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Already the committee has made specific recommendations for omissions in algebra. Among the topics slated to go are highest common factor and lowest common multiple, square and cube root of algebraic expressions, and simultaneous quadratics. “Such omissions will not surprise those who have kept in touch with the recent recommendations of the leaders of mathematical thought in America," says Prof. Hedrick. “We now find other additions to these worst offenders; the theorems on proportion, the theory of exponents, the theory of quadratic equations."

There are other changes suggested that are even more radical than these. Fractions are to be confined, in general, to those simple fractions most used in the world—fractions whose denominators are 2, 3, 4, 5, and simple combinations of these.

“Is, then, algebra and possibly a part of geometry to be abandoned ?" asks Prof. Hedrick. "Far from it. Just as in the teaching of modern languages, when the old drill on conjugations and declensions and rules was swept away, its place was taken by a real study of the living language as such, as a mode of expressions, as a living reality. I venture to say that the disciplinary value of language study has not suffered in the process. And I know that the students taught under the present methods know fully as much about the declensions and the rules a year after they leave the course as did the older students who studied only those rules and declensions.

“Similarly in algebra and geometry, if we sweep aside some of the outworn topics accumulated when discipline was considered to be the entire purpose and aim, we have to substitute something of the real life of mathematics, some of the ways in which people actually use it.

“It is a mistake to imagine that people will think accurately about affairs that concern them deeply without such training as that which is proposed. Mistakes concerning interest on money, mistakes on life insurance, mistakes on estimated costs and values are as common as mistakes in science, due always to lack of training in functional thinking.

“A very interesting book is Sir Oliver Lodge's 'Easy Mathematics, Principally Arithmetic,' written by that great scientist in his prime, before he undertook the more occult studies in which he is now engaged. This is a book for adults. It deals with simple topics in a novel, interesting, and valuable way. In it he refers to the common mistakes that people make in think

ing of relations between quantities. Some of his illustrations, while crude, are striking. Thus he asks:

'If a camel can go six days after drinking twelve gallons of water, how much water would he have to drink to go for three months?'

“He points out that many persons would thoughtlessly solve this problem by ordinary proportion. Or he asks:

'If a boy can slide ten feet on the ice with a running start of fifteen feet, how far can he slide with a running start of half a mile?'"

Again: 'If a horse can carry 300 pounds when standing on four legs, how much can he carry when standing on one leg!'

“Such problems, while ridiculous, illustrate perfectly the commonplace nature of problems not solvable by proportion. The common errors made in such problems exist in very practical affairs. That they may become extremely serious is illustrated by the Quebec Bridge disaster of a decade ago, when hundreds of human lives and $7,000,000 were lost, all because one man supposed that a girder twice as large as another would be twice as strong. A homely case of the same error has become almost proverbial, in the statement that twice as much medicine does not give twice as much benefit to a sick man.

“Between this homely case of doubling the dose of medicine and the awful case of the Quebec Bridge disaster lie hosts of other relations between quantities in everyday life, in business, in science, in which it behooves us to think with care and accuracy. It is our business to see that our mathematical courses in secondary schools do give training in such thinking.

If they do, as they have not in the past, they will be more worthy of recognition by real educators and of retention in school curricula.”—(Reprinted from the New York Evening Post.)

CLIPPINGS FROM THE EUGENICS CONGRESS Severe restriction of immigration is essential to prevent the deterioration of American civilization, according to students of race and biology now taking part in the second International Eugenics Congress at the American Museum of Natural History.

The “melting pot” theory is a compete fallacy, according to eugenists, because it suggests that impurities and baser qualities are eliminated by the intermingling of races, whereas they are as likely to be increased. Speakers who touched on the subject were all on one side, holding that the mixture of poor stock with a good one does as much harm to the good stock as it benefits the poor.

Dr. Charles B. Davenport, Director of the Eugenics Record Office, urged stricter immigration laws than those now in force and suggested that amendments should eventually be made enabling researches to be made into the family history of candidates for admission into the United States in order to bar tainted lines.

Dr. Osborn argued that the state's right to prevent disease implied a similar right to prevent the multiplication of feebleminded, idiocy and moral and intellectual diseases.

“The wisdom of British biologists," he continued, "expressed by Tennyson in his memorable lines:

How careless of the individual.

How careful of the race? has been translated into the fatal reverse,

How careful of the individual,
How careless of the race.

