"slantwise,,' and one common cause of spinal curvature is thus obviated. The erect style is therefore recommended for use in schools in preference to the ordinary sloping lines. At the Seventh International Congress of Hygiene and Demography, London, the following resolution was proposed by Dr. Kotelmann and seconded by Dr. Gladstone, Vice Chairman of the School Board for London, and carried. "That, as the Hygienic advantages of Vertical Writing have been clearly demonstrated and established both by medical investigation and practical experiment and that as by its adoption the injurious postures so productive of spinal curvature and short sight are to a very great extent avoided, it is hereby recommended that Upright Penmanship be introduced and generally taught in our elemetary and secondary schools." The position of the body demanded by vertical writing keeps the trunk of the body upright and the spinal column straight. The forearms, not the elbows, are laid on the desk in a symmetrical position, as they are the shoulder props they bring the transverse axis, the connecting line between the shoulders, and the transverse axis of the head parallel to the edge of the desk. The latter is lowered slightly to obtain a clear view of the paper, and remains a suitable distance from it. The paper is placed a little to the right of the median line of the body. In this position the base line of the eyes remains parallel to the edge of the desk, Fig. 5, and there is no tension or strain on any of the muscles of the body. To sum up,- if it has been clearly proven that vertical writing is more legible, speedy, economic and hygienic, what excuse can longer be urged for training our children in that unsatisfactory and dangerous sloping style ? Who Makes the School. A bright young girl of sixteen came home from school the second day full of enthusiastic happiness, and with such hopeful anticipations of the school year, that it made me young again only to hear her. She was entering upon the third year of high school, and her teachers had been wise enough to share some of their plans with their pupils. "We are to read one of a selected list of books each month, and write a short review of it," she explained; now what is a review like? I never read one." Happily, in a recent journa just at hand, there were several short reviews and she was soon eagerly interested in them. The Latin teacher, the Chemistry teacher, and the English teacher had each opened enchanted gates for her and she was eager to follow them into the wonder land of wisdom. Three weeks later her interest and zeal were unabated, and I knew that the year would be one of happiness and of growth for her. Then I fell to wondering whether the grammar teachers and the primary teachers all over the land were effecting children as intensely as these high school teachers were doing. I wished that I might know just what words of cheer went home from one large school through whose rooms I went back and forth daily. I wished that I might cry out with so clear a voice that every teacher must realize how she made or marred the life of a child who sat before her day by day. I said, "It is not the principal who makes a school useful or great; the average principal is a small factor in the school life of a child. It is his teacher who makes possible his happiness and his growth. Chicago, Nov. 2, 1893. Here is the way a Kansas teacher subdued and refined an unruly school. At the beginning of school, she says, I wrote at the top of the blackboard on one side (the other side was reserved for the alphabet in script) "A rule for self-defense," - followed by, "A soft answer turneth away wrath" in ornamental letters. Then on each morning before the arrival, or on the previous evening after school, I wrote in the middle of the board, following the date, some good quotation, to remain during the day, for instance, Monday, Oct. 9, 1893. "Tis better not to be at all, Than not be noble." I said nothing about them, as I thought that forced attention might destroy some of the good influence they might have, but gradually I noticed the children came to look at the board the first thing in the morning; and as time went on, I could see that the thought had taken root, and in such fertile brains was sure to grow. One of the chief causes of disturbance in school, I think, is the idea a great many children have, that instead of their teacher being their counsellor and friend, she is a ruler, to whom they must always submit their own wills, regardless of any rights they may possess. And who would not rebel against such rule? I sympathize with them because it is the fault of their training, and there are too many teachers who make that impression on the minds of their pupils. That seemed to be the feeling of the majority of my school, and was hard to eradicate. After a particularly restless day among the boys, I wrote for the next day, "Always think of your teacher as your friend." That one sentence, with a few friendly smiles from their teacher did more to quiet those rebellious feelings that day, than a ten minutes lecture would have done the evening before. I tried various means to effect a refining influence on the school, as decorating the walls with paintings, crayon sketches and picture cards; insisting on neatness and order, and kindly remonstrating against all rudeness and