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the top? Some one has called this spelling a column. Or are you more modern yet, and say 5, 25, 55, 60, etc.? This may be called reading a column. This column was put down at random, but the student should be taught to see that the first two figures spell 5, and the next four spell 20, etc., just as h-o-r-s-e spells horse. In short, he should be taught to pick out the 10's, 15's, 20's, etc., at a glance.

Suppose we wish to subtract 368 from 636; this may be done in one of three ways—(1) 8 from 16, 8; 7 from 13, 6; 4 from 6, 2. (2) 8 from 16, 8; 6 from 12, 6; 3 from 5, 2. (3) 8 and 8, 16; 7 and 6, 13; 4 and 2, 6. All of these plans are easily explained, but the third has the great advantage of using the addition table alone in the two processes of addition and subtraction, and as a result much time is saved. The first or second might be used to check the work of the third.

Now suppose we wish to divide 10.3522 by 3.82. The work may be arranged in this way:

382)1035.22(271 794

271.22

267.4

3.82 3.82

Such an arrangement gives no trouble with the decimal, and the explanation of the process is easy. In the above process the entire remainder is brought down, and the decimal point is retained to the end of the work. We think this best until the process

NUMBERS AND ARITHMETIC. That this subject is one of the most important in any course no one doubts. We all see that without it all business would be suspended. It is also a fact that it is one of the most poorly taught subjects in the curriculum. We are constantly making mistakes, and among the most common are the following:

1. We do not give the child credit enough when he enters school.

2. Being a very reflective study, we expect too much before the child reaches the reflective stage.

3. We have swung too far to the other extreme and teach too much written arithmetic and not enough mental.

The young people sent out are abject slaves to the pencil and paper. Let us be more economical and teach our people to use the things that will give power and not the things that cost money and result in lack of power.

Teachers, as a rule, fail to see the central idea of the subject, which seems to be: Like particular quantities as to their ratio. If the central idea is not grasped, the scope of the subject can not be definitely marked. Neither can an intelligent division of the subject be made, nor can the relative importance of the divisions be grasped. This is the weakest point in our teaching of the subject. We have been blindly following the organization of the texts placed in our hands, and have been giving about as much time to the non-essentials as to the essentials. With the central idea, scope and divisions established, we fail to see the rel

ative importance of the divisions. If we could, the following would not receive much stress: partnership, compound interest, foreign exchange, equation of payments, partial payments, present worth and true discount, G. C. D., difficult complex fractions, apothecaries' weight, troy weight, foreign money tables, annual interest, so-called "cases" in percentage, and cube root. With these eliminated, the teacher could give more attention to the modes of approach of the essentials, and the result would be that the pupils would have a clear idea of the essentials, and would leave the subject feeling that each division has an important place.

The teacher of every grade should be able to look backward and forward in the course in every subject, but in no subject is this more imperative than in this subject. In teaching any part the teacher must see just how this will strengthen the work of the previous grade or grades, and how it will prepare for the work to come.

If everything is logically presented, and no new point presented until there is a felt need; and no principle developed until all the conditions are ripe; and the connection of every part clearly shown so we would be weaving a cosmos instead of a chaos; then we could dispense with so many reviews and could turn our attention to more fruitful work.

Just what the work in numbers should be the first three years, there is very little agreement among school people.-Manual, Goodland Schools.

THE NATURE OF NUMBER.

Any number, as three for example, has two phases

1. The multiplicity, or its elementary phase.

2. Ratio, its scientific phase.

Three, in its elementary phase, is simply

an aggregation of three units, defined or undefined, without relation, whereby it has the attribute of three-ness.

Three, in its scientific phase, by which it is an element of pure mathematics, is a multiple of a unit, which is taken or repeated three times. In other words, it is a ratio; it indicates the relation of itself, as a unity, to its constituent unit, whatever that may be.

Number in its multiplicity phase is manifested in two ways

1. In the number series and its applications in space and time. Here it may be limited or unlimited. The counting of pebbles or grains of sand in the earth, or the universe, is as indeterminate and unthinkable as the end of the number series or infinity itself. So the counting of heart beats, or the rising and setting of the sun. But of course the application of the number series may be limited, as in the counting of any reasonable number of objects not thought of specifically as a distinct collection.

