rule. Nor should we ever forget that 
 the child can only derive benefit from its 
 occupation, if we do not over-tax the measure 
 of its strength and ability. The laws of for- 
 mation should, therefore, always be as definite 
 and distinct as simple. As soon as the child 
 cannot trace back the way in which you have 
 led it, in developing any of the forms of life 
 or beauty ; if it cannot discover how it arrived 
 at a certain point, or how to proceed from it, 
 the moment has arrived when the occupation 
 not only ceases to be useful, but commences 
 to be hurtful, and we should always studiously 
 avoid that moment. 
 
 In order to facilitate the child's control of 
 his activity, it is well to give the cubes, which 
 arc, so to say, the representatives of the law 
 
26 
 
 GUIDE TO KINDER-GARTNERS. 
 
 of development, instead of the letters a, b, c, 
 names of some children present, or of friends 
 of the pupils. This enlivens the interest in 
 their movements, and the children follow them 
 with much more attention. 
 
 FORMS OF KNOWLEDGE. 
 
 (plates XV. AND XVI.) 
 
 The representations of the forms of knowl- 
 edge, to which the Fifth Gift offers oppor- 
 tunity, is of great advantage for the develop- 
 ment of the child. To superficial observers, 
 it is true, it may appear as if Froebel not 
 only ascribed too much importance to the 
 mathematical . element to the disadvantage 
 of others, but that mathematics necessarily 
 require a greater maturity of understanding 
 than could be found with children of the 
 Kinder-Garten age. But who thinks of in- 
 troducing mathematics as a science ? Many 
 a child, five or six years of age, has heard 
 that the moon revolves around the earth, that 
 a locomotive is propelled by steam, and that 
 lightning is the effect of electricity. These 
 astronomical, dynamic and physical facts have 
 been presented to him, as mathematical facts 
 are presented to his observation in Froebel's 
 Gifts. Most assuredly it would be folly, if one 
 would introduce in the Kinder-Garten math- 
 ematical problems in the usual abstract man- 
 ner. In the KinderGarten, the child beholds 
 the bodily representation of an expressed 
 truth, recognizes the same, receives it without 
 difficulty, without overtaxing its developing 
 mind in any manner whatsoever. Whatever 
 would be difficult for the child to derive from 
 the mere word, nay, which might under cer- 
 tain circumstances be hurtful to the young 
 mind, is taught naturally and in an easy man- 
 ner by the forms of knowledge, which thus 
 become the best means of e-xercising the 
 child's power of observation, reasoning, and 
 judging. Beware of all problems and ab- 
 stractions. The child builds, forms, sees, 
 observes, compares, and then expresses the 
 truth it has ascertained. By repetition, these 
 truths, acquired by the observation of facts. 
 
 become the child's mental property, and this 
 is not to be done hurriedly, but during tlie 
 last two years in the Kinder-Garten and 
 afterwards in the Primary Department. 
 
 The first seven forms of knowledge on 
 Plate XV. show the regular divisions of the 
 cube in three, nine and twentj'-seven parts, 
 lu cither case, a whole cube was employed, 
 and yet the forms produced by division are 
 different. This shows that the contents may 
 be equal, when forms are different (Figs. 2, 3, 
 4, or 5 and 6). 
 
 This difference becomes still more obvious 
 if the three parts of Fig. 2, are united to a 
 standing oblong, or those of Fig. 3 to a lying 
 oblong, or if a single long beam is formed of 
 Fig. 4. 
 
 Take a cube, children, place it bc'fore you, 
 and also a cube divided in two halves, and 
 place the two halves with their triangular 
 planes or sides, one upon another. 
 
 These two halves united are just as large 
 as the whole cube. 
 
 But the two halves may be united, also, in 
 other ways. They may touch each other with 
 their quadratic and right angular planes. 
 
 Represent these different ways of uniting 
 the two halves of the cube simultaneously. 
 Notwithstanding the difference in the forms, 
 the contents of mass of matter remained the 
 same. 
 
 In a still more multiform manner, this fact 
 may be illustrated with the cubes divided in 
 four parts. Similar exercises follow now with 
 the whole Gift, and the children are led to 
 find out all possible divisions in two, three, 
 four, five, nine and twelve equal parts (Figs. 
 8 to 18). 
 
 After each such division the equal parts 
 are to be placed one upon another, for divid- 
 ing and separating are always to be followed 
 by a process of combining and re-uniting. 
 The child thus receives every time, a trans- 
 formation of the whole cube, representing the 
 same amount of matter in various forms 
 (Fig. 19-22). The child should also be al- 
 lowed to compare with each other the various 
 
GUIDE TO KINDER-GARTNERS. 
 
 27 
 
 thirds, quarters, or sixths, into which whole 
 cubes can be divided, as shown in Figs. 9, 
 10, II, 12, or 14, 15 and 16. 
 
 It is understood that all these exercises 
 should be accompanied by the living word 
 of the teacher ; for thereby, only, will the 
 child become perfectly conscious of the ideas 
 received from perception, and the opportunity 
 is offered to perfect and multiply them. The 
 teacher should, however, be carefuF not to 
 speak too much, for it is only necessary to 
 keep the attention of the pupil to the object 
 represented, and to render impressions more 
 vivid. 
 
 The divisions introduced heretofore, are 
 followed by representations of regular mathe- 
 matical figures, (planes,) as shown in Figs. 
 23-26. The manner in which one is formed 
 from the preceding one is easily seen from 
 the figures themselves. 
 
 As mentioned before, part of the occupa- 
 tion described in the preceding pages, is to 
 
 be introduced in the Primary Department 
 only, where it is combined with other inter- 
 esting but more complicated exercises. Sim- 
 ply to indicate how advantageously this Gift 
 may be used for instruction in geometiy in 
 later years, we have added the Figs. 30" and 
 30'', the representation of which shows the 
 child the visible proof of the well-known 
 Pythagorean axiom, by which the theoretical, 
 abstract solution of the same, certainly, can 
 alone be facilitated. 
 
 For the continuation of the exercises in 
 arithmetic, begun with the previous Gifts, the 
 cubes of the present one are of great use. 
 Exercises in addition and subtraction are con- 
 tinued more extensively, and by the use of 
 these means, the child will be enabled to 
 learn, what is usually called the multiplication 
 table, in a much shorter time and in a much 
 more rational way than it could ever be ac- 
 complished by mere memorizing, without visi- 
 ble objects. 
 
 THE SIXTH GIFT. 
 
 LARGE CUBE, CONSISTING OF DOUBLY DIVIDED OBLONGS. 
 
 (plates XVII. TO XX.) 
 
 As the Third and Fifth Gifts form an 
 especial sequence of development, so the 
 Fourth and Sixth are intimately connected 
 with each other. The latter is, so to say, a 
 higher potence of the former, permitting, the 
 observation in greater clearness, of the quali- 
 ties, relations, and laws, introduced previously. 
 
 The Gift contains twenty-seven oblong 
 blocks or bricks, of the same dimensions as 
 those of the Fourth Gift. Of these twenty- 
 seven blocks, eighteen are whole, six are 
 divided breadthwise, each in two squares, 
 and three by a lengthwise cut, each in t\vo 
 columns ; altogether making thirty-six pieces. 
 
 The children soon become acquainted with 
 this Gift, as the variety of forms is much less 
 than in the preceding one, where, by an ob- 
 lique division of the cubes, an entirely new 
 radical principle was introduced. 
 
 It is here, therefore, mainly the proportions 
 of size of the oblongs, squares, and columns 
 contained in this Gift and the number of each 
 kind of these bodies, about which the child 
 has to become enlightened, before engaging 
 in building — playing, creating — withthis new 
 material. 
 
 The cube is placed upon the table — all parts 
 are disjoined — then equal parts collected 
 
2S 
 
 GUIDE TO KINDER-GARTNERS. 
 
 into groups, and the child is then asked, 
 "How many blocks have you altogether?" 
 How many oblongs? how many squares? 
 how many columns ? Compare the sides of 
 the blocks with another — take an oblong — 
 how many squares do you need to cover it ? 
 how many columns ? 
 
 Place the oblong upon its long edge, now 
 upon its shortest side — and state how many 
 squares or columns you need in order to 
 reach its height, in either case. Exercises of 
 this kind will instruct the child sufficiently, 
 to allow it to proceed, in a short time, to the 
 individual creating, or producing occupation 
 with this new Gift. 
 
 FORMS OF LIFE. 
 
 (PLATES XVri. AND XVIH.) 
 
 It is the forms of life, particularly, for 
 which this Gift provides material, far better 
 fitted, than any previously used. The ob- 
 longs admit of a much larger extension of 
 the plane, and allow the enclosure of a much 
 more extensive hollow space, than was possi- 
 ble, for instance, with the cubes of the Fifth 
 Gift. Innumerable forms can therefore be 
 produced with this Gift, and the attention and 
 interest of the pupil will be constantly in- 
 creased. 
 
 This very variety, however, should induce 
 the careful teacher to prevent the child's 
 purely accidental production of forms. It is 
 always necessary to act according to certain 
 rules and laws, to reach a certain aim. The 
 established principle, that one form should al- 
 ways be derived from another, can be carried 
 out here only with great difficulty, owing to 
 the peculiarity of the material. It is therefore 
 frequently necessary, particularly with the 
 more complicated structures, to lay an entirely 
 new foundation for the building to be erected. 
 
 It is necessary, at all times, to follow the 
 child in his operations, — his questions should 
 always be answered and suggestions made to 
 enlarge the circle of ideas. 
 
 It affords an abundance of pleasure to a 
 child to observe that we understand it and 
 
 its work ; it is, therefore, a great mistake in 
 education to neglect to enter fully into the 
 spirit of the pupil's sphere of thinking and 
 acting; and if we ever should allow our- 
 selves to go so far as to ridicule his pro- 
 ductions, instead of assisting him to improve 
 on them, we would certainly commit a most 
 fatal error. 
 
 The selections of forms of life on Plates 
 XVII. and XVIII., nearly all of which are 
 in the meantime forms of art and knowledge, 
 because of their architectural fundamental 
 forms, and the mathematical proportions of 
 their single parts, can, therefore, not fail to 
 give nourishment to various powers of the 
 mind. 
 
 1. House without roof; back wall has no 
 door, i", ground plan. 
 
 2. Colonnade ; lowest row, five oblongs 
 laid lengthwise, and back wall consisting of 
 ten standing oblongs, upon which ten squares. 
 2', ground plan. 
 
 3. Hall, with columns. 
 
 4. Summer House. 4% ground plan ; ves- 
 tibule formed by six columns. 
 
 5. Memorial Column of the Three Friends. 
 5°, ground plan. 
 
 6. Monument in Honor of "Some Fallen 
 Hero. 6°, ground plan; lowest row, eight 
 oblongs ; second square of nine squares, par- 
 tially constructed of oblongs ; third, four sin- 
 gle squares ; then four columns, four single 
 squares, square of nine squares, square of 
 four squares, etc. 
 
 7. Facade of a Large House. 7°, ground 
 plan. 
 
 8. The Columns of the Three Heroes. 
 8% ground plan. 
 
 9. Entrance to Hall of Fame. 9°, ground 
 plan ; first row, sLx squares and six oblongs ; 
 second row, six oblongs ; third row, six 
 squares, etc. 
 
 10. Two Story House, with yard. io% 
 ground plan. Io^ side view. 
 
 11. Faqade. II^ ground plan. 
 
 12. Covered Summer House. 12°, ground 
 plan. 
 
GUIDE TO KINDER-GARTNERS. 
 
 29 
 
 13. Front View of a Factory. 13°, ground 
 plan. I3^ side view. 
 
 14. Double Colonnade. 14°, ground plan. 
 
 15. An Altar. 15°, ground plan. 
 
 16. Monument. 16°, ground j^lan. 
 
 17. Columns of Concord. 17", ground 
 plan. 
 
 The fantasy of the child is inexhaustibly 
 rich in inventing new forms. It creates gar- 
 dens, yards, stables with horses and cattle, 
 household furniture of all kinds, beds with 
 sleeping brothers and sisters in them, tables, 
 chairs, sofas, etc., etc. 
 
 If several children combine their individual 
 building they produce large structures, perfect 
 barn-yards with all out-buildings in them, nay, 
 whole villages and towns. The ideas that in 
 union there is strength, and that by co-oper- 
 ation great things may be accomplished, will 
 thus early become manifest to the young 
 mind. 
 
 FORMS OF BEAUTY. 
 
 (plates XIX. AND XX.) 
 
 The forms of beauty of this Gift offer far less 
 diversity than those of Gift No. 5 ; owing, how- 
 ever, to the peculiar proportions of the plane, 
 they present sufficient opportunity for charac- 
 teristic representations, not to be neglected. 
 
 We give on the accompanying plates a sin- 
 gle succession of development of such forms. 
 The progressive changes are easily recog- 
 nized, as the oblong, which needs to be moved 
 to produce the following figure, is always 
 marked by a letter. The center-piece always 
 consists of two of the little columns, standing 
 one upon another, and important modifica- 
 
 tions may be produced by using the oblongs 
 in lying or standing positions. By employing 
 the four little columns in various ways, many 
 pleasant changes can be produced by them. 
 
 FORMS OF KNOWLEDGE. 
 (plate XX.) 
 
 These also appear in much smaller num- 
 bers compared with the richness and multi- 
 plicity of the Fifth Gift. By the absence of 
 oblique (obtuse and acute) angles, they are 
 limited to the square and oblong, and exer- 
 cises introduced with these previously, may 
 be repeated here with advantage. 
 
 All Froebel's Gifts are remarkable for the 
 peculiar feature that they can be rendered ex- 
 ceedingly instructive by frequently introduc- 
 ing repetitions under varied conditions and 
 forms, by which means we are sure to avoid 
 that dry and fatiguing monotony which must 
 needs result from repeating the same thing in 
 the same manner and form. And still more, 
 the child, thereby, becomes accustomed to 
 recognize like in unlike, similarity in dissimi- 
 larity, oneness in multiplicit}', and connection 
 in the apparently disconnected. 
 
 In Fig. 16-22, all squares that can be 
 formed with the Sixth Gift are represented. 
 In Fig. 23 we see a transition from the forms 
 of knowledge to those of beauty. 
 
 With the Sixth Gift we reach the end of 
 the two series of development given by 
 Froebel in the building blocks, whose aim 
 is to acquaint the child with the general 
 qualities of the solid body by own observa- 
 tion and occupation with the same. 
 
THE SEVENTH GIFT. 
 
 SQUARE AND TRIANGULAR TABLETS FOR LAYING OF FIGURES. 
 
 (plates XXI. TO XXIX.) 
 
 All mental development begins with con- 
 crete beings. The material world with its 
 multiplicity of manifestations first attracts 
 the senses and excites them to activitj', thus 
 causing the rudimental operations of the 
 mental powers. Gradually — only after many 
 processes, little defined and explained by any 
 science as yet, have taken place — man be- 
 comes enabled to proceed to higher mental 
 activity, from the original impressions made 
 upon his senses by the various surroundings 
 in the material world. 
 
 The earliest impressions, it is true, if often 
 repeated, leave behind them a lasting trace 
 on the m.ind. But between this attained pos- 
 sibility to recall once-made observations, to 
 represent the object perceived by our senses, 
 by mental image (imagination), and the 
 real thinking or reasoning, the real pure ab- 
 straction, there is a very long step, and 
 nothing in our whole system of education is 
 more worthy of consideration than the sud- 
 den and abrupt transition from a life in the 
 concrete, to a life of more or less abstract 
 thinking to which our children are submitted 
 when entering school from the parental 
 house. 
 
 Froebel, by a long series of occupation * 
 material, has successfully bridged over this 
 chasm, which the child has to traverse, and 
 the first place among it, the laying tablets of 
 various forms occupy. 
 
 The series of tablets is contained in five 
 boxes containing— 
 
 A. Quadrangular square tablets. 
 
 B. Right angular (equal sides). ^ „ . 
 
 C. Right angular (unequal sides). I . 
 
 D. Equilateral, and {Tu^t 
 
 E. Obtuse angular (equal sides). J 
 
 The child was heretofore engaged with 
 solid bodies, and in the representation of 
 real things. It produced a house, garden, 
 sofa, etc. It is true the sofa was not a sofa 
 as it is seen in reality ; the one built by the 
 child was, therefore, so to say, an image al- 
 ready, but it was a bodily image, so much so 
 that the child could place upon it 'a little 
 something representing its doll. The child 
 considered it a real sofa, and so it was to the 
 child, fulfilling, as it did, in its little world, 
 the purposes of a real sofa in real life. 
 
 With the tablets, the embodied planes, the 
 child can not represent a sofa, but a form 
 similar to it ; an image of the sofa can be pro- 
 duced by arranging the squares and triangles 
 in a certain order. 
 
 We shall see, at some future time, how 
 Froebel continues on this road, progressing 
 from the plane to the line, from the line to 
 the point, and finally enables the child to 
 draw the image of the object, with pencil or 
 pen in his own little hand. 
 
 A. THE QUADRANGULAR LAYING TAB- 
 LETS (Squares). 
 
 (PLATE XXI.) 
 
 They are given the child first to the num- 
 ber of six. In a similar way as was done 
 with the various building gifts, the child is 
 led to an acquaintance with the various quali- 
 
GUIDE TO KINDER GARTNERS. 
 
 ties of Ihe new material, and to compare it, 
 with other things, possessing similar qualities. 
 It is advisable to let the child understand 
 the connection existing between this and the 
 previous gifts. The laying tablets are nothing 
 but the embodied planes, or separated sides 
 of the cube. Cover all the sides of a cube 
 with square tablets and after the child has 
 recognized the cube in the body thus formed, 
 let it separate the tablets one by one, from 
 the cube hidden by them. 
 
 The following, or similar questions are here 
 to be introduced : — What is the form of this 
 tablet ? How many sides has it ? How 
 many angles ? Look carefully at the sides. 
 Are they alike or unlike each other? They 
 are all alike. Now look at the corners. These 
 also are all alike. Where have you seen sim- 
 ilar figures ? 
 
 What are such figures called ? Can you 
 show me angles somewhere else ? Where 
 the two walls meet is an angle. Here, there, 
 and everywhere you find angles. 
 
 But all angles are not alike, and they are 
 therefore differently named. All these dif- 
 ferent names you will learn successively, but 
 now let us turn to our tablet. Place it right 
 straight before you upon the table. Can you 
 tell me now what direction these two sides 
 have which form the angle ? The one is 
 horizontal, the other perpendicular. An 
 angle which is formed if a perpendicular 
 meets a horizontal line, is called a right an- 
 gle. How many of such angles can you 
 count on your tablet? Four. Show me such 
 right angles somewhere else. 
 
 By the acquisition of this knowledge the 
 child has made an important step forward. 
 Looking for horizontal and perpendicular 
 lines, and for right angles, it is led to investi- 
 gate more deeply the relations of form, which 
 it had heretofore observed only in regard to 
 the size conditioned by it. 
 
 The child's attention should be drawn to 
 the fact that, however the tablet may be 
 placed the angles always remain right angles 
 though the lines are horizontal and perpen- 
 
 dicular only in four positions of the tablet, 
 namely, those where the edges of the tablet 
 are placed in the same direction with the 
 lines on the table before the child. This 
 will give occasion to lead the child to a gen- 
 eral perception of the standing or hanging of 
 objects according to the plummet. 
 
 But the tablet will force still another ob- 
 servation upon the child. The opposite sides 
 have an equal direction ; they are the same 
 distance from each other in all their points ; 
 they never meet, however many tablets the 
 child may add to each other to form the lines. 
 
 The child learns that such lines are called 
 parallel lines. It has observed such lines 
 frequently before this, but begins just now to 
 understand their real being and meaning. 
 It looks now with much more interest than 
 ever before at surrounding tables, chairs, 
 closets, houses, with their straight line orna- 
 ments, for now the little cosmopolitan does 
 not only receive the impressions made by the 
 surroundings upon his senses, but he already 
 looks for something in them, an idea of which 
 lives in his mind. Although unconscious of 
 the fact that with the right angle and the 
 parallel line, h€< received the elements of 
 architecture, it will pleasantly incite him to 
 new observations whenever he finds them 
 again in another object which attracts his 
 attention. 
 
 The teacher in remembrance of oar oft- 
 repeated hints, will proceed slowly, and care- 
 fully, according to the desire and need of the 
 child. She repeats, explains, leads the child 
 to make the same observations in the most 
 different objects, and changing circumstances, 
 or guides the child in laying other forms of 
 knowledge (lying or standing parallelograms 
 Fig. 4 and 5) of life, (steps. Fig. 6 and 8, 
 double steps. Fig. 7 and 9, door, Fig. 10, sofa. 
 Fig. II, cross. Fig. 12), or forms of beauty. 
 
 The number of these forms is on the whole 
 only very limited. It is well now to augment 
 the number of tablets in the hands of the 
 pupil, by two, when a much larger munber of 
 forms can be produced. The various series 
 
32 
 
 GUIDE TO KINDER GARTNERS. 
 
 of forms of beauty, introduced with the third 
 Gift, can be repeated here and enlarged upon, 
 according to the change in tlie material now 
 at the disposal of the child. 
 
 B, RIGHT-ANGLED TRIANGLES. 
 (PLATE XXI.) 
 
 As from the whole cube, the divided cube 
 was produced, so by division the triangle 
 springs from the square. By dividing it 
 diagonally in halves, we produce the rectan- 
 gular triangle with equal sides. 
 
 Although the form of the triangle was pre- 
 sented to the child in connection with the 
 Fifth Gift, it here appears more independentl)-, 
 and it is not only on that account necessary 
 to acquaint the child with the qualities and 
 being of the new addition to its occupation 
 material, but still more so as the forms of 
 the triangles with which, as a natural sequence 
 it will have to do hereafter, were entirely 
 unknown to the pupil. The child places two 
 triangles, joined to a square, upon the table. 
 
 What kind of a line divides your four-cor- 
 nered tablet.' An oblique or slanting line. 
 In what direction does the line cut your 
 square in two ? From the right upper corner 
 to the left lower corner. Such a line we call 
 a diagonal. 
 
 Separate the two parts of the square, and 
 look at each one separately. What do you 
 call each of these parts ? What did you call 
 the whole ? A square. How many corners 
 or angles had the square ? Four. How many 
 corners or angles has the half of the square 
 you are looking at? Three. This half, 
 therefore, is called a triangle, because, as I 
 have explained to you before, it has three 
 angles. How many sides has your tri- 
 angle ? etc. 
 
 Looking at the sides more attentively, 
 what do you observe ? One side is long, the 
 other two are shorter, and, like each other. 
 These latter are as large as the sides of the 
 square, all sides of which were alike. 
 
 Now tell me what kind of angle it is, that 
 is formed by these two equal sides ? It is a 
 
 right angle. Why? and what will you call 
 the other two angles ? How do the sides 
 run which form these two angles ? They run 
 in such a way as to form a very sharp point, 
 and these angles are, therefore, called acute 
 angles, which means sharp-pointed angles. 
 Your triangle has then, how many different 
 kinds of angles ? Two ; one right angle, and 
 two acute angles. 
 
