(Enter Old Mathematics holding a large book in which he seems deeply interested.) Old Mathematics Dear me, dear me! How peculiar it feels to be out of a book! I've been shut in by covers for so many years that my poor old bones are stiff as pokers. I shouldn't be surprised if folks took me for "Father Time" instead of "Old Mathematics." I've been around so long that they think I'm as old as Time. But they're mistaken. Compared with Time I'm quite a young fellow. Besides, there's another difference between us. Time always carries a scythe; I never carry one myself, but I notice almost everybody else gets out a sigh when I'm about. I wonder where my children are! I've become so dependent on them that I'm quite helpless when they are out of sight. Here come the twins, Notation and Numeration. They are the eldest. (Absently.) They are the root of Numeration (stepping forward quickly) Don't say evil, Father. From your tone I should suppose you were about to quote some school boy. We are truly the root of Mathematics. Arithmetic begins with the making of units into groups and dealing with number by some group method. The first idea savage tribes have of numbers is to divide things into groups of more and less. Their first grouping of units is done by the help of the fingers, sometimes of one hand, sometimes of two, and often both fingers and toes are used. This is why the first number groups were fives, tens, and twenties. Some tribes of Africa use two persons for counting purposes; the first to count the units on his hands, the second to count the tens on his toes. Old Mathematics So long as your brother is relating family history, Notation, you tell us how the number idea came to be spoken and written. Notation That would make too long a speech for me; but I'll tell a little. Savage people have difficulty in finding names for their number groups. Some tribes have no words for numbers beyond two. They say, "One, two, many." Other tribes go farther. For three they say, "Two-two"; for five they use the word for hand. Six is "hand-one"; ten, "both hands"; twelve, is "two-on-the-foot"; twenty, is "wholeman." The first written number symbols were probably scratches made on something the sand, wood or stone. (Goes to blackboard and makes symbols as he talks.) The Assyrians used these symbols for numbers: (Addition enters from the side.) Addition Of course I do! I can always add a thing or two to everything. I'm one of the fundamentals, the fundamental, some say. Here's a conundrum for you. Is addition counting or is counting addition? When a pupil says 2, 4, 6, 8, 10, is he counting by 2's or is he adding 2's? familiar with me can never get very far in the good graces I don't believe you can guess the answer. Anyone not of Old Mathematics. I'm his favorite son - he's too absorbed in that problem to hear me - and I appear wherever he does. In fact, I sum up all his difficulties for him. Here's Subtraction, now. (Subtraction enters.) What makes you look so glum, Brother? Subtraction Yes, I'm here, Minuend, Subtrahend, and all, though there's usually nothing left of me but a Remainder. You'd look glum, too, if people were always taking things away from you. Oh, dear! what work some do make of me! No wonder I'm always minus something when they're always borrowing my tens. Addition Cheer up, cheer up, Brother! Look how they carry my tens around, but I don't care at all. Subtraction I can't help getting vexed Old Mathematics (starts up from his book) What's that? "Multiplication is vexation." Where is Multiplication, anyway? Multiplication (entering) Here I am, but I can't stay long. I've got to get some tables set up in the primary department of a big public school. People talk about dissolving the trusts, but though I've had the monopoly of the "Trust Table" for years, I never hear a word about its dissolution. Addition (coming forward) Poof! Don't think you're so important. We could get along without you. (Puts on the blackboard 2 x 3 = 6.) What's that but adding two three times like this? (Puts down) multiply 321 by 249, or add 321 put down 249 times. Old Mathematics Cease your quarreling, children. I want to work this problem. "A man had" (Addition, Subtraction, and Multiplication put hands over ears.) Multiplication Here comes Division. Division (enters hurriedly, holding out a string) Here, tie this around me quickly before some one gets at me and divides me up again. Oh, dear! I'm always being separated into groups. Children search for quotients as carefully as their parents search for dividends. Old Mathematics (excitedly) Here's a good one! “A, B, and C each had" (Children put hands over their ears and hurry out.) Division (as he passes out) He'd work us to death if we'd let him. Old Mathematics (looks around as if bewildered) Oh, dear! those children! As soon as I get a real good problem, they either quarrel about it or run away. I've got to follow them. 