noise. I have the same school this year, and a more quiet, well-behaved school, I think can not be found in the country; and I give the daily quotations a great deal of the credit. An International University. And now, Chicago “pinnacled dim in the intense inane” of the magnificent success of the great Exposition, calls aloud to the United States and "the rest of mankind" to establish a sort of international university on the Fair grounds, through which the learned Pundits of all nations, tribes and tongues shall circulate and everybody have a chance to be a student, with $10,000,000 to float the enterprise. Everybody likes to hear the top-note of American civilization, and the song of Chicago is melodious to the ear and uplifting to the soul. But, after all, man is mortal; and a child is not a man, and few teachers "are born," a few more "made," and the majority are as good as other people, but incapable of rising to the level of the present demand of high expertism even in the university, to say nothing of the people's common school. The most we can reasonably hope from any system of universal education is to abolish gross illiteracy at the bottom of society; give to the majority a lift in mental, moral and executive training; and leave an unlimited realm in the upper story for those who love to climb to scale any height of culture of which they may be capable. But everything over-done is more badly damaged than if under-done. It is on the whole better for a generation of children to go a little too slow in childhood, provided they have a fair appreciation of what is learned and attempted, than to blast the faculties themselves with " excess of " and give to the republic several millions of young people in light that state of superficial intelligence and mental confusion, that it may require another Revolution to bring the country back to the common sense, moral earnestness and stubborn persistence of the fathers. M. METROS The Editors will be pleased to receive contributions for this Department. Τ Rules in Arithmetic. By J. K. ELLWOOD, Pittsburg Pa. HE complaint is very frequently heard that children do not receive the benefit they should from the study of arithmetic; that in their attempt to memorize definitions and rules they lose that development of the reasoning power which a proper study of the subject should give; that, although they may learn how to perform certain operations, they have not learned to determine, from the conditions of a problem, what operations are required for its solution. These criticisms are made not only by parents, but by leaders in educational thought and work. The method employed by a teacher is largely responsible for a child's failure to derive the greatest possible benefit from his study of arithmetic, but the weak teacher is not alone to blame for the failure. She is required to use a textbook prepared perhaps by the president of a college or the chancellor of a university, before whose profound scholarship she bows in meek submission, deeming it presumptuous on her part to omit or criticise anything placed in "the book" by one so superior in rank. She follows the order prescribed by the book, which is her guide, by order of the board. Definitions are frequently given first, and these the unfortunate children are required to memorize as a foundation for the surerstructure that is to follow. Next comes an example, with solution and explanation, which is usually "skipped" because "there is no use wasting time with what is already done." Here follows a rule containing specific directions for the solution of the succeeding problems. Its prominent type is meant to attract the attention. The only apparent purpose of this rule is to prevent the pupil from thinking to make of him a mere operator to manage that piece of labor-saving machinery, whose real function lies hidden behind the magic word - "Rule" The use of rules in the solution of problems, preventing, as it does, the full and free exercise of the pupil's faculties, is a most potent factor in convertng independent effort and healthful mental activity into mere "machine work." True, a child may aquire great facility in mechanical work by the use of rules, but, if properly taught, he will acquire equally as great, if not greater, facility without any rule whatever. Rules in arithmetic, with very few exceptions, are pernicious in their effect, and should be omitted from textbooks. If rules must be printed, the proper place for them is in a teacher's hand-book. The pupil should make his own rules - not depend upon the book for them. He should be led naturally, and logically by progressive steps, to a thorough understanding of the principles and processes involved in a problem, after which he should be led to state the processes in their proper order, and finally to write complete and concise directions for solving all similar problems. These exercises, besides their great educational value as a generalization, serve to fix more permanently in his mind what he has learned, and to stimulate him to independent effort and investigation. Moreover, they afford valuable exercise in language work or composition. The rules written by the pupil may not be so well worded as those in his arithmetic, but they are his own work; he knows where they came from, how they came, and what they are for. In solving other