universities differ considerably. The normal beginning courses now
presuppose a year of geometry and a year and a half of algebra in
addition to the elementary courses in arithmetic, but much higher
requirements are sometimes imposed, especially for engineering
courses. In recent years several of the largest universities have
reduced the minimum admission requirement in algebra to one year's
work, but students entering with this minimum preparation are
sometimes not allowed to proceed with the regular mathematical classes
in the university.
=Variety of college courses in mathematics=
Freshmen courses in mathematics differ widely, but the most common
subjects are advanced algebra, plane trigonometry, and solid geometry.
The most common subjects of a somewhat more advanced type are plane
analytic geometry, differential and integral calculus, and spherical
trigonometry. Beyond these courses there is much less uniformity,
especially in those institutions which aim to complete a well-rounded
undergraduate mathematical course rather than to prepare for graduate
work. Among the most common subjects beyond those already named are
differential equations, theory of equations, solid analytic geometry,
and mechanics.
A very important element affecting the mathematical courses in recent
years is the rapid improvement in the training of our teachers in the
secondary schools. This has led to the rapid introduction of courses
which aim to lead up to broad views in regard to the fundamental
subjects. In particular, courses relating to the historical
development of concepts involved therein are receiving more and more
attention. Indirect historical sources have become much more plentiful
in recent years through the publication of various translations of
ancient works and through the publication of extensive historical
notes in the _Encyclopedie des Sciences Mathematiques_ and in other
less extensive works of reference.
The problem presented by those who are preparing to teach mathematics
may at first appear to differ widely from that presented by those who
expect to become engineers. The latter are mostly interested in
obtaining from their mathematical courses a powerful equipment for
doing things, while the former take more interest in those
developments which illumine and clarify the elements of their subject.
Hence the prospective teacher and the prospective engineer might
appear to have conflicting mathematical interests. As a matter of
fact, these interests are not conflicting. The prospective teacher is
greatly benefited by the emphasis on the serviceableness of
mathematics, and the prospective engineer finds that the generality
and clarity of view sought by the prospective teacher is equally
helpful to him in dealing with new applications. Hence these two
classes of students can well afford to pursue many of the early
mathematical courses together, while the finishing courses should
usually be different.
The rapidly growing interest in statistical methods and in insurance,
pensions, and investments has naturally directed special attention to
the underlying mathematical theories, especially to the theory of
probability. Some institutions have organized special mathematical
courses relating to these subjects and have thus extended still
further the range of undergraduate subjects covered by the
mathematical departments. The rapidly growing emphasis on college
education specially adapted to the needs of the prospective business
man has recently led to a greater emphasis on some of these subjects
in several institutions.
The range of mathematical subjects suited for graduate students is
unlimited, but it is commonly assumed to be desirable that the
graduate student should pursue at least one general course in each one
of broader subjects such as the theory of numbers, higher algebra,
theory of functions, and projective geometry, before he begins to
specialize along a particular line. It is usually taken for granted
that the undergraduate courses in mathematics should not presuppose a
knowledge of any language besides English, but graduate work in this
subject cannot be successfully pursued in many cases without a reading
knowledge of the three other great mathematical languages; viz.,
French, German, and Italian. Hence the study of graduate mathematics
necessarily presupposes some linguistic training in addition to an
acquaintance with the elements of fundamental mathematical subjects.
Historical studies make especially large linguistic demands in case
these studies are not largely restricted to predigested material. This
is particularly true as regards the older historical material. In the
study of contemporary mathematical history the linguistic
prerequisites are about the same as those relating to the study of
other modern mathematical subjects. With the rapid spread of
mathematical research activity during recent years there has come a
growing need of more extensive linguistic attainments on the part of
those mathematicians who strive to keep in touch with progress along
various lines. For instance, a thriving Spanish national mathematical
society was organized in 1911 at Madrid, Spain, and in March, 1916, a
new mathematical journal entitled _Revista de Matematicas_ was started
at Buenos Aires, Argentine Republic. Hence a knowledge of Spanish is
becoming more useful to the mathematical student. Similar activities
have recently been inaugurated in other countries.
=History of college mathematics=
Until about the beginning of the nineteenth century the courses in
college mathematics did not usually presuppose a mathematical
foundation carefully prepared for a superstructure. According to M.
Gebhardt, the function of teaching elementary mathematics in Germany
was assumed by the gymnasiums during the years from 1810 to 1830.[5]
Before this time the German universities usually gave instruction in
the most elementary mathematical subjects. In our own country, Yale
University instituted a mathematical entrance requirement under the
title of arithmetic as early as 1745, but at Harvard University no
mathematics was required for admission before 1803.
On the other hand, _L'Ecole Polytechnique_ of Paris, which occupies a
prominent place in the history of college mathematics, had very high
admission requirements in mathematics from the start. According to a
law enacted in 1795, the candidates for admission were required to
pass an examination in arithmetic; in algebra, including the solution
of equations of the first four degrees and the theory of series; and
in geometry, including trigonometry, the applications of algebra to
geometry, and conic sections.[6] It should be noted that these
requirements are more extensive than the usual present mathematical
requirements of our leading universities and technical schools, but
_L'Ecole Polytechnique_ laid special emphasis on mathematics and
physics and became the world's prototype of strong technical
institutions.
The influence of _L'Ecole Polytechnique_ was greatly augmented by the
publication of a regular periodical entitled _Journal de l'Ecole
Polytechnique_, which was started in 1795 and is still being
published. A number of the courses of lectures delivered at _L'Ecole
Polytechnique_ and at _L'Ecole Normale_ appeared in the early volumes
of this journal. The fact that some of these courses were given by
such eminent mathematicians as J. L. Lagrange, G. Monge, and P. S.
Laplace is sufficient guarantee of their great value and of their good
influence on the later textbooks along similar lines. In particular,
it may be noted that G. Monge gave the first course in descriptive
geometry at _L'Ecole Normale_ in 1795, and he was also for a number of
years one of the most influential teachers at _L'Ecole Polytechnique_.
A most fundamental element in the history of college mathematics is
the broadening of the scope of the college work. As long as college
students were composed almost entirely of prospective preachers,
lawyers, and physicians, there was comparatively little interest taken
in mathematics. It is true that the mental disciplinary value of
mathematics was emphasized by many, but this supposed value did not
put any real life into mathematical work. The dead abstract reasonings
of Euclid's _Elements_, or even the number speculations of the ancient
Pythagoreans, were enough to satisfy most of those who were looking to
mathematics as a subject suitable for mental gymnastics.
On the other hand, when the colleges began to train men for other
lines of work, when the applications of steam led to big enterprises,
like the building of railroads and large ocean steamers, mathematics
became a living subject whose great direct usefulness in practical
affairs began to be commonly recognized. Moreover, it became apparent
that there was great need of mathematical growth, since mathematics
was no longer to be used merely as mental Indian clubs or dumb-bells,
where a limited assortment would answer all practical needs, but as an
implement of mental penetration into the infinitude of barriers which
have checked progress along various lines and seem to require an
infinite variety of methods of penetration.
The American colleges were naturally somewhat slower than some of
those of Europe in adapting themselves to the changed conditions, but
the rapidity of the changes in our country may be inferred from the
fact that in the first half of the nineteenth century Harvard placed
in comparatively short succession three mathematical subjects on its
list of entrance requirements; viz., arithmetic in 1802, algebra in
1820, and geometry in 1844. Although Harvard had not established any
mathematical admission requirements for more than a century and a half
after its opening, she initiated three such requirements within half a
century. It is interesting to note that for at least ninety years from
the opening of Harvard, arithmetic was taught during the senior year
as one of the finishing subjects of a college education.[7]
The passage of some of the subjects of elementary mathematics from the
colleges to the secondary schools raised two very fundamental
questions. The first of these concerned mostly the secondary schools,
since it involved an adaptation to the needs of younger students of
the more or less crystallized textbook material which came to them
from the colleges. The second of these questions affected the colleges
only, since it involved the selection of proper material to base upon
the foundations laid by the secondary schools. It is natural that the
influence of the colleges should have been somewhat harmful with
respect to the secondary schools, since the interests of the former
seemed to be best met by restricting most of the energies of the
secondary teachers of mathematics to the thorough drilling of their
students in dexterous formal manipulations of algebraic symbols and
the demonstration of fundamental abstract theorems of geometry.
