»«:^ A a A O c^ -~i -n 1 m 4 4 9 ^•^^— > 8 =^= X) 7 8 :i 6 Davis Genetic construction work based on intersecting planes THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES G enctic Construction Work BASED ON INTERSECTING PLANES SOUTHERN BRANCH UNIVERSITY OF CALIFORNIA LIBRARY I ' -?, CALIF, By JESSIE DAVIS Instructor in The Chicago Kindergarten College Published by THE CHICAGO KINDERGARTEN COLLEGE 1200 Michigan Boulevard £>54'^<. Copyright 1908 By JESSIE DAVIS Chicago INTRODUCTION All handwork is not educative any more than all books are instructive. Much time and attention have been wasted in many schools by the so-called occupation work. Even much of the handwork which results in the making of definite objects lacks true educative value. The importance of this new handwork of Miss Jessie Davis is that it is based on the eternal and universal forms of geometry and includes the funda- mental principles of all construction. It therefore connects not only with the industrial and art life of mankind (leading directly into the same), but it is genetic, one kind of a work growing out of the mas- tery of the preceding kind, as, for example, the in- tersection of planes leads the child to a familiarity with diametral lines. These are the chief elements used in the second series and thus is emphasized the central point at which the diametral lines meet. The central point becomes a pivot around which the third series swings, and so on, throughout the entire series. Like all fundamental things this work is exceed- ingly simple. When rightly understood, I feel sure 3 that it will form a strong bond between the kinder- garten and the grades of our public schools, as it contains almost unlimited possibilities of new forms and combinations, thus stimulating the creative ac- tivity of children from the kindergarten age to the grammar grades. I need only add that it has been thoroughly tested with children of various ages and approved by eighteen training teachers. However, the work itself is its own best recommendation. In the following pamphlet, the first series, is given. The others will be published in book form later. ELIZABETH HARRISON, Chicago Kindergarten College. Februarv, 1<)0.2 -2- THE Genetic Construction Work is based on the intersecting planes of the Second Gift. It is called Genetic because it is really generated by these intersecting planes. They give the principle of in- tersection, by means of which the surfaces hold each other together. Thus this construction work is based on an inner constructive principle. The intersecting planes, passing through each other, hold each other together and reveal not the solid, but the constructive principle of the solid. Applying this principle of construction, intersec- tion, to surfaces in many different ways we can make a variety of forms which have the three dimensions of a solid, but which are hollow. Most hollow forms made by man can be made by the child with card board, through intersection. Thus the little child can play his way into the constructive work of mankind. For intersection is the principle used by man. All dovetailing, hinging, brick-laying, mortising, nailing, etc., are ways of in- tersecting surfaces and lines so that they hold each other together. And surely the child is educated through construction work, not so much hy producing the outer form or object, as by finding out and using the making-poiver. The intersecting planes of sphere, cube and cyl- inder are made and cut for the child in order that he may put them together and discover for himself, through play, the principles of construction. The child in playing with them is playing with the universal principle of construction before he makes the particu- lar object. This corresponds to the law of develop- ment by which we use the whole before the parts ; the universal before the particular ; for the particular is generated by the universal. Moreover, these inter- secting planes, being those of the Second Gift, whose three forms are two inches in dimension, show three other principles which will be developed throughout this Genetic Construction A\'ork. The first is form. The circle and square are used. Through division other planes, the oblong, the triangle, the half and quarter circle are produced. Thus we have form, the plane with its name to start with. Not an indefinite surface is given the child, but a definite one ; for he can not put indefinite sur- faces together. They do not fit. The second principle is measui'emcut. The planes are measured. Just the two inch circle and two inch square are given first — no other; for the unit of measurement, one inch, is to be developed. We do not each make this imit, and yet through using it each of us remakes it, confirms its use. It is a great thing for a child to begin to use the same unit of measure as his race. He is using the same measure others use, and thereby becoming universal. But this unit is not directly given. Through division the child derives it. He re-gives it to himself; re-makes this measure which is made and given to him. The two inch plane is measured, but the child did not do it. By division he can find this unit, and so gain it for himself, not have it arbitrarily given. xA.lso, the two inch size is easy for little hands to use. A one inch size would be too small, and larger, if much larger, too large, at least to begin with. Possibly a three inch plane would not differ much in point of handling from a two inch one, but the child could never through its easiest division reach the unit of measure. The four inch plane would require too much division to reach the unit of measure, and would besides be a little too large. By actual experience, the two inch size is not