examples he does not work mechanically, by the rule, but uses the knowledge of principles and processes he had before making his rule. This pupil advances, and his progress is two-fold: he is fully as skillful in numerical computations as the one who works by the book rule, and, which is more important, he is constantly gaining in independence and power. If a child lacks either the power or the knowledge necessary to an understanding of the steps of a process, then the teacher is limited to the how the why cannot be introduced. In such cases a well worded rule is an efficient aid to the pupil in retaining the how in memory. For instance, to find the volume of a sphere, one must either understand Geometry or work by rule. Since all arithmetics contain rules, how can the teacher avoid them, or how should she proceed? Suppose a class to have reached "finis" in an elementary arithmetic, and to have arrived at "Reduction of Fractions" in a more advanced work. The lesson for to-day is "to reduce mixed numbers to improper fractions." By the way, the class understand that "improper" fractions are not properly fractions, in fact, not fractions at all. They were told one day to take an apple as the unit of the fraction, to divide it into 4 equal parts, and to show how could be "a number of the equal parts of a unit." As their apples had only each, they said they must cut another apple and take of it." Then," said the teacher, " must be of one unit and of another unit, instead of 4 of 'a unit,' as your book has it. You cannot say 4 of one apple, for an apple has only t. Nor can you say of two apples, for that is 2 apples." After further talk and illustration the conclusion was reached that "no fraction is as great as its unit." An "improper" fraction is a fraction that is not a fraction! Some say is properly a fraction, as it expresses of 5; but in that case it is simply an expression of unexecuted division - not a fraction at all, although written in the form of one. Attention is called to the mixed number 2; it is to be changed to fourths. The how and the why are "questioned" into the minds of the pupils somewhat as follows: How many fourths in 1? Then how many in 2? And & + 2 = how many fourths? Now, what have you done with the integer in the example? (used it as a multiplier.) What was the multiplicand? = How did you find the multiplicand? Will you now let me see your solution, or operation? (2 × 4 fourths 8 fourths, or 4.) Other examples are now given, solved and explained by the class, until the teacher thinks the pupils prepared to tell how such problems are solved, when they are requested to state in their own language how mixed numbers may be changed to fractional form. They will readily tell how a given number may be so changed, but to make their statement general is rather difficult, and here and there should be as much more judicious questioning as the teacher finds necessary. For example: In your first solution, how did you get the 4 fourths? What is the fractional unit in that example? What tells you how many of these fractional units are in 1? (the denominator of the fraction.) When you have found how many fractional units are in 1, what is the next step? The next? Then how do you change a mixed number to fractional form? Eventually the answer comes, multiply the number of fractional units in 1 by the integer, and then add the fraction to the product." we The number of fractional units in 1 is the same as what? (the denominator.) Is 2 × 4 equal to 4 × 2? Does a change in the order of factors change the product? Then might we multiply the integer by the denominator? Now examine the rule given in your book, solve several examples by it, and see whether you get the correct result. Is that method more convenient than yours? Which is the better method? Why? The book rule, it is seen, is not derived from the analysis or from the legitimate operation, but from a substituted operation that is observed to give the same result. In conclusion I quote from the preface of a most excellent elementary arithmetic recently published: "When the more systematic treatment of the science is presented, the pupil is led by natural progressive, and logical steps to an understanding of the definitions, principles, processes, and rules, before he is required to state them; consequently, all definitions, principles, and rules are but the expressions of what he already knows." The latter statement should be true, and would be, if the rules given were all derived from the analysis and corresponding operations. But where these are ignored, and the rule derived from a substitute, as in the example given above, the given rule is rather the expression of what the pupil has not learned. He may be able to solve every problem in a given "case," and yet not have the least understanding as to how the book rule has been derived. After the pupil has formulated and stated his rule, he has no further use for it. A rule should be regarded as an end-not a means. SOME Arithmetic Again. By WM. M. GIFFIN, Chicago. ME one hath said, "We may say there are two kinds of division." Some one should have said, "We may say there are three kinds of division." (1) Dividing a number into an equal number of numbers. This we call division. (2) Dividing a number into a number of equal parts to find the number in one part. This we call partition, (without