=Relation of mathematics in secondary schools and college=
Students who come to college with a solid and broad foundation but
without any knowledge of the superstructure can readily be inspired
and enthused by the erection of a beautiful superstructure on a
foundation laid mostly underground, with little direct evidence of its
value or importance. The injustice and shortsightedness of the
tendency to restrict the secondary schools to such foundation work
would not have been so apparent if the majority of the secondary
school students would have entered college. As a matter of fact it
tended to bring secondary mathematics into disrepute and thus to
threaten college mathematics at its very foundation. It is only in
recent years that strong efforts have been made to correct this very
serious mathematical situation.
Much progress has been made toward the saner view of letting secondary
mathematics build its little structure into the air with some view to
harmony and proportion, and of requiring college mathematics to build
_on_ as well as _upon_ the work done by the secondary schools. The
fruitful and vivifying notions of function, derivative, and group are
slowly making their way into secondary mathematics, and the graphic
methods have introduced some of the charms of analytic geometry into
the same field.
This transformation is naturally affecting college mathematics most
profoundly. The tedious work of building foundations in college
mathematics is becoming more imperative. The use of the rock drill is
forcing itself more and more on the college teacher accustomed to use
only hammer and saw. As we are just entering upon this situation, it
is too early to prophesy anything in regard to its permanency, but it
seems likely that the secondary teachers will no more assume a yoke
which some of the college teachers would so gladly have them bear and
which they bore a long time with a view to serving the interests of
the latter teachers.
As many of the textbooks used by secondary teachers are written by
college men, and as the success of these teachers is often gauged by
the success of their students who happen to go to college, it is
easily seen that there is a serious temptation on the part of the
secondary teacher to look at his work through the eyes of the college
teacher. The recent organizations which bring together the college and
the secondary teachers have already exerted a very wholesome influence
and have tended to exhibit the fact that the success of the college
teacher of mathematics is very intimately connected with that of the
teachers of secondary mathematics.
While it is difficult to determine the most important single event in
the history of college teaching in America, there are few events in
this history which seem to deserve such a distinction more than the
organization of the Mathematical Association of America which was
effected in December, 1915. This association aims especially to
promote the interests of mathematics in the collegiate field and it
publishes a journal entitled _The American Mathematical Monthly_,
containing many expository articles of special interest to teachers.
It also holds regular meetings and has organized various sections so
as to enable its members to attend meetings without incurring the
expense of long trips. Its first four presidents were E. R. Hedrick,
Florian Cajori, E. V. Huntington, and H. E. Slaught.
An event which has perhaps affected the very vitals of mathematical
teaching in America still more is the founding of the American
Mathematical Society in 1888, called the New York Mathematical Society
until 1894. Through its _Bulletin_ and _Transactions_, as well as
through its meetings and colloquia lectures, this society has stood
for inspiration and deep mathematical interest without which college
teaching will degenerate into an art. During the first thirty years of
its history it has had as presidents the following: J. H. Van Amringe,
Emory McClintock, G. W. Hill, Simon Newcomb, R. S. Woodward, E. H.
Moore, T. S. Fiske, W. F. Osgood, H. S. White, Maxime Boecher, H. B.
Fine, E. B. Van Vleck, E. W. Brown, L. E. Dickson, and Frank Morley.
=Aims of college mathematics: methods of teaching=
The aims of college mathematics can perhaps be most clearly understood
by recalling the fact that mathematics constitutes a kind of
intellectual shorthand and that many of the newer developments in a
large number of the sciences tend toward pure mathematics. In
particular, "there is a constant tendency for mathematical physics to
be absorbed in pure mathematics."[8] As sciences grow, they tend to
require more and more the strong methods of intellectual penetration
provided by pure mathematics.
The principal modern aim of college mathematics is not the training of
the mind, but the providing of information which is absolutely
necessary to those who seek to work most efficiently along various
scientific lines. Mathematical knowledge rather than mathematical
discipline is the main modern objective in the college courses in
mathematics. As this knowledge must be in a usable form, its
acquisition is naturally attended by mental discipline, but the
knowledge is absolutely needed and would have to be acquired even if
the process of acquisition were not attended by a development of
intellectual power.
The fact that practically all of the college mathematics of the
eighteenth century has been gradually taken over by the secondary
schools of today might lead some to question the wisdom of replacing
this earlier mathematics by more advanced subjects. In particular, the
question might arise whether the college mathematics of today is not
superfluous. This question has been partially answered by the
preceding general observations. The rapid scientific advances of the
past century have increased the mathematical needs very rapidly. The
advances in college mathematics which have been made possible by the
improvements of the secondary schools have scarcely kept up with the
growth of these needs, so that the current mathematical needs cannot
be as fully provided for by the modern college as the recognized
mathematical needs of the eighteenth century were provided for by the
colleges of those days.
There appears to be no upper limit to the amount of useful
mathematics, and hence the aim of the college must be to supply the
mathematical needs of the students to the greatest possible extent
under the circumstances. In order to supply these needs in the most
economical manner, it seems necessary that some of them should be
supplied before they are fully appreciated on the part of the student.
The first steps in many scientific subjects do not call for
mathematical considerations and the student frequently does not go
beyond these first steps in his college days, but he needs to go much
further later in life. College mathematics should prepare for life
rather than for college days only, and hence arises the desirability
of deeper mathematical penetration than appears directly necessary for
college work.
=Advanced work in college mathematics=
Another reason for more advanced mathematics than seems to be directly
needed by the student is that the more advanced subjects in
mathematics are a kind of applied mathematics relative to the more
elementary ones, and the former subjects serve to throw much light on
the latter. In other words, the student who desires to understand an
elementary subject completely should study more advanced subjects
which are connected therewith, since such a study is usually more
effective than the repeated review of the elementary subject. In
particular, many students secure a better understanding of algebra
during their course in calculus than during the course in algebra
itself, and a course in differential equations will throw new light on
the course in calculus. Hence college mathematics usually aims to
cover a rather wide range of subjects in a comparatively short time.
Since mathematics is largely the language of advanced science,
especially of astronomy, physics, and engineering, one of the
prominent aims of college mathematics should be to keep in close touch
with the other sciences. That is, the idea of rendering direct and
efficient services to other departments should animate the
mathematical department more deeply than any other department of the
university. The tendency toward disintegration to which we referred
above has forcefully directed attention to the great need of
emphasizing this aspect of our subject, since such disintegration is
naturally accompanied by a weakening of mathematical vigor. It may be
noted that such a disintegration would mean a reverting to primitive
conditions, since some of the older works treated mathematics merely
as a chapter of astronomy. This was done, for instance, in some of the
ancient treatises of the Hindus.
=Mathematics and technical education=
The great increase in college students during recent years and the
growing emphasis on college activities outside of the work connected
with the classroom, especially on those relating to college athletics,
would doubtless have left college mathematics in a woefully neglected
state if there had not been a rapidly growing interest in technical
education, especially in engineering subjects, at the same time. Naval
engineering was one of the first scientific subjects to exert a strong
influence on popularizing mathematics. In particular, the teaching of
mathematics in the Russian schools supported by the government began
with the founding of the government school for mathematics and
navigation at Moscow in 1701. It is interesting to note that the
earlier Russian schools established by the clergy after the adoption
of Christianity in that country did not provide for the teaching of
any arithmetic whatever, notwithstanding the usefulness of arithmetic
for the computing of various dates in the church calendar, for land
surveying, and for the ordinary business transactions.[9]
The direct aims in the teaching of college mathematics have naturally
been somewhat affected by the needs of the engineering students, who
constitute in many of our leading institutions a large majority in the
mathematical classes. These students are usually expected to receive
more drill in actual numerical work than is demanded by those who seek
mainly a deeper penetration into the various mathematical theories.