too small and it enables the child himself, through the first and easiest division to find the unit -of measure which he can now use in measuring any size; for three inch and four inch planes are not to be kept from him. As he becomes older and grows in ability to handle different sizes, he should use them and measure them. The two inch plane makes only a beginning; but it really makes the only possible be- ginning for the development of measurement. The third principle is cutting, which is here in- troduced. This is more directly the Occupation side of the work. It is what must be done that these measured surfaces may be divided and put together again. And measure is also to be applied to the cuts. They are to be made more and more definite as the child learns to measure, and can cut the planes so as to fit better and better. The first cut is the easiest. One plane is cut, and the uncut plane intersects the cut plane. The first plane cut should be a folded square. The square is folded once and then cut from the folded edge almost to the open edges as seen in Plate I, Fig. 1. This cut is easy for little children. It requires no measure- ment, and may be cut quite near the edge to which it is parallel, or farther away. It is well to be satisfied with a child's first cutting if it will work at all. In the second cut both planes are cut and inter- sect each other. This gives the dovetailing, Plate I, Fig. 2. This cut is much more difficult, and demands more ability to measure on the part of a child. The two cuts must fit each other. But although it is more difficult, it works better. The two planes hold each other more firmly in place, and make a more permanent object. In the third cut both planes are cut, one from within out and the other from without in. They in- tersect each other making the hinge, Plate I, Fig. 3. This makes the most^ permanent intersection of all, as the two planes when hinged can not be pulled apart. The first cut is a transitional one and may gradu- ally be dropped as a child becomes able to use the two more difficult cuts, dovetailing and hinging. The in- tersecting with the first cut does not hold the forms together very well ; although well enough for a little child who is learning the process of making rather than producing permanent results. All these processes the child is to play with as made, as universal, before he tries to use them in making particular things. So the first step is : I. Undirected Play with intersecting planes. It is important that this be given first, as the PLATE I. The Three Kinds of Cuts, Intersecting, Dove-TaiHng and Hinging, With Application of Same in Objects Made. child should discover beginnings for himself. Then he can be directed by the knowledge of the past, by the teacher, how to use these discoveries. The first set of intersecting planes is given in the following order. Two two inch circles already cut to the center are given to each child. They are not intersected but lie on the table apart from each other. Let the children pick them up and put them together or do with them whatever they wish. The first thing they usually do is to insert one circle in the cut of the other. They do not at once fit the two cuts together, although of course some child might. But they will hold up one circle by the other, will say, "It makes a wheel." Now should begin a sym- bolic play with the circles, which the kindergartner enters into being interested in each new thing sug- gested, until at last some child fits the two cuts to- gether, and perhaps begins to rock them, exclaiming, "It's a cradle !" The general experience with this play has been that all the children now try to put their circles to- gether in the same way, being satisfied with the re- sults. Now the cradles may be rocked, or the planes spun vertically, suggesting a ball or anything else the children may think of. Then laying the two circles together and placing them on the center of the table, give each child two two inch squares each cut to the center. The children will at once fit these together in the same way they have discovered the circles will fit, and will give to the resulting figure various symbolic names. We now have these figures — Plate II. Fig. 1-2. Then let the PLATE II. Geometric Forms Made by Intersecting Planes. children take the planes apart and see if they can put them together again. Also they can take each apart and intersect circle with square, as Plate II, Fig. 3. •Through this play with the intersecting planes, the child not only learns how to intersect, and learns it without direct teaching, but the forms themselves suggest to him some of the things he can afterward make, as troughs, cradles, shelves, chairs, etc. Then by laying the intersected planes flat, they can be moved back and forth like "winding a watch," as one child said. They can be wound apart and then wound together again. When put away they should be left together. Only two planes are intersected at first. Not until much later, especially with young children, are the three planes given, as they are much harder to handle. Besides they are less symbolic and more mathematical, suggesting at once the intersecting planes of sphere, cube and cylinder. When given, the three planes should be already fastened together by intersection, but flattened. The child can then pull the parts out in place, making the intersecting planes. Having done that, he may then pull them apart and see if he can put them together again. It is a little too difficult for a child to have the parts separated the first time. But given in this way he can easily man- age them, taking apart and putting together. As be- fore, the intersecting planes of both sphere and cube are given at