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Aim of instruction.—New branches or new chapters to substitute for useless topics of study in the course, or those of secondary interest, but retained by pure tradition or by routine.

Section III. EXAMINATIONS.—Projects for the transformation of the system of examinations or for their complete suppression.

Section IV. THE METHODS OF TEACHING.—Modern ideas concerning methods at different stages of instruction and in different types of schools. Correlation among mathematical branches. Relation between mathematics and other branches. Problems and practical applications; models and instruments. The use of manuals.

Section V. THE PREPARATION OF TEACHERS.—What are the conditions which a rational preparation of candidates for teaching should fulfil? How are the theoretic courses and the practical preparation to be organized ?

The progress of teaching depends directly on the preparation of the teachers. This is a question of fundamental importance. The studies and the exigencies vary necessarily from one country to another; they depend much on the number of candidates and the facilities at hand in regard to education. Consequently the committee believes that it will be useful to take account of the reforms or the projects for reform which are now being considered with a view to bringing the training of teachers into conformity with modern conditions, not only for the personnel of primary and secondary schools but also for the university.

This inquiry should touch notably:
(a) The mathematical work required of candidates.
(b) Their introduction to scientific research.

(c) The best method of presenting theoretical and practical pedagogy (considered as the science of education).

(d) The question of the sex of the teacher in different

school years.

(e) Questions concerning, for example, the time to be de

voted to the history of mathematics, the history of the teaching of mathematics, the recreational side of mathematics, and general literature touching mathematical education.

Emerson's oft-quoted remark that every man is my master in something and in that I may learn of him, is, it need hardly be said, eminently true in education, and in particular is it true in the teaching of mathematics. Our colleges have not much cause for over-contentment in the progress made in this subject in the past generation, and aside from the fact that our high school teachers are better educated than formerly, we have not progressed in any very marked degree in the development of education in the mathematical subjects in these institutions. It is well, therefore, that we heartily join the rest of the world in seeing just what we are all doing, not for the sake of attaining to uniformity, but for the sake of doing better the work that makes for our diversity. Uniformity is both unattainable and undesirable, but it is most desirable to know the best that our colleagues elsewhere are accomplishing

The members of the Commission include some men who are sure to accomplish noteworthy results in this work. For many years Professor Klein has stood among the great mathematicians of the world, and of late he has been a prime mover in educational progress in Germany. With him are actively associated in this movement men like Professors Stäckel, Gutzmer, Schotten, Treutlein, and Schimmack, all of whom stand among the leaders in German mathematics or education. In Austria, Professors Czuber, Suppantschitsch, and Wirtinger are among the most active workers, and each one is well known wherever the teaching and progress of mathematics is understood. In France, Saint-Germain, Bourlet, Appell, Tannery, André, Borel, and Laisant are a few among the number who are carrying on the work, not to speak of others equally well known who are acting in an advisory capacity. In Italy, Castelnuovo, Enriques, and Scorza are three of the best known men in the field, and they form the Italian Commission. So it is with the various other countries; each is represented by men who are recognized as

leaders in their respective departments, and the result is an international body of great strength and of sound judgment. The work has already begun, not always in the same way in all countries, but always with the same purpose. The conditions not being identical, the plan of attack varies with the different countries, but everywhere the attack is being made with earnestness and with promise of good results.

In one respect the foreign countries have an advantage over us. In most of them a central bureau of education is more generously treated by the government than is the case in the United States, and therefore government aid is more readily secured. Germany, for example, at once appropriated ten thousand marks for carrying on the investigation in that country. Hungary followed with an appropriation of six thousand crowns. Other governments at once paid their subscriptions to the general fund and agreed to meet the expenses of their delegates, and in no case, so far as known, has there been a lack of financial and educational support of the movement abroad. In the United States the Commissioners were aware from the first that government support of this kind was out of the question. The United States Commissioner of Education, Dr. Brown, has offered all of the assistance possible, and has the success of the work very greatly at heart, but the funds of the Bureau are limited and the uses to which they can be applied are strictly circumscribed. It therefore becomes necessary to look elsewhere for the financial means for carrying on a work in which our educational reputation is in no slight degree at stake, and in which we have a national pride. With fifteen large committees and nearly sixty subcommittees at work, and with a vast amount of labor still to be done, it seems proper to appeal to the generosity of those who are most interested in educational progress of the highest type. The committees are closely connected with university work, many of their members or the members of the advisory council are on university faculties; the movement is international, which means that other nations will hold our universities responsible for the high character of the investigation, and it therefore seems most fitting that friends of the corporations that form the Association of American Universities should assist in raising the small amount that each of these institutions might be glad to contribute to such a cause. If this could be undertaken at once the success of the investigation in the United States, and of the educational contribution of our country to the international cause, would be assured.





Two distinct but converging lines of criticism appear to confuse the public mind as to the present position and value of the American college. The one proceeds from those serious-minded and constructive men, within college service or without it, who are jealous for the college and who are anxious promptly to meet and to solve each new problem as it arises, and so to keep the work of the college as nearly perfect as may be. The other is set in motion by the lapping waves of that presently popular tide whose yellow is, as the dictionaries have it, a token or symbol of jealousy, envy, melancholy. Probably thru inadvertence, the dictionaries omit to add the word ignorance.

This crude criticism of the baser sort may be first disposed of. Because ignorant, it is impertinent. Nevertheless, it reaches the public and measurably affects public opinion. One of the most important commercial discoveries of recent years is that, in our American democracy, attack upon the existing order and upon established institutions has a cash value. If it rises to unusual heights of shrill abuse, it is for the moment talked about, and, in so far, important. One thrifty, but hitherto unknown, person recently sold three articles to a confiding editor, the purport of which was that conspicuous teachers in American colleges did not teach their pupils things known not to be true, but did inculcate openness of mind and the habit of scientific inquiry. The business of the world went on without interruption.

Soon after, a presumably good bishop, turning for the moment from the faith once delivered unto the saints, announced

Reprinted by permission from the New York Evening Post, September 25, 1909.

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