The most successful methods of teaching the former students have much
in common with those usually employed in the high schools and are
known as the recitation and problem-solving methods. They involve the
correction and direct supervision of a large number of graded
exercises worked out by the students on the blackboard or on paper,
and aim to overcome the peculiar difficulties of the individual
students.
The lecture method, on the other hand, aims to exhibit the main facts
in a clear light and to leave to the student the task of supplying
further illustrative examples and of reconsidering the various steps.
The purely lecture method does not seem to be well adapted to American
conditions, and it is frequently combined with what is commonly known
as the "quiz." The quiz seems to be an American institution, although
it has much in common with a species of the French "conference." It is
intended to review the content of a set of lectures by means of
discussions in which the students and the teacher participate, and it
is most commonly employed in connection with the courses of an
advanced undergraduate or of a beginning graduate grade.
A prominent aim in graduate courses is to lead the student as rapidly
as possible to the boundary of knowledge along the particular line
considered therein. While some of the developments in such courses are
apt to be somewhat special or to be too general to have much meaning,
their novelty frequently adds a sufficiently strong element of
interest to more than compensate losses in other directions. Moreover,
the student who aims to do research work will thus be enabled to
consider various fields as regards their attractiveness for prolonged
investigations of his own.
=Preparation of the college teacher of mathematics.=
The fact that the college teacher has need of much more mathematical
knowledge than he can possibly secure during the period of his
preparation, especially if he expects to take an active part in
research and in directing graduate work, has usually led to the
assumption that the future teacher of college mathematics should
devote all his energies to securing a deep mathematical insight and a
wide range of mathematical knowledge.[10] On the other hand, students
prepared in accord with this assumption have frequently found it very
difficult to adapt themselves to the needs of large freshman classes
of engineering students entering upon the duties for which they were
supposed to have been prepared.
The breadth of view and the sweep of abstraction needed for effective
graduate work have little in common with accuracy in numerical work
and emphasis on details which are so essential to the young
engineering students. The difficulty of the situation is increased by
the fact that the young instructor is often led to believe that his
advancement and the appreciation of his services are directly
proportional to his achievements in investigations of a high order.
This belief naturally leads many to begrudge the time and thought
which their teaching duties should normally receive.
The young college teacher of mathematics is thus confronted with a
much more complex situation than that which confronts the mathematics
teachers in secondary school work. Here the success in the classroom
is the one great goal, and the mathematical knowledge required is
comparatively very modest. Possibly the situation of the college
teacher could be materially improved if it were understood that his
first promotion would be mainly dependent upon his success as a
teacher, but that later promotions involved the element of productive
scholarship in an increasing ratio.
The schools of education which have in recent years been established
in most of our leading universities have thus far had only a slight
influence on the preparation of the college teachers, but it seems
likely that this influence will increase as the needs of professional
training become better known. It is probably true that the ratio of
courses on methods to courses on knowledge of the subject will always
be largest for the elementary teacher, in view of the great difference
between the mental maturity of the student and the teacher, somewhat
less for the secondary teacher and least for the college teacher; but
this least should not be zero, as is so frequently the case at present,
since there usually is even here a considerable difference between the
mathematical maturity of the student and that of the teacher.
It may be argued that the future college teacher will probably profit
more by noting the methods employed by his instructors than he would
by the theoretic discussions relating to methods. This is doubtless
true, but it does not prove that the latter discussions are without
value. On the other hand, these discussions will often serve to fix
more attention on the former methods and will lead the student to note
more accurately their import and probable adaptability to the needs of
the younger students.
Among the useful features for the training of the future mathematics
teachers are the mathematical clubs which are connected with most of
the active mathematical departments. In many cases, at least, two such
clubs are maintained, the one being devoted largely to the
presentation of research work while the other aims to provide
opportunities for the presentation of papers of special interest to
the students. The latter papers are often presented by graduate
students or by advanced undergraduates, and they offer a splendid
opportunity for such students to acquire effective and clear methods
of presentation. The same desirable end is often promoted by reports
given by students in seminars or in advanced courses.
Prominent factors in the training of the future college teachers are
the teaching scholarships or fellowships and the assistantships. Many
of the larger universities provide a number of positions of this
type. It sometimes happens that the teaching duties connected with
these positions are so heavy as to leave too little energy for
vigorous graduate work. On the other hand, these positions have made
it possible for many to continue their graduate studies longer than
they could otherwise have done and at the same time to acquire sound
habits of teaching while in close contact with men of proved ability
along this line.
It should be emphasized that the ideal college teacher of mathematics
is not the one who acquires a respectable fund of mathematical
knowledge which he passes along to his students, but the one imbued
with an abiding interest in learning more and more about his subject
as long as life lasts. This interest naturally soon forces him to
conduct researches where progress usually is slow and uncertain.
Research work should be animated by the desire for more knowledge and
not by the desire for publication. In fact, only those new results
should be published which are likely to be helpful to others in
starting at a more favorable point in their efforts to secure
intellectual mastery over certain important problems.
Half a century ago it was commonly assumed that graduation from a good
college implied enough training to enter upon the duties of a college
teacher, but this view has been practically abandoned, at least as
regards the college teacher of mathematics. The normal preparation is
now commonly placed three years later, and the Ph.D. degree is usually
regarded to be evidence of this normal preparation. This degree is
supposed by many to imply that its possessor has reached a stage where
he can do independent research work and direct students who seek
similar degrees. In view of the fact that in America as well as in
Germany the student often receives much direct assistance while
working on his Ph.D. thesis, this supposition is frequently not in
accord with the facts.[11]
The emphasis on the Ph.D. degree for college teachers has in many
cases led to an improvement in ideals, but in some other cases it has
had the opposite effect. Too many possessors of this degree have been
able to count on it as accepted evidence of scientific attainments,
while they allowed themselves to become absorbed in non-scientific
matters, especially in administrative details. Professors of
mathematics in our colleges have been called on to shoulder an unusual
amount of the administrative work, and many men of fine ability and
scholarship have thus been hindered from entering actively into
research work. Conditions have, however, improved rapidly in recent
years, and it is becoming better known that the productive college
teacher needs all his energies for scientific work; and in no field is
this more emphatically true than in mathematics. Some departmental
administrative duties will doubtless always devolve upon the
mathematics teachers. By a careful division of these duties they need
not interfere seriously with the main work of the various teachers.
=The mathematical textbook=
The American teachers of mathematics follow the textbook more closely
than is customary in Germany, for instance. Among college teachers
there is a wide difference of view in regard to the suitable use of
the textbook. While some use it simply for the purpose of providing
illustrative examples and do not expect the student to begin any
subject by a study of the presentation found in the textbook, there
are others who expect the normal student to secure all the needed
assistance from the textbook and who employ the class periods mainly
for the purpose of teaching the students how to use the textbook most
effectively. The practice of most teachers falls between these two
extremes, and, as a rule, the textbook is followed less and less
closely as the student advances in his work. In fact, in many advanced
courses no particular textbook is followed. In such courses the
principal results and the exercises are often dictated by the teacher
or furnished by means of mimeographed notes.
The close adherence to the textbook is apt to cultivate the habit on
the part of the student of trying to understand what the author meant
instead of confining his attention 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.
G. A. MILLER
_University of Illinois_
REFERENCES
For articles on the teaching of mathematics which appeared during the
nineteenth century, consult 0050 _Pedagogy_ in the _Royal Society
Index_, Vol. I, 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 Mathematiques_, under V 1. The
volumes of the international review entitled _L'Enseignement
Mathematique_, 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.
Footnotes:
[3] P. Zuehlke. _Zeitschrift fuer Mathematischen und
Naturwissenschuftlichen Unterricht_, Vol. 45 (1915), page 483.
[4] Committee No. XII, American Report of the International Commission
on the Teaching of Mathematics, 1912, page 9.
