Sunshine the center of which hung a huge paper ball of gleaming and have them dragged to the river. The river men send yellow fingers -- a veritable sunshine. them down the stream. The saw-mill man and his helper On the wall we pictured our watchword, get them into the mill, which turns round and ound with loud buzzing. As the logs are thus converted into boards, the carpenter proceeds to build a house with them. Let the game go on until all the trees are felled, the logs sawn, and the house built, and if one wishes it, some of the workmen may live in the house. The logs will have to be told to go down stream on their feet on account of clean clothes and not always clean foors. Enthusiasts invariably wish to roll down the river in this game. The Carpenter (Page 84. Part I.) “ The Woodman" game is naturally followed by a more complicated “Carpenter” game than was possible during the previous process. A simple mode of procedure is to use it as a “motion song,” and perhaps teachers will find it most useful in this way, as it brings. change and rest to the children without much trouble or expense of time. The children stand in the aisle, and as they sing the first its golden rays quite as tall as our tiniest babies. verse they make the hamThen from the center window space the gracious face of mering motion, pounding inour guide and friend looked down upon us, his tender words visible nails into an imagifor the little ones written round about him. Beneath was a nary house. bracket in white and gold, and never a day passed without As the second verse is a blossom for Froebel. Even the prim pillars bore their sung, the children, by a tribute, a bas-relief of Reynolds' “Angel Choir," or a climbing movement of the marble angel caryatid upholding in a golden amber vase hands, represent the carsome feathery branch of blossoms and leaves, making dainty penter going up his ladder. traceries against the dark wood. With the words, Each window lovingly tended some living green thing, while slender lilies and spring blossoms filled bowl and jar. “ He puts a roof above our heads The seasons, with dainty tribute of bird and blossom, To shield when rain doth fall," crossed the blackboards, and above looked tenderly down each child may make a the Babe of Bethlehem in His manger cradle. gable roof of his own upWhat could make us more at home than our beloved raised hands, or may so raise squirrels and comical bunnies — all the friends of field and his hands that they touch farm that the PRIMARY EDUCATION had sent us? So we those of his opposite neighmounted them on dark backgrounds to nestle among the bor, and a long, arching pictured sunflowers, the dainty groups of Black-eyed Susans roof be thus formed. In and the golden wheat, among which piped the gay “ Bob this case two rows of children White." will have to stand in one And then came Iris and threw her rainbow bridges across aisle. floor and wall, and we knew we had come out of the valley During the last verse let the children clap their hands in into the light. time to the music. Another and a less simple rendition of this game was a great favorite in our kindergarten. A number of children so placed themselves as to form a hollow square, a small opening being left on one side. This was a house in process of building. A number of small carpenters worked School-Room V. in and around this structure as the words of the song were An old piano cover served as a roof, and a family was ready to move in as soon as the last ET us now live for a while in a northern lumber reached. Nearly every camp. One of the aisles is a river; in a corner at WARNAR. The carpenter Kindergarten Games in the verse was L collection of kinderthe back of the room is a saw-mill, made by a num garten songs and games ber of children joining hands in a circle ; a man is has in it a carpenter in charge of this mill, and a carpenter conveniently serves play of some sort, so as his assistant. In the front part of the room are two teachers may have a other men who are in charge of ox-teams. Two others are large range of choice. chosen, who stand in the river, pointers in hand. These The music of the one pointers are used in gently assisting the logs as they float in Miss Blow's transdown the stream towards the saw-mill. It is needless to lation of Froebel's say that they should be used with discretion. Several woodmen are chosen, who carry imaginary axes “Mother Play” book is particularly attractThe rest of the children represent trees, and are ive. FD MANER planted in the space in front of the desks. Sing the whole song through while standing in position The Blacksmith ready for work, and point dramatically to the objects and (Page 82. Part I.) groups mentioned in the verses. Then let the industry In the open space in front of the desks arrange most of move on. The woodmen fell the trees one by