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THE END IN EDUCATION,

SUMMER SCHOOLS.

In a recent sermon, Dr. W. F. Oldham, It is reported that, although the enrollof Columbus, Ohio, declared that th ment at the Chicago or Cook county norgreatest cnd in life is living. This was mal school last year was over 900, the probably intended as a sentiment or key- total at both that school and Colonel thought for all of life; but it is worthy of Parker's Chicago institute this year is special emphasis for us as teachers, lest only 800. Of this number 250 have regiswe fall into the error of thinking that tered at the former and 550 at the latter. education is only for the years yet to This decrease in attendance must not be come. Only to the extent that school life taken to indicate a declining interest in is a complete life for school days—the the peculiar advantages that the summer best life that can then be lived-will it school affords, but must rather be asserve its full purpose in preparing for the signed to the rapid increase in such faciliyears that are to be. The chief end is the ties. The summer school has come to be immediate end. If we call it character, an important factor in American educalet us say that the question of character tion, whether reference be had to the local is just as important to a child now as it normal for the benefit of the rural teacher ever can be. The end in all education, in or to the university six or eight weeks' school or out, is life to-day.

course for post-graduates. It is a means of growth for thousands of teachers who

could not possibly let go of their places WHAT DO THE SCHOOLS NEED? for special work during the school year, The West Virginia School Journal for

but who do find it possible to go year after July, printed a group of letters from

year for a few weeks of study and for the

new life and thought that they find in prominent teachers in that State received

contact with larger minds. The summer in answer to the question, “What one

school is more than a passing fad, and its thing, in your opinion, will do the great place in our system is at once manifest. est good for the public schools of West Virginia ? Out of twenty-six replies, there were seven who advocated such special preparation of teachers for their work

WHAT WILL THE COUNTY INSTITUTE as would improve the professional spirit;

DO FOR ME! five favored higher wages; nine saw the need of closer supervision and a more uni- When this issue reaches our readers the fied system; two advocated greater care in institute season will be fairly opened. A the selection of teachers; two felt the need vast quantity of time and energy, with no of closer sympathy between school and small amount of money, will be expended community; five would demand compul- in this very commendable work. The resory education; while one each pleaded re- muneration, the benefit, will depend spectively for uniform examinations, "a chiefly upon the attitude of the teacher. baptism of the teaching spirit,” and “a who, for the week, becomes a student. civil service defense absolutely impregna- Notwithstanding the multiplied facilities ble to the influence of politicians, sectari- for normal and professional training, it is ans and paternalism.” The variety of re- true that the great body of our teachers, plies shows a wider diversity of opinion especially those in the rural schools, rethan should exist among teachers well ceive no other training than the institute qualified for their work. It seems to us affords. It is this consideration that gives that a persistent effort to raise the stand- them such importance; that makes it ard of preparation would be the surest worth while to secure the best available and quickest solution of all the other instruction, and to use every means to problems. Give us teachers of ability and make them a source of real help. Precharacter, and all other things shall be suming that the best possible arrrangeadded.

ments for instruction have been made, the question for each individual teacher is, -a most expensive theory, disastrous to What can I get out of the week's work? the teacher, and especially hard on the It is possible to make it largely a social innocents. affair; it is possible to attend perfunctor- The other ideal is that of service. It ily, and it is rumored that some teachers is the standard of the real teacher. Even find a way to be there and not to be there his salary is regarded as a means of better at the same time, though, considering the preparation and enlarged usefulness. He natural limitations and the high moral believes, as firmly as any other, that the standards of teachers, this appears hardly teacher is worthy of his hire, but he feels credible. On the other hand, it is possible that there are rewards which are not to go to the institute hungry for all that measurable by a money standard. One is to be offered, eager to know more of the might put a value upon the work of teachsubjects presented, and especially to learn ing arithmetic, writing, reading, history of better methods of instruction. This is and the sciences; but who shall measure the commendable attitude. The indiffer- the work of inculcating truthfulness and ent teacher and the half attentive teacher honesty and uprightness and gentleness will doubtless absorb something, but to and economy and industry and frankness get the most the teacher must make the and unselfishness and purity—the work of week a time of earnest thought and work. building character, of making citizens, of

shaping destiny? All of these may or SALARY AND SERVICE.