[5] _Internationale Mathematische Unterrichtskomission_, Vol. 3, No. 6
(1912), page 2.
[6] _Journal de l'Ecole Polytechnique_, Vol. 1 (1896), part 4, page lx.
[7] F. Cajori, _Teaching and History of Mathematics in the United
States_, 1890, page 22.
[8] A. E. H. Love, _Proceedings of the London Mathematical Society_,
Vol. 14 (1915), page 183.
[9] V. V. Bobynin, _L'Enseignement Mathematique_, Vol. 1 (1899), page 78.
[10] The Training of Teachers of Mathematics, 1917, by R. C.
Archibald. Bulletin No. 27, 1917, United States Bureau of Education.
[11] Cf. M. Bocher, _Science_, Vol. 38 (1913), page 546.
IX
PHYSICAL EDUCATION IN THE COLLEGE
=Lessons for physical education from the world war=
The events of the four years between the summer of 1914 and the winter
of 1918 have brought us to a full realization of the real significance
of physical education 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 education 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.
=Aims of physical education=
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, coordination,
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.
=Formulations of aims and scope of physical education in official
documents--By Regents of the State of New York=
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."
=By national committee on physical education=
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.
II. That legislation, similar in purpose and scope to the
provisions and requirements in the laws recently enacted in
California, New York State, and New Jersey, is desirable in every
state, to provide authorization and support for state-wide
programs in the health and physical education field.
III. That the United States Bureau of Education should be
empowered by law, and provided with sufficient appropriations, to
exert adequate influence and supervision in relation to a
nationwide program of instruction in health and physical
education.
IV. That it seems most desirable that Congress should give
recognition to this vital and neglected phase of education, with
a bill and appropriation similar in purpose and scope to the
Smith-Hughes Law, to give sanction, leadership, and support to a
national program of health and physical education; and to
encourage, standardize, and, in part, finance the practical
program of constructive work that should be undertaken in every
state.
V. That federal recognition, supervision, and support are
urgently needed, as the effective means, under the Constitution,
to secure that universal training of boys and girls in health and
physical fitness which are equally essential to efficiency of all
citizens both in peace and in war.
=By five national organizations=
In December, 1918, five national organizations, assembled in regular
annual meeting, adopted resolutions which read in part as follows:
First: That this Society shall make every reasonable effort to
influence the Congress of the United States and the legislatures
of our various states to enact laws providing for the effective
physical education of all children of all ages in our elementary
and secondary schools, public, institutional and private, a
physical education that will bring these children instruction in
hygiene, regular periodic health examinations and a training in
the practice of health habits with a full educational emphasis
upon play, games, recreation, athletics and physical exercise,
and shall further make every possible reasonable effort to
influence communities and municipalities to enact laws and pass
ordinances providing for community and industrial physical
training and recreative activities for all classes and ages of
society.
Second: That this Association shall make persistent effort to
influence state boards of education, or their equivalent bodies,
in all the states of the United States, to make it their
effective rule that on or after June, 1922, or some other
reasonable date, no applicant may receive a license to teach any
subject in any school who does not first present convincing
evidence of having covered in creditable manner a satisfactory
course in physical education in a reputable training school for
teachers.
Third: And that this Association hereby directs and authorizes
its president to appoint a committee of three to take such steps
as may be necessary to put the above resolutions into active and
effective operation, and to cooperate in every practical and
substantial way with the National Committee on Physical
Education, the division of physical education of the Playground
and Recreation Association of America, and any other useful
agency that may be in the field for the purpose of securing the
proper and sufficient physical education of the boys and girls of
to-day, so that they may to-morrow constitute a nation of men and
women of normal physical growth, normal physical development and
normal functional resource, practicing wise habits of health
conservation and possessed of greater consequent vitality, larger
endurance, longer lives and more complete happiness--the most
precious assets of a nation.
=By the United States Interdepartmental Social Hygiene Board=
In January, 1919, the United States Interdepartmental Social Hygiene
Board suggested the following organization of a department of hygiene
for the purpose of establishing such a department in at least one
normal school, college, or university training school for teachers in
each state of the Union.
SUGGESTED ORGANIZATION OF A DEPARTMENT OF HYGIENE
I. _Division of Informational Hygiene._ (Stressing in each of its
several divisions with due proportion and with appropriate
emphasis, the venereal diseases, their causes, carriers, injuries,
and prevention):
(_a_) The principles of hygiene. Required of all students at least
twice a week for at least four terms.
(1) General hygiene. (The agents that injure health, the carriers
of disease, the contributory causes of poor health, the defenses
of health, and the sources of health.)
(2) Individual hygiene. (Informational hygiene, the care of the
body and its organs, correction, and repair, preventive hygiene,
constructive hygiene.)
(3) Group hygiene. (Hygiene of the home and the family, school
hygiene, occupational hygiene, community hygiene.)
(4) Intergroup hygiene. (Interfamily, intercommunity, interstate,
and international hygiene.)
(_b_) Principles of physical training. (Gymnastics, exercise,
athletics, recreation, and play.) Required of all students. To be
given at least twice a week for two terms in the Junior or Senior
Years.
(_c_) Health examinations--
(1) Medical examination required each half year of every student.
(Making reasonable provisions for a private, personal,
confidential relationship between the examiner and the student.)
(2) Sanitary surveys and hygienic inspections applied regularly to
all divisions of the institution, their curriculums, buildings,
dormitories, equipment, personal service, and surroundings.
II. _Division of Applied Hygiene._
(_a_) Health conference and consultations.
(1) Every student advised under "c" above (health examinations)
must report to his health examiner within a reasonable time, as
directed, with evidence that he has followed the advice given, or
with a satisfactory explanation for not having done so.
(2) Must provide student with opportunities for safe, confidential
consultations with competent medical advisors concerning the
intimate problems of sex life as well as those of hygiene in
general.
(_b_) Physical training.
(1) Gymnastic exercises, recreation, games, athletics, and
competitive sports. Required of all students six hours a week
every term.
(2) Reconstructional and special training and exercise for students
not qualified organically for the regular activities covered in
"1" above. It is assumed that every teacher-in-training
physically able to go to school is entitled to and should take
some form of physical exercise.
III. _Division of Research._
(_a_) Investigations, tests, evaluating measurements, records, and
reports required each term covering progress made under each
division and subdivision of the department, for the purpose of
discovering and developing more effective educational methods in
hygiene.
(_b_) Provide facilities for the sifting, selection, and
investigation of problems in hygiene that may be submitted to or
proposed by the department of hygiene.
(_c_) Arrange for frequent lectures on public hygiene and public
health from competent members of municipal, state, and national
departments of health, and from other appropriate sources.
IV. _Personnel requisite for such a department._--Men and women
should be chosen for service in the several divisions of the
Department, who have a sane, well-balanced, and experienced
appreciation of the importance of the whole field of hygiene as
well as of the place and relations of the venereal diseases.
(1) One director or head of department. Must have satisfactory
scientific training and special experience, fitting him for
supervision, leadership, teaching, research, and administrative
responsibility.
(2) One medical examiner for men and one medical examiner for
women. There should be one examiner for each 500 students. Must be
selected with special care because of the presence of
extraordinary opportunities to exercise a powerful intimate
influence upon the mental, moral, and physical health of the
students with whom such examiners come in contact.
(3) One special teacher of physical training (a "Physical
Director") for each group of 500 students. There must be a man for
the men and a woman for the women students. The physical training
instructors employed in this department should be in charge of and
should cover satisfactorily all the directing, training, and
coaching carried on in the department and in the institution in
its relation to athletics and competitive sports. The men and
women who are placed in charge of individual students and groups
of students engaged in the various activities of physical training
(gymnastics, athletics, recreation and play) should be selected
with special reference to their wholesome influence on young men
and young women.
(4) One coordinator (this function may be covered by one of the
personnel covered by "1," "2" or "3" above). Will serve to
influence every teacher in every department on the entire staff of
the institution to meet his obligations, in relation to the
individual hygiene of the students in his classes and to the
sanitation of the class rooms in which he meets his students. The
coordinator should bring information to all teachers and assist
them to meet more satisfactorily their opportunities to help
students in their individual problems in social hygiene.
