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Below are given some lines written by him which correctly interpret the man. reckon him as a teacher although he limited his work to the pulpit; he reminds one of Phillips Brooks, yet was an entirely different type of man. The world is poorer since he left us.

Is it not strange that this man sele tel Pestalozzi as the theme for one of his most eloquent sermons last winter, and yet, that not one in three teachers hive ever read the life of one of the most remarkable personages the world has po duced? Yes, the lamented Babcock had imbibed the spirit of Pestalozzi. It was this spirit that differentiated him from other men in their pulpits. And so it is that the spirit pervading the teacher distinguishes him from others who probably possess as much knowledge as he, but who would fail if they were set to work in the schoolroom.

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child who reaps the consequences of his teacher's lack in this sphere.

It is not to be understood that a child is to read, and to love to read, only those books which add to his stock of knowledge, or which immediately tend to the improvement of his morals; for there is as legitimate a place for amusement, and for the lighter play of the imagination, in a child's reading as there is for recreation and laughter in the sphere of his physical training.

Books should to one of these four ends conduce

For wisdom, piety, delight, or use.

And that reading which conduces merely to "delight" for the time being has its essential part in the formation of a character that includes wisdom, piety and useful knowledge. It is to be understood that no child should be left to read only those books to which his untutored tastes naturally incline him; nor should he be made to read other books simply as a dry task. His tastes for instructive books as well as amusing ones should be so cultivated by the judicious endeavor of his teacher that he will find enjoyment in one class as well as another.

The rhymes of "Mother Gocse" are not to be under-valued, in their place, as a means of amusement and of attraction in the direction of a child's earliest training. Their mission in this realm is as real as that of the toy rattle in the education of a child's ear. But these helps to amusement are to be looked upon only as aids toward something better; not as in themselves sufficient to an end. So, also, it is with the better class of fairy tales. They meet a want in a child's mind in the development and exercise of his imagination and he who has never read them will inevitably lack something of that excitement and enjoyment in the realm of faney which they supply so liberally. But it is only a beginning of good work in the sphere of a child's reading, when he has found that there is amusement there, together with food for his imagination and fancy.

PRACTICAL QUESTIONS. Should whispering be prohibited altogether in school? How shall I prevent it? E. S. B.

Whispering should be prohibited so far as it interferes with good order. There is nothing wrong in a necessary communication performed so quietly that no one is disturbed. It would be a mistake to spend time in planning how to stop or to punish the offense. One would better be devising ways to keep the children so busy that they could find no time for it. Pupils rarely fail to appreciate fair treatment, and it is the wiser and more humane way to allow time for the tongues to relax. Apply to discipline the principle that "you must induce that growth which will grow itself," and let your pupils govern themselves.

Noon Recess.-What can I do with my pupils during the noon recess, when it is too stormy to leave the building? W.

Let there be an entire change from school routine. After luncheon, which, if the teacher eat with the pupils, can be made an occasion for silent instruction in many points of table etiquette, encourage activity of body. Games should then be in order, or singing, or marching exercises, with open windows. Do not allow study, for change of employment is especially necessary, when pupils do not go home. Talk freely with your pupils, for you will thus be training their powers of conversation, besides imparting general information. Discourage all local gossip, by substituting better topics for discussion. Let this hour belong to the pupils, and, so far as possible, let the restraints of school hours be dispensed with.

How to Teach Composition to Beginners.-How should a teacher begin to teach composition work to small children? Teacher.

The first formal composition work should be reproduction from memory. It may be introduced in regular lessons, based on material found in the reader, or elsewhere, or used incidentally to reproduce other lessons. There is no one subject which can be taught so constantly as this. Conversation lessons, though intended to give facility in oral expression, are indirectly training the memory, and the power to reproduce statements. Read

a selection, then without comment, request the class to write the story from memory. The written stories should be corrected at the time, suitable criticisms being made. Vary this plan by the following one: The teacher tells a story, pausing to write new or leading words on the board, instead of uttering them. When she has finished, this list will help the school in reproducing the story.

Reading Lessons.-I am convinced that reading lessons should not consist merely of the time-honored reading around the class, but I am not ingenious enough to devise many other plans. Can you help me? A. R.

Let some recitations be information as well as reading lessons. Select a piece which alludes to noted people or events, or describes some well-known natural wonder, or an invention. Call for all the information your pupils can gain on the subject, supplying all important points not touched upon by them. Make one lesson a study of words, another a simple study of style, if your pupils are old enough to appreciate this. Try to group together lessons in the reader which are naturally connected, as, patriotic poems, war stories, tales of great men, etc.

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casionally make a synopsis of the lesson, by questioning the class so as to bring out the main points. Place this synopsis on the board, and leave it there. It will form an outline for a good reproduction exercise some day in language recitation.

Along the line of smoky hills

The crimson forest stands;
And all day long the blue jay calls
Throughout the autumn lands.
Now by the brook the maple leans
With all his glory spread;
And all the sumachs on the hills

Have turned their green to red.
Now by great marshes, wrapt in mist.
Or by some river's mouth,

Through all the long, still, autumn days,
Wild birds are flying south.

-Selected.

MATHEMATICS.

ROBERT J. ALEY, BLOOMINGTON, INDIANA UNIVERSITY.

HOW TO MAKE A TABLE OF SQUARES.