the same time. The child who can handle the one can handle the other. By taking them apart as before the intersecting planes of the cylinder can be made by the child. It will doubtless take several periods on different days for the children to exhaust the possibiUties of these planes. As they suggest clearly the relationship to the Third Gift, it may be brought out. The children them- selves have frequently called for it and have always taken delight in fitting the cubes into the corners of these mtersecting planes. If a divided cylinder and divided ball are the property of the kindergarten or school, they will greatly add to the interest and com- prehension of these planes, or one might say, of "the insides of things." Some children have made these intersecting planes at home and brought them to the kindergarten, showing how thoroughly they have understood them. But it is not a good plan for the kindergarten children to be taught directly to make these intersecting planes. If they make the planes crudely by themselves, well ancL good ; but a careful making of them involves too much measure- ment for a little child. It must not be forgotten that these intersecting planes are to be given through undirected, not directed play. The forms suggest to the child his own ex- perimenting which the teacher should follow and enter into with appreciation, but should not direct. Also this play with intersecting planes, whenever given, precedes the actual construction work which is di- rected. They should therefore be given the first period and the construction work the second period. But this play with planes need not precede the giving of the actual construction work each time. The play with two planes, circles and squares, should always precede the first giving of construction work, but need not the second. Indeed they need not be given for several weeks when the children may be ready to discover new possibilities in them. And the three planes should not be given until the children are old enough and skillful enough to handle them. Much depends on the teacher, who should understand when her children are ready to grasp both physically and mentally each new step. The intersecting planes form a bridge between the gifts and the occupations. These beginning forms are to be made for the child, played with by him, and returned unaltered to the box. This makes them partly a gift. But they are also an occupation, for the planes are put together, not by external combina- tion, but by internal division. Used in this way, they form the transition from the gifts into the occupa- tions. This transition is made through the two inch tablet, circular and square, which being cut to the center and intersected by another tablet returns to the Second Gift from which it was derived, as it takes up again the dimension it lost as surface and shows now the three dimensions of the solid as the three intersecting planes. And as intersecting planes, con- taining the principles of construction of the solid, it moves forward into the occupations through which that which is given in the gifts, is to be re-given, re- constructed, in the occupations through surface, line and point. The present occupation reconstructs the solid through surface, and so starts with giving the child measured surfaces which he is to learn to measure and put together. II. Directed Play — intersecting of planes in vari- ous ways. The universal principle found in the intersecting planes of the Second Gift, is now to be applied to the making of particular objects. Also the principle which organizes all this directed construction work, is the principle which man uses in organizing all of his work — and also himself: namely, measurement. "Man is the measure of all things." 1. First Set — objects made with two inch planes only, — finding the unit of measure. The first set begins with two inch planes, circles and squares. The first giving of this directed con- struction work should immediately follow the first play with intersecting planes. Two of these inter- sected forms, two circles intersected, and two squares intersected, may be left in the center of the table dur- ing the occupation period, as they serve to suggest objects. Give each child one two inch circle and a pair of scissors. Have each child fold the circle once in the middle and rock it like intersected circles. Then open and see the dividing diametral line. The divi- sion which the intersected planes suggest is now made by the child. Next he is to complete what is begun. The dividing diametral line is used for division. Let the children cut on this folded line. In order to cut well, the fold should be smoothed out and then cut. Never cut on a fold doubled up. It always makes poor edges, and admits of little, if any, improvement. And besides this, the child should see the line he cuts on. The folded line has this advantage over the drawn line, in that the child can feel it as well as see it. And again, he can easily fold a line, a straight one, whereas it would be more difficult to draw a good true line. Now we have two half circles. Then fold a square in the same way. As the folded circle would rock, so the folded square will. look like a part of the intersected squares. Now the folded square is to be cut up each side from folded edge toward open edges, using the first cut. By intersecting in these cuts the two half circles, a cradle is made. Plate I. If the kindergartner precedes each process of folding and cutting on the part of the children, by a play of intersecting — interlocking the fingers, and finally by having the children fasten their hands be- hind their backs in this position, while she quickly and definitely shows them how to fold and cut, she