 It is not necessary to mention that the 
 above is not to be taught in one lesson. It 
 should be presented in various conversations, 
 lest the acquired knowledge might not be 
 retained by even the brightest child. The 
 attention of the pupil may also be led, in 
 subsequent con\^ersations to the fact that the 
 largest side is opposite the largest angle, and 
 that the two acute angles are alike, etc. 
 Sufficient opportunity for these and additional 
 remarks will offer itself during the represen- 
 tations of forms of life, of knowledge, and of 
 beauty, for which the child will employ its 
 tablets, according to its own free will, and 
 which are not necessarily to be separated, 
 neither here nor in any other part of these 
 occupations, although it is well to observe a 
 certain order at any time. 
 
 Whenever it can be done, elementary knowl- 
 edge may well be imparted, together with the 
 representations of forms of life, and forms of 
 beauty. 
 
 In order to invent, the child must have 
 observed the various positions which a trian- 
 gle may occupy. It will find these acting 
 according to the laws of opposites, already 
 familiar to the child. 
 
 The right angle, to the right below, (Fig. 17) 
 it will bring into the opposite direction to the 
 left above, (Fig. 18) then into the mediative 
 positions to the left below, (Fig. 19) and to 
 the right above, (Fig. 20). By turning, it 
 comes aboi'e\h& long side, (Hypothenuse, Fig. 
 21) then opposite below it, (Fig. 22) then to 
 the right, (Fig. 23) and finally to the left of 
 it, (Fig. 24). 
 
 The various positions of two triangles are 
 easily found by moving one of them around 
 
GUIDE TO KINDER-GARTNERS. 
 
 33 
 
 the other. Fig. 26-31 are produced from 
 Fig. 25, by moving the triangle marked a, 
 always keeping it in its original position, 
 around the otlier triangle. 
 
 In Figs. 32-37, the changes are produced, 
 alternating regularly between a turn and a 
 move of the triangle a. In Figs. 38-47, 
 simply turning takes place. 
 
 After the child has become acquainted with 
 the first elements from which its formations 
 develop, it receives for a beginning four of 
 the triangled tablets. It then places the 
 right angles together, and thereby forms a 
 standing full square, (Fig. 48.) 
 
 By placing the tablets in an opposite posi- 
 tion', turning the right angles from within to 
 without, it produces a lying square with the 
 hollow in the middle, (Fig. 49). This hollow 
 space has the same shape and dimensions as 
 Fig. 48. The child will fancy Fig. 48 into the 
 place of this hollow space, and will thereby 
 transfer the idea of a full square upon an 
 empty or hollow one, and will consequently 
 make the first step from the perception of the 
 concrete to its idea, the abstraction. 
 
 The child will now easily find mediative 
 forms between these two opposites. It places 
 two right angles v.'ithin and two without, 
 (Fig. 58 and 59) two above, and two below, 
 (Fig. 50) two to the right, and two to the left, 
 (Fig. 50- 
 
 So far, two tablets always remained con- 
 nected with one another. By separating 
 them we produce the new mediative forms, 
 52, 53, 54 and 55. in which again two and 
 two are opposites. But instead of the right. 
 the acute angles may meet in a point also, 
 and thus Figs. 56 and 57 are produced, 
 which are called rotation forms, because the 
 isolated position of the right angle suggests, 
 as it were, an inclination to fall, or turn, or 
 rotate. 
 
 The mediation between these two oppo- 
 site figures is given in Figs. 50 and 5 1 — 
 between them and Figs. 49 and 50 in Figs. 
 58 and 59 ; and it should be remarked in 
 this connection, that these opposites are con- 
 5 
 
 ditioned by the position of the right angle in 
 all these cases. 
 
 All these exercises accustom the pupil to a 
 methodic handling of all his material. They 
 develop a correct use of his eye, because 
 regular figures will only be produced when 
 his tablets are placed correctly and exactly 
 in their places shown by the net-work on the 
 table. The precaution which must be exer- 
 cised by the child not to disturb the easily 
 movable tablets, and the care employed to 
 keep each in its place, are of the greatest 
 importance for future necessary dexterity of 
 hand. In a still greater degree than by these 
 simple elementary forms just described, this 
 will be the case, when the pupil comes into 
 possession of the following boxes, containing 
 a larger number — up to sixty-four — tablets for 
 the formation of more complicated figures, 
 according to the free exercise of his fantasy. 
 
 FORMS OF LIFE. 
 (plate xxiii.) 
 All hints given in connection with the build- 
 ing blocks, are also to be followed here, with 
 this difference only, that we produce now . 
 images of objects, whereas, heretofore, we 
 united the objects themselves. 
 The child here begins — 
 
 A, WITH FOUR TABLETS. 
 
 And forms witli them — 
 I. A flower-pot. 2. A little garden-house. 
 3. A pigeon-house. 
 
 B, WITH EIGHT TABLETS. 
 
 4. A cottage. 5. A canoe or boat. 6. 
 A covered goblet. 7. A lighthouse. 8. A 
 clock. 
 
 C, WITH SI.XTEEN TABLETS. 
 
 9. A bridge with two spans. 10. A large 
 gate. II. A church. 12. A gate with bel- 
 fry. 13. A fruit basket. 
 
 D, WITH THIRTY-TWO TABLETS. 
 
 14. A peasant's house. 15. A forge with 
 high chimney. 16. .'\ coffee-mill. 17. A cof- 
 fee-pot without handle. 
 
34 
 
 GUIDE TO KINDER-GARTNERS. 
 
 E, WITH SIXTY-FOUR TABLETS. 
 
 i8. A two-Story house. 19. Entrance to a 
 railroad depot. 20. A steamboat. 
 
 In No. 21, we see the result of combined 
 activity of many children. Although to some 
 grown persons it may appear as if the images 
 produced do not bear much resemblance to 
 what they are intended to represent, it should 
 be remembered that iu most cases, the chil- 
 dren themselves have given the names to 
 the representations. Instructive conversation 
 should also prevent this drmvmg with planes, 
 as it were, from being a mere mechanical pas- 
 time ; the entertaining, living word must in- 
 fuse soul into the activity of the hand and its 
 creations. Each representation, then, will 
 speak to the child and each object in the 
 world of nature and art will have a story to 
 tell to the child in a language for which it 
 will be well prepared. 
 
 We need not indicate how these conversa- 
 tions should be carried on, or what they 
 should contain. Who would not think, in 
 connection with the pigeon-house, of the 
 beautiful white birds themselves, and the nest 
 they build ; the white eggs they lay, the ten- 
 der young pigeons coming from them, and 
 the care with which the old ones treat the 
 young ones, until they are able to take care 
 of themselves. An application of these re- 
 lations to those between parents and children, 
 and, perhaps, those between God and man, 
 who, as his children enjoy his kindness and 
 love every moment of their lives, may be 
 made, according to circumstances — all de- 
 pending on the development of the children. 
 However, care should always be taken not to 
 present to them, what might be called ab- 
 stract morals, which the young mind is unable 
 to grasp, and which, if thus forced upon it 
 cannot fail to be injurious to moral develop- 
 ment. The aim of all education should be 
 love of the good, beautiful, noble, and sub- 
 lime ; but nothing is more apt to kill this 
 very love, ere it is born, than the monotony 
 of dry, dull preaching of morals to young 
 children. Words not so much as deeds — 
 
 actual experiences in tiie life of the child, are 
 its most natural teachers in this important 
 branch of education. 
 
 FORMS OF BEAUTY. 
 
 (PLATES XXI. AND XXII.) 
 
 Owing to the larger multiplicity of ele- 
 mentary forms to be made with the triangles, 
 the number of Forms of Beauty is a very large 
 one. Triangle, square, right angle, rhomb, 
 hexagon, octagon, are all employed, and the 
 great diversity and beauty of the forms pro- 
 duced lend a lasting charm to the child's 
 occupation. Its inventive power and desire, 
 led by law, will find constant satisfaction, and 
 to give satisfaction in the fullest measure 
 should be a prominent feature of all systems 
 of education. 
 
 FORMS TO BE BUILT WITH FOUR TABLETS 
 
 have already been mentioned on page 33, as 
 contained on Plate XXI — D, 48-59. We find 
 more satisfaction by employing 
 
 EIGHT TABLETS. 
 
 In working with them, we can follow the 
 most various principles. Series E, 60-69, is 
 formed by doubling the forms produced by 
 four tablets ; series F, starting from the fun- 
 damental form 70, making one half of the 
 tablets move from left to right, the length of 
 one side, with each move. A new series 
 would be produced, if we move from right to 
 left in a similar manner. In these figures, 
 sides always touch sides, and corners touch 
 corners — consequendy, parts of the same kind. 
 
 The transition or mediation between these 
 two opposites, the touching of corners and 
 sides, would be produced by shortening the 
 movement of the traveling triangle one-half, 
 permitting it to proceed one-half side only. 
 
 But let us return to fundamental form 70. 
 In it, either large sides (hypothenuses) or 
 small sides (catheti) constantly touch one 
 another. The opposite — large side touching 
 small — we have in Fig. 82, and by traveling 
 from right to left of half the triangles, series 
 
GUIDE TO KINDER-GARTNERS. 
 
 35 
 
 G, 82 to 87, is produced. We would have 
 produced a much larger number of forms, if 
 we had not interrupted progress by turning 
 the triangles produced by Fig. 86. 
 
 In the fundamental forms 70 and 82, the 
 sides touched one another. Fig. 88 shows 
 that they may touch at the corners only. In 
 this figure, the right angles are without ; in 
 89 and 90, they are within. Fig. 90 is the 
 mediation between 70 and 89, for four tablets 
 touch with their sides (70) four with the cor- 
 ners (89). No. 91 is the opposite of 90, full 
 center, (empty center.) and mediation between 
 88 and 89 — (four right angles without, as in 
 88, and four within, as in 89.) It is already 
 seen, from these indications, what a treasure 
 of forms enfolds itself here, and how, with 
 
 SIXTEEN TABLETS, 
 
 it again will be multiplied. 
 
 It would be impossible to exhaust them. 
 Least of all, should it be the task of this 
 work to do this, when it is only intended to 
 show how the productive selfoccupation of 
 the pupil can fittingly be assisted. We be- 
 lieve, besides, that we have given a .suffi- 
 cient number of ways on which fantasy may 
 travel, perfectly sure of finding constantly 
 new, beautiful, eye and taste developing for- 
 mations. We, therefore, simply add the series 
 J and K, the first of which is produced by 
 quadrupling some of the elementary forms 
 given at D, 48 to 59, and the second of which 
 indicates how new series of forms of beauty 
 may be developed from each of these forms. 
 It must be evident, even to the casual ob- 
 ser\-er, how here also the law of opposites, 
 and their junction, was obsen^ed. Opposites 
 are 92 and 93 ; mediation, 94 and 95 :' oppo- 
 sites, 96 and 97 ; mediation, 98, 99, and 100: 
 opposites, loi and 102 ; mediation, 103, etc. 
 
 WITH THIRTY-TWO TABLETS. 
 
 As heretofore, we proceed here also in the 
 same manner, by multiplying the given ele- 
 ments, or by means of further development, 
 according to the law of opposites. As an 
 
 example, we give Series L, the members of 
 which are produced by a four-fold junction 
 of the elements 68 and 69. no and iii are 
 opposites; 112 and 113 mediative forms. 
 
 WITH SIXTV-FOUR TABLETS. 
 
 Here, also, the combined activity of many 
 children will result in forms interesting to be 
 looked at, not only by little children. There 
 is another feature of this combined activity 
 not to be forgotten. The children are busy 
 obeying the same law ; the same aim unites 
 them — one helps the other. Thus the condi- 
 tions of human society — family, community, 
 states, etc., — are already here shown in their 
 effects. A system of education which, so to 
 speak, by mere play, leads the child to appre- 
 ciate those requisites, by compliance with 
 which it can successfully occupy its position 
 as man in the future, certainly deserves the 
 epithet of a natural and rational one. 
 
 Figures 114, 115, 116, are enlarged pro- 
 ductions from 96 and 97. They are planned 
 in such a way, as to admit of being continued 
 in all directions, and thus serve to carry out 
 the representation of a veiy large design. 
 
 After having acted so far, according to in- 
 dications made here, it is now advisable to 
 start from the fundamental forms presented 
 in the Fifth Gift, and to use them, with the 
 necessary modifications, in forther occupying 
 the pupils with the tablets. Fig. 117 gives 
 a model, showing how the motives of the 
 Fifth Gift can be used for this purpose. 
 
 FORMS OF KNOWLEDGE. 
 
 (plate XXII.) 
 
 By joining two, four, and eight tablets, we 
 have already become acquainted with the 
 regular figures which may be formed with 
 them, namely, triangle, quadrangle (square), 
 right angle, rhomboid, and trapezium (Plate 
 XXII., Figs. 1 18-123). 
 
 The tablets are, however, especially quali- 
 fied to bring to the observation of the child 
 different sizes in equal forms (similar figures), 
 and equal sizes in different forms. 
 
36 
 
 GUIDE TO KINDER- GARTNERS. 
 
 Figures 124, 125, and 126 show triangles 
 of wliich each is the half of the following, 
 and Nos. 129, 127, and 128, three squares 
 of that kind. Figures 1 19-123, and 129- 
 131, show the former five, the latter three 
 times the same size in different forms. 
 
 That the contemplation of these figures, 
 the occupation with them, mu'st tend to facili- 
 tate the understanding of geometrical axioms 
 in future, who can doubt? And who can 
 gainsay that mathematical instruction, by 
 means of Froebel's method, must needs be 
 facilitated, and better results obtained ? That 
 such instruction, then, will be rendered more 
 fruitful for practical life, is a fact which will 
 be obvious to all, who simply glance at our 
 figures, even without a thorough explanation. 
 They contain demonstratively the larger num- 
 ber of the axioms in elementary geometry, 
 which relate to the conditions of the plane in 
 regular figures. 
 
 For the present purpose, it is sufficient if 
 the child learns to distinguish the various kinds 
 of angles, if it knows that the right angles 
 are all equally large, the acute angles smaller, 
 and the obtuse angles larger than a right 
 angle, which the child will easily understand 
 by putting one upon another. A deeper in- 
 sight in the matter must be reserved for the 
 primary department of instruction. 
 
 C. THE EQUILATERAL TRIANGLE. 
 
 (plates XXIV. AND X.XV.) 
 
 So far the right angle has predominated in 
 the occupations with the tablets, and the 
 acute angle only appeared in subordinate 
 relations. Now it is the latter alone which 
 governs the actions of the child in producing 
 forms and figures. 
 
 The child will compare the equilateral 
 triangle, which it receives in gifts of 3, 6, 9, 
 and 12, first with the isosceles, right-angled 
 tablet already known to him. Both have three 
 sides, both three angles, but on close observa- 
 tion not only their similarities, but also their 
 dissimilarities will become apparent. The 
 three angles of the new triangle are all smaller 
 
 than a right angle, are acute angles and the 
 three sides are just alike,- hence the name — 
 equilateral — meaning "■ eqtcal sided" triangle. 
 
 Joining two of these equilateral tablets the 
 child will discover that it cannot form any 
 of the regular figures previously produced. 
 No triangle, no square, no right angle, no 
 rhomboid, can be produced, but only a form 
 similar to the latter, a rhomboid with four 
 equal sides. To undertake to produce forms 
 of life with these tablets would prove very 
 unsatisfactory. Of particular interest, how- 
 ever, because presenting entirely new forma- 
 tions, are 
 
 THE FORMS OF BEAUTY. 
 The child first receives three tablets and 
 will find the various positions of the same 
 towards one another according to the law of 
 opposites and their combination. Vide Plate 
 XXIV., 1-9. 
 
 SIX TABLETS. 
 
 The child will unite his tablets around one 
 common center (Fig. 10), form the opposite 
 (Fig 11), and then arrive at the forms of me- 
 diation 12, 13, 14, and 15, or it unites three 
 elementary forms each composed of two tab- 
 lets as done in 16, and forms the opposite 
 17 and the mediations 18 and 19, or it starts 
 from No. 10, turning first i, then 2, then 3 
 tablets, outwardly. By turning one tablet, 
 21 and 22, by turning two tablets, 23, 24, 25, 
 26, 27, 28 and 29, are produced from No. 20. 
 This may be continued with 3, 4, and 5 tab- 
 lets. All forms thus received give us ele- 
 mentary forms which may be employed as 
 soon as a larger number of tablets are to be 
 used. ^ 
 
 NINE TABLETS. 
 
 As with the right-angled triangle, small 
 groups of tablets were combined to form 
 larger figures, so we also do here. The ele- 
 mentary forms under A give us in threefold 
 combination the series of forms under C, 30 — 
 40, which in course of the occupation may be 
 multiplied at will. 
 
GUIDE TO KINDER-GARTNERS. 
 
 37 
 
 TWELVK TABLETS. 
 (PLATE XXV.) 
 
 Half of the tablets are painted brown, the 
 balance l)lue By this difterence in color, op- 
 positis are rendered more conspicuous, and 
 these twelve tablets thus aftbrd a splendid 
 opportunity for illustrating more forcibly the 
 law of opposites and their combination. 
 Plate XXV. shows how, by combination of 
 opposites in the forms a and b, every time 
 the star c is produced. Entirely new series of 
 forms may be produced by employing a larger 
 number of tablets, i8, 24 or 36. We are, 
 however, obliged to leave these representa- 
 tions to the combined inventive powers of 
 • teacher and pupil. 
 
 FORMS OK RXOWl.EDGE. 
 
 It has been mentioned before, that the 
 previously introduced regular mathematical 
 tlgures do not appear here as a whole. How- 
 ever, a triangle can be represented by four or 
 nine tablets, a rhomboid by four, six or eight 
 tablets, a trapezium l)y three, and manifold 
 instructive remarks can be made and experi- 
 ences gathered in the construction of these 
 figures. But above all, it is the rhombus 
 and hexagon, with which the pupil is to be 
 made acquainted here. The child unites two 
 triangles by joining side to side, and thus 
 produces a rhombus. 
 
 The child compares the sides — are they 
 alike ? What is their direction ? Are they 
 parallel ? Two and two have the same di- 
 rection, and are therefore parallel. 
 
 The child now examines the angles and 
 finds that two and two are of equal size. 
 'I'hey are not right angles. Triangles, smaller 
 than right angles, he knows, are called acute 
 angles, and he hears now that the larger 
 ones are called olMuse angles. The teacher 
 may remark that the latter are twice the size 
 of the former ones. By these remarks the 
 pupil will gradually receive a correct idea of 
 the rlionibus and of the qualities by which it 
 is distinguished from the quadrangle, right 
 angle, trapezium and rhomboid. 
 6 
 
 In the same manner, the hexagon gives 
 occasion for interesting and instructive ques- 
 tions and answers. How many sides has it ? 
 How many are parallel ? How many angles 
 does it contain ? What kind of angles are 
 the)- ? How large are they as compared with 
 the angles of the equal sided triangle.' Twice 
 as large. 
 
 The power of observation and the reason- 
 ing faculties are constantly developed by such 
 conversation, and the results of such exer- 
 cises are of more importance than all the 
 knowledge that may be acquired in the mean- 
 time. 
 
 The greater part of this occupation, how- 
 ever, is not within the Kinder-Garten proper, 
 but belongs to the realm of the Primary' 
 School Department. If thej' are introduced 
 in the former, they are intended only to swell 
 the sum of general experience in regard to 
 the qualities of things, whereas in the latter, 
 they serve as a foundation for real knowledge 
 in the department of mathematics. 
 
 D. THE OBTUSE-ANGLED TRIANGLE WITH 
 
 TWO SIDE.S ALIKE. 
 
 (plates xxvl and xxvil) 
 
 The child receives a box with sixty-four 
 obtuse-angled tablets. It examines one of 
 them and compares it with the right-angled 
 triangle, with two sides alike. It has two 
 sides alike, has also two acute angles, but the 
 third angle is larger than the right angle ; it 
 is an obtuse angle, and the tablet is, there- 
 fore, an obtuse-angled triangle with two sides 
 alike. 
 
 The pupil then unites two and two tablets 
 by joining their sides, corners, sides and 
 corners, and vice versa, as shown in Figs. 1-8, 
 on Plate XXVI. 
 
 The next preliminary exercise, is the com- 
 bination, by fours, of elementary forms thus 
 produced. Peculiarly beautiful, mosaic-like 
 forms of beauty result from this process. 
 The Pigs. 9-15 aftbrd examples which were 
 produced by combination of two opposites, 
 a and b, or by mediative forms c and d. In 
 
38 
 
 GUIDE TO KINDER-GARTNERS. 
 
 Figs. 16-22 we have finally some few sam- 
 ples of forms of life. 
 
 The forms of knowledge which may be 
 produced, afford opportunity to repeat what 
 has been taught and learned previously about 
 proportion of form and size. In the Primary 
 School the geometrical proportions are further 
 introduced, by which irjeans the knowledge 
 of the pupils, in regard to angles, as to the 
 position they occupy in the triangle, can be 
 successfully developed by practical observa- 
 tion, without the necessity of ever dealing in 
 mere abstractions. 
 
 E. THE RIGHT-ANGLED TRIANGLE WITH 
 NO EQUAL SIDES. 
 
 (PLATES XXVIII. AND XXIX.) 
 
 The little box with fifty-six tablets of the 
 above description, each of which is half the 
 size of the obtuse-angled triangle, enables the 
 child to represent a goodly number of forms 
 of life, as shown on Plate XXIX. 
 
 In producing them, sufficient opportunities 
 will present themselves, to let the child find out 
 the qualities of the new occupation material. 
 
 A comparison with the right angled triangle 
 with two equal sides will facilitate the matter 
 greatly. 
 
 On the whole, howe^■er, the process of de- 
 velopment may be pursued, as repeatedly in- 
 dicated on previous occasions. 
 
 The variety of the forms of beaut)' to be laid 
 with these tablets, is especially founded on 
 their combination in twos. Plate XXVIII., 
 Figs. 1-6, shows the forms produced by join- 
 ing equal sides. 
 
 In similar manner, the child has to find out 
 the forms which will be the result of joining 
 unlike sides, like corners, unlike corners, and 
 finally, corners and sides. 
 
 By a fourfold combination of such element- 
 ary forms the child receives the material, 
 (Figs. 7-18,) to produce a large number of 
 forms of beauty similar to those given under 
 19-22. 
 
 For the purpose, also, of presenting to the 
 child's observation, in a new shape, propor- 
 tions of form and size, in the production of 
 forms of knowledge, these tablets are very 
 serviceable. 
 
 Like the previous tablets, these also, and a 
 following set of similar tablets, are used in 
 the Primary Department for enlivening the 
 instruction in Geometry. It is believed that 
 nothing has ever been invented to so facilitate, 
 and render interesting to teacher and pupil, 
 the instruction in this so important branch of 
 education as the tablets forming the Seventh 
 Gift of Froebel's Occupation Material, the use 
 of which is commenced with the children when 
 they have entered the second year of their 
 Kinder-Garten discipline. 
 
THE EIGHTH GIFT. 
 
 STAFFS FOR LAYING OF FIGURES. 
 
 (PLATES XXX. TO XXXIII.) 
 
 As the tablets of the Seventh Gift are 
 nothing but an embodiment of the planes sur- 
 rounding or limiting the cube, and as these 
 planes, limits of the cube, are nothing but 
 the representations of the extension in length, 
 breadth, and height, already contained in the 
 sphere and ball, so also the staffs are derived 
 from the cube, forming as they do, and here 
 bodily representing its edges. But they are 
 also contained in the tablets, because the 
 plane is thought of, as consisting of a con- 
 tinued or repeated line, and this may be 
 illustrated by placing a sufficient number of 
 one inch long staffs side by side, and close 
 together, until a square is formed 
 
 The staffs lead us another step farther, 
 from the material, bodily, toward the realm 
 of abstractions. 
 