an exclamation point.) (4) Dividing a number into two numbers, one of which is known. This we call subtraction. There are those, however, who insist upon calling all of these by one name, because each time the number is divided, though differently. There are others who give each a name in order that the child may the better understand each. Dear Reader, take your choice. For some eighteen years the writer was blind. He now sees the light and is happy, because he is now able to simplify the processes of fractional arithmetic! (N. B., with an exclamation point.) Let us suppose that some professor of method, (there being no such high office in the Cook County Normal School, we cannot mean anyone there) desires to find out how many four dollars he has. Counting his money he finds that he has $12. He places them before himself thus: $ $ $ He takes one four $ $ $ He takes another four ($$$$) He takes still another four ($$$$). He finds that he has (alas! not 3, four dollars) but 3 "what is its?" Why three abstracts! to be sure. He buys a $4 hat, and he takes one of his abstracts and it pays his bill. He buys a $4 vest, and again takes one of his abstracts and it pays his bill. He buys a $4 work on "The Philosophy of Arithmetic ", and his last abstract pays this bill. He then exclaims, "O, Lord, grant that I may some day get a hold of some more abstracts!" The writer has often called a question like the following, an example in multiplication, viz.: .5 times .5 = ? Let us look at it a little in detail. .5 the multiplicand. N. B. tenths. .5 the multiplier. N. B. tenths. .25 the product. N. B. hundredths. Why not say, 5 apples 5 apples 25 potatoes? If in one case the product can be something which the multiplicand is not; why not in another case? Why not? Because arithmetic is a science and we have no right to teach a child one thing today and tomorrow mystify him with something that is "unadulterated nonsense." Such questions should never be given as questions in multiplication but as questions in Partition (with a capital "P" the reader will please notice), viz.: .5 of .5. If we ask of 12 ? We know that we must first find of 12 or 3 and then or 9. So, too, when we ask, .5 of .5=? We must first find .1 of .5 or .05 and then .5 or .25. The child can be made to discover a truth here if the teacher will take the time "to present the proper conditions for his growth." (The disciple again follows his master.) "One hundredth." "One row equals what part of one layer?" "One tenth." "Of what is this a picture?" "A cube." "Of what is it composed?" "Of layers and rows of little cubes." "One layer equals what part of the large cube?" "One tenth. "One row equals what part of the large cube?" .1 of .8.08. .3=3X.08 or .24. Thousands, my dear Doubter, will tell you that in multiplication of decimals, we multiply as in simple numbers, and point off as many decimal places in the product as there are decimal places in the multiplier and multiplicand taken together." But they never did know, do not know, and never will know, WHY. In view of these "basic" truths it is not at all surprising that so unrelated processes require separate names to mark properly the distinction between them. Any child even though "niggard nature" has not endowed the poor thing with the minimum thirty ounces of brains knows why .3 of .3 give .09. Even though it be written:3. Figures, FIGURES, FIGURES, that is what we are teaching our children, figures, figures and but little numbers. The late Dr. R. H. Quick, once said in a personal letter to the writer, "There is no subject worse taught than arithmetic, and This comes there is no subject in which failures are so common. of our putting children to 'do sums' before they have any proper grasp or conception of numbers." WRITING. Lessons in Penmanship.—XV. By CLARENCE E. SPAYD, Harrisburg, Pa. (The business-man wants business penmanship. Copy-book styles and the snail-like manner in which all copy-book students as a rule write, are practically back numbers. Practical writing, which can be utilized in every department of business, or perhaps it would be more clearly understood if it was said that the teacher should endeavor to teach writing so that all that he teaches will be available to the student when he enters the business world. Teachers in the public schools must be relied upon to give this instruction to a great extent. The teacher in the public school gives the first lesson in writing and upon these lessons depends, to a great extent, the pupil's success in becom. ing a free, and easy writer. If a pupil is properly started it is hardly likely that he will lose the enthusiasm and consequently all interest in penmanship. The first impressions are always best. Surely the psychological conditions of the young pupil in school are not so different that he cannot and must not be brought into touch with prac tical business methods. Quick, light, elastic movement from the muscles of the arm, is the basis upon which every teacher must base his system if he contemplates teaching business penmanship success. fully. Teach whatever will be of practical value to the pupil in after life, but nothing more and nothing less.) M OVEMENT is the life of penmanship and not until every pupil has been thoroughly instructed in movement will be be a free and easy writer. Move smoothly and regularly