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OCTOBER, 1866.

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How the INTERESTS OF EDUCATION ARE ADVANCED. T HE Teachers' Association of this State met at Geneva, July 31st,

for the purpose of advancing the interests of Education. The discrepancy between the purpose avowed, and the means adopted to accomplish it, deserves a passing notice.

In the reports of the Association we hear very much of "attractions," “ brilliant performances," and the like, but very little of earnest discussion, or hearty endeavor to grapple with the practical questions which should have engaged every attention. “Considerable music was interspersed,” reports say, “but the most welcome treat of all was the reading of Miss Potter.” In the evening, Linden Hall was crowded to overflowing, Miss Potter being again "the main attraction.” There were besides, Mrs. Randall, and the “still further attraction of singers, male, female, and professional.”—Truly, we hope the teachers of New York are not responsible for the foregoing classification of the singers who so kindly entertained them.--During the evening, poems were read ; professional readings delivered ; an operatic air was sung; and, probably, as an interlude to enable the "attractions” to recover breath, Dr. Miller read an Address on our Common Schools. On the following day, the Geneva Select Choir, and a choir of girls, “ entertained the assembly” with some of their choicest songs ; Prof. Mills“ delighted the Association” with a performance on the harp ; and Miss Potter and Mrs. Randall further advertised their elocutionary proficiency.

That all these exercises had a primary reference to education is evident from the titles of the various pieces. Prof. Baker, upon invitation, gave a “brilliant performance" of " True love can ne'er forget ;" Miss Potter read “ High Tide ;" and Mrs. Randall, “ The Vagabonds."

These intellectual and artistic entertainments were, no doubt, very agreeable ; but when we compare such misuse of time with the serious discussions and business-like action of the Association of School Commissioners and Superintendents, which met at the same place earlier in the week, the contrast is any thing but creditable to the Association of Teachers. If teachers seek relaxation and amusement, and choose to assemble as teachers for that purpose, they have a perfect right to do so; but we protest against their meeting in the name of the Association of the Teachers of the State of New York, ostensibly to discuss important educational questions, and then making such meeting solely the occasion of mutual admiration and personal display. We do not wish the world to look upon teachers as incapable of discussing intelligently the questions to which their profession gives rise; or less interested in the details of their calling, than jurists, physicians, and clergymen are with theirs. Members of these professions do not find it necessary to engage the services of singers and dramatic performers to insure a respectable attendance upon their conventions. And it is a disgrace to the teachers of New York that the Association of the Teachers of the State does not possess sufficient professional spirit and ability to sustain its conventions without so much extraneous and comparatively frivolous aid.

THE BEGINNING OF Our Common School SYSTEM. TN bis message to the Legislature which met in Ponghkeepsie, January 1 6, 1795, Gov. George Clinton reminded that body, that while provision had been made for the endowment of colleges and other seminaries in which the higher branches of learning were taught, no legislative aid had been given to common schools, and he recommended that provision should be made for their improvement and encouragement.

This was the first official movement made in this State in behalf of these institutions-institutions upon which, under God, depends the preservation of the rights and liberties of the people of these States. Thus speaks the chronicler of those times.

The Legislature passed a law appropriating annually, for five years, the sum of fifty thousand dollars. The act further provided, that a sum equal to one-half the sum received from the State by the several towns should be raised by à tax and added to the appropriation.

From such beginnings our Common School System was developed. This happened seventy-one years ago—threescore years and ten-the allotted life of man ; and many an old man of to-day remembers with what joy the news was received in each little hamlet. And they will tell us how munificent they deemed the bounty of the State, and what visions of winter schools, reached through miles of long tramping, filled the imagination, and begot all sorts of vague yearnings.

Since those times, what wonderful accessions have been made to the general mass of information ; what changes in educational systems ; how has wealth increased and altered all the old relations and long-established ways of business! The boy of to-day has the culture of the man of yesterday; the girl surprises the woman with her wonderful advancement, and knowledge of things unknown in her girlhood, until the mother doubts that this is a child of her begetting. But we are sometimes led to think that this is not all improvement, and that what we are pleased to style culture is, to a certain extent, mechanical expertness. We sometimes think that we may have a vast deal more learning, but, at the same time, less earnest thought ; and earnest, well-directed thought, makes the man.

Those were the days of Jay, of Livingston, of Josiah Ogden Hoffman, of Ambrose Spencer, of Samuel Jones, of Stephen Van Rensselaer, of Yates, of Philip Schuyler, of Rufus King, of Alexander Hamilton, and of many others whose integrity and patriotism should pat to shame the time-servers and trimmers of to-day.

They were men who endeavored earnestly and truly to carry out those two precepts of that greatest of men, Plato ; "first, to make the safety and interest of their fellow-citizens the great aim and design of all their thoughts and actions, without ever considering their own personal advantage ; secondly, so to take care of the whole collective body of the republic, as not to serve the interests of any one party to the prejudice or neglect of all the rest ; for the government of a State is much like the office of a guardian or trustee, which should always be managed for the good of the pupil, and not of the persons to whom he is intrusted ; and those men who, whilst they take care of one, neglect or disregard another part of the citizens, do but occasion sedition and discord.”