 By means of the tablets, we were enabled 
 to produce flat images of bodies ; the slats, 
 which, as previously mentioned, form a tran- 
 sition from plane to line, gave, it is true, the 
 outlines of forms, but these outlines still re- 
 tained a certain degree of the plane about 
 them ; in the staffs, however, we obtain the 
 material to draw the outlines of objects, by 
 bodily lines, as perfectly as it can possibly 
 be done. 
 
 The laying of staffs is a favorite occupa- 
 tion with all children. Their fantasy sees in 
 them the most different objects, — stick, yard 
 measure, candle ; in short, they are to them 
 representatives of every thing straight. 
 
 Our staffs are of the thickness of a line 
 (one twelfth of an inch), and are cut in vari- 
 7 
 
 ous lengths. The child, holding the staff in 
 hand, is asked : What do you hold in your 
 hand.? How do you hold it? Perpendicu- 
 larly. Can you hold it in any other way.' 
 Yes ! I can hold it horizontally. Still in 
 another way? Slanting from left above, to 
 right below, or from right above to left 
 below. 
 
 Lay your staff upon the table. How does 
 it lie ? In what other direction can you place 
 it? (Plate XXX. A.) 
 
 The child receives a second staff. How 
 many staffs have you now ? Now try to form 
 something. The child lays a standing cross, 
 (Fig. 4.) You certainly can lay many other 
 and more beautiful things ; but let us see 
 what else we may produce of this cross, by 
 moving the horizontal staff, by half its lengfth, 
 (Fig. B. 4 to 14.) Starting from a lying cross, 
 (C. 15 — 23) or from a pair of open tongs, 
 (where two acute and two obtuse angles are 
 formed by the crossing staffs,) and proceeding 
 similarly as w-ith B, we will produce all posi- 
 tions which two staffs can occupy, relative to 
 one another, except the parallel, and this will 
 give ample opportunit}- to refresh, and more 
 deeply impress upon the pupil's mind, all that 
 has been introduced so far, concerning per- 
 pendicular, horizontal, and oblique lines, and 
 of right, acute and obtuse angles. With two 
 staffs, we can also form little figures, which 
 show some slight resemblance with things 
 around us. By them we enliven the power of 
 recollection and imagination of the child, ex- 
 ercise his abilit}' of comparison, increase his 
 
40 
 
 GUIDE TO KINDER-GARTNERS. 
 
 treasure of ideas, and develop, in all these 
 his power of perception and conception — the 
 most indispensable requisites for disciplining 
 the mind. 
 
 Our plates give representations of the fol- 
 lowing objects : 
 
 WITH TWO STAFFS. 
 Fig. 24. A Playing Table. 
 Fig. 25. A Weather-vane. 
 Fig. 26. A Pickax. 
 
 Fig. 27. An Angle measure. (Carpenter's 
 square.) 
 
 Fig. 28. A Candle stick. 
 Fig. 29. Two Candles. 
 Fig. 30. Rails. 
 Fig. 31. Roof 
 
 WITH THREE STAFFS. 
 Fig. 32 A Kitchen Table. 
 Fig. 33. A Garden Rake. 
 
 Fig. 34 
 
 A Flail. 
 
 WITH SEVEN STAFFS. 
 
 Fig. 35- 
 
 An Umbrella. 
 
 Fig. 74. A Window. 
 
 Fig. 36. 
 
 A Hay Fork. 
 
 Fig. 75. A Stretcher. 
 
 Fig. 37- 
 
 A Small Flag. 
 
 Fig. 76. A Dwelling-house. 
 
 Fig. 38. 
 
 A Steamer. 
 
 Fig. 77. Steeple with Lightning-rod. 
 
 Fig. 39- 
 
 A Whorl. 
 
 Fig. 78. A Balance. 
 
 Fig. 40. 
 
 A Star. 
 
 Fig. 79. Piano-forte. 
 
 Fig. 80. A Bridge with Three Spans 
 
 
 WITH FOUR STAFFS. 
 
 Fig. 81. An Inn Sign. 
 
 Fig. 41- 
 
 A Small Looking-glass. 
 
 Fig. 82. Crucifix and Two Candles. 
 
 Fig. 42. 
 
 A Wooden Chair. 
 
 Fig. 83. Tombstone and Cross. 
 
 Fig. 43- 
 
 A Wash-bench. 
 
 Fig. 84. Rail Fence. 
 
 Fig. 44- 
 
 Kitchen Table with Candle. 
 
 Fig. 85. Garret Window. 
 
 Fig. 45- 
 
 A Crib. 
 
 Fig. 86. Flower Spade. 
 
 Fig. 46. 
 
 A Kennel. 
 
 Fig. 87. A Star Flower. 
 
 Fig. 47- 
 
 Sugar-loaf. 
 
 
 Fig. 48. 
 
 Flower pot. 
 
 WITH EIGHT STAFFS. 
 
 Fig. 49- 
 
 . Signal-post. 
 
 Fig. 88. Book-shelves. 
 
 Fig. 5°- 
 
 Flower-stand. 
 
 Fig. 89. Church, with Steeple. 
 
 Fig. 51- 
 
 Crucifix. 
 
 Fig. 90. Tombstone and Cross. 
 
 Fig 52- 
 
 A Grate. 
 
 Fig. 91. Gas Lantern. 
 Fig. 92. Windmill. 
 
 
 WITH FIVE STAFFS. 
 
 Fig. 93. A Tower. 
 
 Fig. S3- 
 
 Signal Flag of R. R. Guard. 
 
 Fig. 94. An Umbrella. 
 
 Fig. 54. 
 
 Chest of Drawers. 
 
 Fig. 95. A Carrot. 
 
 Fig- 55- 
 
 A Cottage. 
 
 Fig. 96. A Flower-pot. 
 
 Fig. 56 
 
 A Steeple. 
 
 Fig. 57- 
 
 A Funnel. 
 
 Fig. 58. 
 
 A Beer Bottle. 
 
 Fig. 59. 
 
 A Bath Tub. 
 
 Fig. 60. 
 
 A (broken) Plate. 
 
 Fig. 61. 
 
 A Roof 
 
 Fig. 62. 
 
 A Hat. 
 
 Fig. 63. 
 
 A Chair. 
 
 Fig. 64. 
 
 A Lamp Shade. 
 
 Fig. 65. 
 
 A Wine-glass. 
 
 Fig. 66. 
 
 A Grate. 
 
 WITH SIX STAFFS. 
 Fig. 67. A Large Frame. 
 Fig. 68. A Flag. 
 Fig. 69. A Barn. 
 Fig. 70. A Boat. 
 Fig. 71. A Reel. 
 Fig. 72. A Small Tree. 
 Fig 73. A Round Table. 
 
GUIDE TO KINDER-GARTNERS. 
 
 Fig. 97. A large Wash tub. 
 Fig. 98. A large Rail Fence. 
 Fig. 99. A large Kitchen Table. 
 Fig 100. A Shoe. 
 Fig. 1 01. A Butterfly. 
 Fig. 102. A Kite. 
 
 WITH NINE STAFFS. 
 
 Fig. 103. Church with Two Steeples. 
 
 Fig. 104. Dwelling-house. 
 
 Fig. 105. Coffee-mill. 
 
 Fig. 106. Kitchen Lamp. 
 
 Fig. io7. Sail-boat. 
 
 Fig. loS. Balance. 
 
 
 WITH TEN STAFFS. 
 
 Fig. 
 
 109. A Tower. 
 
 Fig. 
 
 no. A Drum. 
 
 Fig. 
 
 III. Grave-yard Wall. 
 
 Fig. 
 
 112. A Hall. 
 
 Fig. 
 
 113. A Flowerpot. 
 
 Fig. 
 
 114. A Street Lamp. 
 
 Fig. 
 
 115. A Satchel. 
 
 Fig. 
 
 116. A Double Frame. 
 
 Fig. 
 
 117. A Bedstead. 
 
 Fig. 
 
 118. A row of Barns. 
 
 Fig. 
 
 119. A Flag. 
 
 
 WITH ELEVEN STAFFS. 
 
 Fig. 
 
 1 20. A Kitchen Lamp. 
 
 Fig. 
 
 121. A Pigeon-house. 
 
 Fig. 
 
 122. A Farm-house. 
 
 Fig. 
 
 123. A Sail-boat. 
 
 Fig. 
 
 124. A Student's Lamp. 
 
 
 WITH TWELVE STAFFS. 
 
 Fig. 
 
 125. A Church. 
 
 Fig. 
 
 126. A Window. 
 
 Fig. 
 
 127. Chair and Table. 
 
 Fig. 
 
 128. A Well with Sweep. 
 
 These exercises are to be continued with a 
 larger number of staffs. The hints given 
 above, will enable the teacher to conduct the 
 laying of staffs in a manner interesting, as well 
 as useful, for her pupils. 
 
 It is advisable to guide the activity of the 
 
 child occasionally in another direction. The 
 pupils may all be called upon to lay tables, 
 which can be produced from two to ten staffs, or 
 houses which can be laid with eighteen staffs. 
 
 Another change in this occupation can be 
 introduced by employing two, four, or eight 
 times, divided staffs. It is obvious that, in 
 this manner, the figures may often assume a 
 greater similarity and better proportions than 
 is possible if only staffs of the same length are 
 employed. 
 
 If a staff is not entirely broken through, 
 but only bent with a break on one side, an 
 angle is produced. If a staff forms several 
 such angles, it can be used to represent a 
 curved or rounded line, and by so doing a new 
 feature is introduced to the class. 
 
 Staffs are also employed for representing 
 forms of beauty. The previous, or simulta- 
 neous occupation with the building blocks, 
 and tablets, will assist the child in producing 
 the same in great variety. Figures 121 — 124 
 on Plate XXXIII. belong to this class of repre- 
 'sentations. 
 
 Combination of the occupation material of 
 several, or all children taking part in the ex- 
 ercises, will lead to the production of larger 
 forms of life, or beauty, which in the Primary 
 Department, can even be extended to repre- 
 senting whole landscapes, in which the mate- 
 rial is augmented by the introduction of saw- 
 dust to represent foliage, grass, land, moss, 
 etc. Plate XXXIII. gives, un(3er Fig. 120, a 
 specimen of such a production-^-on a very re- 
 duced scale. 
 
 By means of combination, the children 
 often produce forms which afford them great 
 pleasure, and repay them for the careful per- 
 severance and skill employed. .They often 
 express the wish that they might be able to 
 show the production to father, or mother, or 
 sister, or friend. But this they cannot do, as 
 the staffs will separate when taken up. 
 
 We should assist the little ones in carrying 
 out their desire, of giving pleasure to others, 
 by showing to, or presenting them with the 
 result of their own industry, in portable form. 
 
42 
 
 GUIDE TO KINDER-GARTNERS. 
 
 By wetting the ends of the staffs with mucil- 
 age, or binding them together with needle 
 and thread, or placing them on substantial 
 paper, we can grant their desire, and make 
 them happy, and be sure of their thanks for 
 our efforts. 
 
 We employ the same means of rendering 
 permanent the production of staff-laying in 
 our instruction in reading, where letters are 
 fastened to paper by mucilage, thus impress- 
 ing upon the child's mind more lastingly, the 
 visible signs of the sounds he has learned. 
 
 But we have still another means of render- 
 ing these representations permanent, and it is 
 by drawing, which, on its own account, is to 
 be practiced in the most elementary manner. 
 We begin the drawing, as will hereafter be 
 shown, as a special branch of occupation, as 
 soon as the child has reached its third or 
 fourth year. 
 
 The child is provided with a slate, upon 
 whose surface, a net-work of horizontal and 
 perpendicular lines is drawn. Instead of lay- 
 ing the staff upon the table, the child places 
 it upon the slate. Taking the staff from its 
 place, he draws with the slate pencil, in its 
 stead, a line as long as the staff, in the same 
 direction. He draws the perpendicular staff. 
 The horizontal, slantingly laid staff, is drawn 
 in all its variations in like manner, perpendic- 
 ular, and horizontal ; perpendicular and ob- 
 lique, or horizontal and oblique staffs are 
 brought in contact with one another, and 
 these connections reproduced by drawing. 
 
 The method of laying staffs is in general 
 the same, applied for drawing, the latter, how- 
 ever, progresses less rapidly. It is advisable 
 to combine staffs in regular figures, triangles 
 and squares, and to find out in a small num- 
 ber of such figures all possible combinations 
 according to the law of opposites. Plates 
 XXIV. and XXV. will furnish material for this 
 purpose. 
 
 All these occupations depend on the larger 
 or smaller number of staffs employed ; they 
 therefore afford means for increasing and 
 strengthening the knowledge of the child. 
 
 The pupil, however, is much more decidedly 
 introduced into the elements of ciphering, 
 when the staffs are placed into his hands for 
 this specific purpose. We do not hesitate to 
 make the assertion that there is no material 
 better fitted to teach the rudiments in figures, 
 as also the more advanced steps in arithme- 
 tic, than Froebel's staffs, and that by their in- 
 troduction, all other material is rendered use- 
 less. A few packages of the staffs in the 
 hands of the pupil is all that is needed in the 
 Kinder Garten proper, and the following De- 
 partment of the Primary. 
 
 The children receive a package with ten 
 staffs each. Take one staff and lay it per- 
 pendicularly on the table. Lay another at 
 the side of it. How many staffs are now be- 
 fore you ? Twice one makes two. 
 
 Lay still another staff upon the table. 
 How many are there now? One and one 
 and one — two and one are three. 
 
 Still another, etc., etc., until all ten staffs 
 are placed in a similar manner upon the 
 table. Now take away one staff. How many 
 remain ? Ten less one leaves nine. Take 
 away another staff from these nine. How 
 many are left.' Nine less one leaves eight 
 
 Take another; this leaves ? seven, etc., 
 
 etc., until all the staffs are taken one by one 
 from the table, and are in the child's hand 
 again. Take two staffs and lay them upon 
 the table, and place two others at some dis- 
 tance from them. (|| ||) How many are now 
 on the table ? Two and two are four. Lay 
 two more staffs beside these four staffs. How 
 many are there now ? Four and two are six. 
 Two more. How many are there now ? Six 
 and two are eight. And still another two. 
 How many now ? Eight and two are ten. 
 
 The child has learned to add staffs by twos. 
 If we do the opposite, he will also learn to 
 subtract by twos. In similar manner we pro- 
 ceed with three, four, and_;?z.'^. After that, we 
 alternate, with addition and subtraction For 
 instance, we lay three times two staffs upon the 
 table and take away twice two, adding again 
 four times two. Finally we give up the 
 
GUIDE TO KINDER- GARTNERS. 
 
 43 
 
 equality of the number and alternate, by ad- 
 ding different numbers. We lay upon the 
 table 2 and 3 staffs=5, adding 2=7 adding 
 3=10. This affords opportunity to intro- 
 duce 6 and 9, as a whole, more frequently 
 than was the case in previous exercises. In 
 subtraction we observe the same method, and 
 introduce exercises in which subtraction and 
 addition alternate with unequal numbers. 
 Lay 6 staffs upon the table, take 2 away, add 
 4, take away i, add 3, and ask the child how 
 many staffs are on the table, after each of 
 these operations. 
 
 In like manner, as the child learned the 
 figures from one to ten, and added and sub- 
 tracted with them as far as the number of 10 
 staffs admitted, it will now learn to use the 
 lo's up to 100. Packages of 10 staffs are 
 distributed. It treats each package as it did 
 before the single staff. One is laid upon the 
 table, and the child says, "Once ten ;" add a 
 second, " Twice ten ; " a third, " Three times 
 ten," etc. Subsequently it is told, that it is 
 not customary to say twice, or two times ten, 
 but twenty; not three times ten, but thirty, 
 etc. This experience will take root so much 
 the sooner, in his memory, and become 
 knowledge, as all this is the result of his own 
 activity. 
 
 As soon as the child has acquired sufficient 
 ability in adding and subtracting by tens, the 
 combination of units and tens is introduced. 
 
 The pupil receives two packages of ten 
 staffs — places one of them upon the table, 
 opens the second and adds its staffs one by 
 one to the ten contained in the whole pack- 
 age. He learns 10 and i = ii, 10 and 2=12, 
 10 and 3 = 13, until 10 and 10 = 20 staffs. 
 Gathering the 10 loose staffs, the child re- 
 ceives another package and places it beside 
 the first whole package. 10 and 10=20 
 staffs. Then he adds one of the loose staffs, 
 and says 20 and 1=21,20 and 2 = 22, etc. 
 Another package of 10 brings the number to 
 31, etc., etc., up to 91 staffs. In this manner 
 he learns 22, 32, up to 92, 23 to 93, and 100, 
 and to add and subtract within this limit. 
 
 To be taught addition and subtraction in 
 this manner, is to acquire sound knowledge, 
 founded on self-activity and experience, and 
 is far superior to any kind of mind-killing 
 memorizing usually employed in this connec- 
 tion. 
 
 If addition and subtraction are each other's 
 opposites, so addition and multiplication on 
 the one hand, and subtraction and division 
 on the other, are oppositionally equal, or, 
 rather, multiplication and division are short- 
 ened addition and subtraction. 
 
 In addition, when using equal numbers of 
 staffs, the child finds that by adding 2 and 2 
 and 2 and 2 staffs it receives 8 staffs, and is 
 told that this may also be expressed by saying 
 4 times 2 staffs are 8 staffs. It will be easy 
 to see how to proceed with division, after the 
 hints given above. 
 
 It has been previously mentioned that for 
 the representation of forms of life and beauty, 
 the staffs frequently need to be broken. This 
 provides material for teaching fractions, in the 
 meantime. The child learns by observtion 
 i staff, i, -J, i, etc. The proportion of the 
 part or of several equal parts to the whole, 
 becomes clear to him, and finally it learns to 
 add and subtract equal fractions, in element- 
 ary form, in the same rational manner. 
 
 Let none of our readers misunderstand us 
 as intimating that all this should be accom- 
 plished in the Kinder-Garten proper. 
 
 Enough has been accomplished if the child 
 in the Kinder Garten, by means of staffs and 
 other material of occupation, has been en- 
 abled to have a clear understanding of figures 
 in general. 
 
 This will be the basis for further develop- 
 ment in addition, subtraction, multiplication 
 and division in the Primaiy Department. 
 
 It now remains to add the necessary advice 
 in regard to the introduction and representa- 
 tion with staffs of the nuvierah. In order to 
 make the children understand what nnmerals 
 are, use the blackboard and show them that 
 if we wish to mark down how many staffs, 
 blocks, or other things each of the children 
 
44 ■ 
 
 GUIDE TO KINDER-GARTNERS. 
 
 have, we might make one Hne for each staff, 
 block, etc. Write then one small perpendicu- 
 lar line on the blackboard, saying in writing, 
 Charles has one staff; making hiw lines below 
 the first, continue by saying, Emma has two 
 blocks; again, making three lines, Ernest has 
 three rubber balls, and so on until you have 
 written ten lines, always giving the name of 
 the child and stating how many objects it has. 
 Then write opposite each row of lines to the 
 right, the Arabic figure expressing the number 
 of lines, and remark that instead of using so 
 many lines, we can also use these figures, 
 which we call numerals. Then represent with 
 the little staff these Arabic figures, some of 
 which require the bending of some of the 
 staffs, on account of the curved lines. 
 
 After the children have learned that the 
 figures which we use for marking down the 
 number of things are called numerals, exer- 
 cises of the following character may be intro- 
 duced : 
 
 How many hands has each of you .' Two. 
 The numeral 2 is written on the board. How 
 many fingers on each hand ? Five. This is 
 written also on the board — 5. How many 
 walls has this room ? Four. Write this figure 
 also on the board. How many days in the 
 week are the children in the Kinder-Garten ? 
 Six days. The 6 is also written on the board. 
 
 Then repeat, and let the children repeat 
 after you, as an exercise in speaking, and at 
 the same time, for the purpose of recollecting 
 the numerals : 
 
 Each child has 2 hands, on each hand are 
 5 fingers ; this room has 4 walls, — always 
 emphasizing the numerals, and pointing to 
 them when they are named. 
 
 The children may then count the objects in 
 the room, or elsewhere, and then lay, with 
 their staffs, the numerals expressing the num- 
 ber they have found, speaking in tlie mean- 
 time, a sentence asserting the fact which they 
 have stated. 
 
 After having introduced the numerals in 
 this manner, the teacher, on some following 
 day, may proceed to reading exercises. 
 
 The second part of this Guide contains 
 systematically arranged material for instruc- 
 tion in reading, according to the phonetic 
 method. 
 
 Suffice it to say, tliat it is begun in the 
 same manner in which numerals were intro- 
 duced. As by means of numerals, I could 
 mark on the blackboard the number of things, 
 so I can also mark on the board the names of 
 things, their qualities and actions. In doing 
 this I write words, and zcords consist of let 
 ters. Besides the words expressing names of 
 things, their qualities and actions, which are 
 the most important words in every language, 
 there are other words which are used for 
 other purposes. Such words are, for example, 
 no, now, never. Should I ask you, is any one 
 of you asleep, what would you answer ? " No, 
 sir. We are all awake." I will write the lit- 
 tle word " no," on the blackboard, because it 
 is the most important word in your answer. 
 There it stands, " no." And now I will ask you : 
 "Have you ever been in a Kinder-Garten?" 
 " Yes, sir, we are now in a Kinder-Garten 
 school." I will write on the board the little 
 wox^," now." There it stands, " w^w ;" and 
 another question I will now ask you : " Should 
 we ever kill an animal for the mere pleasure 
 of hurting it ? " " No, sir, «67rr." I will also 
 write the word " nex'er" on the board. There 
 it is, '■'■never." I will now pronounce these 
 three words for you, and each of you will 
 repeat them in the same manner in which I 
 do. N o! N ow! N ever! Chil- 
 dren, in repeating, always dwell on the n 
 sound longer than on any other part of the 
 word. They are then led to observe the 
 similarity of sound in pronouncing the three 
 words, then to observe the similarity of the 
 first letter in all of them, and finally the dis- 
 similarity of the remaining part of the words 
 in sound, and its representations — the letters. 
 
 I will now take away these words from 
 the blackboard, and write something else upon 
 it. I again write the " n" and the children 
 will soon recognize it as the letter previously 
 shown. 
 
GUIDE TO KINDER-GARTNERS. 
 
 45 
 
 For the continuation of instruction in read- 
 ing, we refer tlie reader to the second part of 
 the " Guide," where all necessary information 
 on this important branch of instruction will 
 be found. 
 
 As the occupation with laying staffs, is one 
 
 of the earliest in the Kinder Garten, and is em- 
 ployed in teaching numerals, and reading and 
 writing, and drawing also, it is evident how 
 important a material of occupation was sup- 
 plied by Froebel, in introducing the staffs as 
 one of his Kinder-Garten Gifts. 
 
 THE NINTH GIFT. 
 
 WHOLE AND HALF RINGS FOR LAYING FIGURES. 
 