one, and saw the children in a hollow square or oblong, open at one end. off the branches. The drivers fasten the logs to the oxen This is a blacksmith's shop. In it are two little black* Part II. “Songs and Games for the Kindergarten." Smith. smith's, one chair for a forge, another for an anvil, and a and saws. Horses and driver boy to blow the bellows. Two children serve as hitching- The blacksmiths continue to work until the song is finposts, for it is very difficul: for a two-legged horse to stand ished, until the chorus has been repeated several times, or on one foot without support while the other is being shod. until all the horses have been shod, as may be expedient. A few old horseshoes and a hammer will add much to the When in doubt as to any of the details of this game, or realism of the sound of the work, and give great pleasure any other, let the children themselves step into the breach to the children beside. with suggestions and help. Indeed the more entirely the Several children are ckosen for drivers and others for games can be planned as well as executed by them the horses. These people reside in remote parts of the room, better. The details given in these articles have most of them come to the writer in this way, but other more original or better adapted methods should always be substituted for them when developed by any particular set of children. As a song to be sung at the seats, sitting or standing, this becomes a great favorite with an “ anvil chorus ” accompaniment. Ask the children to bring old horseshoes and nails to school. Distribute as many as you see fit among your pupils and let them beat time on a horseshoe with a nail during the chorus. To get the resonance from the iron it will be necessary to pass a loop of strong string through each shoe by which it may be held while it is being struck. Let the few who hold the horseshoes during the first chorus pass them to their neighbors for the second one. By rapid striking, a very pretty sleigh-bell accompaniment may be made for any sleighing song in use. The Tailor (Page 7. Part II. ing near their desks, are to be the cutters; standing near their and drive their horses into the shop to be shod. While the desks, are to be the work of shoeing is going on, the children who form the pressers. The third walls of the shop sing : part should be seated “Busy blacksmith, what are you doing cross-legged, and on At your anvil all day long?” the desks, if possible, To which the blacksmith; 1 eply: to represent the sew This arrange“ Horses now you see I'm shoeing, ment holds for the Making shoes so good and strong." first verse. After it is We substitute the word “shoes” for “nails,” as it is in sung, the sewers be MARNER the book, because the blacksmith no longer makes his own come cutters, the cutnails. ters pressers, and the pressers sewers. At All join in the chorus: the end of the second verse still another change is made, “ Cling, clang, clir.g, clang, giving each group an opportunity of doing each kind of Hear the anvil ringing,” etc. work. ers. The tailor Description of Simple Objects F and very bright. I have a white face. My two hands are not alike. I lie down a great deal. Every one thinks I am M. F. HALL nice.” A Game in Composition [A WATCH] (Second Grade) JOR the child who describes an object not previously “ It has six square faces. It has eight corners. It is named, the exercise is, primarily, one of orderly, made of wood. It cannot roll, but it can stand. We draw [A CUBE] (First Grade) may tell from the descripticn what the narrator has in mind. Both these things, and in this order, are essential to real These are suffcient to show the possibilities of this form constructive work in language. of language exercise when used with children. It need The children who listen ale to hold in mind the various scarcely be said that a description of Dr. Johnson at tea; features, or attributes, described, and to think of objects The Three Kings of Longfellow; Robinson Crusoe ; Ivanhaving the characteristics given. hoe; or other characters of life or of literature will form an This exercise, with a suitable theme, is useful in any grade inspiring theme for a game with advanced classes. or class. In the literature cłass it may become a fine test It is understood, of course, that this exercise need not be both of knowledge and skill. limited in its range or theme. Some exercises by the youngest children are given as Its greatest value is probably found in the style of clearillustrations : cut, related, and complete thinking which it requires. The “What I am thinking of is something in this room. It difficulty of the lesson is forgotten because the exercise takes has a flat top and four legs. It is small and brown. Miss the form of a game. Clear oral narration" is more discipliuses it every day. We all have them at home.” nary than