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Coal, Petroleum, Natural Gas, Metals, Gold, Silver, Copper, Zinc, Lead, Tin, Iron, The Story of Your House, Lumber, Ship-Building, Marble and Granite, Slate and Brick, A Visit to the Glass-Works, House Building, Pottery. CONTENTS OF VOL. II. Clothing, Cotton, Calico Printing, Linen, Wool. Carpets, Silk, Furs, Leather, India-Rubber, Corn, Wheat and Grass, Meats, Milk and Butter, Fish, Coffee, Sugar, Fruit. EDUCATIONAL PUBLISHING COMPANY Boston New York Chicago San Francisco AND INDUSTRY For Upper Grammar Grades BY W. F. ROCHELEAU A DIRECTORY OF "An honest, painstaking, efficient teachers' agency is a very serviceable institution for school boards and schools, colleges and private schools, have been put there by means of teachers' agencies. The following excellent "THE RIGHT TEACHER IN THE RIGHT POSITION MEANS Eastern Teachers' Agency BOOKS MANUAL OF PLAY. By William Byron Forbush. Philadelphia: George W. Jacobs &Co. 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Inexperienced teachers will welcome a book which frankly recognizes the sometimes disputed fact, that discipline is a definite and distinct phase of school work and must be studied as such. The author believes that fairly concrete means of achieving good results may be passed from one teacher to another, as truly as a concrete manner of teaching a geography lesson may be taught one teacher by another. After reviewing the general theory of discipline, the author takes up the various concrete problems of school life and offers suggestions for their successful ALBANY TEACHERS' AGENCY solution. Her ideas are always practical has good positions for good teachers with good records Harlan P. French, Pres., Vincent B. Fisk, Sec'y., 81 Chapel St., Albany, N. Y. It is always wise to have "a friend at the Court of Cæsar." Register Now! Of THE TEACHER'S EXCHANGE of Boston, RECOMMENDS TEACHERS, TUTORS AND SCHOOLS. An Agency registration increases your chances for securing work entirely congenial. 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This is a welcome book to those of us Competition for positions grows sharper each year- use every help POSITIONS OF ALL KINDS FOR TEACHERS CO-OPERATIVE INSTRUCTORS' ASS'N who believe that the handwork done by THE THURSTON TEACHERS' AGENCY Recommends teachers in answer to direct calls from Employers. Has good teachers for any position at any time. Our free Booklet tells how to apply for a position. ANNA M. THURSTON, Mgr. E. R. NICHOLS, Asst. Mgr. 623 So. Wabash Avenue, Chicago, Ill. little children should possess real usefulness and beauty, however simple its character. It tells boys and girls how to make all sorts of delightful things, boxes, candle shades, bags, curtains, bindings for books, etc., with little outlay for materials or implements. At the same time the articles are truly artistic, and are not simply "busy work" for restless fingers. The book is charmingly illustrated by the author. CONLEY'S PRINCIPLES OF COOKING. 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NOTES To the Editor's desk there has ar- HISTORY HELPS Ready in January let compiled for the use of tourists and HISTORY IN STORY, SONG travelers in Latin-America. Its time 224 N. Hamlin Ave., Chicago liness must impress those who realize SACRED HEART SANITARIUM Nervous, Mental and Drug Cases DEBATE OUTLINES any subject $1.00. Essays, Orations, and special articles written to order on any subject. JOHN H. ARNOLD, Cedar Falls, Iowa. AMERICAN COLLECE OF PHYSICAL EDUCATION AND ACTION By FLORENCE M. MILLER. tory. the necessity of acquiring some knowledge Teachers everywhere, who are interested in the decoration of their schoolrooms, should not fail to take advantage of the offer made by the Greenfield Art Association, and advertised in POPULAR EDUCATOR and Primary Education from VOL. II. contains Lessons and Entertain- The idea and purpose of this book is first to group material and outlines for history work in Primary and Rural Schools in a convenient form for the teacher's use. 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