 Immediately connected with the staffs, or 
 straight lines, Froebel gives the representa- 
 tives of the rounded, curved lines, in a box 
 containing twenty-four whole and fort}'-eight 
 half circles of two different sizes made of 
 wire. We have heretofore introduced the 
 curved line by bending the staff; this, how- 
 ever, was a rather imperfect representation. 
 The rings now introduced supply the means 
 of representing a curved line perfectly, be- 
 sides enabling us by their different sizes to 
 show " the one within another " more plainly 
 than it could be done with the staffs, as the 
 above, upon, below, aside of each other, etc., could 
 well be represented, but not the " within " in 
 a perfectly clear manner. 
 
 This Gift is introduced in the same way as 
 all other previous Gifts were introduced, and 
 the rules by which this occupation is carried 
 on must be clear to every one who has fol- 
 lowed us in our " Guide " to this point. 
 
 The child receives one whole ring and two 
 half rings of the larger size. Looking at the 
 whole ring the children obser\'e that there is 
 neither beginning nor end in the ring — that it 
 represents the circle, in which there is neither 
 beginning nor end. With the half ring, they 
 have two ends ; half rings, like half circles 
 and all other parts of the circle or curved 
 lines, have two ends. Two of the half rings 
 
 form one whole ring or circle, and the chil- 
 dren are asked to show this by experiment, 
 (Fig. I, Plate XXXIV). Various observations 
 can be made by the children, accompanied by 
 remarks on the part of the teacher. When- 
 ever the child combined two cubes, two tablets, 
 staffs or slats with one another, in all cases 
 where corners and angles and ends were con- 
 cerned in this combination, corners and angles 
 were again produced. The two half rings or 
 half circles, however, do not form any angles. 
 Neither could closed space be produced by 
 two bodies, planes, nor lines ! — the two half 
 circles, however, close tightly up to each 
 other, so that no opening remains. 
 
 The child now places the two half circles 
 in opposite directions, (Fig. 2.) Before the 
 ends touched one another, now the middle of 
 the half circles ; previously a closed space 
 was formed, now both half circles are open, 
 and where they touch one another, angles 
 appear. 
 
 Mediation is formed in Fig. 3, where both 
 half circles touch each other at one end and 
 remain open, or, as indicated by the dotted 
 line, join at end and middle, thereby enclosing 
 a small plane and forming angles in the mean- 
 time. 
 
 Two more half circles are presented. The 
 child forms Fig. 4, and develops by moving 
 
46 
 
 GUIDE TO KINDER-GARTNERS. 
 
 the half circles in the direction from without, 
 to within Fig 5, 6, 7, and 8. 
 
 The number of circles is increased. Fig. 
 9, 10, and II show some forms built of 8 half 
 circles. 
 
 All these forms are, owing to the nature of 
 the circular line, forms of beauty, or beauti- 
 ful forms of life, and, therefore, the occupa- 
 tion with these rings, is of such importance. 
 The child produces forms of beauty with 
 other material, it is true, but the curved line 
 suggests to him in a higher degree than any- 
 thing else, ideas of the beautiful, and the 
 simplest combinations of a small number of 
 half and whole circles, also bear in themselves 
 the stamps of beauty. 
 
 If the fact cannot be refuted, that merely 
 looking at the beautiful, favorably impresses 
 the mind of the grown person, in regard to 
 direction of its development, enabling him to 
 more fully appreciate the good, and true, and 
 noble, and sublime, this influence, upon the 
 tender and pliable soul of the child, must 
 needs be greater, and more lasting. Without 
 believing in the doctrine of two inimical 
 natures in man, said to be in constant con- 
 flict with each other, we do believe that the 
 
 talents and disposition in human nature are 
 subject to the possibility of being developed 
 in two opposite directions. It is this possi- 
 bility, which conditions the necessity of edu- 
 cation, the necessity of employing every 
 means to give the dormant inclinations and 
 tastes in the child, a direction toward the 
 true, and good, and beautiful, — in one word, 
 toward the ideal. Among these means, stands 
 pre-eminently a rational and timely develop- 
 ment of the sense of beauty, upon which 
 Froebel lays so much stress. 
 
 Showing the young child objects of art which 
 are far beyond the sphere of its appreciation 
 however, will assist this development, much 
 less than to carefully guard that its surround 
 ings contain, and show the fundamental req 
 uisites of beauty, viz. : order, cleanliness, sim 
 plicity, and harmony of form, and giving as^ 
 sistance to the child in the active representa 
 tion to the beautiful in a manner adapted to 
 the state of development in the child himself. 
 
 Like forms laid with staffs, those repre 
 sented with rings and half rings also, are 
 imitated by the children by drawing them on 
 slate or paper. 
 
 THE TENTH GIFT. 
 
 THE MATERIAL FOR DRAWING. 
 
 (PLATES XXXV. TO 
 
 •) - 
 
 One of the earliest occupations of the child 
 should be methodical drawing. Froebel's 
 opinion and conviction on this subject, de- 
 viates from those of other educators, as much 
 as in other respects. Froebel, however, does 
 not advocate drawing, as it is usually prac- 
 ticed, which on the whole, is nothing else but 
 a more or less thoughtless mechanical copy- 
 
 ing. The method advanced by Froebel, is in- 
 vented by him, and perfected in accordance 
 with his general educational principles. 
 
 The pedagogical effect of the customary 
 method of instruction in drawing, rests in 
 many cases simply in the amount of trouble 
 caused the pupil in surmounting technical 
 difficulties. Just for that reason it should be 
 
GUIDE TO KIXDER-GARTNERS. 
 
 47 
 
 abandoned entirely for the youngest pupils, 
 for the difficukics in many cases are too great 
 for the child to cope with. It is a work of 
 Sisyphus, labor without result, naturally tend- 
 ing to extirpate the pleasure of the child in its 
 occupation, and the unavoidable consequence 
 is that the majority of people will never reach 
 the point where they can enjoy the fruits of 
 their endeavors. 
 
 If we acknowledge that Froebel's educa- 
 tional principles are correct, namely, that all 
 manifestations of the child's life are manifes- 
 tations of an innate instinctive desire for 
 development, and therefore should be fos. 
 tered and developed by a rational education, 
 in accordance with the laws of nature. Draw- 
 ing should be commenced with the third year; 
 nay, its preparatory principles should be intro- 
 duced at a still earlier period. 
 
 With all the gifts, hitherto introduced, the 
 children were able to study and represent 
 forms and figures. Thus they have been 
 occupied, as it were, in drawing with bodies. 
 This developed their fantasy, and taste, giving 
 them in the meantime correct ideas of the 
 solid, plane, and the embodied line. 
 
 A desire soon awakes in the child, to rep- 
 resent by drawing these lines and planes, 
 these forms and objects. He is desirous of 
 representation when he requests the mother 
 to tell him a story, explain a picture. He is 
 occupied in representation when breathing 
 against the window-pane, and scrawling on it 
 with its finger, or when trying to make figures 
 in the sand with a little stick. Each child is 
 delighted to show what it can make, and 
 should be assisted in every way to regulate 
 this desire. 
 
 Drawing not only develops the power of 
 representing things the mind has perceived, 
 but affords the best means for testing how far 
 they have been perceived correctly. 
 
 It was Froebel's task to invent a method 
 adapted to the tender age of the child, and 
 its slight dexterity of hand, and in the mean- 
 time to satisfy the claim of all his occupa- 
 tions, i. €., that the child should not simply 
 
 imitate, but proceed, self-actingly, to perform 
 work which enables him to reflect, reason, 
 and finally to invent himself. 
 
 Both claims have been most ingeniously 
 satisfied by Froebel. He gives the three 
 years' old child a slate, one side of w^hich is 
 covered by a net-work of engraved lines (one- 
 fourth of an inch apart), and he gives him in 
 addition, thereto, the law of opposites and 
 their mediation as a rule for h's activity. 
 
 The lines of the net-work guide the child in 
 moving the pencil, they assist it in measuring 
 and comparing situation and position, size 
 and relative center, and sides of objects. 
 This facilitates the work greatly, and in con- 
 sequence of this important assistance the 
 childs' desire for work is materially increased ; 
 whereas, obstacles in the earliest attempts at 
 all kinds of work must necessarily discourage 
 the beginner. 
 
 Drawing on the slate, with slate pencil is 
 followed by drawing on paper with lead 
 pencil. The paper of the drawing books is 
 ruled like the slates. It is advisable to begin 
 and continue the exercises in drawing on 
 paper, in like manner as those on the slate 
 were begun and continued, with this differ- 
 ence only, that owing to the progress made 
 and skill obtained by the child, less repeti- 
 tions may be needed to bring the pupil to 
 perfection here, as was necessary in the use 
 of the slate. 
 
 It has been repeatedly suggested, that 
 whenever a new material for occupation is 
 introduced, the teacher should comment upon, 
 or enter into conversation with the children, 
 about the same ; the difference between draw- 
 ing on the slate and on paper, and the mate- 
 rial used for both may give rise to many 
 remarks and instructive conversation. 
 
 It may be mentioned that the slate is first 
 used, because the children can easily correct 
 mistakes by wiping out what they have made, 
 and that they should be much more careful in 
 drawing on paper, as their productions can 
 not appear perfectly clean and neat if it 
 should be necessary to use the rublier often. 
 
48 
 
 GUIDE TO KINDER- GARTNERS. 
 
 Slate and slate pencil are of the same mate- 
 rial ; paper and lead pencil are two very differ- 
 ent things. On the slate the lines and figures 
 drawn, appear white on darker ground. On 
 the paper, lines and figures appear black on 
 white ground. 
 
 More advanced pupils use colored lead 
 pencils instead of the common black lead 
 pencils. This adds greatly to the appear- 
 ance of the figures, and also enables the child 
 to combine colors tastefully and fittingly. For 
 the development of their sense of color, and 
 of taste, these colored mosaic like figures are 
 excellent practice. 
 
 Drawing, as such, requires observation, at- 
 tention, conception of the whole and its parts, 
 the recollection of all, power of invention and 
 combination of thought. Thus, by it, mind 
 and fantasy are enriched with clear ideas and 
 true and beautiful pictures. For a free and 
 active development of the senses, especially 
 eye and feeling, drawing can be made of in- 
 calculable benefit to the child, when its natu- 
 ral instinct for it is correctly guided at its 
 very awakening. 
 
 Our Plates XXXV. to XLVI. show the sys- 
 tematic course pursued in the drawing depart- 
 ment of the Kinder-Garten. The child is first 
 occupied by 
 
 THE PERPENDICULAR LINE. 
 
 (PLATES XXXV. TO XXXVIII.) 
 
 The teacher draws on the slate a perpen- 
 dicular line of a single length (^ of an inch), 
 saying while so doing, I draw a line of a single 
 length downward. She then (leaving the line 
 on the slate, or wiping it out) requires the 
 child to do the same. She should show that 
 the line she made commenced exactly at the 
 crossing point of two lines of the net-work, 
 and also ended at such a point. 
 
 Care should be exercised that the child 
 hold the pencil properly, not press too much 
 or too little on the slate, that the lines drawn 
 be as equally heavy as possible, and that each 
 single line be produced by one single stroke 
 of the pencil. The teacher should occasion- 
 
 ally ask : What are you doing ? or, what have 
 you done? and the child should always an- 
 swer in a complete sentence, showing that it 
 works understandingly. Soon the lines may 
 be drawn upwards also, and then they may 
 be made alternately up and down over the 
 entire slate, until the child has acquired a cer- 
 tain degree of ability in handling the pencil. 
 
 The child is then required to draw a per- 
 pendicular line of two lengths, and advances 
 slowly to lines of three, four and five lengths, 
 (Plate XXXV., Figs. 2—5). 
 
 With the number five Froebel stops on 
 this step. One to five are sufficiently known, 
 even to the child three years old, by the 
 number of his fingers. 
 
 The productions thus far accompHshed are 
 now combined. The child draws, side by 
 side of one another, lines of one and two 
 lengths (Fig. 6), of one, two and three lengths 
 (Fig. 7), of one, two, three and four lengths 
 (Fig. 8), and finally lines of one, two, three, 
 four and five lengths (Fig. 9.) It always forms 
 by so doing a right-angled triangle. We 
 have noticed already, in using the tablets, that 
 right-angled triangles can lie in many different 
 ways. The triangle (Fig. 9 and 10) can also 
 assume various positions. In Fig. 10 the 
 five lines stand on the baseline — the smallest 
 is the first, the largest the last, the right an- 
 gle is to the right below. In Fig. 1 1 the op- 
 posite is found — the five lines hang on the 
 base-line, the largest comes first, the smallest 
 last, and the right angle is to the left above. 
 Figs. 12 and 13 are forms of mediation of 10 
 and II. 
 
 The child should be induced to find Figs. 
 IT to 13 himself Leading him to understand 
 the points of Fig. 10 exactly, he will have no 
 difficulty in representing the opposite. Instead 
 of drawing the smallest line first, he will draw 
 the longest ; instead of drawing it downward, 
 he will move his pencil upward, or at least 
 begin to draw on the line which is bounded 
 above, and thus reach 11. By continued re- 
 flection, entirely within the limits of his capa- 
 bilities, he will succeed in producing 12 and 13. 
 
GUIDE TO KINDER-GARTNERS. 
 
 49 
 
 Thus, by a different way of combination of 
 five perpendicular lines, four forms have been 
 produced, consisting of equal parts, being, 
 however, unlike, and therefore oppositionally 
 alike. 
 
 Each of these figures is a whole in itself. 
 But as every thing is always part of a larger 
 whole, so also these figures serve as elements 
 for more extensive formations. 
 
 In this feature of Froebel's drawing method, 
 in which we progress from the simple to the 
 more complicated in the most natural and 
 logical manner, unite parts to a whole and 
 recognize the former as members of the latter, 
 discover the like in opposites, and the media- 
 tion of the latter, unquestionable guarantee 
 is given that the delight of the child will be 
 renewed and increased, throughout the whole 
 course of instruction. Let Figs. lo — 13 be 
 so united that the right angles connect in 
 the center (Fig. 14), and again unite them so 
 that all right angles are on the outside (Fig. 
 15.) Figs. 14 and 15 are opposites. No. 14 
 is a square with filled inside and standing on 
 one corner; No. 15 one resting on its base, 
 with hollow middle. In 14 the right angles 
 are just in the middle; in 15 they are the 
 most outward corners. In the forms of medi- 
 ation (16 and 17), they are, it is true, on the 
 middle line, but in the meantime on the out- 
 lines of the figures formed. In the other 
 forms of mediation, (Figs. 18, 19, etc) they 
 lie altogether on the middle line ; but two in 
 the middle, and two in the limits of the 
 figure. 
 
 Thus we have again, in Figs. 18 — 22, four 
 forms consisting of exactly the same parts, 
 which therefore are equal and still have qual- 
 ities of opposites. In the meantime, they 
 are fit to be used as simple elements of fol- 
 lowing formations. In Fig. 22, they are com- 
 bined into a star with filled middle ; in Fig. 
 23, it is shown how a star with hollow middle 
 may be formed of them. (The Fig. 23, on 
 Plate XXXVI., does not show the lower part; 
 on Plate XXII., Fig. 97, Gift Seventh, the 
 whole star is shown.) Here, too, numerous 
 
 forms of mediation may be produced, but we 
 will work at present with our simple elements. 
 
 Owing to the similarity in the method of 
 drawing to that employed in the laying of the 
 right angled, isosceles triangle, it is natural 
 that we should here also arrive at the so-called 
 rotation figures, by grouping our triangles with 
 their acute angles toward the middle (Figs. 
 24 and 25), or arrange them around a hollow 
 square (Figs. 26 and 27.) 
 
 Figs. 28 and 29 are forms of mediation 
 between 24 and 25, and at the same time 
 between 14 and 15. 
 
 All these forms again serve as material for 
 new inventions. As an example, we produce 
 Fig. 30, composed of Figs. 28 and 29. 
 
 The number of positions in which our orig- 
 inal elements (Figs. 10 — 13) can be placed 
 by one another, is herewith not exhausted by 
 far, as the initiated will observ^e. Simple and 
 easy as this method is rendered by natural 
 law^s, it is hardly necessary to refer to the tab- 
 lets (Plates XXI. to XXIX..) which will sug- 
 gest a sufficient number of new motives for 
 further combinations. 
 
 As previously remarked, the slate is ex- 
 changed for a drawing-book as soon as the pro- 
 gress of the child warrants this change. It 
 aflfords a peculiar charm to the pupil to see his 
 productions assume a certain durability and 
 permanency enabling him to measure, by thera, 
 the progress of growing strength and ability. 
 
 So far the triangles produced by co arrange- 
 ment of our five lines, were right-angled. 
 Other triangles, however, can be produced 
 also. This, however, requires more practice 
 and security in handling the pencil. 
 
 Figs. 31 and 32 show an arrangement of 
 the 5 lines, of acute angled (equilateral) tri- 
 angles ; Figs. 31 and 32 being opposites. 
 Their union gives the opposites 33 and 34 ; 
 finally, the combination of these two. Fig. 35. 
 
 In the last three figures we also meet now 
 the obtuse angle. This finds its separate 
 representation in the manner introduced in 
 Fig. 36 ; opposition according to position is 
 given in Fig. 37 ; mediation in Figs. 38 and 
 
50 
 
 GUIDE TO KINDER-GARTNERS. 
 
 39, and the combination of these four ele- 
 ments in one rhomboid in Fig. 40. The four 
 obtuse angles are turned inwardly. Fig. 42, 
 the opposite of 40, is produced by arranging 
 the triangles in such a manner that the obtuse 
 angles are turned outwardly. Fig. 41 pre- 
 sents the form of mediation. Another one 
 might be produced by arranging the 4 obtuse 
 angled triangles represented in Nos. 36, 37, 
 38, and 39 in such a manner as to have 39 
 left above, 37 right above, 36 left below, and 
 
 39 I 37 
 
 38 right below. Thus : ~r\—^ 
 
 36 I 38 
 
 It is evident that with obtuse angled trian- 
 gles, as with right angled triangles, combina- 
 tions can be produced. Indeed, the pupil 
 who has grown into the systematic plan of 
 development and combination will soon be 
 enabled to unite given elements in manifold 
 ways ; he will produce stars with filled and 
 hollow middle, rotation forms, etc., and his 
 mental and physical power and capacity will 
 be developed and strengthened greatly by 
 such inventive exercise. 
 
 Side by side with invention of forms of 
 beauty and knowledge, the representation of 
 forms of life, take place, in free individual ac- 
 tivity. The child forms, of lines of one length, 
 a plate, (Fig. 43,) or a star, (Fig. 44,) of lines 
 of one and two lengths a cross, (Fig. 45,) of 
 lines up to 4 lengths, it represents a coffee- 
 mill, (Fig. 46,) and employs the whole material 
 of perpendicular lines at his command, in the 
 construction of a large building with part of a 
 wall connected with it. (Fig. 47.) Equal 
 consideration, however, is to be bestowed 
 upon the opposite of the perpendicular, 
 
 THE HORIZONTAL LINE. 
 
 (PLATE XXXIX.) 
 
 The child learns to draw lines of a single 
 length below each other, then lines of 2, 3, 4, 
 and 5 lengths, (Figs, i — 5.) It arranges them 
 also beside each other, (Figs. 6 — 8) unites 
 lines of i and 2 lengths, (Fig. 9,) of i, 2, and 
 3 lengths, (Fig. 10,) of i to 4 lengths, (Fig. 1 1,) 
 finally of i to 5 lengths, thereby producing 
 
 the right angled triangle 12, its opposite 13, 
 and forms of mediation 14 and 15. The 
 pupil arranges the elements into a square 
 with filled middle, (Fig. 16) with hollow mid- 
 dle, (Fig. 17) produces the forms of mediation, 
 
 cl a dib 
 
 (Fig. 18, — — and — — ) and continues to 
 
 b I d a j c 
 
 treat the horizontal line just as it has been 
 taught to do with the perpendicular. ( By turn- 
 ing the Plates XXXV. to XXXVIII., the 
 figures on them will serve as figures with hori- 
 zontal lines.) Rotation forms, larger figures, 
 acute and obtuse angled triangles can be 
 formed ; forms of beauty, knowledge and life 
 are also invented here, (Fig. 19, adjustable 
 lamp J Fig. 20, key; Fig. 21, pigeon-house;) 
 and after the child has accomplished all this, it 
 arrives finally, in a most natural way, at the 
 
 COMBINATION OF PERPENDICULAR AND 
 HORIZONTAL LINES. 
 
 (plates XL. TO XLIL) 
 
 First, lines of one single length are com- 
 bined ; we already have four forms different 
 as to position, (Fig. i.) Then follow the 
 combination of 2, 3, 4, 5 — fold lengths, (Figs. 
 2 — 5) with each of which 4 opposites as to 
 position are possible. As previously, lines of i 
 to 5 — fold lengths are united to triangles, so 
 now the angles are united and Fig. 6 is pro- 
 duced. Its opposite, 7 and the forms of medi- 
 ation, can be easily found. A union of "these 
 four elements appears in the square, Fig. 8; 
 opposite Fig. 9. In Fig. 8, the right angles are 
 turned toward the middle, and the middle is 
 full. In Fig. 9, the reverse is the case. Forms 
 of mediation easily found. We have in Figs. 
 
 a i c bid 
 
 8 and 9 the combinations — 1 — and — |---- 
 
 Let the following 
 
 dib 
 be constructed : 
 alb die dl 
 
 dib 
 
 b|d d|b b |d d 
 b I c aid 
 
 b ' b c ' a I d ' 
 
GUIDE TO KINDER-GARTNERS. 
 
 If perpendicular and horizontal lines can 
 be united only to form right angles, we have 
 previously seen that perpendicular as well as 
 horizontal lines may be combined to obtuse 
 and acute angled triangles. The same is pos- 
 sible, if they are united. Fig. lo gives us an 
 e-xample. All perpendicular lines are so ar- 
 ranged as to form obtuse angled triangles. By 
 their combination with the horizontal lines, 
 the element lo" is produced, its opposite lo'', 
 and the forms of mediation io'= and lo'' whose 
 combination forms Fig. lo. 
 
 As in Fig. lo, the perpendicular lines form 
 an obtuse angled triangle, so the horizontal 
 lines, and finally both kinds of lines can at 
 the same time be arranged into obtuse angled 
 triangles. 
 
 Thus a series of new elements is produced, 
 whose systematic employment the teacher 
 should take care to facilitate. (The scheme 
 given in the above may be used for this 
 purpose.) 
 
 So far we have only formed angles of lines 
 equal in length ; but lines of unequal lengths 
 may be combined for this purpose. Exactly 
 in the same manner as lines of a single length 
 were treated, the child now combines the line 
 of a single length with that of two lengths, 
 then, in the same way, the line of two lengths 
 with that of four lengths, that of three with 
 that of six, that of four with that of eight, and 
 finally, the line of five lengths with that of ten. 
 ■ The combination of these angles affords new 
 elements with which the pupil can continue 
 to form interesting figures in the already well- 
 known manner. Figs, ii and 12, on Plate 
 XL., are such fundamental forms ; the de 
 velopment of which to other figures will give 
 rise to many instructive remarks. These fig- 
 ures show us that for such formations the 
 horizontal as well as the perpendicular line 
 may have the double length. Fig. 11 shows 
 the horizontal lines combined in such a way 
 as if to form an acute-angled triangle. They, 
 however, form a right-angled triangle, only the 
 right angle is not, as heretofore, at the end 
 of the longest line, but where? An acute- 
 
 angled triangle would result, if the horizontal 
 lines were all two net-squares distant from 
 each other. Then, however, the perpendicular 
 lines viould form an obtuse-angled triangle. 
 