written descriptions, because of the readiness and The children said : “ It is a table." command of resources that it necessitates. (First Grade) The efforts of young children are like these : “ I am in many places. Miss has one. I am round “I build my house in the bushes or in a hollow tree. I I can build it of grass and soft moss. My coat is white. run very fast. I like cabbage. I shall soon take a long sleep." [RABBIT] “I live on a tree with my brothers and sisters. When cold weather comes we change our dresses. We drop off on the sidewalks, and the children pick us up and give us to their friends." [MAPLE LEAVES] “I like to stay on a pond. I can swim and dive and walk and fly. I can say, “Quack! Quack' I have a web between my toes, anu I use it for a paddle. Don't you think I am smart?" [Duck] 2 to n. It is the purpose of the following exercises to denote how the more difficult inferences of mathematical relation may be connected with and developed out of primary ones which may be observed directly. Exercise I Tell all you can of the size of the units in Fig. 1. Ex. p is f as large as n. Find all the ratios you can in Figs. 1-5. Ex. s is the ratio of m 3 Make equations. Ex.c = of p. h = 4 times d. (Fig. 4.) 1 of 6 = of 4. (Fig. 5.) 8 +4= 12. (Fig. 5.) 1 +υ = 1. (Fig. 3.) 4 i is the ratio of what? Ex. I is the ratio of 4 of d to b. (Fig. 2.) i is the ratio of } of v to of y: (Fig. 3.) i is the ratio of 3 times 8 to 0. (Fig. 4.) 1 is the ratio of of 120 of 6. (Fig 5.) 5 Fill the blanks: m = and 2 times of c=of of n. (Fig. 1.) is the ratio of to y.' (Fig. 3.) of <=-- (Fig. 2.) is the ratio of to is the ratio of 6 Find the units that have the relative size (ratio) $; those that show the ratios , 3, 1, #, 3, 4, 6, }, }, 4, 3, 5, 2, }, 5, 6, 4, 5, 3, $, . Ex. is the ratio of m to p. (Fig. 1); of d to e, (Fig. 2); of y tol, (Fig. 3); etc. = f of - of -of P, 9 to of а a S Fractions II (Continued from December number) ary, on beginning the study of mathematics, to turn at once to its abstract technique, as these processes may be termed. So long has this practice obtained and so justifiable does it seem that we have accepted it heretofore unquestioningly and styled the processes fundamental. Regarding them in this light, we are thereby predisposed to look with suspicion upon an attempt to substitute for the study of operations with figures, that which is really fundamental, visz.: relations of quantity. Yet we know very well that the things of prime importance are not letters, figures, or signs, but ideas; moreover it is written in the words of those we dare not dispute that thinking is comparing, that numerical symbols are purely representative, and that number cannot furnish a basis upon which to develop the science of mathematics. (See quotations in Primary Book.) Fig. 2 IO 5.) Sums and Differences 7 p equals the sum of what units? (Fig. 1.) (Give several pairs.) 3 The sum of n and b (Fig. 1) equals the sum of what? 9 Two times I equals the sum of what? (Fig. 3.) c and what unit equal p? (Fig. 1) d and what nnit equal 3 times c? (Fig. 2.) 6 and what unit equal the sum of 10 and 2? (Fig. up is how much more than c? (Fig. 1) How much more than r? What unit equals the difference between c and p? between 6 and 10? (Fig. 5.) What unit equals m less b? Names of Terms 12 Use the integral names in Fig. 5 like the letter names in the other figures. 13 Draw Fig. 5 on blackboard; instead of writing in the names 2, 4, 6, etc., write in the names, 3, 6, 9, etc. Give ratios, find missing terms, sums, differences, etc., as above. 14 Use other sets of names, similarly; 4, 8, 12, etc. 20, 40, 60, etc. 25, 50, 75, etc. 32, 64, 96, etc. Fix these names by applying them to other magnitudes showing the same ratio. Constantly vary the forms but preserve the same ratios. Return over and over with new sets of units to be named by the same series of names until the names become significant of certain relations of magnitude. Exercise II Call the largest unit 1 (Figs. 1-4) and name each of the other units. Call the next largest unit i and name the others; the next largest, etc. Draw units bearing the same relations as above and write in these names, - •, }, 1, 3, , 1. (Fig 6.) 