But though men have grown mechanical ; though individual endeavor has lost its potency ; thongh processes have taken the place of thought; though men are more guided by selfish interests-yet a great work has been effected. Information has become as necessary as the air we breathe ; and every day the feeling is growing stronger, that ignorance and selfgovernment cannot go hand in hand. Woman is reaching forward to the higher functions of her nature, and man is every year gaining a deeper insight into the laws that should govern human actions and relations.

We honor thee, first governor of the Empire State, among the great names of those times—and they are great for all time; not least on the scroll of honor shall thy name be written.

EDITORIAL MISCELLANY. W E purpose from this time to devote a few pages of our Magazine to the consider

V ation of mathematical problems, questions in English analysis, and such other kindred matter as may be of use to the teacher.

Teachers having difficult questions to propose, or elegant and peculiar solutions of problems, will please direct to

MATHEMATICAL EDITOR,
AMERICAN EDUCATIONAL MONTHLY,

430 Broome Street, New York city.

PROBLEM I. Demonstrate that, if upon the three sides of a right-triangle, any three similar figures be described, the figure described upon the hypothenuse is equal to the sum of the other two.

PROBLEM II. Demonstrate mathematically that the minute-hand of a clock must overtake the hour-hand.

PROPERTIES OF NUMBERS. Every square number is either divisible by 5, or will leave for a remainder plus or minus 1.

Every cube number is either divisible by 7, or will leave for a remainder plus or minus 1.

Geometrical construction for a very close approximation to the cir. cumference of the circle.

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Let BD be the diameter of a circle ; erect at its extremity B, the perpendicular BC, and make it equal to the radius ; prolong BD, and make Da=ab=bc=one-fifth of the radius; draw aC and cC, and make BA= aC. Now if we draw from A the line AE parallel to CC, BE will be only one-half millionth part smaller than 7.

DEMONSTRATION.
As BD=l Ba=1.1 Bc=1.3 -
Ca=Ba? BC=146 and Ca= 146
BC : Be :: BA : BE or 1: 1: :: 1148 : BE from which
BE=1347146=13V0.0584=V9.8696=3.14159.

EDITORIAL CORRESPONDENCE.

GERMAN GEOGRAPHICAL PUBLICATIONS.

NUREMBERG, August 1, 1866. YERMANY, though pre-eminently a land of books, is not a land of CT school-books, for, as I have said in previous letters, the method of giving instruction is so different from that employed in American schools, that books are almost unneeded. Whatever can be taught by familiar lectures, is communicated to the child's mind in that way, and the Germans prefer this mode of teaching to that in vogue in America. There is an abundance of reading-books, because that is a department which can not be taught by oral communication. But the great variety of school histories, geographies, arithmetics, algebras, and grammars, which form a conspicuous part of the stock of an American bookstore, is not found in Germany; or if it be too strong an expression to say not found, let me word it, not thrust into the foreground as with us. Little text-books, in pamphlet form, there are indeed; but they are as unpretentious as possi. ble, and bear the humble name of Leitfadens, or Rudimentary Hints. The so-called Hand-books which the German press issues are not works for the pupils of the schools, but for the use of the teachers, and contain the materials which are drawn upon to furnish the familiar lectures of the class-room. In one word, the method of instruction employed in our theological seminaries is adopted in all, or nearly all, the schools of Germany; a lecture is given, the pupils take notes, and answer questions the next day upon the instruction imparted. On some accounts this is a good system; it is better at any rate than that of committing the words of a text-book to memory, and repeating them by rote, in the manner prescribed in some schools.

There is one class of text-books known in which Germany excels, and it is to them that I propose to devote a part at least of this letter. It is the Atlases which are used. The teacher may dispense with manuals of descriptive geography, but he can not dispense with the aid of good maps. The method of instructing in this department has called out two classes of works, which are in their respective ways among the most perfect that are known—the Geographical Hand-books, which are to be used by the teachers, and the Atlases, which are to be used by the scholars. Of the Hand-books I do not propose to speak at any length, excepting to say that there is not in the United States or in England, so far as I am aware, any thing so perfect in its way, as the Hand-books of Daniel and Klöden. They are each in three volumes, of about eight hundred pages to the volume, and form an admirable and thoroughly digested summary of all matters connected with geography--not executed in the manner of a gazetteer, but thoroughly worked out in a natural and not an alphabetical order. The authors are thorough geographers. I am personally acquainted with both Klöden and Daniel, and know that they are conscientiously giving the best years of their lives to those admirable manuals, and are keeping the new editions level with the advance of geographical science.

The reader is probably not aware of the fact, that the most of the maps which he sees are mere copies of maps previously existing. Sometimes

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