 Important progress is made, when we com- 
 bine horizontal and perpendicular lines in 
 such a way that by touching in two points 
 they form closed figures, squares and oblongs. 
 
 First, the child draws squares of one- 
 length's dimension, then of two-lengths, of 
 three, four and five lines. These are combined 
 then as perpendicular lines were combined 
 also I- with 2-, the i^, 2^ and 3^ etc. These 
 combinations can be carried out in a perpen- 
 dicular direction, when the squares will stand 
 over or under each other; or in horizontal, 
 when the squares will stand side by side ; or, 
 finally, these two opposites may be combined 
 with one another. 
 
 Fig. 13° shows as an example a combina- 
 tion of four squares in a horizontal direction ; 
 13'' is the opposite ; c and d are forms of me- 
 diation. 
 
 In Fig. 14*, squares of the first, second and 
 third sizes are combined, perpendicularly and 
 horizontally, forming a right angle to the 
 right below ; b is the opposite, (angle left 
 above ;) c and d are forms of mediation. The 
 same rule is followed here as with the right 
 angle formed by single lines. The simple 
 elements are combined with each other into a 
 square with full or hollow middle, etc. ; and 
 from the new elements thus produced larger 
 figures are again created, as the example Fig. 
 15, Plate XLL, illustrates. From the four 
 elements 14"''"', the figure 15* and its opposite 
 B are constructed, (analogous to the manner 
 employed with Fig. 28, Plate XXXVII.,) a two- 
 fold combination of which resulted in Fig. 15. 
 Squares of from one to five length lines of 
 course admit of being combined in similar 
 manner. Each essentially new element should 
 give rise to a number of exercises, conditioned 
 only by the individual ability of the child. It 
 must be left to the faithful teacher, by an 
 earnest observation and study of her pupils, 
 to find the right extent, here as everywhere in 
 
52 
 
 GUIDE TO KINDER- GARTNERS. 
 
 their occupations. Indiscriminate skipping 
 is not allowed, neither to pupil nor teacher ; 
 each following production must, under all cir- 
 cumstances be derived from the preceding one. 
 
 As the square was the result of angles 
 formed of lines of equal length, so also with 
 the oblong. Here too the child begins with 
 the simplest. It forms oblongs, the base of 
 which is a single line, the height of which is a 
 line of double length. It reverses the case 
 then. Base line 2, height single length. Re- 
 taining the same proportions, it progresses to 
 larger oblongs, the height of which is double 
 the size of its base, and vice versa, until it 
 has reached the numbers 5 and 10. 
 
 It is but natural that these oblongs, stand- 
 ing or lying, should also be united in perpen- 
 dicular, and horizontal directions. Each form 
 thus produced again assumes four different 
 positions, and the four elements are again 
 united to new formations, according to the 
 rules previously explained. Fig. 16" shows an 
 arrangement of standing oblongs, in horizontal 
 directions. The opposite would contain the 
 right angle, at a to the right below — to the 
 left above ; 16° would be one form of media- 
 tion, a second one, (opposite of 16^) would 
 have its right angle to the right above. 
 
 Fig. 17 shows a combination of lying ob- 
 longs, in a perpendicular direction. Fig. iS, 
 shows oblongs in perpendicular and horizon- 
 tal directions. Fig. 19, a combination of stand- 
 ing and lying oblongs, the former being ar- 
 ranged perpendicularly, the latter, horizon- 
 tally. 
 
 In Fig. 20, we find standing oblongs so 
 combined that the form represents an acute 
 angled triangle ; a and b are the only possible 
 opposites in the same. 
 
 These few examples may suffice to indicate 
 the abundance of forms which may be con- 
 structed with such simple material as the 
 horizontal and perpendicular lines, from i to 
 5 lengths, (and double.) 
 
 It is the task of the educator to lead the 
 learner to detect the elements, logically, in 
 order to produce with them, new forms in 
 
 unlimited numbers, within the boundaries of 
 the laws laid down for this purpose. 
 
 But even without using these elements, the 
 child will be able, owing to continued practice, 
 to represent manifold forms of life and beauty, 
 partly by its own free invention, partly by 
 imitating the objects it has seen before. As 
 samples of the former, Plate XLIL, Fig. 27, 
 shows a cross. Fig. 29, a triumphal gate. Fig. 
 30, a wind-mill, of the latter, Fig. 21 — 24, and 
 28, show samples of borders ; Fig. 25 and 26, 
 show other simple embellishments. As the 
 perpendicular line conditioned its opposite, 
 the horizontal line, both again condition their 
 mediation. 
 
 THE OBLIQUE LINE. 
 (plates xliii. to xlv.) 
 
 Our remarks here can be brief as the ope- 
 rations are nothing but a repetition of those 
 in connection with the perpendicular line. 
 
 The child practices the drawing of lines 
 from I to 5 lengths, (Plate XLIII., i to 5,) 
 and combines these, receiving thereby 4 op- 
 positionally equal right angled triangles, (Fig. 
 6 — 9,) of which it produces a square, (Fig. 10,) 
 its opposite, (Fig. 11,) forms of mediation, and 
 finally large figures. 
 
 Then the lines are arranged into obtuse 
 angles, and the same process gone through 
 with them. 
 
 With these, as in Fig. 13, its opposite 16, 
 and its forms of mediation, 14 and 15, the 
 obtuse angles will be found at the perpendic- 
 ular middle line, or as in 17, at the horizontal 
 middle line. By a combination of 15 and 17, 
 we produce a star, 19. Finally we have also, 
 reached here the formation of the acute 
 angled triangle, (Fig. 18.) The oblique line 
 presents particular richness in forms, as it 
 may be a line of various degrees of inclina- 
 tion. It is an oblique of the first degree 
 whenever it appears as the diagonal of a 
 square, as in Figs, i — 19. When it appears 
 as the diagonal of an oblong, it is either an 
 oblique of the 2d, 3d, 4th, or 5lh degree, ac- 
 cording to the proportions of the base line. 
 
GUIDE TO KINDER-GARTNERS. 
 
 53 
 
 and height of tlie oblong, i to 2, i to 3, i to 
 4, I to 5. 
 
 In Fig. 20°, obliques of the second degree 
 are united to a right-angled triangle. 20" is 
 the opposite, 20° and d form mediations. 
 
 In Fig. 21, the same lines are united in an 
 obtuse angled triangle. In Fig. 22, they finally 
 form an acute angle. 
 
 In all these cases, the obliques were diag- 
 onals of standing oblongs. They may just as 
 well be diagonals of lying oblongs. Fig. 23, 
 in which obliques from the first to the fifth 
 degree are united, will illustrate this. The 
 obliques are here arranged one above the 
 other. In Fig. 24, the members a and b show 
 a similar combination ; the obliques, however, 
 are arranged beside one another ; the mem- 
 bers, c and d, are formed of diagonals of stand- 
 ing oblongs. 
 
 Obliques of various grades can be united 
 with one point, when the elements in Fig. 25, 
 will be produced, which requires the other 
 elements, b, c, and d, to form this figure, the 
 opposite of which would have to be formed 
 
 bid 
 according to the formula, — — , beside which 
 c I a 
 
 c I a 
 the forms of mediation would appear as — — 
 b 1 d 
 dlb 
 (Fig. 26) and — — . 
 a 1 c 
 
 As in this case, lying figures are produced, 
 standing ones can be produced likewise. 
 Each two of the elements thus received may 
 be united, so that all obliques issue from one 
 point, as in Fig. 27, and in its opposite. Fig. 28. 
 
 An oppositional combination can also take 
 place, so that each two lines of the same 
 grade meet, (Fig. 29.) The combination of 
 obliques with obliques to angles, to squares 
 and oblongs now follow, analogous to the 
 method of combining oblongs, perpendicular 
 and horizontal lines. Finally the combination 
 of perpendicular and oblique, horizontal and 
 oblique lines to angles, rhombus and rhomboid 
 ■is introduced. 
 
 With these, the child tries his skill in pro- 
 
 ducing forms of life : Fig. 40, gate of a for- 
 tress; 41, church with school-house and cem- 
 etery wall, and forms of beauty: Figs. 30 — 39. 
 The task of the Kinder -Garten and the 
 teacher has been accomplished, if the child 
 has learned to manage oblique lines of the 
 first and second degree skillfully. All given 
 instaiction which aimed at something beyond 
 this, was intended for the study of the teacher 
 and the Primary Department, which is still 
 more the case in regard to — 
 
 THE CURVED LINE. 
 (plate -\LVI.) 
 
 Simply to indicate the progress, and to give 
 Froebel's system of instruction in drawing 
 complete, we add the following, and Plate 
 XLVI. in illustration of it. 
 
 First, the child has to acquire the ability to 
 draw a curved line. The simplest curved line 
 is the circle, from which all others may be 
 derived. 
 
 However, it is difficult to draw a circle, and 
 the net on slate and paper do not afford suffi- 
 cient help and guide for so doing. But on 
 the other hand, the child has been enabled to 
 draw squares, straight and oblique lines, and 
 with the assistance of these it is not difficult 
 to find a number of points which lie on the 
 periphery of a circle of given size. 
 
 It is known that all corners of a quadrangle 
 (square or oblong) lie in the periphery of a 
 circle whose diameter is the diagonal of the 
 quadrangle. In the same manner all other 
 right angles constructed over the diameter, 
 are periphery angles, affording a point of the 
 desired circular line. It is therefore nec- 
 essary to construct such right angles, and this 
 can be done very readily with the assistance 
 of obliques of various grades. 
 
 Suppose we draw from point a (Fig. i) an 
 oblique of the third degree, as the diagonal 
 of a standing oblong ; draw then, starting 
 from point c, an oblique of the third degree, as 
 diagonal of a lying oblong, and continue both 
 these lines. They will meet in point a, and 
 there form a right angle. 
 
54 
 
 GUIDE TO KINDER-GARTNERS. 
 
 All obliques of the same degree, drawn 
 from opposite points, will do the same as 
 soon as the one approaches the perpendicular 
 in the same proportion in which the other 
 comes near the horizontal, or as soon as the 
 one is the diagonal of a standing, the other 
 of a lying oblong. 
 
 The lines Aa and Cc are obliques of the 
 third, Ab and Cb of the second, Af and C/ 
 of the third degree, etc., etc. In this manner 
 it is easy to find a number of points, all of 
 which are points in the circular line, intended 
 to be drawn. Two or three of them over 
 each side, will suffice to facilitate the drawing 
 of the ciRCUMscribing circle, (Fig. 2.) In like 
 manner, the iNXERscribing circle will be ob- 
 tained by drawing the middle transversals of 
 the square, (Fig. 3,) and constructing from 
 their end-points angles in the previously de- 
 scribed manner. 
 
 After the pupil has obtained a correct idea 
 of the size and form of the circle, whose ra- 
 dius may be of from one to five lengths, it 
 will divide the same in half and quarter cir- 
 cles, producing thereby the elements for its 
 farther activity. 
 
 The course of instruction is here again the 
 same as that in connection with the perpen- 
 dicular line. The pupil begins with quarter 
 circles, radius of which is of a single length. 
 Then follow quarter circles with a radius of 
 from two to five lengths. By arrangement of 
 these five quarter circles, four elements are 
 produced, which are treated in the same man- 
 ner as the triangles produced by arrangement 
 of five straight lines. The segments may be 
 parallel, and the arrangement may take place 
 in perpendicular and horizontal direction, (Fig. 
 4 and 5,) or they may, like the obliques of va- 
 rious degrees, meet in one point, as in Fig. 8, 
 of which Figs. 4 and 5 are examples. 
 
 Fig. 6 represents the combination of the 
 elements a and (/ as a new element ; Fig. 7, 
 the combination of d and c. In Fig. 8 the 
 arrangement finally takes place in oblique 
 direction, and all lines meet in one point. 
 
 The quarter circle is followed by the half 
 circle 9, 10, 11 ; then the three-fourths circle 
 (Fig. 12), and the whole circle, as shown in 
 Fig. 13- 
 
 With the introduction of each new line, the 
 same manner of proceeding is observed. 
 
 Notwithstanding the brevity with which we 
 have treated the subject, we nevertheless 
 believe we have presented the course of in- 
 struction in drawing sufficiently clearly and 
 forcibly, and hope that by it we have made 
 evident : 
 
 1. That the method described here is per- 
 fectly adapted to the child's abilities, and fit 
 to develop them in the most logical manner ; 
 
 2. That the abundance of mathematical 
 perceptions offered with it, and the constant 
 necessity for combining according to certain 
 laws, can not fail to surely exert a wholesome 
 influence in the mental development of the 
 pupil ; 
 
 3. That the child thus prepared for future 
 instruction in drawing, will derive from such 
 instruction more benefit than a child prepared 
 by any other method. 
 
 Whosoever acknowledges the importance 
 of drawing for the future life of the pupil — 
 may he be led therein by its significance for 
 industrial purposes, or resthetic enjoyment, 
 which latter it may afford even the poorest ! — 
 will be unanimous with us in advocating an 
 early commencement of this branch of in- 
 struction with the child. 
 
 If there be any skeptics on this point, let 
 them try the experiment, and we are sure they 
 will be won over to our side of the question. 
 
THE ELEVENTH AND TWELFTH GIFTS. 
 
 MATERIAL FOR PERFORATING AND EMBROIDERING. 
 
 (PLATES .\LVII. TO L.) 
 
 It is claimed by us that all occupation ma- 
 terial presented by Froebel, in the Gifts of the 
 Kinder-Garten, are, in some respects, related 
 to each other, complementing one another. 
 What logical connection is there between the 
 occupation of perforating and embroidering, 
 introduced with the present and the use of 
 the previously introduced Gifts of the Kinder- 
 Garten ? This question may be asked by 
 some superficial enquirer. Him we answer 
 thus : In the first Gifts of the Kinder-Garten, 
 the solid mass of bodies prevailed ; in the fol- 
 lowing ones the plane ; then the embodied line 
 was followed by the drawn line, and the occu- 
 pation here introduced brings us down to the 
 point. With the introduction of the per- 
 forating paper and pricking needle, we have 
 descended to the smallest part of the whole — 
 the extreme limit of mathc?natical divisibility ; 
 and in a playing manner, the child followed 
 us unwittingly, on this, in an abstract sense, 
 difficult journey. 
 
 The material for these occupations is a 
 piece of net paper, which is placed upon 
 some layers of soft blotting paper. The 
 pricking or perforating tool is a rather strong 
 sewing needle, fastened in a holder so as to 
 project about one-fourth of an inch. Aim of 
 the occupation is the production of the beau- 
 tiful, not only by the child's own activity, but 
 by its own invention. Steadiness of the eye 
 and hand are the visible results of the occu- 
 pation which directly prepares the pupil for 
 various kinds of manual labor. The per- 
 forating, accompanied by the use of the 
 
 needle and silk, or worsted, in the way em- 
 broidery is done, it is evident in vi'hat direc- 
 tion the faculty of the pupil may be developed. 
 
 The method pursued with this occupation 
 is analogous to that employed in the drawing 
 department. Starting from the single point, 
 the child is gradually led through all the 
 various grades of difficulty ; and from step to 
 step its interest in the work will increase, 
 especially as the various colors of the em- 
 broidered figures add much to their liveliness, 
 as do the colored pencils in the drawing 
 department. 
 
 The child first pricks perpendicular lines 
 of two and three lengths, then of four and five 
 lengths, (Figs. 2 and 3.) They are united to 
 a triangle, opposites and forms of mediation 
 are found, and these again are united into 
 squares with hollow and filled middle, (Figs. 
 4 and 5.) The horizontal line follows, (Figs. 
 6 — 8,) then the combination of perpendicu- 
 lar and horizontal to a right angle in its four 
 oppositionally equal positions, (Figs. 9 — 12.) 
 The combination of the four elements present 
 a vast number of small figures. If the exter- 
 nal point of the angle of 9 and 10 touch one 
 another, the cross (Fig. 13) is produced; if 
 the end points of the legs of these figures 
 touch, the square is made, (Fig. 14.) By 
 repeatedly uniting 9 and 12 Fig. 15 is pro- 
 duced, and by the combination of all four 
 angles Figs. 16 and 17. According to the 
 rules followed in laying figures with tab- 
 lets of Gift Seven, and in drawing, or by a 
 simple application of the law of opposites, the 
 
56 
 
 GUIDE TO KINDER-GARTNERS. 
 
 child will produce a large number of other 
 figures. 
 
 The combination of lines of i and 2 lengths 
 is then introduced, and standing and lying 
 oblongs are formed, (Figs. 18 and ig,) etc. 
 The school of perforating, per se, has to con- 
 sider still simple squares and lying and 
 standing oblongs, consisting of lines of from 
 2 to 5 lengths.- In order not to repeat the 
 same form too often, we introduce in Pigs. 
 2 1 — 3 1 a series of less simple ; containing, 
 however, the fundamental forms, showing in 
 the meantime the combination of lines of 
 various dimensions. 
 
 In a similar way, the oblique line is now 
 introduced and employed. The child pricks 
 it in various directions, commencing with a 
 one length line, (Figs. 32 — 35,) combines it to 
 angles, (Figs. 36 — 39,) the combination of 
 which will again result in many beautiful 
 forms. Then follows the perforating of ob- 
 lique lines of from 2 to 5 lengths, (a single 
 length containing up to seven points,) which 
 are employed for the representation of bor- 
 ders, corner ornaments, etc., (Figs. 42 — 45, 
 61.) The oblique of the second degree is 
 also introduced, as shown in Figs. 46 and 47, 
 and the peculiar formations in Figs. 48 — 51. 
 
 Finally, the combination of the oblique 
 with the perpendicular line, (Figs. 52 and 54,) 
 and with the horizontal, (Figs. 53 and 55,) or 
 with both at the same time, (Figs. 56 — 60,) 
 takes place. The conclusion is arrived at in 
 the circle (Fig. 62) and the half circle (Figs. 
 63-69.) 
 
 All these elements may be combined in 
 the most manifold manner, and the inventive 
 activity of the pupil will find a large field in 
 producing samples of borders, corner-pieces, 
 frames, reading marks, etc., etc. 
 
 When it is intended to produce amything of 
 a more complicated nature, the pattern should 
 be drafted by pupil or teacher upon the net 
 paper previous to pricking. In such cases, 
 it is advisable and productive of pleasure to 
 the pupils, if beneath the perforating paper 
 another one doubly folded is laid, to have the 
 
 pattern transferred by perforation upon this 
 paper in various copies. Such little produc- 
 tions may be used for various purposes, and 
 be presented by the children to their friends 
 on many occasions. To assist the pupils in 
 this respect, it is recommended that simple 
 drawings be placed in the hands of the pupils, 
 which, owing to their little ability, they cer- 
 tainly could not yet produce by drawing, but 
 which they can well trace with their per- 
 forating tool. These drawings should repre- 
 sent objects from the animal and vegetable 
 kingdoms, and may thus be. of great service 
 for the mental development of the children. 
 The slowly and carefully perforated forms 
 and figures will undoubtedly be more last- 
 ingly impressed upon the mind and longer 
 retained by the memory, than if they were 
 only described or hurriedly looked at. Plate 
 XLIX. presents a few of such pictures, which 
 can easily be multiplied. 
 
 A particular explanation is required for 
 Fig. 84, on Plate L. In this figure are con- 
 tained shaded parts, indicating plastic forms, 
 which so far have not been introduced, all 
 previous figures presenting mere outlines to 
 be perforated. It is supposed to be known 
 that each prick of the needle causes some- 
 what of an elevation on the reverse (wrong 
 side) of the paper. If a number of very fine, 
 scarcely visible pricks are made around a 
 certain point, an elevated place will be the 
 result, so much more observable, the larger 
 the number of pricks concentrated on the 
 spot. In this wise it is possible to represent 
 certain parts of a design as standing out in 
 relief It is understood that very young chil- 
 dren could not well succeed in such kind of 
 work. The older ones find material in Figs. 
 72, 74 and 76 to try their skill in this direc- 
 tion, and thereby prepare themselves for fig- 
 ures like 84. 
 
 All figures of Plates XXXIX., XLIL, and 
 XLIX. may well be used for samples of per- 
 forating and embroidering. 
 
 It should be mentioned that the embroider- 
 ing does not begin simultaneously with the 
 
GUIDE TO KINDER-GARTNERS. 
 
 57 
 
 perforating, but only after the children have 
 acquired considerable skill in the last named 
 occupation. For purposes of 
 
 EMBROIDERING, 
 The same net paper which was used for e.xer- 
 cises in perforating may be employed, by fill- 
 ing out the intervals between the holes with 
 threads of colored silk or worsted. It will be 
 sufficient for this purpose to combine the 
 points of one net square only, because other- 
 wise the stitches would become too short to 
 be made wilh the embroideiy needle in the 
 hands of children yet unskilled. For work, to 
 be prepared for a special purpose, the perfor- 
 ated pattern should be transferred upon stiff 
 paper or bristol-board. 
 
 Course of instruction just the same as with 
 perforating. 
 
 Experience will show that of the figures 
 contained on our plates, some are more fit for 
 perforating, others better adapted for embroid- 
 ering. Either occupation leads to peculiar 
 results. Figures in which strongly rounded 
 lines predominate may be easily perforated, 
 but with difficulty, or not at all be embroid- 
 ered, as Figs. 75 and 77. By the process of 
 embroidering, however, plain forms, as stars, 
 and rosettes, are easily produced, which could 
 hardly be represented, or, at best, very imper- 
 fectly only, by the perforating needle. Figs. 
 87 — 92, and Fig. 39 on Plate XLII. are ex- 
 amples of this kind. 
 
 To develop the sense of color in the chil- 
 dren, the paper on which they embroider, 
 should be of all the various shades and hues, 
 through the whole scale of colors. If the 
 paper is gray, blue, black, or green, let the 
 worsted or silk be of a rose color, white, or- 
 ange or red, and if the pupil is far enough 
 advanced to represent objects of nature, as 
 fruit, leaves, plants, or animals, it will be very 
 proper to use in embroidering, the colors 
 
 shown by these natural objects. Much can 
 be thereby accomplished toward an early de- 
 velopment of appreciation and knowledge of 
 color, in which grown people, in all countries 
 are often sadly deficient. It has appeared to 
 some, as if this occupation is less useful than 
 pleasurable. Let them consider that the ordi- 
 nary seeing of objects already is a difficult 
 matter, nay, really an art, needing long prac- 
 tice. Much more difficult and requiring much 
 more careful exercise, is a true and correct 
 perception of color. 
 
 If the bcatttifid is introduced at all as a 
 means of education — and in Froebel's institu- 
 tions it occupies a prominent place — it should 
 approach the child in various ways ; not only 
 mform, but in color, and tone also. To insure 
 the desired result in this direction, we begin 
 in the Kinder-Garten, where we can much 
 more readily make impressions upon the 
 blank minds of children, than at a later pe- 
 riod when other influences have polluted their 
 tastes. 
 
 For this reason, we go still another step 
 farther, and give the more developed pupil a 
 box with the three fundamental colors, show- 
 ing him their use, in covering the perforated 
 outlines of objects with the paint. Children 
 like to occupy themselves in this manner, and 
 show an increased interest, if they first pro- 
 duce the drawing and are subsequently al- 
 lowed to use the brush for further beautifying 
 their work. 
 