3 Find ratios; arrange the statement of them in order. Ex. $ = } of }, } of }, 1 of 3, s of , andof 1. = 2 times , s of}, į of }, } of and f of 1. I 2 Fig. 1 Direct study of quantity reveals the real fundamentals of mathematics as products of comparative magnitudes. Convenient processes of reckoning quantity with figures are needed, but their use should develop, like all habits, from internal pressure for expression, not from external imposition nor dictation. Calculating can be done by machines; education deals with brains. Few magnitudes can be perceived entire, yet upon the few ratios that can be directly sensed, depends the estimate of all those vast or subtle units that the hand cannot reach for nor the eye take in. (See article in May issue.) Upon the seen rests the unseen. “ The importance of bringing simple basic ratios definitely into the consciousness is better understood when we look beyond them. By means of perceived relations we must pass to the inferring of relations." Primary Book “The higher processes in mathematics lie at the very foundation of the subject." Sylvester “ Equations constitute the true starting point of arithmetic.” Comte “ Upon these equations made known by the activity of mind upon the magnitudes themselves, all mathematical deduction depends.” Primary Book Fig. 3 4 Observe the magnitudes in Fig. 6 before replying; į is the ratio of what units? į is the ratio of what? 2 is the ratio of what? Find the ratios in Fig. 6, which are given in question 6 Exercise I. 5 g of the unit = what unit? of the unit j = what unit? of = what?of= what? of the unit j = į of what unit? Ask questions similar to these. 6 What is the ratio of į to ? Then how many t's are there in ? How many in j? in 3? 7 How many s's in ? (What is the ratio ?) How many l's in 1? of 64 { 7 64 II 9 I 2 4 8 Observe the relative magnitude of ff and 1. e., Compare with 1. Note. When the child observes the magnitudes and concludes that How many f's in $? Or, better, what part of a f equals a ?? 8, the teacher writes Similarly with d of 64, the teacher seeks to form an inci. dental association of the Applications 9 A bottle holds ļ a pt. It is full of water. How much water is there form with the thought. in the bottle? What is the quantity relation of the water to į pint? j is 8 the ratio of what to pt.? Then what part of a pint of water is there in When this has been done repeatedly and sufficient impression made, the bottle? the child may reproduce such forms from memory. Later he will easily 10 If $25 is . of the cost of my horse, what is the cost? What is the infer that if } of 64 and many other calculations with figures agree with size relation of to d? 2 is the ratio of what to $25? facts observed, that ft of 576 may be found by a similar process and the Represent by drawings or by blocks units that may be named 1, ļ, result may be depended upon although the fact is not easily observed. 4, 1, $, 8, 5, . Give their ratios as in problem 3 of Exercise II. 3 What is the cost of 23 tons of coal at $6 a ton? 12 f is the ratio of what to j? is the ratio of what? 13 At the rate of 1 yd. for 27c what is the cost of yd. of ribbon? 7 27 03 151. How much is ß as compared with ?? (Compare the magnitudes.) 3: 4 Keep distinctly in mind the fact that the terms }, }, , , Exercise VI etc., must not unvaryingly call up any particular size or What is the ratio of m to n (Fig. 1)? of n to m? special units. It is imperative that the experience of the What is the ratio of ļ to § (Fig. 6)? off to ?? children should connect them with such a variety of forms 3 What is the magnitude of $ as compared with the magnitude of 1, that the particular forms shall sink out of sight and the terms (Fig. 6)? If the names in Fig. 6 be changed so as to make become i, what must i become? What must it become if s becomes 1 ?' shall stand for relations that can be represented in new What is the ratio of i to j? What is the quantity i as compared forms freely selected or created. with ? with 7? with A ? with 24? with 4? with 7%? 5 What is the ratio of a yard to % of a yard. If $ yard cloth cost F $1.05, what cost i yard? Solution : 1 yard bears what relation to of a yard? It should cost what fraction as much? 6 When 23 dozen eggs are worth 40c, how much are eggs a dozen? Solution : How much is i as compared to aj or f? What part of g 400 then is the value of a dozen eggs? 7 At $j a pound, how much citron can be bought for $2 for $63? Solution : What is the ratio of $1 to $$? How much can be bought h for $1? Then how much for $2? for $6% or $84? 8 How many in 24? Solution : What unit will measure both & and }? What then, is the ratio ofto ? $ pound costs what fraction of 13}c, or 4c? Sums and Differences 14 What unit equals the sum of į and f? (Observe the magnitudes, Fig. 6, then other magnitudes in the same ratio. 15 the sum of what? f = the sum of what? f= the sum of Á and what? Then what is the difference between $ and f? between ; and f? 16 33 and how much = 41? blo 2 Call c I and name the units in Fig. I as above. Call b. $,: tc. 3 Deal with the other magnitudes similarly. If 8 in Fig. 5 represents a square yard of oilcloth what do th: other units represent? 4 What other way of expressing , ], $. 1, $, 1, 4, 75, etc.; 19, ij, 23, 74, 251}, etc.? Another solution: What is the ratio of 1 pound to pound? 1 pound costs what fraction as much? á pound costs what fraction of of sc? 17 5° 3 08 145. 