may not be included in the teaching of A few weeks ago, when Superintendent

the curriculum, according as the teacher Maxwell succeeded in getting a bill passed Earnestness, faithfulness, patience and

a true teacher or a mere hireling. by the New York Legislature and signed by Governor Roosevelt, providing an in

that quality almost akin to the mother's crease of nearly $2,000,000 in the yearly

love are not commercial commodities. The salaries of New York city teachers, there

teacher who has them may have to regret was great rejoicing, as there should have

the smallness of her salary, but she does been. Either fortunately or unfortunate

not lose her reward. She has her part, as ly, teachers, like other men and women,

Professor Scott puts it, "in doing the high are subject to physical needs and to those

things.” There are faithful teachers even requirements of home and society which

in humble places to whom opportunity demand financial means. To teachers, as

itself is reward. The late venerable teachto others, subsistence for self and family

er, Henry Barnard, as Dr. Winship vells is the first consideration. Salaries for

us, used a fortune of $50,000 in the publiteaching have been notoriously inade

cation of an educational work which quate. The long campaign for better pay

will be of untold value for generations to is defensible on the simple ground of ne

come. It was a work of love and a noble cessity; and rejoicing over such an

sacrifice. His ideal was one of service. achievement as that just mentioned and

So let us teach. So let us live. Success over the substantial recognition of pro

means more than salary, and character is fessional ability in many places surely

greater than wealth. needs no apology.

But there is always danger of commer- Extolling that which is pure is a better cialism. It is easy to look askance at aid to virtue than denouncing that which teachers who are accustomed to speak and is vile. When a guide shows a traveler think of teaching as something higher through a perilous region he is likely to than most other occupations. It is easy show him along the right way rather than to measure a teacher's worth or a teacher's to take him from pitfall to pitfall and success by the salary paid. No less is it pointing out to him just what to avoid in easy for a teacher to measure out the serv- his course. Many a bad book would never ice to be rendered in proportion to the have done one-half the harm it has, had salary received. Too many times small an emphasis not been placed upon its pay means correspondingly small service worst phase by its reviewer.

MATHEMATICS.

ROBERT J. ALEY, BLOOMINGTON, IND.

HISTORY OF ARITHMETIC.

XXV. ARITHMETIC IN THE COLONIES-Continued.

Dilworth's Schoolmaster's Assistant, mentioned in the July Inland Educator, is worthy of some further notice. It was the authority in the latter colonial days. All arithmetical arguments were settled by an appeal to Dilworth. Many English editions were issued, and at least seven American ones.

Thomas Dilworth was a school-master in Wapping. He was the author of several other school books besides the arithmetic, notably a grammar and a work on bookkeeping. In his book he follows the general lines laid down by Cocker. All the theory is propounded in the form of question and answer. The book contains three distinct divisions: whole numbers, vulgar fractions and decimals, to which is added a large collection of questions and a chapter on duodecimals.

The rhyme for the months is:

the day of marriage, it happened that the gentleman's age was just double to that of the lady's; that is, as 2 to 1. After they had lived together thirty years, the gentleman observed that his lady's age drew nearer to his and that his was only in such proportion to hers as 2 to 1 3-7. Thirty years after this the same gentleman found his and his lady's ages to be as near as 2 to 135, at which time they both died. I demand their several ages at the day of their marriage, and of their death; also the reason why the lady's age, which was continually gaining upon her busband's, should, notwithstanding, be never able to overtake it."

In the list of pleasant and diverting questions we find many of the old friends that were used to while away our own boyhood evenings. It is interesting to know that the boys of one hundred twenty-five years ago were puzzling their heads over the same questions. Here are a few of them given by Dilworth:

1. Place the nine digits in a quadrangular form, so that any three figures in a right line may add just fifteen.

2. A gentleman's servant went to market with an order to buy twenty fowls for 20d. He did so, and brought home pigeons at 4d. apiece, larks at a halfpenny apiece, and sparrows at a farthing apiece. I demand how many there were of each sort.

