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tion to trying to understand the subject. In view of the fact that the American secondary mathematics teachers usually follow textbooks so slavishly, the college teacher of mathematics who believes in emphasizing the subject rather than the textbook often meets with considerable difficulty with the beginning classes. On the other hand, it is clear that as the student advances he should be encouraged to seek information from all available sources instead of from one particular book only. The rapid improvement in our library facilities makes this attitude especially desirable.

An advantage of the textbook is that it is limited in all directions, while the subject itself is of indefinite extent. In the textbook the subject has been pressed into a linear sequence, while its natural form usually exhibits various dimensions. The textbook presents those phases about which there is usually no doubt, while the subject itself exhibits limitations of knowledge in many directions. From these few characteristics it is evident that the study of textbooks is apt to cultivate a different attitude and a different point of view from those cultivated by the unhampered study of subjects. The latter are, however, the ones which correspond to the actual world and which therefore should receive more and more emphasis as the mental vision of the student can be enlarged.

The number of different available college mathematical textbooks on the subjects usually studied by the large classes of engineering students has increased rapidly in recent years. On the other hand, the number of suitable textbooks for the more advanced classes is often very limited. In fact, it is often found desirable to use textbooks written in some foreign language, especially in French, German, or Italian, for such courses. This procedure has the advantage that it helps to cultivate a better reading knowledge of these languages, which is in itself a very worthy end for the advanced student of mathematics. This procedure has, however, become less necessary in recent years in view of the publication of various excellent advanced works in the English language.

The greatest mathematical treasure is constituted by the periodic literatures, and the larger colleges and universities aim to have complete sets of the leading mathematical periodicals available for their students. This literature has been made more accessible by the publication of various catalogues, such as the Subject Index, Volume I, published by the Royal Society of London in 1908, and the volumes "A" of the annual publications entitled International Catalogue of Scientific Literature. All students who have access to large libraries should learn how to utilize this great store of mathematical lore whenever mathematical questions present themselves to them in their scientific work. This is especially true as regards those who specialize along mathematical lines.

In some of the colleges and universities general informational courses along mathematical lines have been organized under different names, such as history of mathematics, synoptic course, fundamental concepts, cultural course, etc. Several books have recently been prepared with a view to meeting the needs of textbooks for such courses. College teachers of mathematics usually find it difficult to interest their students sufficiently in the current periodic literature, and one of the greatest problems of the college teacher is to instill such a broad interest in mathematics that the student will seek mathematical knowledge in all available sources instead of confining himself to the study of a few textbooks or the work of a particular school.

University of Illinois

G. A. MILLER

REFERENCES

For articles on the teaching of mathematics which appeared during the nineteenth century, consult 0050 Pedagogy in the Royal Society Index, Vol. 1, Pure Mathematics, 1908. For literature appearing during the first twelve years of the present century the reader may consult the Bibliography of the Teaching of Mathematics, 1900-1912, by D. E. Smith and Charles Goldziher, published by the United States Bureau of Education, Bulletin, 1912, No. 29. More recent literature may be found by consulting annual indexes, such as the International Catalogue of Scientific Literature, A, Mathematics, under 0050, and Revue Semestrielle des Publications Mathématiques, under V 1. The volumes of the international review entitled L'Enseignement Mathématique, founded in 1899, contain a large number of articles relating to college teaching. This subject will be treated in the closing volumes of the large French and German mathematical encyclopedias in course of publication.

IX

PHYSICAL EDUCATION IN THE COLLEGE

THE of four y 1913 have brought us to a physical

world war

HE events of the four years between the summer of Lessons for 1914 and the winter of 1918 have br a education full realization of the real significance of physical edu- from the cation in the training of youth. America and her allies have had very dramatic reasons for regretting their careless indifference to the welfare of childhood and youth in former years. Only yesterday, we were told that the great war would be won by the country that could furnish the last man or fight for the last quarter of an hour. America and her allies looked with a new and fearful concern upon the army of young men who were found physically unfit for military service.

With the danger of war past, there is no lack of evidence that we and our allies will make practical application of this particular lesson. It will be fortunate indeed if the enlightened people of the earth are really permanently awake to the importance of the physical education of their citizens-in-the-making.

Governmental agencies have already started the movement to guarantee to the coming generation more extensive and more scientific physical education. Public and private institutions are joining forces so that the advantages of this extended program of physical education will be enjoyed by the young men and young women in industry and commerce as well as by those in schools and colleges.

It is to be hoped that the American college will do its full share and neglect no reasonable measure whereby the college graduate may be developed into the vigorous and healthy human being that the mentally trained ought to be. It must be admitted that our findings by the military draft boards, as well as other evidences secured through physical examinations, are not such as to make the American college proud of the quality or the extent of physical edu

Aims of physical education

Formulations of aims and scope of physical education in official documents - By Re

gents of the State of New York

By national committee on physical education

cation which it has given in the past. We must express our keen disappointment at the prevalence of under-development, remediable defects, and unachieved physical and functional possibilities in our college graduates.

Physical training is concerned with the achievement and the conservation of human health. It has to do with conditioning the human being for the exigencies of life in peace or in war. Its standards are not set by a degree of health which merely enables the individual to keep out of bed, eat three meals a day, and run no abnormal temperature. Physical training is concerned with developing vigorous, enduring health that is based upon the perfect function, coördination, and integration of every organ of the human body; health that is not found wanting at the military draft; health that meets all its community obligations; health that is not affected by diseases of decay; and health that resists infection and postpones preventable death.

Official statements and information from reliable sources indicate that physical education and hygiene and physical training are regarded by authorities as covering about the same general field. The general plan and syllabus for physical training adopted by the Regents of the University of the State of New York in 1916 interprets physical training as covering "(1) Individual health examinations and personal health instruction (medical inspection); (2) instruction concerning the care of the body and the important facts of hygiene (recitations in hygiene); (3) physical examinations as a health habit, including gymnastics, elementary marching, and organized, supervised play, recreation, and athletics."

In March of 1918 a National Committee on Physical Education, formed of representatives from twenty or more national organizations, adopted the following resolutions:

I. That a comprehensive, thoroughgoing program of health education and physical education is absolutely needed for all boys and girls of elementary and secondary school age, both rural and urban, in every state in the Union.

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