 We only give three fundamental colors, in 
 order not to confound the beginner by need- 
 less multiplicity, as also to teach how the sec- 
 ondary colors,may be produced by mixing the 
 primarj'. 
 
 The perforating and embroidering are be- 
 gun with the children in the Kinder-Garten, 
 when they have become sufficiently prepared 
 for the perception of forms by the use of their 
 building-blocks and staffs. 
 
THE THIRTEENTH GIFT. 
 
 MATERIAL FOR CUTTING PAPER AND MOUNTING PIECES TO PRODUCE 
 FIGURES AND FORMS. 
 
 (PLATES 
 
 The labor, or occupation alphabet, pre- 
 sented by Froebel in his system of education, 
 cannot spare the occupation, now introduced 
 — the cutting of paper — the transmutation of 
 the material by division of its parts, notwith- 
 standing the many apparently well-founded 
 doubts, whether scissors should be placed into 
 the hands of the child at such an early age. 
 It will be well for such doubters to consider : 
 Firstly, that the scissors which the children 
 use, have no sharp points, but are rounded at 
 their ends, by which the possibilities of doing 
 harm with them are greatly reduced. Sec- 
 ondly, it is expected that the teacher employs 
 all possible means to watch and superintend 
 the children with the utmost care during their 
 occupation with the scissors. Thirdly, as it 
 can never be prevented, that, at least, at times 
 scissors, knives and similar dangerous objects 
 may fall into the hands of children, it is of 
 great importance to accustom them to such, 
 by a regular course of instruction in their use, 
 which, it may be expected, will certainly do 
 something to prevent them from illegitimately 
 applying them for mischievous purposes. 
 
 By placing material before them from which 
 the child produces, by cutting according to 
 certain laws, highly interesting and beautiful 
 forms, their desire of destroying with the scis- 
 sors will soon die out, and they, as well as 
 their parents, will be spared many an unpleas- 
 ant experience, incident upon this childish in- 
 stinct, if it were left entirely unguided. 
 
 As material for the cutting, we employ a 
 square piece of paper of the size of one-six- 
 
 teenth sheet, similar to the folding sheet. 
 Such a sheet is broRen diagonally, (Plate 
 LXIX., Fig. 5,) the right acute angle placed 
 upon the left, so as to produce four triangles 
 resting one upon another. Repeating the same 
 proceeding, so that by so doing the two upper 
 triangles will be folded upwards, the lower 
 ones downwards in the halving line, eight 
 triangles resting one upon another, will be 
 produced, which we use as our first funda- 
 mental form. This fu7ida7nental form is held, 
 i?i all exercises, so that the open side, where no 
 plane connects with another is always turned 
 toivard the left. 
 
 In order to accomplish a sufficient exact- 
 ness in cutting, the uppermost triangle con-. 
 tains, (or if it does not, is to be provided with) 
 a kind of net as a guide in cutting. Dotted 
 lines indicate on our plates this net-work. 
 
 The activity itself is regulated according 
 to the law of opposites. We commence with 
 the perpendicular cut, come to its opposite, 
 the horizontal and finally to the mediation of 
 both, the oblique. 
 
 Plates 51 — 53 indicate the abundance of 
 cuts which may be developed according to 
 this method, and it is advisable to arrange for 
 the child a selection of the simpler elements 
 into a school of cutting. 
 
 The following selection presents, almost 
 always, two opposites and their combination, 
 or leaves out one of the former, as is the case 
 with the horizontal cut, wherever it does not 
 produce anything essentially new. 
 
 a. Perpendicular cuts, 2, 3, 4 — 5, 6, 7. 
 
GUIDE TO KINDER- GARTNERS. 
 
 59 
 
 b. Horizontal cuts, 8, 9— (above ; above 
 and below). 
 
 c. Perpendicular and horizontal, 18, 19, 
 20 — 21, 22, 23. 
 
 d. Oblique cuts, 34, 35—36, 37, 38. 
 
 e. Oblique and perpendicular, 51, 52, 53, 
 —54, 55- 56—58- 59. 60. 
 
 / Oblique and horizontal, 65, 66, 67. 
 
 g. Half oblique cuts, where the diagonals 
 of standing and lying oblongs, formed of two 
 net squares, serve as guides — 117, 118, 119 — 
 121, 122, 123 — 125, 126, 127. 
 
 Here ends the school of cutting, perse, for 
 the first fundamental form, the right angled 
 triangle. The given elements may be com- 
 bined in the most manifold manner, as this 
 has been sufficiently carried out in the forms 
 on our plates. 
 
 The fundamental form used for Plates LIV. 
 and LV. is a six fold equilateml triangle. It 
 also is produced from the folding sheet, by 
 breaking it diagonally, halving the middle of 
 the diagonal, dividing again in three equal 
 parts the angle situated on this point of halv- 
 ing. The angles thus produced will be an- 
 gles of 60 degrees. The leaf is folded in the 
 legs of these angles by bending the one acute 
 angle of the original triangle, upwards, the 
 other downwards. By cutting the protruding 
 corners, we shall have the desired form of the 
 si.x fold equilateral triangle, in which the en- 
 tirely open side serves as basis of the triangle. 
 The net for guidance is formed by division of 
 each side in four equal parts, uniting the points 
 of division of the base, by parallel lines with 
 the sides, and drawing of a perpendicular 
 from the upper point of the triangle upon its 
 base. It is the oblique line, particularly which 
 is introduced here. The designs and patterns 
 from 133 — 145, will suffice for this purpose. 
 The same fundamental form is used for prac- 
 tising and performing the circular cuts, al- 
 though the right angular fundamental form 
 may be used for the same purpose. Both find 
 their application subsequently, in a sphere of 
 development only, after the child by means 
 of the use of the half and whole rines, and 
 
 drawing, has become more familiar with the 
 curved line. These exercises require great 
 facility in handling the scissors, besides, and 
 are, therefore, only to be introduced with 
 children, who have been occupied in this de- 
 partment quite a while. For such it is a cap- 
 ital employment, and they will find a rich 
 field for operation, and produce many an in- 
 teresting and beautiful form in connection 
 with it. The course of development is indi- 
 cated in figures 164 — 172. 
 
 After the child has been sufficiently intro- 
 duced into the cutting school, in the manner 
 indicated in the above ; after his fantasy 
 has found a definite guidance in the ever-re- 
 peated application of the law, which protects 
 him against unbounded option and choice, it 
 will be an easy task to him, and a profitable 
 one, to pass over to free invention, and to 
 find in it a fountain of enjoyment, ever new, 
 and inexhaustibly overflowing. To let the 
 child, entirely without a guide, be the master 
 of his own free will, and to keep all discipline 
 out of his way, is one of the most dangerous 
 and most foolish principles to which a misun- 
 derstood love of children, alone, could bring 
 us. This absolute freedom condemns the 
 children, too soon, to the most insupportable 
 annoyance. All that is in the child should be 
 brought out by means of external influence. 
 To limit this influence as much as possible is not 
 to suspend it. Froebel has limited it, in a most 
 admirable way by placing this guidance into the 
 child itself, as early as possible ; that from one 
 single incitement issues a number of others, 
 within the child, by accustoming it to a lawful 
 and regulated activity from its earliest youth. 
 
 With the first perpendicular cut, which we 
 made into the sheet (Fig. i,) the whole course 
 of development, as indicated in the series of 
 figures up to No. 132 is given, and all subse- 
 quent inventions are but simple, natural com- 
 binations of the element presented in the 
 '■^school." Thus a logical connection prevails 
 in these formations, as among all other means 
 of education, hardly any but mathematics 
 may afford. 
 
60 
 
 GUIDE TO KINDER- GARTNERS. 
 
 Whereas the activity of the cutting itself, 
 the logical progress in it advances a most 
 beneficial influence upon the intellect of the 
 pupil, the results of it will awaken his sense 
 of beauty, his taste for the symmetrical, his 
 appreciation of harmony in no less degree. 
 The simplest cut already yields an abundance 
 of various figures. If we make as in Fig. 5, Plate 
 LI., two perpendicular cuts, and unfold all 
 single parts, we shall have a square with 
 hollow middle, a small square, and finally the 
 frame of a square. If we cut according to 
 Fig. 6, we produce a large octagon, four 
 small triangles, four strips of paper of a trape 
 zium form, nine figures altogether. 
 
 All these parts are now symmetrically ar- 
 ranged according to the law: union of op- 
 posites — here effected by the position or direc- 
 tion of the parts, relative to the center — 
 and after they have been arranged in this 
 manner, the pupils will often express the de- 
 sire to preserve them in this arrangement. 
 This natural desire finds its gratification by 
 
 MOUNTING THE FIGURES. 
 As separation always requires its opposite, 
 uniting, so the cutting requires mounting. 
 Plates LVI. to LVIII. present some examples 
 from which the manner in which the results 
 of the cutting may be applied, can be easily 
 derived. With the simpler cuts, the clippings 
 are to be employed, but if a main figure is 
 
 complete and in accordance with the claims 
 of beauty in itself, itwould be foolish to spoil 
 it, by adding the same. 
 
 This occupation, also, can be made sub- 
 servient to influence the intellectual develop- 
 ment of the child by requiring it to point 
 out all manners in which these forms may 
 be arranged and put together. (Plate LVI., 
 Fig- S-) 
 
 In order to increase the interest of the chil- 
 dren, to give a larger scope to their inventive 
 power, and at the same time, to satisfy their 
 taste and sense of color, they may have paper 
 of various colors and be allowed to e.xchange 
 their productions among one another. 
 
 Both these occupations, cutting and mount- 
 ing, are for Kinder Garten as well as higher 
 grades of schools. For older pupils, the cut- 
 ting out of animals, plants and other forms of 
 life will be of interest, and silhouettes even 
 may be prepared by the most expert. 
 
 It is evident that not only as a 'simple 
 means of occupation for the children, during 
 their early life, but as a preparation for many 
 an occupation in real life, the cutting of paper 
 and mounting the parts to figures, as intro- 
 duced here, are of undeniable benefit. 
 
 The main object, however, is here, as in all 
 other occupations in the Kinder-Garten, de- 
 velopment of the sense of beauty, as a prep- 
 aration for subsequent performance in and 
 enjoyment of art. 
 
 THE FOURTEENTH GIFT. 
 
 MATERIAL FOR BRAIDING OR WEAVING. 
 
 (tlates lix. to lx>v.) 
 
 Braiding is a favorite occupation of chil- 
 dren. The child instinctively, as it were, likes 
 everything contributing to its mental and 
 bodily development, and few occupations may 
 
 claim to accomplish both, better than the oc- 
 cupation now introduced. It requires great 
 care, but the three year old child may already 
 see the result of such care, whereas even from 
 
GUIDE TO KINDER-GARTNERS. 
 
 6l 
 
 twelve to fourteen years old pupils often have 
 to combine all their ingenuity and persever- 
 ance to perform certain more complicated 
 tasks in the braiding or weaving department. 
 It does not develop the right hand alone, the 
 left also finds itself busy most of the time. It 
 satisfies the taste of color, because to each 
 piece of braiding, strips of at least two differ- 
 ent colors belong. It excites the sense of 
 beauty because beautiful, /. e , symmetrical, 
 forms are produced ; at least their production 
 is the aim of this occupation. The sense and 
 appreciation of number are constantly nour- 
 ished, nay, it may be asserted, that there is 
 hardly a better means of affording percep- 
 tions of numerical conditions, so thorough, 
 founded on individual experience and ren- 
 dered more distinct by diversity in form and 
 color, than '^braiding." The products of the 
 child's activity, besides, are readily m.ade use- 
 ful in practical life, affording thereby capital 
 opportunities for expression of its love and 
 gratitude, by presents prepared by its own 
 hand. 
 
 The material used for this occupation are 
 sheets of paper prepared as shown on Plate 
 LIX., strips of paper, and the braiding needle, 
 also represented on Plate LIX. 
 
 A braid work is produced by drawing with 
 the needle a loose strip (white) through the 
 strips of the braiding sheet, (green) so that a 
 number of the latter will appear over, another 
 under the loose strip. These numbers are 
 conditioned by the form the work is to as- 
 sume. As there are but two possible ways 
 in which to proceed, either lifting up, or pres- 
 sing down, the strips of the braiding sheet, 
 the course to be taken by the loose strip is 
 easily expressed in a simple formula. All 
 varieties of patterns are expressible in such 
 formulas, and therefore easily preserved and 
 communicated. 
 
 The simplest formula of course, is when one 
 strip is raised and the next pressed down. 
 We express this formula by i u (up), i d 
 (down). All such formulas in which only two 
 figures occur, are called simple formulas ; 
 
 combination formulas, however, are such as 
 contain a combination of two or more such 
 simple formulas. 
 
 But with a single one of such formulas, no 
 braid work can yet be constructed. If we 
 should, for instance, repeat with a second, 
 third, and fourth strip, i u, i d, the loose 
 strips would slip over one another at the 
 slightest handling, and the strips of the braid- 
 ing sheet and the whole work, drop to pieces 
 if we should cut from it, the margin. In do- 
 ing the latter, we have, even with the most 
 perfect braidwork, to employ great care ; but 
 it is only then a braid or weaving work exi^sts 
 — when all strips are joined to the whole by 
 other strips, and none remain entirely de- 
 tached. 
 
 To produce a braid work, we need at least 
 two formulas, which are introduced alternately. 
 Proceeding according to the same fundamen- 
 tal law which has led us thus far in all our 
 work, we combine first with i ;/, i d, its oppo- 
 site \ d, \ u. 
 
 Such a combination of braiding formulas 
 by which not merely a single strip, but the 
 whole braid work, is governed, is a braiding 
 scheme. 
 
 Braiding formulas, according to which the 
 single strip moves, are easily invented. Even 
 if one would limit one's self to take up or press 
 down no more than five strips, (and such a 
 limitation is necessary, because otherwise the 
 braiding would become too loose,) the follow- 
 ing thirty formulas M'ould be the result : 
 
 1, lu id 9, 3u id 17, 4u 2d 24, 5d lu 
 
 2, id lu 10, 3d lu 18, 4d 2u 25, 5u 2d 
 
 3, 2u 2d n, 3u 2d 19, 4U 3d 26, 5d 2u 
 
 4, 2d 2u 12, 3d 2u 20, 4d 3u 27, 5u 3d 
 
 5, 2u id 13, 4u 4d 21, 5u 5d 28, 5d 3U 
 
 6, 2d lu 14, 4d 4u 22, 5d 5u 29, 5U 4d 
 
 7, 3u 3d 15, 4U id 23, 5u id 30, 5d 4U 
 
 8, 3d 3u 16, 4d lu 
 
 From these thirty formulas, among which are 
 always two oppositionally alike, as for in- 
 stance, I and 2, 9 and 10, 25 and 26, hun- 
 dreds of combined, or combination formulas 
 can be formed by simply uniting two of them. 
 In the beginning it is advisable to combine 
 
62 
 
 GUIDE TO KINDER-GARTNERS. 
 
 such as contain equally named numbers either 
 even or odd. The following are some ex- 
 amples : 
 
 Formulas i and 3, lu id, 2u 2d. 
 
 " I and 5, III id, 2u id. 
 
 " I and 7, III id, 3U 3d. 
 
 " I and 9, lu id, 3U id. 
 
 " I and II, lu id, 3U 2d. 
 
 " I and 13, III id, 4U 4d. 
 
 " I and 15, lu id, 411 id. 
 
 " I and 17, lu id, 4U 2d. 
 
 " I and 19, lu id, 4U 3d. 
 
 " I and 21, lu id, 5U 5d. 
 
 " I and 23, lu id, 5U id. 
 
 I and 25, III Id, 511 2d. 
 
 " I and 27, lu id, 5U 3d. 
 
 " I and 29, lu id, 5u 4d. 
 
 If we also add the formulas under the even 
 numbers in the given thirty, we have to read 
 them inversely. Thus : 
 
 Formulas I and 6, lu id, lu 2d. 
 
 " I and 10, lu id, lu 3d. 
 
 " I and 12, III id, 2u 3d. 
 
 " I and 16, lu id, lu 4d. 
 
 " I and iS, lu id, 2u 4d. 
 
 " I and 20, ui id, 3U 4d. 
 
 " I and 24, III id, lu 5d. 
 
 " I and 26, lu id, 2u 5d. 
 
 I and 28, lu id, 3U 5d. 
 
 " I and 30, lu id, 4U 5d. 
 
 By a combination of one single formula 
 with the twenty-four others, we receive new 
 combination formulas and see that inventing 
 formulas is a simple mathematical operation, 
 regulated by the laws of combination. 
 
 Much more difficult it is to invent braiding 
 schemes. Not to dwell too long on this point, 
 we introduce the reader to the course shown 
 in pictures on our plates, which is arranged so 
 systematically that either as a whole or with 
 some omissions, it may be worked through 
 with children from three to six years, as a 
 braiding school. It begins with simple formu- 
 las and by means of the law of oppbsites is 
 carried out to the most beautiful figures. 
 
 Formula i, lu id, (Fig. i,) is first intro- 
 duced; opposite in regard to number is 2u 
 2d, (Fig. 2). In Fig. 3 the numbers i and 2 
 are combined ; Fig. 4 is a combination of 
 Figs. I and 2 ; Fig. 5 a combination of Figs. 
 
 I and 3 by combining the simple formulas. 
 If we examine Fig. 5, the number 3 makes 
 itself prominent in the strips running ob- 
 liquely. In Fig. 6 it occurs independently as 
 opposite to I and 2, and then follows in Figs. 
 7-15 a series of mediative forms all uniting 
 the opposites in regard to number. In all 
 these patterns the squares or oblongs pro- 
 duced, are arranged perpendicularly under, or 
 horizontally beside, one another. Except in 
 Fig. I, the oblique line appears already be- 
 side the horizontal and perpendicular. Thus, 
 this given opposite of form is prevailing on 
 Plate LXL, and we apply here the same for- 
 mulas as on Plate LX., with the difference, 
 however, that we need only one formula, 
 which in the second, third strip, etc], always 
 begins one strip later or earlier. Thus in 
 Fig. 16, the formula 2U 2d (as in Fig. 2) is 
 carried out. The dark and light strips of the 
 pattern run here from right above to left be- • 
 low. Opposite of positioji to Fig. 16, is 
 shown in Fig. 17, where both run the oppo- 
 site way. Fig. 18 shows combination, and 
 Fig. 19 double combination. In opposition 
 to the connected oblique lines, the broken line 
 appears in Fig. 20. As the formula 2U 2d 
 has furnished us five patterns, so the formula 
 of Fig. 3, lu 2d, furnishes the series 21 — 25. 
 Nos. 21 and 22 are opposites as to direction. 
 Fig. 23 shows the combination of these op- 
 posites. Figs. 24 and 25, opposites to one 
 another, are forms of mediation between 21 
 and 22. With them for the first time a mid- 
 dle presents itself. 
 
 While in Figs. 21 — 26 the dark color is 
 prevailing. Figs. 26 — 28 show us predom- 
 inantly, the light strip, consequently the op- 
 posite in color. In 29 — 32, formulas from Figs. 
 3 — 5 are employed. Fig. 29 requires an op- 
 posite of direction, a pattern in which the strips 
 run from left above to right below. Fig. 30 
 gives the combination of both directions and 
 Figs. 31 and 32 are at the same time op- 
 posites as to direction and color. 
 
 It is obvious that each single formula can 
 be used for a whole series of divers patterns, 
 
GUIDE TO KINDER-GARTNERS. 
 
 63 
 
 and the invention of these patterns is so easy 
 that it will suffice if we introduce each new 
 formula very briefly. • 
 
 Fig- 33 's a form of mediation for the for- 
 • mula 3U 3d ; Fig. 34 shows a different appli- 
 cation of the same formula. In Fig. 35 the 
 broken line appears again, but in opposition 
 to 20, it changes its direction with each break. 
 In Figs. 36 — 40 the formulas of Figs. 7, 8, 
 10, II, and 13 are carried out. The braiding 
 school, J>er se, is here concluded. Whoever 
 may think it too extensive may select from it 
 Nos. I, 2, 3, 6, 7, 10, 16, 17, 18, 21, 26, 24, 
 25, 33, and 34. 
 
 But if any one would like still to enlarge 
 upon it, she may do so by working out, for 
 each single formula the forms or patterns 
 16, 17, 18, 19, 24 and 25, and continue the 
 school to the number 5. The number of pat- 
 terns will be made, thereby, ten times larger. 
 
 Another change, and enlargement of the 
 school may be introduced by cutting the 
 braiding strips, as well as those of the braiding 
 sheet, of different widths. We can, thereby, 
 represent quite a number of patterns after 
 the same formula, which are, however, essen- 
 tially different. This is particularly to be 
 recommended with very small children, who 
 necessarily will have to be occupied longer 
 with the simple formula lu id. But for more 
 developed braiders, such change is of interest, 
 because by it a great variety of forms may 
 be produced which may be rendered still 
 more interesting and attractive, by a variety 
 of colors in the loose braiding strips. 
 
 With patterns that have a middle, as 24 
 and 28, it is advisable to let the braiding be- 
 gin (especially with beginners,) with the mid- 
 dle strip, and then to insert always one strip 
 above, and one below it. 
 
 It is not unavoidably necessary that the 
 school should be finished from beginning to 
 end, as given here. Quite the reverse. The 
 pupil, after having successfully produced some 
 patterns, may be afforded an opportunity for 
 developing his skill by his own invention, in 
 trying to form, by braiding a cross, with hol- 
 low middle, (Fig. 41,) a standing oblong, (42,) 
 a long cross, (43,) a small window, (45,) etc. 
 
 Plate LXIIL, presents some patterns which 
 may be used for wall-baskets, lamp tidies, 
 book-marks, etc., and which may easily be 
 augmented by such as have acquired more 
 than ordinary skill. 
 
 Finally, Plate LXIV. shows in figures i — 3, 
 obliquely intertwined strips, representing the 
 so called free-braiding, the braiding without 
 braiding sheet. This is done in the following 
 manner : Cut two or more long strips (Fig. 4) 
 of a quarter sheet of colored paper, (green,) 
 and fold to half their length, (Fig. 5,) cut 
 then, of differently colored paper, (white,) 
 shorter strips, afso fold these to half their 
 length. Put the green strips side by side of 
 one another, as shown in Fig. 7, so that the 
 closed end of the one strip lies above, and 
 that of the other below, (7^^.) Then take 
 the white strip, bend it around strip i, and 
 lead it through strip 2, (Fig. 8.) The second 
 strip is applied in an opposite way, laying it 
 around 2, and leading it through i. Em- 
 ploying four instead of two green strips, the 
 bookmark. Fig. 9, will be the result. The 
 protruding ends are either cut or scolloped. 
 By introducing strips of different widths, 
 a variety of patterns can also here be pro- 
 duced. 
 
 Instead of paper, glazed muslin, leather, 
 silk or woolen ribbon, straw and the like may 
 be used as material for braiding. 
 
THE FIFTEENTH GIFT. 
 
 THE INTERLACING SLATS. 
 
 (plates lxv. and lxvi.) 
 