Number,

Square,

1st difference,

0 1 0 1 4 1

2

3

2d difference,

3 4 5 6 7 8 9 16 25 36 49 64 5 7 9 11 13 15 2 2 2 2 2 2 2 The first difference row is gotten by taking the differences between the successive squares. The second difference row is gotten by taking the differences between the successive first differences. The second differences are constant, for they are all 2's. By extending the second row of differences we are able to extend the row of first differences and then the row of squares. In the table above the next second difference is 2, and therefore the next first difference is 17, and hence the next square is 64-17=81, which is the square of the next number, 9. The next first difference is 19, the next square 81+19=100, which is the square of the next number, 10 In this way a table of squares can be rapidly made by addition.

The row of second differences consists of the series of odd integers 1, 3, 5, 7, 9,.. We have:

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x2 = x (by multiplying both sides by x). x2-1=x-1 (by subtracting 1 from both sides).

x+1=1 (by dividing both sides by x-1).

21 (by putting in the value of x).

This is frequently given as a mathematical paradox. At first sight the reasoning seems legitimate. The fallacy is in the step when both sides are divided by x 1. This divisor according to the hypothesis is 0. The right-hand number of the equation instead 0

0'

of being 1 should be which may have any value, and which in this problem has the value 2. It is always safe in mathematics to assume that a paradoxical result is based upon some fallacy in the argument.

SOME USEFUL APPROXIMATIONS.

1

1+3

1 +3 +5

1+3+5+7

1+3+5+7+9

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= 25=52 1+3+5+7+9+11=36 = 62 This may be extended indefinitely. We see that the sum of any number of terms of the series of odd integers (beginning with 1), is equal to the square of that number.

If n is any number, then n+1 is the next consecutive number. The squares of these consecutive numbers are n2 and n2+20+1. Hence, if we know the square of any number, we can form the square of the next number by addition.

122-144

132=(12+1)2=141+2×12+1=141+

25=169.

142=(13+1)2=169+2×13+1=169+

27-196.

V10 V

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152 (14+1)2=196+2×14+1=196+ a mental training to the pupil. The com29-225.

And so on.

2=1.

mercial, technical, or professional applications of the subject are of secondary importance in general education.

2. That there should be no undue haste to begin the study of the calculus with a view to its practical applications.

3. That pupils should not be encouraged in the unscientific practice of placing dependence on rules or formulae which they do not understand.

4. That, in teaching any branch of mathematics, concrete illustrations and verifications, including experimental, graphical, and other methods, should, wherever practicable, accompany theory.

5. That in examinations particular methods of solution or demonstration should not as a rule be demanded, e. g., the use of algebra should not be prohibited in answering questions in arithmetic or geometry.

6. That there should not be imposed upon schools in any branch of mathematics a syllabus which does more than indicate the order in which the main divisions of a subject are to be taught.

NOTES.

Mr. J. C. Boldt was offered an instructorship in mathematics at the State University. He declined to accept and will stay in charge of the mathematics in the Anderson high school.

Lee Driver, principal of the Winchester high school, attended the Indiana University summer session, and did advanced work in mathematics.

Dr. E. W. Rettger, formerly high school principal at Rensselaer, has accepted a position in the mathematical faculty of Lehigh University.

Mr. Bertram Sanders, A. B., mathematics, Indiana, '02, will superintend the Jasper schools and teach mathematics in the high school.

Miss Madge McKee is the new teacher of mathematics in the Rockville high school.

Miss Kate Meek, after six years' successful work in the Bloomington high school, has resigned and will spend next year in advanced study at Chicago University. She is succeeded by Roy E. Roudebush.

Mr. O. E. Glenn, for the past year teacher in the Elwood high school, has

accepted an instructorship in mathematics at Indiana University for next year.

Mr. Edgar C. Hinkle has resigned his position as teacher of mathematics in the Goshen high school to accept a similar position at Winona, Minn.

L. E. Wheeler continues at Monticello. He is a splendid student in mathematics. and an inspiring teacher.

Mr. J. W. Heath, of Clay county, received the degree of A. M. in mathematics at the Indiana University in June. His thesis was on "The Theory of Parallels." He acted as an instructor in the department during the spring term.

Albert M. Wilson, principal and teacher of mathematics in the Covington high school, was married in June to Miss Hunter, of Bloomington.

Frank Masters, teacher of mathematies in the Brookville high school during the past year, has resigned and will enter Sibley College at Cornell in September. He will study engineering.

Mr. H. C. Brandon, who received the degree of A. B. in mathematics at Indiana in June, will continue in charge of the mathematics in the Fairmount high school.

Curtis Merriman, A. B., in philosophy, Indiana University, '02, will have charge of the mathematics in the Crawfordsville high school, 1902-03.

Mr. Charles A. Unnewehr is the new high school principal at Cannelton. He will teach the mathematics and physics. He is a strong man.

J. H. Shock will superintend the schools at Warren, and teach the mathematics in the high school.

Mr. W. I. Early continues to do most excellent work in mathematics at Spencer.

Prof. Jacob Westlund, of the mathematical department at Purdue, has recently published a very interesting note on "Multiple Perfect Numbers."

SOLUTIONS.

112. A circular farm of 160 acres is divided among a wife and three daughters, the daughters receiving circles tangent to each other and to the boundary of the farm, and the wife the remainder. How much

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