along, slowly at first but gradually increasing the speed until finally every pupil will write with surprising rapidity and beauty and smoothness that will convince the most skeptical that movement exercises are essential in learning to become a good writer. Every successful teacher of penmanship says "bear in mind that an easy action of the arm is developed only by frequent drilling on movement exercises." As has been stated several times in these lessons, every lesson should be begun with a movement exercise of some kind. Exercise No. LXXX. the work must be regular and the careful teacher does not neglect to count. Take other simple letters and carry the class through the same exercises. Teachers will soon find that their pupils are thoroughly aroused and will be wanting the teacher to give "special" lessons after school hours. In this way many teachers secure for themselves a raise in their salaries as well as the support of every patron. Teachers are frequently at a loss to know how to entertain their pupils, to hold their attention and make the lesson interesting. Exercise No. LXXXIII. u w W The teacher can spend a period in no more profitable manner and at the same time hold the attention, entertain and instruct everyone present, than by placing the simplest of the small letters on the black-board, making it six or eight inches in height so that all can readily see every line, point and turn. When the small letter "i" has been written, say to the class, "Whe can tell me what small letter is composed only of 'i's'?" Some may be able to answer while many will not know that it is "u". Without telling them pass to the board and add a neat dotted line to the “i” as shown in the above exereise, Then turn to the class and ask, "Who can tell me now?" All will now be ready to give the correct answer. Take a piece of crayon and strengthen the dotted line on the board and you have a perfect "u". Now ask what other letter can be made out of "u". If no answer comes, add the dotted line to "u" as shown in the engraving and you have another unanimous answer from the class. Again strengthen the dotted line and the " " is perfect.. The entire class will be convinced at once and be able to reproduce the lesson at home and with much pride and satisfaction tell his parents how three letters grew from one. NN All members of the class have had this letter some time since, but it is not given for that purpose, but to teach each writer to be able to write a line of "i's" across the page without lifting the pen and at the same time make each letter well. When the paper is turned upside-down the letters should have the same regular appearance, and look like so many "m's" connected without observing the proper right-curved line which should connect them. Now try this exercise: Exercise No. LXXXI. Exercise No. LXXXIV, wn п The same lesson can be given by using “u” and then asking each of the pupils to make the letter of good size, between the blue lines, on their foolscap paper. Having done this add the dotted line and ask each one to do the same. No one will be able to tell what letter it is. Give them all a surprise by telling them to turn their paper around. At the same time the teacher strengthens the dotted line and writes another letter, "n". Show how "m" is produced. Make this a result sheet. Draw two views of a sphere. Draw two views of a spheroid or ovoid. Sheet IV. Drawing In Grammar Schools. By N. L. BERRY, Supt. of Drawing, Newton, Mass. HE ends to be attained in teaching Working Drawing should be:-first, to enable pupils to understand constructive drawings of others; second, to give them the power to express their own ideas by means of similar drawings. First steps towards the accomplishment of this result may be taken by leading pupils in the fourth grade to see 1. That objects have facts of form. 2. That these facts may be expressed by views. 3. That two views of an object when placed in proper relation may give a clear idea of its shape. 4. That in the representation of objects by means of views certain peculiar lines are used. Full lines represent visible outlines or edges. Dot and dash or construction lines represent the axis of an object. Date Pupil's Name. Dotted or working lines are used to connect different views or show the relation between parts. The drawings in this grade will be wholly freehand, and drill lessons with the little people, in pencil-holding and free movement, will prove time wisely spent. Give practice in drawing straight lines, circles, ellipses and ovals. The sphere, alike in all views, and without edges or corners, is the simplest model for first study. Afterward, study the spheroids and ovoid, comparing with the sphere, as to views. After the study of the models, follow this order in drawing: 1. centre line or axis, 2. location and proportion of views, adapted to the space, 3. sketch, 4. correct, 5. finish. During first lessons, work with the pupils using the blackboard; gradually leading them to depend on themselves, and with-holding black-board helps as the lessons advance. In the sketch, all lines should be light and continuous. In finishing make them full, dot and dash or dotted. See that the dot and dash line always extends beyond the views, and the dashes are made long. Also that the dotted line is really a broken line in which spaces and lines are of equal length. |