 Froebel, in his Gifts of the Kinder-Garten, 
 does not present anything perfectly new. All 
 his means of occupation are the result of care- 
 ful observation of the playing child. But he 
 has united them in one corresponding whole ; 
 he has invented a method, and by this method 
 presented the possibility of producing an ex- 
 haustless treasure of formations which, each 
 influencing the mind of the pupil in its pecu- 
 liar way, effect a development most harmoni- 
 ous and thorough of all the mental faculties. 
 The use of slats for interlacing is an occupa- 
 tion already known to our ancestors, and who 
 has not practiced it to some extent in the 
 days of childhood ? But who has ever suc- 
 ceeded in producing more than five or six 
 figures with them ? Who has ever derived, 
 from such occupation, the least degree of that 
 manual dexterity and mental development, 
 inventive power and talent of combination, 
 which it affords the pupils of the Kinder-Gar- 
 ten, since Froebel's method has been applied 
 to the material ? 
 
 Our slats, ten inches long, three-eighths of 
 an inch broad and one-sixteenth of an inch 
 thick, are made of birch or any tough wood, 
 and a dozen of them are sufficient to produce 
 quite a variety of figures. They form, as it 
 were the transition from the plane of the tab- 
 let to the line of the staffs, (Ninth Gift) differ- 
 ing, however, from both, in the fact that forms 
 produced by them are not bound to the plane, 
 but contain in themselves a sufficient hold to 
 be separated from it. 
 
 The child first receives one single slat. Ex- 
 
 amining it, it perceives that it is flexible, that 
 its length surpasses its breadth many times, 
 and again that its thickness is many times 
 less than its breadth. 
 
 Can the pupil name some objects between 
 which and the slat, there is any similarity ? 
 
 The rafters under the roof of a house, and 
 in the arms of a wind-mill, and the laths of 
 which fences, and certain kinds of gates, and 
 lattice work are made, are similar to the slat. 
 
 The child ascertains that the slat has two 
 long plane sides and two ends. It finds its 
 middle or center point, can indicate .the upper 
 and lower side of the. slat, its upper and lower 
 end, and its right and left side. After these 
 preliminaries, a second slat is given the child. 
 On comparison the child finds them perfectly 
 alike, and it is then led to find the positions 
 which the two slats may occupy to each other. 
 They can be laid parallel with each other, so 
 as to touch one another with the whole length 
 of their sides, or they may not touch at all. 
 
 They can be placed in such positions that 
 their ends touch in various ways, and can be 
 laid crosswise, over or under one another. 
 
 With an additional slat, the child now con- 
 tinues these experiments. It can lay various 
 figures with them, but there is no binding or 
 connecting hold. Therefore as soon as it at- 
 tempts to lift its work from the table, it falls 
 to pieces. 
 
 By the use oifour slats, it becomes enabled 
 to produce something of a connected whole, 
 but this only is done, when each single slat 
 coines in contact with at least three other slats. 
 
GUIDE TO KINDER-GARTNERS. 
 
 65 
 
 Two of these should be on one side, the third 
 or middle one should rest on the other side 
 of the connecting slat, so that here again the 
 law of opposites and their mediation is fol- 
 lowed and practically demonstrated in every 
 figure. 
 
 It is not easy to apply this law constantly 
 in the most appropriate manner. But this 
 ver}' necessity of painstaking, and the reason- 
 ing, without which little success will be at- 
 tained, is productive of rich fruit in the de- 
 velopment of the pupil. 
 
 The child now places the slat aa horizon- 
 tally upon the table. £b is placed across it 
 in a perpendicular direction ; cc in a. slanting 
 direction under a and b, and eld is shoved under 
 aa and over bb and under cc, as shown in Fig. i. 
 
 This gives a connected form, which will not 
 easily drop apart. The child investigates 
 how each single slat is held and supported — 
 it indicates the angles, which were created, 
 and the figures which are bounded by the va- 
 rious parts of the slats. 
 
 To show how rich and manifold the material 
 for obse'rvation and instruction given in this 
 one figure is, we will mention that it contains 
 twenty-four angles, of which 8 (i — 8) are 
 right, 8 (9 — 16) acute, and 8 (17 — 24) obtuse 
 — formed by one perpendicular slat, bb, one 
 horizontal, aa, one slanting from left above 
 to right below, cc, and another slanting from 
 right above to left below, dd. 
 
 Each single slat touches each other slat 
 once ; two of them, aa and bb, pass over two 
 and under one, and the others, cc and dd, pass 
 under two and over one of the other slats, by 
 which interlacing, three small figures are 
 formed within the large figure, one of which 
 is a figure with two right, one obtuse and one 
 acute angle, (3, 6, 22, 10), and four unequal 
 sides, and two others, one of which is a right 
 angled triangle with two equal sides, and the 
 other is a right angled triangle with no equal 
 sides. 
 
 By drawing the slats of Fig. i apart. Fig. 
 2, an acute angled triangle is produced — by 
 drawing them together, Fig. 3 results, from 
 
 which the acute angled triangle, Fig. 4, can 
 again be easily formed. Each of these fig- 
 ures present? abundant matter for* investiga- 
 tion and instructive conversation, as shown 
 above in connection with Fig. i. 
 
 The child now receives a fifth slat. Sup- 
 pose we have Fig. 2, consisting of four slats 
 — ready before us — we can, by adding the 
 fifth slat, easily produce what appears on 
 Plate LXV. as Fig. 8. 
 
 If the five slats are disconnected, the child 
 may lay two, perpendicularly at some distance 
 from each other, a third in a slanting position 
 over them from right above to left below, and 
 a fourth in an opposite direction, v.heu the 
 two latter will cross each other in their mid- 
 dle. By means of the fifth slat the interlac- 
 ing then is carried out, by sliding it from 
 right to left under the perpendicular over the 
 crossing two, and again under the other perpen- 
 dicular slat, and thereby the figure 5 made firm. 
 
 By bending the perpendicular slats together. 
 Fig. 6 is produced; when the horizontal slat 
 assumes a higher position, a five angled fig- 
 ure appears — one of the slanting slats, how- 
 ever, has to change its position also, as shown 
 in Fig. 7. In Fig. 8, the horizontal slat is 
 moved downward. In Fig. 9, the original 
 position of the crossing slats is changed ; in 
 the triangle. Fig. lo, still more, and in Figs. 
 II and 12, other changes of these slats are 
 introduced. 
 
 The addition of a sixth slat enables us still 
 further to form other figures from the previous 
 ones — Fig. 17 can be produced from 9, 18 
 from 10 or 11, 22 from 12, and then a fol- 
 lowing series can be obtained by drawing 
 apart and shoving together as heretofore. 
 
 Let us begin thus : the child lays (Fig. 13) 
 two slats horizontally upon the table — two 
 slats perpendicularly over them ; a large 
 square is produced. A fifth slat horizontally 
 across the middle of the two perpendicular 
 slats, gives two parallelograms, and by con- 
 necting the si.xth slat from above to below with 
 the three horizontal slats, so that the middle 
 one is under and the two outside slats over it, 
 
66 
 
 GUIDE TO KINDER-GARTNERS. 
 
 the child will have formed four small squares, 
 of equal size. 
 
 The figures 17 and 18, (triangles,) and 19 
 and 23, (hexagons,) deserve particular atten- 
 tion, because they afford valuable means for 
 mathematical observations. 
 
 On Plate LXVI. we find some few ex- 
 amples of seven intertwined slats, (Figs. 25 — 
 28,) of eight slats, (Figs. 29 — 36,) of nine slats, 
 (Figs. 37 — 40,) and often slats, (Figs. 41 — 43.) 
 
 All we have given in the above are mere 
 hints to enable the teacher and pupil to find 
 more readily by individual application, the 
 richness of figures to be formed with this oc- 
 cupation material. 
 
 It is particularly mathematical forms, reg- 
 ular polygons, (Figs. 28, 31, 40, 42,) contem- 
 plation of divisions, produced by diagonals, 
 etc., planes and proportions of form, which, 
 informs of knowledge, are brought before the 
 eye of the pupil, with great clearness and dis- 
 tinctness, by the interlacing slats. 
 
 In the meantime, it will afford pleasure to 
 behold the forms of beauty, as given in Figs. 
 3°) 33; 37; nor should \\i^ forms of life be 
 forgotten, as they are easily produced by a 
 larger number of slats, (Fig. 39 — a fan ; 35 
 and 36 — fences,) by combining the work of 
 several pupils. 
 
 The figures are not simply to be constructed 
 and to be changed to others, but each of them 
 is to be submitted to a careful investigation 
 by the child, as to its angles, its constituent 
 parts, and their qualities, and the service each 
 individual slat performs in the figure as indi- 
 cated with Fig. I, on page LXV. 
 
 The occupation with this material will fre- 
 quently prove perplexing and troublesome 
 to the pupil ; oftentimes he will try in vain 
 to represent the object in his mind. 
 
 Having almost successfully accomplished 
 the task, one of the slats will glide out from 
 his structure, and the whole will be a mass 
 of ruins. It was the one slat, which, owing to 
 its dereliction in performing its duty, des- 
 troyed the figure, and prevented all the others 
 from performing theirs. 
 
 It will not be difficult for the thinking 
 teacher to derive from such an occurrence, 
 the opportunity to make an application to 
 other conditions in life, even within the sphere 
 of the young child, and its companions in and 
 out of school. The character of this occu- 
 pation does not admit of its introduction be- 
 fore the pupils have spent a considerable time 
 in the Kinder-Garten, in which it is only be- 
 gun, and continued in the primary depart- 
 ment. 
 
 THE SIXTEENTH GIFT. 
 
 THE SLAT WITH MANY LINKS. 
 
 This occupation material, which may be 
 used at almost any grade of development in 
 the Kinder Garten, the primary and higher 
 school departments, is so rich in its applica- 
 tions, that we cannot attempt to describe it 
 extensively, nor give illustrations of the vari- 
 ous ways in which it can be rendered useful. 
 Suffice it to say, that it may be employed in 
 representing all various kinds of lines, angles 
 
 and mathematical figures, and that even forms 
 of life and beauty may be presented by it. 
 
 We have slats with 4, 6, 8 and 16 links, 
 which are introduced one after the other when 
 opportunities offer. In placing the first. into 
 the hand of the child, we would ask him to 
 unfold all the links of the slat, and to place 
 it upon the table so as to represent a perpen- 
 dicular, horizontal, and then an oblique line. 
 
GUIDE TO KINDER-GARTNERS. 
 
 67 
 
 By bending two of the links perpendicularly, 
 and the two others horizontally, we form a 
 right angle. Bending one of the legs of the 
 angle toward, or from the other, we receive 
 the acute and obtuse angles, which grow 
 smaller or larger, the nearer or farther the 
 legs are brought to, or from each other, until 
 we reduce the angles to either a perpendicular 
 line of two links' length, or a horizontal line 
 of the length of four links. 
 
 We may then form a square. Pushing two 
 opposite corners of it toward each other, and 
 bending the first link so as to cover with 
 it the second, and, by then joining the 
 end of the fourth link to where the first 
 and second are united, we shall form an 
 equilateral triangle. (Which other triangle 
 can be formed with this slat, and how ?) 
 
 The capital letters V, W, N, M, Z, and the 
 figure 4 can be easily produced by the chil- 
 dren, and many figures be constructed by the 
 teacher in which the pupils may designate the 
 
 number and kinds of angles, which they con- 
 tain, as is done with the movable slats on 
 other occasions. 
 
 The slats with 6, 8 and 16 links, to be 
 introduced one after the other, if used 
 in the manner here indicated, can be ren- 
 dered exceedingly interesting and instruct- 
 ive to the pupils. Their ingenuity and in- 
 ventive power will find a large field in the 
 occupation with this material if, at times, 
 they are allowed to produce figures them- 
 selves, of which the more advanced pupils 
 may make drawings and give a description 
 of each orally. 
 
 It would be needless to enlarge here upon 
 the richness of material afforded by this gift, 
 as half an hour's study of and practice with it 
 will convince each thinking teacher fully of 
 the treasure in her hand and certainly make 
 her admire it on account of the simplicit)' of 
 its application for educational purposes in 
 school and family. 
 
 THE SEVENTEENTH GIFT. 
 
 MATERIAL FOR INTERTWINING. 
 
 (PLATES LXVII., LXVIII.) 
 
 Intertwining is an occupation similar to 
 that of interlacing. Aim of both is repre- 
 sentation of plane — outlines. In the occupa- 
 tion with the interlacing slats we produced 
 forms, which were to be destroyed again, or 
 whose peculiarities, at least, had to be changed 
 to produce something new ; here, we produce 
 permanent results. There, the material was 
 in everj' respect a ready one ; here, the pupil 
 has to prepare it himself There, hard slats 
 of little flexibility ; here, soft paper, easily 
 changed. There, production of purely math- 
 ematical forms by carefully employing a given 
 material ; here, production of similar forms 
 
 by changing the material, which forms, how- 
 ever, are forms of beauty. 
 
 The paper strips, not used when preparing 
 the folding-sheets, are used as material, adapted 
 for the present occupation. They are strips 
 of white or colored paper, from eight to ten 
 inches long and varying in breadth. Each 
 strip is subdivided in smaller strips of three- 
 quarters of an inch wide, which by folding 
 their long sides are transformed to threefold 
 strips of eight to ten inches long and one- 
 quarter of an inch wide. 
 
 The children will not succeed well, in form- 
 ing regular figures from these strips at first. 
 
GUIDE TO KINDER-GARTNERS. 
 
 As the main object of tliis occupation is to 
 accustom the child to a clean, neat and cor- 
 rect performance of his task, some of the 
 tablets of Gift Seven are given him as pat- 
 terns to assist liim ; or the child is led to draw 
 on his slate the three, four, or many cornered 
 forms, and to intertwine his paper strips ac- 
 cording to these. 
 
 First, a right angled isosceles triangle is used 
 for laying around it one of these strips so as 
 to enclose it entirely. We begin with the left 
 cathetus, put the tablet upon the strip, folding 
 it toward the right over the right angle. The 
 break of the paper is well to be pressed down, 
 and then the strip is again folded around the 
 acute angle toward the left. Where the hy- 
 potenuse (large side) touches the left cathetus 
 (small side), the strip is cut and the ends of 
 the figure there closed by gluing them to- 
 gether by some clean adhesive matter. Care 
 should be taken that the one end of each side 
 be under, the other over, that of the other. 
 
 Thus the various kinds of triangles, (Figs. 
 I — 3,) squares, rhombus, rhomboids, etc., are 
 produced. 
 
 Two like figures are combined, as shown in 
 Figs. 4 — 6. If strips prove to be too short, 
 the child is shown how to glue them together, 
 to procure material for larger and more com- 
 plicated forms. Thus, it produces, with one 
 long strip. Figs. i6, i8, 19, 20; with two long 
 strips. Figs. 17, 21. Fig. 22 shows the natu- 
 ral size ; all others are drawn on a somewhat 
 reduced scale. It cannot be difficult to pro- 
 duce a great variety of similar figures, if one 
 will act according to the motives obtained with 
 and derived from the occupation with the in- 
 terlacing slats. 
 
 This occupation admits of still another and 
 very beautiful modification, by not only pinch- 
 ing and pressing the strip where it forms 
 angles, but by folding it to a rosette. This 
 process is illustrated in Figs. 7 — 9. The strip 
 is first pinched toward the right, (Fig. 7,) then 
 follows the second pinch downward, (Fig. 8,) 
 then a third toward the left, when the one end 
 of the strip is pushed through under the other, 
 (Fig- 9-) 
 
 Here, also, simple triangles, squares, pen- 
 tagons and hexagons are to be formed, then 
 two like figures combined, and finally more 
 complicated figures produced. (Compare ex- 
 amples given in Figs. 10 — 15.) 
 
 Whatever issues from the child's hand suffi- 
 ciently neat and clean and carefully wrought, 
 may be mounted on stiff paper or bristol 
 board, and disposed of in many ways. 
 
 The occupation of intertwining shows 
 plainly how by combination of simple mathe- 
 matical forms, forms of beauty may be pro- 
 duced. These latter should predominate in 
 the Kinder-Garten, and the mathematical are 
 of importance as they present the elements for 
 their construction. The mathematical ele- 
 ment of all our occupations is in so far of 
 significance, as the child receives from it 
 impressions of form ; but of much more im- 
 portance is the development of the child's 
 taste for the beautiful, because with it, the 
 idea of the good is developed in the mean- 
 time. 
 
 As the various performances of this occu- 
 pation, cutting, folding and mounting, require 
 a somewhat skilled hand, it is introduced 
 in the upper section of the Kinder-Garten 
 only. 
 
THE EIGHTEENTH GIFT. 
 
 MATERIAL FOR PAPER- FOLDING. 
 
 (plates lxix. to lxxi.) 
 
 Froebel's sheet of paper for folding, the 
 simplest and cheapest of all materials of oc- 
 cupation, contains within it a great multitude 
 of instructive and interesting forms. Almost 
 every feature of mathematical perceptions, ob- 
 tained by means of previous occupations, we 
 again find in the occupation of paper-folding. 
 It is indeed a compendium of elementary 
 mathematics, and has, therefore, very justly 
 and judiciously been recommended as a use- 
 ful help in the teaching of this science in 
 public schools. 
 
 Lines, angles, figures, and forms of all 
 varieties appear before us, after a few mo- 
 ments' occupation with this material. The 
 multitude of impressions, however, should 
 not misguide us ; and we should always, and 
 more particularly in this work, be careful to 
 accompany the work of the children with nec- 
 essarj' conversation and pleasant entertain- 
 ment, for the relief of their young minds. 
 
 We prepare the paper for folding in the fol- 
 lowing manner : 
 
 Take half a sheet of letter paper, place it 
 upon the table in such a manner as to have 
 the longest sides extend from left to right. 
 Then halve it by covering the upper corners 
 with the lower ones, (Fig. i.) Then turn the 
 now left and right upper (previously lower) 
 corners back, towards the center ; invert the 
 paper ; turn also the two other corners toward 
 the center, and then we have the form of a 
 trapezium, (Fig. 2.) Unfolding the sheet at 
 its base line, a hexagon, (Fig. 3,) will show 
 itself; in which we obsen'e four triangles, of 
 
 which two and two lie together, forming a 
 larger triangle. At the base lines of these 
 larger triangles, the sheet is again folded, and 
 neatly and accurately cut, severing thereby 
 the two large double, lying triangles from the 
 single and oblong strips of paper. 
 
 Each of these triangles we cut through 
 from where the sides of the small triangles 
 touch each other, unfold the small triangles, 
 and we now have four square pieces, and one 
 oblong piece of paper, (Fig. 4.) The former 
 w^e employ for folding, the latter we keep for 
 future use, in the occupations of intertwining, 
 braiding, or weaving. 
 
 The child should be accustomed to ±e 
 strictest care and cleanliness in the cutting as 
 well as the folding. 
 
 This is necessary, because paper carelessly 
 folded and cut, will not only render more 
 difficult every following task, nay, make im- 
 possible ever}' satisfactory result ; especially, 
 should this be the case, because, we do 
 not intend simply to while away our own 
 and the child's precious time, but are en- 
 gaged in an occupation whose final aim is 
 acquisition of ability to work, and to work 
 well — one of the most important claims 
 hum.in society is entitled to make upon each 
 individual. 
 
 The child prepares for himself, in the man- 
 ner described, a number of folding sheets, 
 and submits them to a series of regular 
 changes, by bending and folding, in conse- 
 quence of which the fundamental forms are 
 produced, from w^hich sequels of forms of 
 
^o 
 
 GUIDE TO KINDER-GARTNERS. 
 
 life and beauty are subseqently developed, 
 by means of the law of opposites. 
 
 On the road to this goal, a surprising num- 
 ber of forms of knowledge present them- , 
 selves. 
 
 The sheet is now folded once more, fol- 
 lowing the diagonal, (Fig. 5,) and will then 
 present, when unfolded, the division of the 
 square, in two right-angled isosceles triangles. 
 
 Folded once more according to the other 
 diagonal, (Fig. 6,) and again unfolded, we find 
 each of the large triangles, halved by a per- 
 pendicular, (Fig. 7.) Now the lower corner 
 is bent upon the left, and the right one upon 
 the upper, and the sheet is so folded, that it 
 is divided into equal oblong halves by a 
 transversal. The same is done to the op- 
 posite transversal, and we have the Fig. 9, 
 affording a multitude of mathematical object 
 perceptions. 
 
 If we now take the lower corner, (Fig. 9,) 
 bend it exactly toward the center of the sheet 
 and fold it, the pentagon, (Fig. 10,) will be the 
 result. We fold the opposite corner in like 
 manner and produce the hexagon, (Fig. 11,) 
 and finally with the two remaining corners, 
 Fig. 12" is formed containing four triangles, 
 touching one another with their free sides, 
 each of them again showing a line halving 
 them in two equal triangles. 
 
 If we invert 12% we have 12'', a connected 
 square, in which the outlines of eight congru- 
 ent triangles appear. If 12° is unfolded we 
 shall see beside a multiplication of previous 
 forms, parallelograms also. If we start from 
 12°, fold the corners toward the middle, (Fig. 
 15,) we shall receive a form consisting of 
 double layers of paper, and showing four tri- 
 angles, under which again, four separate 
 squares are found. This is the fundamental 
 form for a series of forms of life, (Fig. 16.) 
 
 It is utterly impossible to give a minute de- 
 scription how forms of life may be produced 
 from this fundamental form. Practical at- 
 tempts and occasional observation in the 
 Kinder-Garten will be of more assistance tljan 
 the most detailed illustrations and descrip- 
 
 tions. Froebel's Manual mentions, among 
 others, the following objects : A table-cloth 
 with four hanging corners, a bird, a sail boat, 
 a double canoe, a salt-cellar, flower, chemise, 
 kite, wind-mill, table, cigar-holder, flower-pot, 
 looking glass, boat with seats, etc. Still richer 
 become the forms of life, if we bend the cor- 
 ners of the described fundamental form, once 
 more toward the middle. In connection with 
 this, the manual mentions the following forms : 
 the knitting-pouch, the chest of drawers, the 
 boots, the hat, the cross, the pantaloons, the 
 frame, the gondola, etc. For the construction 
 of these forms, it is advisable to use a larger 
 sheet of paper, perhaps half a sheet of letter 
 paper. 
 
 But the simple fundamental form, for the 
 forms of life, is also the fundamental form for 
 the forms of beauty, contained on Plate LXX., 
 (Fig. 16.) Unfold the fundamental form, do 
 not press the corners but first the middle of 
 the upper and lower side, then the two other 
 sides toward the middle of the sheet, and the 
 double canoe will be the result, (hexagon with 
 two long and four short sides.) If the over- 
 reaching triangles are now bent back toward 
 the middle. Fig. 17 appears, from which, up 
 to Fig. 21, the following forms are easily con- 
 structed according to the law of opposites. 
 
 From quite a similar fundamental form, the 
 series 22 — 27 originates. 
 
 If we finally take the sheet as represented, 
 in 12'' fold the lower right corner toward the 
 middle, also the left upper, (Fig. 13,) also the 
 two remaining corners, we shall have four 
 triangles, consisting of a double layer of pa- 
 per which may be lifted up from the square 
 ground and which upper layer again is divi- 
 ded in two triangles, (Fig. 14.) 
 
 Invert this figure and you will have Fig. 28, 
 four single squares, the fundamental form of 
 a series of forms of beauty on Plate LXXI. ; 
 the latter easily to be derived from this former, 
 under the guidance of the well known law of 
 opposites. 
 
 The hints given in the above might be aug- 
 mented to a considerable extent and still not 
 
GUIDE TO KINDER-GARTNERS. 
 