6 4 3 It is hoped that the foregoing exercises indicate in some degree not only the sufficiency of observing ratio for solving all ordinary problems in fractions, but also the necessity of some primary and immediate knowledge of quantity as a basis for inference and operations with figures. Though the reader may miss the familiar nomenclature such as improper fractions, mixed numbers, least common denominator, inverting divisor, etc., it will be remarked that these things appear above, all involved in simple observations of quantity and too closely intermingled to be proper subjects for separate treatment. 6 Fig. 5 1 2 Exercise IV What is the ratio of y to t (Fig, 3)? of į of y to 1 of t? of } of y to } of t? of of y to of t? of ģ of y to an g of t? of 27 of y to 27 of ? What is true of the comparative value of all these ratios? Ans. They are equal. Express in simplest form the ratio of 10 to 25. Compare the ratio of } of 10 to $ of 25 to the ratio of 10 to 25. Are these ratios equal? What is the ratio of 2 to 5? of 10 to 25? Child-Study in the Home The average American child needs tranquilizing rather than stimulating, and through the ear he may be soothed. The lullaby of the mother has a physiological significance, the soft rhythmical cadences seem to excite pleasurable vibrations in the nerves that by their monotonous recurrence soothe and quiet the infant although he can have no real consciousness of music. As he grows older and the sense of hearing can bear more intense sounds, he seems to delight in them for their very intensity. He enjoys noise for the sake of noise. Now is the time that he can be trained to the appreciation of musical sounds. If left to himself he will be noisy only, if directed he may be made musical.- Northwestern Monthly. 3 What units are exact measures of n? Ans. b, r, and c. (Fig. 1.) 4 Wbat units are common measures of m and n? Ans. b and r. 5 What units will measure both 8 and 12 (Fig 5)? What is the greatest common measure of 8 and 12? 6 Reduce 89 Ti to its simplest form. What units will measure both 84 and 1442 Will the unit 7? the unit 2? the unit 3? Give other What is the greatest common measure? What is the ratio of this G. C. M. to 1447 84 how many 12ths of 144? Then what is the ratio of 84 to 144 expressed in its simplest form? Exercise V 1 is the ratio of what magnitude to the magnitude 12? (Fig. 5.) is the ratio of what magnitude to the magnitude 4? (Fig. 5.) 2 4 is the ratio of what to $? (Fig 6.) 4 times $ = ? } is the ratio of what to 64? } of 64 = ? measures. brightening the rooms of the dingy school, crowded with children, representing the decided foreign element characteristic of that section of the city. From the nature of the environment of the children it seemed imperative to the teachers of the school that something should be done to give them a little glimpse of the beautiful. With the cooperation of Mi tarr and Others who became interested in the work, the school-room walls were beautifully tinted, and in every room a picture or a cast was placed. The A Klondike School Woman's Club of Chicago, becoming alive to the import of the subject, formed an association of the members of The newspapers say a Boston teacher has gone to Dawson the educational and literature sections. Other agencies are at city. She has carried her school-house and all necessary work and many of the Chicago schools are tastefully equipments with her, intending to teach all the winter decorated through. They tell us the name is Mrs. L. C. Howland, and that she is a graduate of Harvard Annex. The schoolhouse is a portable building made in sections that can be Enterprise and Interest of Chicago Teachers easily fitted together. If there are no children at the During the first week of last September over three Klondike then she will teach the miners. When a teacher thousand five hundred teachers voluntarily took a week out once gets the fever, it never dies out. Teach she must in of their vacations, and contributed money besides, to mainsome form or other, to the end of her days. tain and attend a series of institutes lasting for five days. At these institutes were lecturers from all parts of the country, and the attendance was large and enthusiastic at The Public School Art League every session. In what other city could this scheme be was organized in the city of Boston in 1892. It was duplicated ? composed of artists and lovers of art who believed in the educational value of an association with works of art. With The Committee of Sixty the aid of the Boston school committee the League began appointed last year by the Chicago Institute of Education, its labors by decorating two school-rooms, and has pushed for the promotion of outdoor study of nature, did wonders. steadily forward ever since with a broadening and beneficient influence. Mr. Ernest Fenallosa says of the basic Committee on Maps told the teachers wnere to go. Comidea of the League : mittee on Syllabi outlined