Major Darwin also urged that the sound and fit and superior people should, by a campaign of patriotism, be induced to raise larger families. Racial deterioration seems evident among all highly civilized peoples, he said, because of the thinning out of the descendants of highly endowed stock and the multiplication of those of inferior endowment.

Dr. Louis I. Dublin, Statistician of the Metropolitan Life Insurance Company, said that a great racial loss resulted from the fact that women with higher education often remained unmarried and seldom raised many children. He deplored the action of school authorities here in discriminating against mothers among school teachers as “a reflection of the unintelligent attitude of the community.” He urged the college bred woman to look on matrimony as a career with great and inspiring possibilities.

After drawing a black picture of post-war conditions in Europe, and particularly in France, Dr. de Lapouge continued :

“America, it depends on you, I solemnly declare, to save civilization and to produce a race of demigods.

“In France the war gave a blow to superior elements that may be mortal. The best of our young men have perished or been invalided in the proportion of at least two to three. Many of the aristocratic families have been wiped out, the last male having been killed. In the same circles, the young women will not find husbands, partly because the young men have disappeared and partly because the high cost of living has made their dowries, even if added to the usual earnings of a husband, insufficient to found a family. Among us generally the salaries of intellectuals are lower than those of the workers.

I have every reason to believe that the disastrous results of selection exercised by the last war are the same among the other peoples of Europe. In Russia, eugenical inheritance may be considered destroyed."

Dr. Andrew Edson sent a notice to all Principals of schools in Greater New York having ungraded classes, to ask that the ungraded teachers be permitted to attend one session of the Congress. Many took advantage of this opportunity.

An examination of eligible men and women applicants for license as teacher of an ungraded class (of mentally sub-normal pupils) in elementary schools, will be conducted by the Board of Examiners in Room 422 of the Hall of the Board of Education, Park Avenue and 59th St., Borough of Manhattan, at each of the following times: Thursday and Friday, November 3 and 4, 1921, and Thursday and Friday, March 16 and 17, 1922, beginning at 9 A. M. each day. The prospectus may be obtained by writing to 500 Park Ave., New York City.

EXCHANGES AND PAMPHLETS RECEIVED Prison Leaflets. 1920. The Psychology of Prison Cruelty, by Frank

Tannenbaum. Reprinted from the Atlantic Monthly, April, 1920,

by the National Committee on Prisons and Prison Labor, N. Y. C. Education. June, 1921. Infant Education, by James L. Stockton. Edu

cation in Recent Sociology, by J. T. Williams. Health News. July, 1921. Some Special Educational Needs of Chil

dren, by Sanger Brown, 2d, M. D. Manuel General de l'Instruction Primaire. Juillet, 1921. Catholic World. September, 1921. A complete Dante number. Journal of the N. E. A September, 1921. The Situation in Congress

Educationally. School Life. September, 1921. Eradication of Illiteracy, by John J.

Tigert. Bibliographie des Livres francais de Medecine et de Sciences. 1908-1921. Immigrant Contributions to the American Nation. Published by Ameri

ca's Making, Inc., 7 West 16th Street, New York City. Education of Mental Defectives in State and Private Institutions and in

Special Classes in Public Schools in the U. S., by V. V. Anderson,

M. D. Published by National Committee for Mental Hygiene. Education. September, 1921. Choosing an Occupation, by H. E. Stone.

America's Making, by Ella K. Jelliffe.

STATEMENT OF THE OWNERSHIP, MANAGEMENT, ETC., OF UNGRADED

Published monthly at Albany, N. Y., required by the Act of August 24, 1912. Name of stockholders or Oficers: Post Office

Address:
Editor, E. E. Farrell,

17 Lexington Ave., New York City Managing Editor, M. B. Ecob,

17 Lexington Ave., New York City Business Manager, M. C. Major,

34 Jefferson Ave., Brooklyn, N. Y. Publisher, The Upgraded Teachers Association of New York City

27 Columbia St., Albany, N. Y.

17 Lexington Ave., New York City Owners (if a corporation, give names and ad

dresses of stockholders holding 1 per cent or more of total amount of stock). The Ungraded Teachers Association of New York

City. Known bondholders, mortgagees, and other

security holders, bolding 1 per cent or more of total amount of bonds, mortgages, or

other securities. None. The Ungraded Teachers Association of New York City,

ELIZABETH E. FARRELL, Editor Sworn to and subscribed before me this 1st day of October, 1921. K. ECOB, Commissioner of Deeds,

New York City. Term expires December 2, 1921.

No. 65

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