 71 
 
 exhaust the matter. They are given espe- 
 cially to stimulate teacher and child to indi- 
 vidual practical attempts in producing forms 
 by folding. The best results of their activity 
 can be improved by cutting out or coloring, 
 which adds a new and interesting change to 
 this occupation. A change of the fundamental 
 form in three directions yields various series 
 of forms of beautj', which may be multi- 
 plied ad infinitum. Thereby, not only the idea 
 of sequel in representations is given, but also 
 the understanding unlocked for the various 
 orders in nature. 
 
 Furthermore, this occupation gives the pu- 
 
 pil such manual dexterity as scarcely any 
 other does, and prepares the way to various 
 female occupations, besides being immediately 
 preparatory to all plastic work. Early training 
 in cleanliness and care is also one of the re- 
 sults of a protracted use of the folding sheet. 
 It is evident that only those children who 
 have been a good while in the Kinder-Garten, 
 can be employed in this department of occu- 
 pation. The peculiar fitness of the folding 
 sheet for mathematical instruction beyond the 
 Kinder-Garten, must be apparent after we 
 have shown how useful it can be made in this 
 institution. 
 
 THE NINETEENTH GIFT. 
 
 MATERIAL FOR PEAS-WORK. 
 
 (plates lxxii. and lxxiii.) 
 
 We have already tried, in connection with 
 the Ninth Gift, (the laying staffs,) to render 
 permanent the productions of the pupils, by 
 stitching or pasting them to stiff paper. We 
 satisfied, by so doing, a desire of the child, 
 which grows stronger, as the child grows 
 older — the desire to produce by his own activ- 
 ity certain lasting results. It is no longer the 
 incipient instinct of activity which governs 
 the child, the instinct which prompted it, ap- 
 parently without aim, to destroy everything 
 and to reconstruct in order to again de- 
 stroy. A higher pleasure of production has 
 taken its place ; not satisfied by mere doing, 
 but requiring for its satisfaction also delight 
 in the created object — if even unconsciously — 
 the delight of progress, which manifests itself 
 in the production, and which can be observed 
 only in and by the permanency of the object 
 which enables us to compare it with objects 
 previously produced. 
 
 To satisfy the claims of the pupil in this 
 
 direction in a high degree, the working with 
 peas is eminently fitted, although considerable 
 manual skill is required for it, not to be ex- 
 pected in any child before the fifth year. The 
 material consists of pieces of wire of the thick- 
 ness of a hair-pin, of various sizes in length, 
 and pointed at the ends. They again represent 
 lines. As means of combination, as embodied 
 points of junction, peas are used, soaked about 
 twelve hours in water and dried one hour pre- 
 vious to being used. They are then just soft 
 enough to allow the child to introduce the 
 points of the wires into them, and also hard 
 enough to afford a sufficient hold to the latter. 
 
 The first exercise is to combine two wires, 
 by means of one pea, into a straight line, an 
 obtuse, right, and acute angle. What has been 
 said in regard to laying of staffs in connection 
 with Fig. I — 23 on Plate XXX. will sen'e 
 here also. 
 
 Of three wires, a longer line is formed ; 
 angles, with one long, and one short side. 
 
72 
 
 GUIDE TO KINDER- GARTNERS. 
 
 The three wires are introduced into one pea, 
 so that they meet in one point ; two parallel 
 lines may be continued by a third ; finally the 
 equilateral triangle is produced. 
 
 Then follows the square, parallelogram, 
 rhomboid ; diagonals may be drawn and the 
 forms shown on Plate LXXIL, figures i — lo, 
 be produced. The possibility of representing 
 the most manifold forms of knowledge, of life 
 and of beauty, is reached, and the forms pro- 
 duced may be used for other purposes. The 
 child may produce six triangles of equal size, 
 and repeat with them all the exercises, gone 
 through with the tablets, and may enlarge 
 upon them. 
 
 Or the child may prepare 4, 8, 16 right an- 
 gled triangles, or obtuse angled, or acute an- 
 gled triangles and lay with them the figures 
 given on Plate LXXIL, etc., for the course of 
 drawing, and carry them out still further. 
 
 After these hints it seems impossible not 
 to occupy the child in an interesting and in- 
 structive manner. 
 
 But the condition attached to each new Gift 
 of the Kinder-Garten is some special progress 
 in its course. 
 
 We produced outlines of many objects with 
 the staffs ; all formations, however, remained 
 planes, whose sides were represented by staffs. 
 In the working with peas, the wires represent 
 edges, the peas serve as corners, and these 
 skeleton bodies are so much more instructive 
 as they allow the observation of the outer 
 forms in their outlines, and the inner structure 
 and being of the body at the same time. 
 
 The child unites two equilateral triangles 
 by three equally long wires, and forms thereby 
 a prism, (Fig. 14;) four equilateral triangles, 
 give the three-sided pyramid ; eight of them, 
 the octahedron. (Figs. 15 and 16.) 
 
 From two equal squares, united by four 
 wires of the length of the sides, the skele- 
 ton cube. Fig. 17, is formed; if the uniting 
 wires are longer than the sides of the square, 
 the four-sided column (Fig. 8); is one of the 
 squares larger than the other, a topless pyra- 
 mid will be produced, etc. 
 
 It is hardly possible that pupils of the 
 KinderGarten should make any further prog- 
 ress in the formation of these mathematical 
 forms of crystallization, as the representation 
 of the many-sided bodies, and especially the 
 development of one from another, requires 
 greater care and skill than should be expected 
 at such an early period of life. It will be re- 
 served for the primary, and even a higher 
 grade of school, to proceed farther on the 
 road indicated, and in this manner prepare 
 the pupil for a clear understanding of regular 
 bodies. (Fig. 19 shows how the octahedron 
 is contained in the cube.) 
 
 This, however, does not exclude the con- 
 struction by the more advanced pupils of the 
 Kinder-Garten, of simple objects, in their 
 surroundings, such as benches, (Fig. 21,) 
 chairs, (Fig. 23,) baskets, etc., or to try to 
 invent other objects. 
 
 Whoever has himself tried peas-work, will 
 be convinced of its utility. Great care, much 
 patience, are needed to produce a somewhat 
 complicated object ; but a successful structure 
 repays the child for all painstaking and per- 
 severance. By this exercise, the pupils im- 
 prove in readiness of construction, and this 
 is an important preparation for organiza- 
 tion. 
 
 More advanced pupils try also, successi.- 
 fully, to construct letters and numerals, with 
 the material of this Gift. 
 
 The bodies produced by peas-work may 
 be used as models in the modeling depart- 
 ment. The one occupation is the comple- 
 ment of the other. The skeleton cube allows 
 the observation of the qualities of the solid 
 cube, in greater distinctness. The image of 
 the body becomes in this manner more per- 
 fect and clear, and above all, the child is 
 led upon the road, on which alone it is 
 enabled to come into possession of a true 
 knowledge and correct estimate of things; 
 the road on which it learns, not only to ob- 
 serve the external appearance of things, but 
 in the meantime, and always, to look at their 
 internal being. 
 
THE TWENTIETH GIFT. 
 
 MATERIAL FOR MODELING. 
 
 (plate lxxiv.) 
 
 Modeling, or working in clay, held in high 
 estimation by Froebel, as an essential part of 
 the whole of his means of education is, strange 
 to say, much neglected in the Kinder-Garten. 
 As the main objection to it named is that the 
 children, even with the greatest care, can not 
 prevent occasionally soiling their hands and 
 their clothes. Others, again, believe that an 
 occupation, directly preparing for art, very 
 rarely can be continued in life. They call it, 
 therefore, aimless pastime without favorable 
 consequences, either for internal development 
 or external happiness. 
 
 If it must be admitted that the soiling of 
 the hands and clothing cannot always be 
 avoided, we hold that for this very reason, 
 this occupation is a capital one, for it will 
 give an opportunity to accustom the children 
 to care, order and cleanliness, provided the 
 teacher herself takes care to develop the sense 
 of the pupils, for these virtues, in connection 
 with this occupation ; as on all other occasions, 
 she should strive to excite the sense of clean- 
 liness as well as purity. Certainly, parts of 
 the adhesive clay will stick to the little fingers 
 and nails of the children, and their wooden 
 knives ; but, pray, what harm can grow out of 
 this? The child may learn even from this 
 fact. It may be remarked in connection with 
 it, that the callous hand of the husbandman, 
 the dirty blouse of the mechanic, only show 
 the occupation, and cannot take aught from 
 the inner worth of a man. As regards the ob- 
 jection to this occupation as aimless and 
 without result, it should be considered that 
 
 occupation with the beautiful, even in its 
 crudest beginnings, always bears good fruit, 
 because it prepares the individual for a true 
 appreciation and noble enjoyment of the 
 same. Just in this the significance of Froebel's 
 educational idea partly rests, that it strives to 
 open every human heart for the beautiful 
 and good — that it particularly is intended to 
 elevate the social position of the laboring 
 classes, by means of education, not only in 
 regard to knowledge and skill, but also, in 
 regard to a development of refinement and 
 feeling. 
 
 Representing, imitating, creating, or trans- 
 forming in general, is the child's greatest en- 
 joyment. Bread-crumbs are modeled by it 
 into balls, or objects of more complicated 
 form, and even when biting bits from its 
 cooky, it is the child's desire to produce 
 for?n. If a piece of wax, putty, or other plia- 
 ble matter, falls into its hands, it is kneaded 
 until it assumes a form, of which they may 
 assert that it represents a baby, — the dog 
 Roamer, or what not ! Wet sand, they press 
 into their little cooking utensils, when playing 
 "house-keeping," and pass off the forms as 
 puddings, tarts, etc. ; in one word, most chil- 
 dren are born sculptors. Could this fact have 
 escaped Froebel's keen observation? He 
 has here provided the means to satisfy this 
 desire of the child, to develop also this talent, 
 in its very awakening. 
 
 According to Froebel's principle, the first 
 exercises in modeling are the representation 
 of the fourteen stereometric fundamental forms 
 
74 
 
 GUIDE TO KINDER- GARTNERS. 
 
 of crystallization, which he presents in a box, 
 by themselves as models. Starting from the 
 cube the cylinder follows — then the sphere 
 pyramid with 3, 4 and 6 sides, the. prism in its 
 various formations of planes, the octahcdro?t 
 or decahedron and cosahedron, or bodies with 
 8, 12 and 20 equal sides or faces, etc., etc. 
 However interesting and instructive this course 
 may be, we prefer to begin with somewhat 
 simpler performances, leaving this branch of 
 this department for future time. 
 
 The child receives a small quantity of clay, 
 (wa.x may also be used,) a wooden knife, a 
 small board, and a piece of oiled paper, on 
 which it performs the work. If clay is used, 
 this material should be kept in wet rags, in 
 a cool place, and the object formed of it, 
 dried in the sun, or in a mildly-heated stove, 
 and then coated with gum arabic, or var- 
 nish, which gives them the appearance of 
 crockery. 
 
 First, the child forms a sphere, from which it 
 may produce many objects. If it attaches a 
 stem to it, it is a cherry ; if it adds depressions 
 and elevations, which represent the dried calyx, 
 it will look like an apple ; from it the pear, nut, 
 potato, a head, may be molded, etc. Many 
 small balls made to adhere to one another 
 may produce a bunch of grapes, (Figs. 
 
 i-S.) 
 
 From the ball or sphere, a cylindrical body 
 may be formed, by rolling on the board, usu- 
 ally called by the children a loaf of bread, 
 cigar, a candle, loaf of sugar, etc. 
 
 A bottle, a bag filled with flour or some- 
 thing else, can also easily be produced. 
 
 Very soon the child will present the cube, 
 an old acquaintance and playmate. From it, 
 it produces a house, a bo.x, a coffee-mill and 
 similar things. Soon other forms of life will 
 grow into existence, as plates, dishes, animals 
 and human beings, houses, churches, birds' 
 nests, etc., etc. If this occupation is intended 
 to be more than mere entertainment, it is 
 necessary to guide the activity of the child in 
 a definite direction. 
 
 The best direction to be followed in Froe- 
 
 bel's occupations is that for the development 
 of regular forms of bodies. Fundamental 
 form, of course, is the sphere. The child 
 represents it easily, if perhaps not exactly 
 true. 
 
 By pressing and assisted by his knife, the 
 one plane of the sphere is changed to several 
 planes, corners, edges, which produces the 
 cube. If the child changes its corners to 
 planes (indicated in Fig. 12,) a form of four- 
 teen sides is produced. If this process is 
 continued so that the planes of the cube are 
 changed to corners, the octahedron is the re- 
 sult, (Fig. 13.) By continued change of edges 
 to planes and of planes to corners, the most 
 important regular forms of crystallization will 
 be produced, which occupation, however, as 
 mentioned before, belongs rather to a higher 
 grade of school, and is therefore better 
 postponed until after the Kinder-Garten 
 training. 
 
 Some regular bodies are more easily 
 formed from the cylinder, the mediation be- 
 tween the sphere and cube. By a pressure of 
 the hand, or by means of his knife, the child 
 changes the one round plane to three or four 
 planes, and as many edges, producing thereby 
 the prism and the four-sided column. 
 
 If we change one of the planes of the cyl- 
 inder to a corner, by forming a round plane 
 from its center to the periphery of the plane, 
 we produce a cone. If we change the sur- 
 face of the cone to three or four planes, we 
 shall have a three or four sided pyramid. If 
 we act in the same manner with the other end 
 of the cylinder, we shall form a double cone, 
 and from it we may produce a three or four- 
 sided double pyramid, etc. If we act in an 
 opposite manner, destroy the edges of the 
 cylinder, we shall again have the sphere. 
 
 Well formed specimens may, to acquire 
 greater durability, be treated as indicated 
 previously. The production of forms and fig- 
 ures from soft and pliable material belongs, 
 undoubtedly, to the earliest and most natural 
 occupations of the human race, and has served 
 all plastic arts as a starting-point. The occu- 
 
GUIDE TO KINDER-GARTNERS. 
 
 75 
 
 pation of modeling, then, is eminently fit to 
 carry into practice Froebel's idea that chil- 
 dren, in their occupations, have to pass through 
 all the general grades of development of hu- 
 man culture in a diminished scale. The 
 natural talent of the future architect or sculp- 
 tor, lying dormant in the child, must needs be 
 called forth and developed by this occupation, 
 as by a self-acting and inventing construction 
 and formation, all innate talents of the child 
 are made to grow into visible reality. 
 
 If we now cast a retrospective look upon 
 the means of occupation in the Kinder- 
 Garten, we find that the material progresses 
 form the solid and whole, in gradual steps to 
 its parts, until it arrives at the image upon 
 the plane, and its conditions as to line and 
 point. For the heavy material, fit only to be 
 placed upon the table in unchanged form, 
 (the building blocks,) a more flexible one 
 is substituted in the following occupations : 
 7vood is replaced hy paper. The paper plane 
 of the folding occupation, is replaced by the 
 paper strip of the weaving occupation, as line. 
 The wooden staff, or very thin ivire, is then 
 introduced for the purpose of executing per- 
 manent figures in connection with peas, repre- 
 senting the point. In place of this material 
 the dratcn line then appears, to which colors 
 are added. Perforating and embroidering 
 introduces another addition to the material 
 to create the images of fantasy, which, in the 
 paper cutting and mounting, again receive 
 new elements. 
 
 The modeling \n clay, or wax, affords the im- 
 mediate plastic artistic occupation, with the 
 most pliable material for the hand of the 
 child. Song introduces into the realm of 
 sound, when movement plays, gymnastics, and 
 dancing, help to educate the body, and insure 
 a harmonious development of all its parts. 
 In practicing the technical manual perform- 
 ances of the mechanic, such as boring, 
 piercing, cutting, measuring, uniting, forming, 
 drawings painting, and modeling, a foundation 
 of all future occupation of artisan and artist 
 
 — synonymous in past centuries — is laid. For 
 ornamentation especially, all elements are 
 found in the occupations of the Kinder-Gar- 
 ten. The forms of beauty in the paper-fold- 
 ing,/. /., serve as series of rosettes and or- 
 naments in relief, as architecture might em- 
 ploy them, without change. The productions 
 in the braiding department contain all con- 
 ditions of artistic weaving, nor does the cut- 
 ting of figures fail to afford richest material 
 for ornamentation of various kinds. 
 
 For every talent in man, means of develop- 
 ment are provided in the Kinder-Garten ma- 
 terial, opportunity for practice is constantly 
 given, and each direction of the mind finds 
 its starting-point in concrete things. No more 
 complete satisfaction, therefore, can be given 
 to the claim of modern pedagogism, that all 
 ideas should be founded on previous percep- 
 tion, derived from real objects, than is done in 
 the genuine Kinder-Garten. 
 
 Whosoever has acquired even a superfi- 
 cial idea only of the significance of Froebel's 
 means of occupation in the Kinder-Garten, 
 will be ready to admit that the ordinary play- 
 things of children can not, by any means, as 
 regards their usefulness, be compared with 
 the occupation material in the Kinder-Gar- 
 ten. That the former may, in a certain de- 
 gree, be made helpful in the development of 
 children, is not denied ; occasional good re- 
 sults with them, however, mostly always will 
 be found to be owing to the child's own in- 
 stinct rather than to the nature of the toy. 
 Planless playing, without guidance and super- 
 vision cannot prepare a child for the earnest 
 sides of life as well as for the enjoyment of 
 its harmless amusements and pleasures. 
 Like the plant, which, in the wilderness even, 
 draws from the soil its nutrition, so the child's 
 mind draws from its surroundings and the 
 means, placed at its command, its educational 
 food. But the rose-bush, nursed and cared 
 for in the garden by the skillful horticulturist 
 produces flowers, far more perfect and beau- 
 tiful than the wild growing sweet-briar. With- 
 out care neither mind nor body of the child 
 
76 
 
 GUIDE TO KINDER-GARTNERS. 
 
 can be expected to prosper. As the latter 
 can not, for a healthful development, use all 
 kinds of food without careful selection, so 
 the mind for its higher cultivation requires a 
 still more careful choice of the means for its 
 development. The child's free choice is lim- 
 ited only in so far as it is necessary to limit 
 the amount of occupation material in order 
 to fit it for systematic application. The child 
 will find instinctively all that is requisite for 
 its mental growth, if the proper material only 
 be presented, and a guiding mind indicate its 
 most appropriate use in accordance with a 
 certain law. 
 
 Froebel's genius has admirably succeeded 
 in inventing the proper material as well as in 
 pointing out its most successful application to 
 prepare the child for all situations in future 
 life, for all branches of occupation in the 
 useful pursuits of mankind. 
 
 When the Kinder-Garten was first estab- 
 lished by him, it was prohibited in its original 
 form and its inventor driven from place to 
 place in his fatherland on account of his lib- 
 eral educational principles, to be carried out 
 in the Kinder Garten. The keen eye of mo- 
 narchial government officials quickly saw that 
 such institution could not turn out willing 
 subjects to tyrannical oppression, and the ru- 
 lers "-^by the grace of God,'' tolerated the 
 Kinder-Garten, only when public opinion de- 
 clared too strongly in its favor. 
 
 In pleading the cause of the Kinder-Gar- 
 ten on the soil of republican America, is it 
 asking too much that all may help in extend- 
 ing to the future generation the benefits which 
 may be derived from an institution so emi- 
 nently fit to educate free citizens of a free 
 country ? 
 
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P A- R T T . 
 
 PARADISE OF C!HlLDHOOD 
 
 A MAMAI. Kdli SKl.|--IXSTl!L-ClIo.\ l.V I'KIKDUICII KUOKIil- L'; 
 KDrCATloNAl, I'UIXCll'I.KS. 
 
 (jiiide to Kinder-Gartners. 
 
 E I) W A R D W I E B E . 
 
 WITH SEVENTY- FOUR PLATES OF ILLUSTRATIONS. 
 
 .MILTON ]}KAULEY >!c COMPANY. 
 
 SIMilN(il-lKLl). .MASS. 
 
PART IV. 
 
 PARA DISE OF CHILDHOOD : 
 
 A MANUAL Fol! SKLF-TN'STRUCTIOX IX FRIEnRICII FliOEBEL'S 
 EDUCATIONAL PRINCIPLES, 
 
 AND A PRACTfCAr 
 
 (jiiide toKinder-Grartners. 
 
 E D W A Pv D \V I E B PJ 
 
 WITH SEVENTY- FOUR PLATES OF ILLUSTRATIONS. 
 
 MILTON BllADLKY & COMPANY 
 
 SPUINCI'IKLl). MASS. 
 
GIFTS. OR OCCUPATION MATERIAL FOR THE 
 
 IK I H D E m«ll A»1PS». 
 
 O0R high' estimation nl' llic tiiorits of tills system of education, lias iiuliicoil us to fit up tlic macliincr.v and 
 fixtures necessary for the |ir.idiutl(in of the Occiipatiox Matkkiai. in an economical and superior manner. 
 
 As the several (iifts have lneii prepared under the direction and liy tlie sii^'sestions of the most conipolent 
 teachers of Kinder-lJartcn in tliis country, we believe they will meet with universal favor; hut any sugiiestions 
 from Practical Kinder-Gartners, will be" thankfully received, and, if considered advantageous, will immediately 
 be embodied in our manufactures. Price Lists furnislied to Dealers and Teachers on application. 
 
 THE GREAT EDUCATIONAL CxAME OF 
 
 Wi: have purchased from the Inventor the entire Patent on the above Wii\-i)i;Rrt:i, ('o.miu 
 STROCTios AM) AJirsF.MF.NT, bv wliicli the jiriiiciples of 
 
 ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION 
 
 Are embodied in one of the most fascinating Games ever devised for Youth or Adults. There 
 this will ]irove the most popular I'arlor Amu.sement even invented. Price §0.(K). 
 
 THE NEW SCRIPTURE GAME OF 
 
 A Combination- op 
 
 CfniflOlli* Bible Qli®^1li#«|i 
 
 In a very pleasine; and Instructive Game. 
 
 -^JVIaqic ^quare^ and -^o^aic ^ablet^, 
 
 Fon Recreation, Kntertainineiit and Instruction, presenting some curious puzzles in the iirojierties of numbers; 
 
 adapted for use in families and school>, 
 
 HY 
 
 EDWARn W. OII.MAM. 
 
 Prof. Lyman of Yale College says in a note to the author of this work : 
 
 "Your device of 'Magic T.tblets' strikes me as one well fitted to aflbrd instruction ,and entertainment for tlie 
 young, and to become popular as an evening amusement. If it shall give to the lovers of mathematical puzzles 
 half Tlie gratification which I received when a boy from Magic S(|uares as commonly exhibited, the young people 
 will have abundant reason tft thank you for your imjiroved method of presentation. 
 
 " The talili'ts and book of problems are put u)) in a neat box complete." Price each, .SLOO. 
 
 THE ZOETROPE, 
 
 TImt OPTICAL WOXOKR— always new, with New Pictures. 
 
 ritOF. BOVEJR'S 
 
 LATEST MANUAL OF CROQUET, 
 
 FOR THE FIELD OR THE PARLOR, ILLUSTRATED. 
 
 Send 10 CEN-TS for the CnOQiin .Maxuat, and complete I'rice List of Games, etc. : or a Stamji for the Price Lists. 
 
 MILTON BRADLKV k (()., 
 
 Spi'iDff/ield. Mass. 
 
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