will find it an easy way of directing. And if she keeps her own hands fastened in the same way while the children fold and cut, helping no one until all have tried, she will find it will help the children to be independent. It is also a good plan to say, "Can you each make another cradle?" And without direc- tion hand each child another circle and square, letting them make another cradle all by themselves. Little children have taken great delight in making three or four in this way, and have done it well. Then holding up a square, fold and cut in half as the circle was cut. Let the children do the same. Then give each child a square to fold and cut up the sides as before, making the first cut. Let the children intersect these oblongs in the cut square, finding out what they can make. Children no older than four years have made four or five forms this way in half an hour. Most of them are, of course, repeated, the children making several of the same form. This first making of objects may be carried as far in one period as the children are able to do the work. The second time the construction work is given it need not be preceded by the play with intersecting planes. This time the children should make the same things as before, aiming now at better work. A whole half hour can be well spent in making one good cradle, throwing away mistakes. Have a small paper doll, less than two inches long to sleep in the cradle. To this construction work is thus added free-hand cut- ting, for the children can cut out their own toys to go with the furniture. Or, if the teacher cuts out the dolls, the child can cut out the covers to put over them, or carpet for the cradle to rest on. Thus he puts the things he makes to a real utilitarian use, and also becomes better able to use the scissors. To the cradle might be added a chair for the mother to sit in. In this first set of two inch planes the circle and square are used together. At first they are cut only in halves, the new planes thus obtained being the half circle and the oblong. Later they can be cut into quarters. In this way the child makes his new planes from the old and that too by the simplest divisions. With a circle and square and their divi- sions, a number of forms can be made ; in fact, almost all household furniture, as well as houses, sheds, 17 troughs, and many things used out of doors. See Plate III. But the Hmitation of the two inch planes is their size. All the things made are about the same size, and the objects when grouped together lack propor- tion. However, in this they correspond to the little child who also lacks the sense of proportion, and must learn it. 2. So the Second Set is — any inch plane, — using the unit of measure. As soon as the child is ready, the step is taken to the next set which is, objects made with any inch plane. Now we can use three, four and five inch circles and squares w'ith their divisions. Beyond five inches it is not well to go, as the paper used at first is necessarily easily folded or the child could not handle it. If too large a plane is used the object will not stand up well. To these circles and squares are added ob- longs of any length or width as 2x3, 4x5, etc. The planes are divided into halves and quarters as in the first set. The same objects made in the first set can now be made in tHe second. This gives opportunity for repe- tition, and also for better work, and, more than all, difiference in size. The same things can be made larger or smaller. Now the tables and chairs are not the same height, but can be proportioned. The child is thus to progress in doing better work. The cradle made in the first set has not a flat bottom, being folded only once. But the cradle made in the second set of larger size can be folded three times, giving a flat bottom and so a better cradle. One of ts PLATE III. Two-Inch Measurement. 19 the things which can be made much better in the second set than the first, is a rocking chair. To make this, the seat can be the oblong from a two inch square, and the rockers the quarters of a three inch circle. This gives a proportion to the curve which brings it far enough below the seat. See Plate IV. The rocker made in the two inch set is not good, yet it satisfies a little child in his first attempts. These two sets are very closely connected, the same objects being made in each, and the principle of the inch measure underlying" both. By providing for the making of simple crude forms at first, we give to the child the opportunity to do what he can. And by providing for a gradual development through measurement, by which the same object can be better and better made, we provide for the development of the child's growing ability. He can and should grow out of crude beginnings, and learn to do better work. But also, he must begin with the crude. In the first two sets the child has been using the inch measure, becoming familiar with it, but not actu- ally measuring much himself, so the next set must pro- vide for that. 3. Third Set — any plane — relative measurement. In this set new forms can. be made for which the first two sets do not provide. Give each child a four inch square. Let him fold it three times. Stand the resulting form on end, so that it looks like a cupboard without shelves. It will be four inches high, two inches wide, and one inch deep. Give each PLATE IV. Any Inch Measurement. 