2. In groups of units, in groups of things. in convention, and in nature. In this manifestation of the multiplicity phase of number we may include any well-defined groups of objects observable in the experience of the child or the adult, in our homes, on the street, in school, in nature.

Defined or undefined number, then, may characterize multiplicity.

The ratio phase of number exists under any of the conditions of multiplicity, but will be perceived only by the mind sufficiently trained. A state of mind modified by number training being the condition for such insight, the perception of ratio, number is in a sense psychical. It is internal as well as external.

Our problem is to find a method which will duly recognize the intrinsic nature of number in both its phases and not do violence to the nature and susceptibilities of the child. Journal of Education.

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Be cheerful.

Look on the bright side.

Editorial Department

Avoid the complaining habit.

If some things go wrong in school think of the things that go right.

No cause of worry is ever removed by lengthening the face and thinking of it.

Some teachers annoy their friends by continually harping on the unpleasant things connected with their work.

If there is not enough good cheer in school work to keep one sweet, he has surely missed his calling. He should resign and become an undertaker.

It pays to follow the advice of Sam Walter Foss: "When you see a man in woe, walk right up and say, 'Hullo!' Say 'Hullo!' and 'How d'ye do! How's the world a-using you?' Slap the fellow on his back. Bring your han' down with a whack; waltz right up, an' don't go slow grin and shake an' say 'Hullo!"""

The school is happy when the teacher takes a cheerful view, and so manages the program that every moment is full of useful work. One great secret of happiness is keeping busy at something worth while. The teacher who attempts to spread ten minutes' work over thirty minutes' time will soon sour both self and school.

(112)

Commercial Club Building

Much educational writing is characterized by length. Many performers at educational meetings use forty minutes to produce five minutes' worth of stuff. Time is too precious to be wasted in this way. It is surprising how long it takes some teachers to conduct a poor recitation, and just as surprising how much some others can accomplish in a few minutes.

Superintendent Greenwood of Kansas City says: "A large per cent. of persons, who intentionally or accidentally slip into or drop into the school room as teachers, get their full growth in three or four years and never render any better service thereafter. They stand still after that, and then their services begin to depreciate." We should all take frequent inventories of self, and if we belong to Greenwood's large per cent. we should reform or quit teaching.

The ideals insisted upon in the administration of the Philippine schools include instruction in the common English branches, but more than that, "a large, general purpose to raise the spiritual character, the industrial efficiency, and the political capacity of the entire people." Might not every American teacher profitably remember that the best ideal of the American school includes all these?

The "School City" is being tried this year in some of the Boston schools. It has been remarkably successful in many of the schools of New York and Phila

delphia. It is a form of self-government, in which the school becomes a miniature city with a full set of legislative, executive and judicial officers. The transforming influence of this form of government in some of the worst districts of New York is almost beyond belief. Its effect in cultured Boston will be watched with interest.

The largest salaries paid to public school men in the United States are as follows: Chicago, $10,000; New York, $8,000; Boston, Pittsburg and Milwaukee, $6,000; St. Louis, $5,500; Philadelphia, Cleveland, Buffalo, Rochester, Denver and Baltimore, $5,000. In all other cities of the country the superintendents receive less than $5,000. No other class of men having so responsible work receive so little pay.

The largest salaries paid to high school principals are as follows: New York, $5,000; Boston, $4,200; Philadelphia and Hartford, $4,000; St. Louis, $3,600; Cleveland and Brooklyn, $3,500; Newton, Mass., $3,300; Denver and New Haven, $3,200; Chicago, San Francisco, Pittsburg, Detroit, Kansas City, St. Paul, Worcester, Los Angeles, Syracuse, Fall River, Lowell, Cambridge, Albany, New Bedford, Somerville, Springfield, Mass., Duluth and Newport, $3,000. All other cities pay less.

There has never been a more opportune time for teaching civic duty. The whole country is thinking upon this subject as never before. Every school boy should be made familiar with the fight against graft and civic dishonor that is being waged by President Roosevelt, Governor Hanly, Governor Folk, Mayor Weaver and others. The story of the achievements of these men, if told properly, will stir every schoolboy to high resolves.

There are only four cities in the United States where the average pay of elementary teachers is better than the pay of street cleaners. This does not mean that the pay of the street cleaner is too high,

but rather that the community must be aroused so that the pay of the teacher will be raised. The work of the teacher calls for skill and careful and expensive preparation. It is surely worth more than the unskilled work of the scavenger.