(5) Special lectures on the principles and progress of public
hygiene and public health. A close coordination should be secured
between this department and community agencies like the Department
of Health that are concerned with public hygiene.
(6) Sufficient clerical, stenographic and filing service to meet
the needs of the department.
In February, 1919, the field service of the National Committee on
Physical Education issued a tentative outline for a state law for
physical education, suggested for use in planning future legislation.
The purposes of physical education as stated in the preamble of this
law read as follows:
1. In order that the children of the State of .... shall receive
a quality and an amount of physical education that will bring to
them the health, growth and a normal organic development that is
essential to their fullest present and future education,
happiness and usefulness; and in order that the future
citizenship of the State of .... may receive regularly from the
growing and developing youth of the Commonwealth a rapidly
increasing number of more vigorous, better educated, healthier,
happier, more prosperous and longer lived men and women, we, the
people of the State of .... represented in the Senate and
Assembly do enact as follows:
=By Legislative Committee of National Committee on Physical Education=
In February, 1919, the legislative committee of the National Committee
on Physical Education prepared a bill for federal legislation for the
purpose of assisting the states in establishing physical education in
their schools. This proposed federal law stated the purpose and aim of
physical education as follows:
The purpose and aim of physical education in the meaning of this
act shall be: more fully and thoroughly to prepare the boys and
girls of the nation for the duties and responsibilities of
citizenship through the development of bodily vigor and
endurance, muscular strength and skill, bodily and mental poise,
and such desirable moral and social qualities as courage,
self-control, self-subordination and obedience to authority,
cooperation under leadership, and disciplined initiative. The
processes and agencies for securing these ends shall be
understood to include: comprehensive courses of physical training
activities, periodical physical examination; correction of
postural and other remediable defects; health supervision of
schools and school children; practical instruction in the care of
the body and in the principles of health; hygienic school life,
sanitary school buildings, playgrounds, and athletic fields and
the equipment thereof; and such other means as may be conducive
to these purposes.
An analysis of these several authoritative and more or less official
documents indicates very clearly a unanimity as to scope and aims of
physical education, for they all seek to promote and conserve, in the
broadest sense of the term, the health of the nation.
=Poor type of physical education in secondary schools intensifies problem
in the college=
The problem of physical education in the college is intensified by the
fact that freshmen come to their chosen institutions with a variety of
experience in physical training, but unfortunately this experience is,
too often, either inadequate or ineffective. The natural physical
training of the earlier age periods produces whatever neuro-muscular
development, whatever neuro-muscular coordination, whatever
neuro-muscular control, and whatever other organic growth,
development, or functional perfection is achieved by the young human
concerned. A program of physical training wisely planned with
reference to infancy, childhood, and early youth would include types
of exercises, play, games, and sports, that would perfect the
neuro-muscular and other functions far more completely than is
commonly accomplished through the natural unsupervised and undirected
physical training of those early age periods either in city or in
rural communities. The force of modern habits of life has led to the
destruction of those natural habits of work, play, and recreation that
gave a proportion of our forebears a fairly complete natural program
of physical exercise during the plastic or formative periods of life.
As a result, many students reach college nowadays with stunted growths
and with poorly developed, poorly trained, or poorly controlled
neuro-muscular equipment. Some of these matriculates are physically
weak. They lack alertness; their response is slow. Others are awkward
and muscularly inefficient, though their physical growth is
objectively--height and weight--normal or even above normal.
The College Department faces these problems through special provisions
made for the purpose of supplying a belated neuro-muscular training to
such cases. It often happens that successful training along these
lines is possible only through individual instruction of a most
elementary sort, taking the student through simple exercises that
ought to have been a part of his experience in early childhood.
=Individual needs of students augment problem of department of physical
education=
For the same reasons that are stated above, the College Department of
Physical Training finds it necessary to concern itself with individual
students who need special attention directed to specified organs or
groups of organs whose training or care could have been accomplished
ordinarily far better at an earlier period. These students present
problems of posture, lung capacity, and regional weakness.
=Supervision of athletics and recreation adds further to its problem=
The College Department of Physical Training finds also a significant
opportunity and an urgent duty in the fact that various types of
physical exercise are intimately associated with social, ethical, and
moral consequences. No other human activity gives the same opportunity
for the development of a social spirit and personal ethical standards
as do play, games, and sports of children and adolescents.
Unsupervised, these activities degenerate and bring unmoral practices
and an anti-social spirit in their wake.
Because of these opportunities and obligations, College Departments of
Physical Training are including within their programs and
jurisdictions more and more supervision of college athletics, and
assume an ever increasing role in the direction of recreational
activities of college students. It remains true, however, that these
influences of supervised play and athletics should operate long before
the individual reaches college age.
The intense interest of college students in athletic competitions,
united with the opportunity which athletics offer for social and
character training, has decided a number of colleges to turn athletic
training over to the Department of Physical Training. This preparation
for the supreme physical and physiological test must be built upon a
foundation of safe and sound health. There is no more fitting place
in the collegiate organization for these athletic and recreational
activities.
=Organization of Department of Physical Education=
The college departments that cover this field in whole or in part are
known by various names. We have departments of Physical Training; of
Physical Education; of Physical Culture; of Hygiene; of Physiology and
Physical Education; of Hygiene and Physical Education; of Physical
Training and Athletics, and so on.
An analysis of these college departments shows that they all concern
themselves with much the same important objects, although they differ
in their lines of greater emphasis. We find, too, that in some
colleges the department includes activities that form separate, though
related departments in other institutions.
The activities of such departments fall into three large divisions,
each one of which has its logical subdivisions. One of these large
divisions may be called the division of health examination. It has to
do with the health examination of the individual student and with the
health advice that is based on and consequent to such examination. The
second division has to do with health instruction covering the subject
matter of physical training. The third division covers directed
experiences in right living and the formation of health habits, and
includes the special activities noted above.
We often refer to the first division noted above as the division of
medical inspection, physical examination, or health examination; to
the second as hygiene, physiology, biology, or bacteriology; and to
the third as gymnastics, physical exercise, organized play,
recreation, athletics, or narrowly as physical training.
The prime purpose of collegiate physical training, then, is to furnish
the student such information and such habit-forming experiences as
will lead him to formulate and practice an intelligent policy of
personal health control and an intelligent policy of community health
control. The collateral and special objects of physical training vary
with the individual student under the influence of his previous
training and his present and future life plans.
The Collegiate Department of Physical Training is primarily concerned,
therefore, with the acquisition and conservation of human
health--mental, moral, and physical health. Because of his physical
training, the college man should live longer; he should meet his
environments obligations more successfully; he should be better able
to protect himself from, and better able to avoid, injury; he should
lose less time on account of injury, poor health, and sickness; he
should get well more rapidly when he is sick; he should be better able
to recover his health and strength after injury or illness; and he
should therefore give to society a fuller, happier, and more useful
life.
Such a department is concerned secondarily with (_a_) those special
defects of earlier physical training that bring to college, students
in need of neuro-muscular training and organic development, (_b_) with
social, ethical, and character training, and (_c_) with the
conditioning and special training of students for athletic competition
or for other extraordinary physical and physiological demands.
In the light of the above statements, the objects of physical training
may be summarized as follows:
I. The fundamental and ever present object of physical training
is the acquisition and conservation of vigorous, enduring health,
the summated effect of perfect functions in each and every organ
of the human body.
II. The special objects of physical training vary in their needs
for emphasis at different age periods and under the changing
stresses of life. Among the more important of these special
objects are:
(1) General, normal growth. An object in the early age periods.
(2) Neuro-muscular development, coordination, and control.
Accomplished best in early age periods.
(3) Special organic (anatomical and functional) development.
Optimum period in childhood and youth.
(4) Social, ethical, and moral training. Character building.
Objects more easily secured in childhood and youth.