21 child a two inch square, which he is to fold once and cut in half. There will then be oblongs 2x1. These oblongs fit exactly in the cupboard as shelves, but cannot be intersected. So the oblong cannot be used as a shelf, but it can be used as a measure. Lay it on another paper and cut out shelves of the same width but a little longer at each end, as Plate V. As many shelves as desired may be cut in this way. Then laying the measure on several shelves cut half way along each side close to measure. The shelves should now fit, having been measured to fit. Fold over the cupboard part on center fold. Cut from without (open edges) in half way to fold. Inter- sect shelves by dovetailing. By cutting cupboard from within out half way beyond the fold, the shelves can be intersected from the back. This gives oppor- tunity to put on a door in front by hinging. Plate V. From these two cupboards by modification, can be made all articles of furniture having shelves ; as wardrobes, bureaus, writing desks, chiffoniers, also using two end shelves only, all sorts of boxes with or without lids. See Plate A^. Also the house, which can be made with the measured planes, can be better made by using this principle of relative measurement. It can be made as wide or as narrow as desired, and so any kind of a house is made. By using the third cut, a door can be hinged on, and a floor put in. Plate VI. As the child learns to measure his own planes, he can learn also to cut them ; to measure them, and thus to apply his own measuring in making over pre- vious sets. PLATE V. 23 Inventing can be begun very early with this work. First, let the children try other ways of intersecting. They may produce forms already made by themselves as well as new ones. Second, they can transform ob- jects made by modifying them so as to look more like chairs, tables, etc. ; as, by cutting out the legs to chairs, cutting out the rockers to rocking chairs, etc. See Plate Yl. Everything a child makes with the planes can be thus modified, and thus become his own invention. Also, older children will study new ways of using the methods of intersecting; new ways of fastening planes together. III. Self-Directed Work — Proportion. In this last work come the sets of furniture, houses, barns with fences and other surroundings. Now a table may be made, and chairs to go with it. A house with fence, a barn with fence and other buildings, etc., can be made. These sets are an application, made by the' child, of the principles of making things, to the grouping of these things together. It varies from the small trough surrounded by a fence, or the cradle with a chair beside it, to all the complex furnishings of rooms. It varies from the work a four year old child can do, to work that would test the skill of a grammar grade pupil. See Plates VII, VIII, IX. In this work the children receive, through meas- urement, a mathematical training which will greatly aid their abstract number work. They will gain skill of hand through cutting, and develop inventive power in fastening the planes together. They will learn to observe how things are made in the world about PLATE VI. Any Inch Planes, Modified. 25 them. And finally, owing to the constructive prin- ciple of intersection, and the use of the inch measure, this work will make a good preparation for the later Manual Training. And more valuable still, it helps the child to understand the work of man. MATERIALS USED A heavy paper should be used. It must be flexible enough to fold easily, yet stiff enough to hold its shape. Prang's Construction Paper has been found to answer the purpose very well. Heavy manilla drawing paper may be used for a while in the first work. But it is hardly stiff enough for good work, and besides lacks color to make it attractive. In the later work of making sets of objects, a heavier paper than Prang's is desirable, and more- over the child will begin to want a more permanent material than the Prang's Construction Paper. Sheets of stiffer paper will enable the older child to do more satisfactory work. TOOLS USED. Good scissors are necessary, for no one can do good work with poor tools. The scissors should be small and blunt. No paste or glue is used. PLATE VII. Objects Made in Relative Proportion. 27 PLATE VIII. Proportion Shown in Groups of Furniture. r^ 1- L^ OUTLINE GENETIC CONSTRUCTION WORK I. Undirected — Play with intersecting planes. II. Directed — ^Measurement. 1st Set — Two inch planes used, — tinding unit of measurement. 2nd Set — Any inch planes used, — using unit of measurement. 3r(l Set — x^ny plane used.— relative meas- urement. Self-directed — Proportion, — making of sets of ob- jects proportioned to each other. Outline of Kindergarten Occupations I Moulding Plastic, -{ of (forma- I material, bility) I, Utilitarian. Mathematical. Artistic. ■ II. Indus- trial, form- making r Utilita- rian. ^ Mathe- matical. L Artistic. \ Industrial I processes. 1. Taking apart. -! 2. Putting to- gether. 3. Both. ( Pricking. -; Tearing. / Cutting. ^ Pasting. Sewing. ( Weaving. -i Folding. Quantitative occupations. Qualitative occupations. Quantitative and Qualitative. Occupations based on 1. Intersecting j Genetic con- plane. / struction. 2. Diametral line. ( Transformation ( of one surface. 3. Central point. i. point. / Wheel making. ( 1. Point making — pricking. ^ 2. Line making — sewing. I I 3. Surface making — weaving. Color work. f Form used — -Quantitative. Making of ob- | jectsbasedon J How used— Qualitative, mathematical principles. | L Color used. III. f r Utilitarian. Graphic, i , . i Mathematical, form- I making. | revealing. I. L Artistic. JAN 1 1 taeo UNIVERSITY OF CALIFORNIA LIBRARY Los Angeles This book is DUE on the last date stamped below. Foi-iii L9-37;;i-3,'57(C5424s'l)4.1.1 \-iia.pL\_x . »^%_^v^**^ $1.00; plus postage, 9 cents. ORGANIZED HAND WORK FOR PRIMARY GRADES— BEAD STRINGING. BY ELIZABETH HARRISON. Price, $0.50; plus postage, 2 cents. 32 THE LIBRARY UNIVERSITY OF CALIFORNIA Los ANGELES LB IIMIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII L 009 513 500