the localities for field work. Committee on Libraries secured a nature study alcove in “ It seems to me the term art is too often identified by the public with the John Crerar Library, in which books will be placed for the more special professional mark of making pictures and sculpture. the benefit of students. No doubt this is an important portion of art, but it does not give the key Committee on Instruction and to the work of the league, which aims to train the faculty and taste, and School Exhibits has presented to the monthly meetings educate the young to the uses, the public function, all the discipline specimens of work done in schools the city nature study in even, of art as a whole. The purpose of art education in general is no and supplied schools with materials from the suburbs. It more to turn the whole nature into professional makers of oil paintings has also made it possible for the schools to secure a cheap than the general education in music is to train a world of composers. “ It is to make more cultivated and well-rounded citizens by stimulat. air pump and aquarium. Committee on City Industries ing a most important part of their nature, and a desire for a knowledge has prepared a list of the industrial and commercial interof beauty. The development of the faculty of taste throughout the ests in the city. Committee on Transportation looked to community would help to bring about right and helpful living, and is secure cheap rates for the children to go to the suburbs. second only in importance to religion.” Public Information Committee put newsy accounts in the daily papers as to what was being done in the schools along The Beginning of the Movement these lines. The movement to introduce art into the school-room by bringing children into daily familiarity with examples of The Free Lecture System in the Public Schools good art originated in Manchester, England. The first of New York City attempt in this country was made some twenty-odd years ago, in Boston, by a committee of the American Social “ For some years past the Board of Education of the Science Association. The girls' high school was selected as city of New York has carried on under its immediate affording perhaps the most promising conditions for success auspices a systematic series of free lectures upon various in such an experiment. The walls of the school hall were branches of Literature, Science and Art. These lectures painted in terra cotta, and more than fifteen hundred dollars have been given in the public school buildings chiefly, was raised for the purchase of casts of the Parthenon frieze, although in one or two instances private halls, which had together with statues, busts and pictures. From time to been placed at the disposal of the Board of Education, time additions have been made to the collection, and the have been utilized for this purpose. During the last season, graduating classes of the school leave behind them as a which was the seventh winter's work, 1065 lectures were memento of their interest various beautiful and appropriate delivered at thirty-four different centres in the city of New examples of art. Though for nearly twenty years the Girls' York, with an attendance of 426,927. This represents an High school of Boston stood as the only representative of average of over thirty lectures at each centre, with an such an experiment in school-room decoration, it is certain average attendance of 400 at each lecture. Of the 1065 that the subtle influence exerted on the minds and hearts, lectures, 772 were illustrated by stereopticon views, 52 by manners and morals of the young people who have gathered scientific experiments and 241 were not illustrated. The there from year to year has created an atmosphere which is subjects upon which lectures were delivered were grouped making it possible for similar enterprises to prosper else- under the following six heads : Physiology and Hygiene; where. Natural Science ; Travel and Geography; American History and Civics ; General History; Art, Literature and Social Science. Most of the lectures were single lectures, but The Chicago Public School Art Society many of the individual lectures were grouped together in This society has the same object in view as the Art such a way as to constitute a series relating to the same League — that of making the school-rooms beautiful in general subject. The success of the New York experiment color and Alling them with the right sort of pictures and has been so marked that school authorities in all parts of casts. It began with the efforts of a principal of one of the country have been raising the question whether it is not Hull house district. She appealed to Miss Ellen Gates possible to carry out in the territory subject to their jurisStarr, one of the workers of the community, for help in diction, a somewhat similar plan.” |