(5) Preparation for some supreme physical and physiological test;
e.g., athletic competition, police or fire service, military
service. Most desirable training period in late youth and early
maturity. Must depend, however, on the effects of earlier
physical training.
(6) The formation of health habits. Best accomplished in early
life but commonly an important function of the College
Department of Physical Training.
(7) The conservation of health. Always an object, but more
particularly so in the middle and later life.
THE MEDICAL EXAMINATION
In the American college of today, the student's first contact with the
Department of Physical Training is very likely to be in the examining
room. In the College of the City of New York[12] it has become the
established custom to require a satisfactory health examination before
admitting the applicant to registration as a student in the college.
Entering classes are enrolled in this institution at the beginning of
each term, and in each list of applicants there are always a few to
whom admission is denied because of unsatisfactory health conditions.
In each case in which admission is denied because of unsatisfactory
health, the individual is given careful advice relative to his present
and probable future condition, and every effort is made to help the
applicant plan his life so that he may be able at a later time to
enter the college. Of course, it occasionally happens that applicants
are found with serious and incurable health defects which make it very
improbable that they will ever be in condition to attempt a college
education.
=Scope of health examination=
The health examination of the student should cover those facts in his
family and personal health history that are likely to have a bearing
upon his present or future health, and the examination should include
a very careful investigation of the important organs of his body. This
examination calls for expert medical and dental service.
=How to conduct health examination=
The most useful examiner is he who is at the same time a teacher.
Nowhere else is a better or even an equally good opportunity given to
drive home impressively, and sometimes dramatically, important lessons
in individual hygiene. Through a pair of experimental lenses placed by
his examiner before his hitherto undiscovered visual brain cells, the
young student who has had poor vision and has never known it, may
obtain, for the first time, a glimpse of the beauty in his
surroundings.
The dental examiner who finds bad teeth and explains bad teeth to the
student whose health is being, or may be, destroyed by such teeth, has
before him all the elements necessary for very effective health
instruction.
The health examination should be a personal and private affair. It is
often best not to have even a recorder present. The student should
understand that whatever passes between him and his examiner is
entirely confidential.
All advice given a student at these examinations should be followed up
if it is the kind of advice that can be followed up. If the advice
involves the attention of a dentist or treatment by a physician, time
should be allowed for making arrangements and for securing the
treatment necessary. After that time has elapsed the student should be
called upon to report with information from his parent or guardian, or
from his family health adviser, indicating what has been done or will
be done for the betterment of the conditions for which the advice was
originally given. In the hands of a tactful examiner--one who is a
teacher as well as an examiner--the student and parent, particularly
the parent, will cooperate effectively in this plan for the
development of health habits of the student. Less than three tenths
of one per cent of the parents of City College students refuse to
secure special health attention for their boys when we do so advise.
These examinations should be repeated at reasonable intervals
throughout the entire college course. We have found in the College of
the City of New York that a repetition every term is none too
frequent. Visual defects, dental defects, evidences of heart trouble
and signs of pulmonary tuberculosis, and other defects, not
infrequently arise in cases of individuals who have been seen several
times before without showing any evidence of poor health. It is hoped
that these repeated examinations may lead to the continuation of such
habits of bodily care in postgraduate years.
A careful and concise record must be made covering the main facts of
each examination and of each conference with the student subsequent to
his examination. These memoranda enable the examiner at each later
examination to talk to the student with a knowledge of what has been
found and what has been said and what has been done on preceding
examinations, and on preceding follow-up conferences. As a result, the
examiner-teacher is in position to be very much more useful not only
because of significant facts before him concerning the student with
whom he is talking, but also because of the greater confidence which
the student will necessarily have in an examiner who is obviously
interested in him and who possesses such an accurate record of his
health history.
These examinations should apply to every student in a college or a
university, regardless of the division to which he belongs. The need
for health instruction or for the establishment of health habits, in
order that one may be physically trained for the exigencies of life,
is not peculiar to any student age period or to any academic or
technicological group, or to a college for men or a college for women.
One of the dangers present in these college examinations is the
tendency of the examiner to become more interested in the number of
students examined and the number of diagnoses made than in the good
influence he may have upon the health future of the student.
Every "case" should be treated by the health examiner as if it were
the first and only case on hand for the day. The student certainly
classifies the examiner as the first and only one he has had that day.
The examiner should plan to make every contact he has with a student a
help to the student.
HEALTH INSTRUCTION
A second large division of physical training deals with health
instruction. As has been pointed out above, the division of health
examination produces a very important and very useful opportunity for
individual health instruction.
=Content of hygiene instruction=
Hygiene, however, is presented commonly to groups of students in class
organization rather than individually. Anatomy, physiology,
psychology, bacteriology, pathology, general hygiene, individual
hygiene, group hygiene, and intergroup hygiene are sciences, or
combinations of sciences, from which physical training draws its
facts. These sciences and those phases of economics and sociology that
have to do with the economic and social influences of health and
disease, of physical efficiency and physical degeneracy, supply
physical training with its general subject matter.
Health instruction, then, as a part of physical training, draws its
content from these sources. A logical plan of class instruction would,
therefore, include the elements of anatomy, physiology, psychology,
bacteriology (and general parasitology), pathology, economics, and
sociology, as a basis for a more complete presentation of the facts of
general hygiene, individual hygiene, group hygiene, and intergroup
hygiene.
=Method of health instruction=
The most satisfactory presentation of these subjects involves the
grouping of students into small classes, the employment of laboratory
methods, the use of reference libraries, and the assignment of
problems for investigation and study, with a general group discussion
of these problems.
Unfortunately, college classes are large and the number of teachers
employed in the department of physical training, or in those
departments from which physical training draws its science and its
philosophy, is small, so that it is impractical to plan to give this
instruction to small groups of students covering this range of subject
matter.
As a result, the lecture method with its obvious defects and
shortcomings is the common medium for the health instruction of
college students organized into classes. The more intimate and
detailed instruction in these subjects is secured in special courses
and in professional schools.
In the College of the City of New York, we expect that students who
come to us from high schools and preparatory schools have had the
elements of anatomy and physiology either in courses on those subjects
or in courses in biology.[13] Our health instruction, therefore, has
been developed along the lines of lectures on general hygiene,
individual hygiene, group hygiene, and intergroup hygiene running
through the four terms of the freshman and sophomore years.
These lectures are given in periods of from ten to fifteen minutes
each, preceding class work in various forms of physical exercise. They
are often called "floor talks." The shortness of the presentation
favors vigor of address; necessitates a concise organization of
material and a clarity and brevity of statement; and is more likely to
command student attention and concentration. It has, however, its
obvious defects. In these lectures persistent effort is made to
influence the daily habits of the student. The lecture content is
selected with reference to the practical problems of the daily life of
the individual and of the community of which he is a part. It is
obvious that the amount of time devoted to the presentation of the subject
matter is utterly inadequate.
Short written tests are given once each month, and a longer written
test is given at the end of each term. These examinations stimulate
the student to organize his information and make it more completely
his own property. The classes are too large[14] and the instructional
force relatively too small to permit the assignment of references,
presentation of reports, and the conduct of investigations.
Further instruction in physiology and bacteriology is secured in this
institution through elective courses open to students in their junior
and senior years. These elective courses, however, are not planned
primarily for the health education of the student, but rather for his
partial preparation as a teacher of physical training, a student of
medicine, a scientific specialist, or for public health work.
HEALTH-FORMING ACTIVITIES OF THE DEPARTMENT OF PHYSICAL EDUCATION
The third division of activities contains the health-habit-forming
influences covered by the Department of Physical Training. These
influences are formed partly in connection with the follow-up
activities associated with the health examinations and advice noted
above; partly through impressions made by way of individual and class
instruction concerning the laws of health (also noted above); and
partly through systematic class work, group work, and individual work
in gymnastics, organized recreation, games, play, and athletics.
The student who has been given a health examination each term
throughout his college career will be very likely to continue the
practice as a habit after graduation. This habit will follow more
surely if the examiner has been a real health teacher and not a
perfunctory recorder of observations made upon the student. A lack of
sympathy and tact may easily prejudice the student against the
examination.