The following resolution was passed recently by a city board of education:

"Resolved, That every teacher signing a contract to teach in the schools in this district be notified that the board will from this day decline to accept his or her resignation and will insist that the contract be carried out as signed, and that all superintendents of schools or any member of the board as to standing or qualification of any teacher under contract be notified of such contract, and that this board will refuse to release such teacher.".

This certainly puts a premium upon mediocrity. Such a board will soon have a set of teachers who will stay simply because no calls from elsewhere will come. The board that will deliberately stand in the way of a teacher's progress deserves only the poorest teachers.

The question of athletics in schools is one of great importance. What the final solution of the many problems presented by the subject will be no one is wise enough to say. At present thoughtful men are agreed that athletic interests consume time and energy out of all proportion to the value returned. The athletically inclined student is too often like Uncle Peter's Percy. When asked about Percy, and whether he had gone into athletics or not, Uncle Peter replied: "Yes, he's quarterback on the football team and he's fullback in his studies."

The Bryan Banquet.

On the evening of September 22 the business men of Franklin gave a banquet in honor of Dr. E. B. Bryan, the new president of Franklin College. About two hundred men were in attendance, nearly all of them being citizens of Franklin. The menu was so excellent and

so elegantly served that it made a splendid introduction to the speechmaking that followed. Toasts were responded to by Lieutenant-Governor Hugh Th. Miller, David M. Parry, Honorable Robert M. Miller and Professor Robert J. Aley. The real theme in every toast was the college and its new president. The response from the audience was such as to leave no doubt that the city of Franklin will do her part in helping to lift the college to still higher usefulness. President Bryan's response was earnest and direct. He pledged his heart, his intellect and his life to the interests of the college with which he has deliberately cast his lot. Franklin College has a noble history. She has played her part well in the educational affairs of Indiana. The Bryan banquet means that her history yet to be written will be nobler than her past, and her part in public affairs yet to be played will be better than anything yet accomplished. Ex-President Stott in his happy and genial way made an ideal toastmaster.

State Teachers' Association.

The time, December 27, 28 and 29. The place, Indianapolis, with headquarters at the Claypool. This will be a great meeting, one that a teacher can hardly afford to miss. Look up the standing of your county in the Directory of Members. of the last meeting of the association. It may be that you can personally help to make the showing of your county better this year. Fountain County has been head for three years and Monroe next to head for two years. Three counties were not represented in the association last year. The Executive Committee is making great efforts this year to have every county represented and to have a total enrollment of more than 2,500. We should all help the committee by our interest and attendance.

The program is unusually good. Wednesday, December 27, forenoon and afternoon, will be devoted to the section meetings. In these, every teacher can find just what he is interested in and meet

those who are working on the same problems that have given him trouble. It will pay to spend all day Wednesday in section meetings. The general program will begin Wednesday at 8 p. m. with the address of the retiring president, W. L. Bryan, and the inaugural address of the new president, E. H. Hughes. On Thursday there will be a symposium on the Disproportion Between Boys and Girls in the Higher Grades of Our Elementary Schools. The speakers will be President E. B. Bryan, Superintendent George H. Tapy, Principal Rosa R. Mikels, President W. E. Stone and Mrs. Sarah Tarney Campbell. The evening address will be given by Governor Hanly. The speakers on Friday are State Superintendent Cotton, President Kelly and Bishop John H. Vincent.

High School Fraternities.

No question in the administration of high school affairs promises more trouble or will require greater wisdom for its proper settlement than that of high school fraternities. The N. E. A. at its recent meeting put itself on record in no uncertain terms. A report from a special committee gave the following reasons why such organizations should be discouraged:

"Because they are unnecessary in high schools; because they are factional and stir up strife and contention; because they form premature and unnatural friendships; because they are selfish; because they are snobbish; because they dissipate energy and proper ambition; because they set wrong standards of excellence; because they are narrow; because rewards are not based on merit, but on fraternity Vows; because they inculcate a feeling of self-sufficiency in the members; because they lessen frankness and cordiality toward teachers; because they are hidden and inculcate dark-lantern methods; because they foster a feeling of self-importance; because high school boys are too young for club life; because they foster the tobacco habit; because they are expensive and foster habits of extravagance: because of the changing membership from

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