3. Let 12 be set down in four figures, and let each figure be the same.

4. Three jealous husbands, with their wives, being ready to pass by night over a river, do find at the waterside a boat which can carry but two persons at once, and for want of a waterman, they are necessitated to row themselves over the river at several times. The question is, how these six persons shall pass two by two, so that none of the three wives may be found in the company of one or two men unless her husband be present?

5. Says Jack to his brother Harry, I can place four threes in such a manner that they shall make just 31; can you do so, too?

"Thirty days hath September,
April, June and November;
All the rest have thirty-one,
Except February alone,
Which claimeth just eight and a score,
But every leap year one more.”

ones.

For the time the book contains an unusually large collection of problems. The problems in the main are good. In the miscellaneous lists are found some rather difficult

The following are examples:
“A gentleman a chaise did buy,

An horse and harness, too;
They cost the sum of three score pound;

Upon my word 'tis true.
The harness came to half of the horse,

The horse twice of the chaise;
And if you find the price of them,

Take them and go your ways."

“A gentleman courted a young lady; and as their birthdays happened together, they agreed to make that their wedding day. On

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THE POWER OF LOGARITHMS. The following example will illustrate the great advantage of logarithms in abridging arithmetical labor. In the higher parts of analysis the use of logarithms is indispensable. It would not be difficult to propose questions, which by logarithms might be wrought in a few moments, but if wrought by arithmetical rules, would require years.

How many figures will be required to ex

press 90%?

The esponent of the above expression is

99 = 387420499.: 999—9387420489 Putting it into logarithms, we have

log. 9:34 12049 = 357420489 X log. 9 =387420139 0.954212509439=369693099.63-L.

Hence, the number answering to this logarithm may consist of 369693100 figures. The number, if printed, would fill upwards of 256 volumes of 400 pages each, allowing 60 lines to a page and 60 figures to a line.July, Notes and Queries.

From these we readily get y+z 1

1 h2

+

ho V 16 - h2 y +z=3. A. Then 3 1

1
h2

+
V 25 h? V 16 – h
Let 1=x+y or + 1'16 -- h?.
Then ho=16 - 12.

Substituting in A, reducing and simplifying, we have 15 +314 — 719 - 31312 — 1411 +381=0.

By methods given in algebra we find l=3.227. Then ho = 5.5864.

z+w=V 25 h2 = 4.406.

1+z+w=5,5864 + 4. 106 = 7633. Multiplying by 10, we have AE=76.33.

-Robert McDill, Newcastle. 18. (16— p. 305.)

It requires 3, 21% and 2 minutes, respectively, for the first, second and third boy to ride around the block. They will be together at the starting point at a time equal to the L. C. M. of these numbers, which is 30 minutes. -P. G. Huston, Weirtown. 19. (32-p. 302.) 36 X 10 X 9 X 1728

= 2603.57 bu.
2150.1
2603.57 x 24 ct. = $637.87.
11% of $637.87 = $9.57
$637.87 – $9.57 = $628.30.

Eva Chaney, Atkinsonville.
(9-p. 351.)
Amount of $600 @ 6% for 2 years = $672.
From Sept. 1, 1890 to June 1, 1892, is 14 yr.
Amount of $1 for 18 yr, at 10% = $1.175.
$672 ; $1.175 = $571.91.

-Alice Irene Clem, Monroeville. 21. (11-p. 355.)

The amounts are to be on interest 9, 6 and 3 years respectively. From table on page 276, the compound amounts of $1.00 at 4% for 9, 6 and 3 years

are $1.423312, $1.265319 and $1.124864. The sum of these amounts is $3.813495.

1.423312 The oldest son receives

of $10,000 =

3.813495 $3,731.50.

1.265319 The next son receives

of $10,000

3.813495 $3,318.50.

1.124864 The youngest son receives

of $10,000

3.813195 = $2,950.00.

-C. E. Walts, Union.

SOLUTIONS.

6 and 7.