The student who has been led regularly to care for defects of one sort
or another; whose contact with his examiner-teacher in conferences
following up the advice that has been given at the time of examination
has been accompanied by the right sort of explanation and mutual
understanding, will be more likely to continue to exercise that sort
of care for the welfare of his body after he is no longer under the
influence of the college.
The student who has seen the application of class health talks to his
everyday problems is likely to be influenced to the practice of
consequent health habits, particularly if those short lectures serve
to correlate his various habit-forming experiences while in college.
And finally, the student who is brought into contact with regular
systematic exercise may, if the exercise is attractive and
interesting, achieve a health habit that will be carried out into his
postgraduate life.
The existence of the Department of Physical Training would be amply
justified if its influence upon the health and vigor of the student
were limited to the period of his stay in college. The full success of
this department, however, like that of all other college departments,
must be measured by its influence upon the life of the student after
he has left college. The formation of lasting health habits is,
therefore, the most important object of this department.
=Place of physical exercise in program for physical education=
Regular appropriate physical exercise is one of our most important
health habits. It is perhaps safe to say that for the average
individual it is the most important health habit. This is true because
of its intimate and impressive influence upon all the fundamental
organic functions of the body. Physical exercise in the American
college is provided either as organized class work in the gymnasium,
or by means of voluntary recreational opportunities, or through
athletics.
=Class work in physical exercise=
Class work may include: marching, mass drills with or without light
apparatus, work on heavy apparatus, games, dancing, swimming, and
track and field work. This class work may be indoors or outdoors,
depending on the season or climate.
=Additional facilities for physical exercise=
Voluntary recreational opportunities are offered through free mass
drills open to all students who may desire to take them regularly or
irregularly; through open periods for apparatus work; and through
facilities and space for games, swimming, mass athletics, and so on.
=Recreational activities and athletics=
Competitive athletics are typical of the American college.
Theoretically, athletics are open to all students. Practically, in
many of our colleges athletics are made available only to the student
with leisure time and exceptional physique. Consistent effort is being
made today by college authorities to provide opportunities for
intramural (interclass, intergroup, and mass) athletics for the whole
student body; at the same time preserving the desirable features of
the more specialized intercollegiate competitions.
=Inculcating habits of physical exercise=
Physical exercise in these various forms has its immediate and
valuable influence upon the health condition of the individual
student, if taken in sufficient quantity. It has its lasting and very
much more important influence in those cases in which physical
exercise becomes a habit. It has, therefore, become the increasing
concern of the college teacher of physical training to develop
activities in physical exercise that the student may use after
graduation. Teachers of physical training have become more and more
impressed with the importance of interesting exercise, not only
because interesting exercise is more likely to become habitual
exercise, but also because exercise that is accompanied by the play
spirit, by happiness and joy, is physiologically and therefore
healthfully of very much more value to the individual. The
relationship between cheerfulness and good health has become very
firmly established through the scientific researches of the modern
physiologist. We know that health habits which are associated with
cheerfulness and happiness are bound to be more effective.
=Opportunities for character building=
The teacher of physical training finds opportunity for incidental and
yet very important instruction leading to the formation of fine
qualities of character and fine standards of personal conduct. These
opportunities arise constantly in the various general types of
physical exercise found in the curriculum of the department of
physical training. They are especially present in those activities in
which competition occurs, as in play, games, and athletics. These
activities do not in themselves produce excellent qualities of
character or high standards of conduct, but the teacher--whether he be
called a coach or a trainer or a professor of hygiene--who sets a good
example and who insists that every game played, and every contest,
whether it be in a handball court between college chums or on the
football field between college teams, shall be clean and fair, is
using in the right way one of the opportunities present in the entire
college life of the student, for the formation of fine character.
SPECIAL EXERCISES FOR SPECIAL GROUPS
In any given group of college students one will find a number of
individuals in need of special or modified physical exercise. These
students may be grouped commonly under the following heads: (1)
undeveloped, (2) bad posture, (3) awkward, (4) originally weak, (5)
deformed.
Some of these students suffer from defects that are remediable, Some
of these defects are due to poor physical training in earlier years.
Some are the results of disease. All of them call for modified
exercise and recreation. The fact that a student may fall into one of
these groups in no way justifies the assumption that he is therefore
no longer subject to the laws of health or to the need for rational
health habits. As a matter of fact, such cases generally call for
greater care and attention in the formulation and operation of a
rational policy of right living.
Every student physically able to go to college is physically able to
exercise. No student in attendance on recitations anywhere can offer a
rational plea for exemption from exercise, The individual whose
physical condition contraindicates all forms of exercise needs
careful medical advice and probably needs hospital or sanitarium
treatment.
College Departments of Physical Training are planning for cases in
need of special or modified exercise, through the organization of
special classes and through individual attention. In the College of
the City of New York we attempt to group the weak students in a given
class, into squads of four such students with a squad leader, a
student. The awkward students are grouped in the same manner. The
exercise of the cripple and the student with serious organic weakness
is individualized. These special individualized cases are under the
direct supervision of a physician on the staff.
ORGANIZATION OF THE STUDENTS FOR PRESCRIBED WORK IN THE COLLEGE
COURSES
In this college, organized, directed physical exercise as outlined
above is covered in the division of physical training, the division of
recreation, and the division of athletics, all of which are
subdivisions of the Department of Hygiene.
The enrollment in the required classes in the division of Physical
Training varies from thirty in the smaller classes to over two hundred
in the larger. The total enrollment has been approximately eleven
hundred each term for several years. These courses are required of all
students during the first four collegiate terms. Each of these four
courses requires three hours a week, distributed over two or into
three periods, and credits the student with one half point toward
graduation. This time allowance is, however, inadequate.
The class organization in the division of the Department of Hygiene is
based on a unit composed of five students. Each of these units or
squads contains one student who is designated as the "leader" of that
unit.
Persistent effort is made to assign students of like physical
development and needs to the same squads. In this manner a single
class of a hundred young men will have a graduation on the basis of
proficiency which makes it possible for the teacher to come very near
to the rational application of exercise for the individual student.
These units or squads are organized into divisions, each division
being made up of four squads. Each division is under the supervision
and instruction of a member of the departmental staff. In any given
class, then, there is a regular instructor for each group of twenty
students, and a student leader for each group of four students. The
aim in this organization is to establish a relationship between the
instructor and his twenty students that will secure for him an
intimate knowledge of each young man, relating to his physical
training needs, general and special.
=A class period in physical exercise=
A typical class period is made up of a short health talk, 10 minutes;
a mass drill, 10 minutes; apparatus period, two changes, 20 minutes;
and a play period, 15 minutes. If the health talk is not given the
play period is lengthened.
The mass drills referred to above are made up of drill in marching and
in gymnastics with and without hand apparatus. These drills are graded
within the term and from term to term so that a desirable variety is
secured. They are devised for disciplinary, postural, developmental,
and health purposes. During the progress of the drill the instructors
present inspect the posture and work of the students in their
divisions.
The apparatus periods referred to include work on the conventional
pieces of gymnastic apparatus, with the addition of chest weights, an
indoor track, and a swimming pool. The squad organization for this
work gives opportunity for the development of student leadership which
is often of extraordinary educational value to the individual boy.
These periods, because of this squad organization, may be utilized for
such _special exercise_ emphasis as may be decided upon for any given
group of students. It is here that _special conditioning_ may be given
those young men who are planning for military training or who need
selected exercise for neuro-muscular development.
The play period in the regular class program is devoted largely to
looser games that contain a predominating element of big muscle
activities. Competition is a fairly constant factor. Here, again, our
squad unit permits us to assign selected groups of students to special
types of games. It is feasible, in this organization, to satisfy a
need for the training that is furnished by highly organized games,
fighting games, and by games and out-of-door events that develop
special groups of muscles and special coordinations.