B

20.

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22. A field whose length is to its width as 2 to 3 contains 15 acres. A man plows around it until he has plowed one-half of it. Find the dimensions of the unplowed part:

Solutions for these problems should be sent to R. J. Aley, 203 Forest Place, Bloomington, Ind., on or before September 14th. Persons desiring credit for their solutions should sign their names to the same. We should like to have some good elementary problems in algebra and geometry.

15 A. = 2400 sq. rd.

If the dimensions are as 2:3, they are 10 rd. and 60 rd.

Let x=width of plowed strip.
60 — 25= length of unplowed part.
40 2x = width of unplowed part.

(60 — 2x) (40 -- 2x)= 1200. Multiplying out and simplifying x? — 50x + 300 = 0.

From which x= 6.97.
40 — 2x = 21.06.
60 – 2x = 41.06.

-John Morrow, Charlestown.

CREDITS

John Morrow, Charlestown, 18, 19, 20, 21, 22; Carol Beard, Terre Haute, 22; C. E. Crawford, Michigantown, 19; Colonel Sentman, Stone Bluff, 22; A. F. Malmstone, Lake Sta., 18; Augusta Sayler, Rensselaer, 18, 19; R. H Baummirk, Saline City, 18; Geo. C. Carothers, Kentland, 18, 19; E. E. Walker, Hardinsburg, 18, 19; Homer Scott, Van Buren, 18; John F. Hoeing, Huntingburg, 18, 21; H. A. Blunk, Crown Centre, 22; L. W. Clements, Elnora, 18, 19, 20; J. L. Allen, Henryville, 19, 20, 21; Thos. Singleton, Washington, 18, 19; W. A. Mayfield, Youngs Creek, 18; B. F. Scott, Bluffton, 18, 19, 20, 21; Wiley Hamilton, Sandborn, 18, 19, 20; J. B. Schwartz, Collingwood, 18, 19, 21; Eva Chaney, Atkinsonville, 18, 19; P. G. Huston, Weirtown, 18, 19, 20, 21, 22; Alice I. Clem, Monroeville, 18, 19, 20; Clarence Walts, Union, 21; H. H. Williamson, Sandborn, 18, 20, 22; Ella G. Warner, Carlisle, 19.

NEW BOOKS. Fairchild's Solution Book.-This book is by Prof. J. T. Fairchild, of Crawfis College, Ohio. It is prepared for the common-school teacher. It contains complete solutions of 471 problems in arithmetic and mensuration. The solutions are notable for their clearness and conciseness. The reader will find good examples of nearly every kind of problem that can come up in arithmetic or mensuration. The historical notes, definitions and suggestions made at various places in the book are very helpful. A splendid list of 142 miscellaneous problems is given at the end of the book. Every teacher who possesses a copy of this book will certainly de. rive much benefit from it. It is published by the author at Crawfis College, Ohio.

Bemarı and Smith's Elements of Algebra.This book comes from Ginn & Co., and is prepared by Professor Beman, of Michigan University, and Principal Smith, of the Brockport Normal, N. Y. The authors hare followed the general plan of their geometry and have introduced as much of the modern spirit of mathematics as is compatible with a good elementary text-book. Factoring is not only fully treated, but it is made use of in the solution of equations and the treatment of fractions. The remainder theorem is given before factoring, as it should be, although many books do not so place it. The whole book is arranged so as to hold the interest of the reader. There are frequent reviews and an unusually large number of fresh and interesting exercises.

Hinds & Noble, New York, have recently come into possession of the University Tutorial Series. The following are some of the mathematical books of the series: Deakin's Euclid.-The author, Rupert Deakin, headmaster of King Edward's grammar school, Stourbridge. The book is issued in two forms, books I and II separate, and

SOLUTIONS REQUESTED. 27. Solve No. 9, page 355. 28. Solve No. 62, page 305. 29. A man plows 19 acres, which is in the form of a rectangle whose dimensions are as 125 to 152. How wide a strip must he plow around this in order to double the plowed land?

30. Reduce 8.36741 to an improper fraction.

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