A well-organized Collegiate Department of Physical Training could
cooperate very effectively with a Collegiate Department of Military
Training. The squad organization in apparatus periods and in play
periods offers the best possible avenue for a successful emphasis of
several of the very important phases of military physical training.
=Recreational facilities in addition to prescribed work=
The division of recreation in the Department of Hygiene in the College
of the City of New York, takes charge of all recreational and athletic
space and all recreational and intramural athletic activities in those
periods of the day in which regular class work does not take
precedence. Students of all classes are admitted freely throughout
their four collegiate years to these activities, and a studied effort
is made to increase their attractiveness as well as to secure from
them their full social and character-training values. Such values
depend to a very large degree upon the experienced supervision and
direction given these activities. It does not follow that the creation
of play opportunity is bound to produce good citizenship. The quality
of the product depends upon the quality of the man or men in charge of
the enterprise.
The most important mission of the Recreational Division is its purpose
to furnish the student lasting habits of play and recreation based
upon the physical development he has secured in his earlier
experiences in physical training. After all, one's physical training
should begin at birth and continue throughout life.
The Division of Athletic Instruction is concerned with all plans for
intercollegiate athletics, including organization, financing,
training, coaching, and scheduling. All these activities are under the
direction of members of the staff of the Department of Hygiene. There
is no one employed in this relationship who is not a member of the
staff. Constant attempts are made, in every reasonable way, to
accomplish the athletic ideals that have been set up by the National
Collegiate Athletic Association. Clean play, honorable methods, and
sportsmanly standards dominate the theory and practice of this
athletic instruction and supervision.
The scope and content of physical training which I have attempted to
present in these pages is brought out more clearly by the following
announcement of the Department of Hygiene of the College of the City
of New York:
HYGIENE (1916-17)
The Department of Hygiene is made up of the divisions of Physical
Training, Physiology, Bacteriology, Health Examination,
Recreational Instruction, and Athletics.
Through these divisions the Department attempts to train young
men for the exigencies of life through the establishment of
enduring habits of health examination and repair, health
information and individual and community protection against the
agents that injure health and cause disease, and through the
establishment of wise habits of daily life.
This organization gives opportunity for the development of
neglected organic and neuromuscular growth, coordination and
control; for the social, ethical, and moral training (character
building influences) inherent in wisely supervised athletic and
recreational experiences; and for the special conditioning that
accompanies training for severe physical and physiological
competition and other tests.
Finally, preparation may be secured for life work along certain
lines of research, certain medical sciences, various phases of
public health, physical training and social work.
In addition, this Department is concerned with all those
influences within the College which affect the health of the
student. Every reasonable effort is made to keep the institution
safe and attractive to the clean, healthy individual.
DIVISION OF PHYSICAL TRAINING
1. _Course One._
(_a_) Lectures. "Some of the common causes of disease."
(_b_) Physical Exercise.
i. Graded mass drills.
(_a_) Elementary drills are used in order to develop obedience,
alertness, and ready response to command, accurate execution,
good posture and carriage and facility of control.
(_b_) More advanced drills are given in which movements are made
in response to commands. Strength, endurance, and coordination
are brought into play.
ii. Apparatus work. Continuation of graded exercises for squads of
five students each.
iii. Selected, graded, recreative indoor and outdoor games and play.
iv. Swimming. Each student is required to learn to swim with more than
one variety of stroke.
Prescribed. Freshman, first term; three hours a week; counts 1/2.
2. _Course Two._
(_a_) Lectures. "The carriers of disease."
(_b_) Physical Exercise.
i. Graded mass drills. Two-count movements. These drills are
continuations of, but more advanced than those given in the
preceding term.
ii. Apparatus work. Continuation of graded exercises for squads of five.
iii. Selected, graded, recreative indoor and outdoor games and play.
iv. Swimming. Each student is required to develop endurance in swimming.
Prerequisite: Hygiene 1.
Prescribed. Freshman, second term; three hours a week; counts 1/2.
3. _Course Three._
(_a_) Lectures. "The contributory causes and carriers of disease."
(_b_) Physical Exercise.
i. Graded mass drills. Four-count movements. More advanced work.
ii. Apparatus work. Continuation of graded exercises for squads of five.
iii. Selected, graded, recreative indoor and outdoor games and play.
iv. Swimming. Diving, rescue and resuscitation of the drowning.
Prerequisite: Hygiene 2.
Prescribed. Sophomore, first term; three hours a week; counts 1/2.
4. _Course Four._
(_a_) Lectures. "Defenses against poor health and disease."
(_b_) Physical Exercise.
i. Advanced graded mass drills. Eight-count movements.
ii. Advanced graded apparatus work. For squads of five.
iii. Selected, graded, recreative indoor and outdoor games and play.
iv. Swimming. Advanced continuation of requirements outlined for
Courses 2 and 3.
Prerequisite: Hygiene 3.
Prescribed. Sophomore, second term; three hours a week; counts 1/2.
_Modified Course._
In each of the above required courses provision is made for those
students whose organic condition may permanently disqualify them for
the regular scheduled work. This special work is under the immediate
direction of a medical member of the Staff.
5. _Intermediate Physical Training._
This course is planned to supply the student with such organic
development and efficiency as will enable him to demonstrate
successfully as a teacher various type exercises for classes in
elementary and intermediate indoor and outdoor gymnastics, aquatics,
games, play and athletics.
Prerequisite: Hygiene 4. Three hours a week; counts 1/2.
6. _Advanced Physical Training._
This course is a continuation of Course 5, and is designed for the
physical equipment of teachers of more advanced physical work.
Prerequisite: Hygiene 5. Three hours a week; counts 1/2.
7. _Class Management._
This course supplies the practical instruction and experience needed
for the training of special teachers in the management of elementary
and intermediate classes in various forms of physical exercise.
Prerequisite: Hygiene 6 and 32. Fall term, three hours a week; counts 1.
8. _Class Management._
This course is a continuation of Course 7. It is planned to give a
training in the management of more advanced classes.
Prerequisite: Hygiene 7. Spring term, three hours a week; counts 1.
9. _Control of Emergencies and First Aid to the Injured._
This course supplies instruction concerning the management and
protective care of common emergencies. The instruction is practical
and rational. It covers such emergencies as: sprains, fractures,
dislocations, wounds, bruises, sudden pain, fainting, epileptic
attacks, unconsciousness, drowning, electric shock, and so on.
Prerequisite: Hygiene 32. Fall term, two hours a week; counts 1.
10. _Theory and Practice of Individual Instruction in Hygiene and
in Departmental Sanitation._
Students taking this subject will be given practical first hand
experience of special use to teachers; (a) in connection with health
examination, inspection, conference, consultation, and follow up
service carried on in the departmental examining room; and (b) in
connection with the sanitary supervision carried on by the department.
Prerequisites or Co-requisites: Hygiene 32, 41 and 48. Spring term,
six hours a week in two periods of three hours each; counts 2.
DIVISION OF PHYSIOLOGY
32. _Elements of Physiology._
This subject deals with the general concepts of the science of
physiology, the chemical and physical conditions which underlie and
determine the action of the individual organs, and the integrative
relationship of the parts of the body.
One lecture, one recitation and two laboratory hours a week; counts 3.
33. _Special Physiology._
A study of the fundamental facts of physiology and methods of
investigation. The aim is to give a complete study of certain topics:
the phenomena of contraction, conduction, sense perception and the
various mechanisms of general metabolism. Laboratory work is arranged
to show the methods of physiologic experimentation and to emphasize
the necessity of using care and accuracy in their application.
Spring term, two lectures and three laboratory hours a week; counts 3.
34. _Physiology of Nutrition._
The aim of this subject is to study broadly the metabolism of the
human body. In the development of this plan the following topics will
be considered: the food requirements of man, the nutritive history of
the physiologic ingredients, the principles of dietetics and their
application to daily living.
Fall term, two lectures and three laboratory hours a week; counts 3.
DIVISION OF BACTERIOLOGY
41. _General Bacteriology._
Lectures, recitations and laboratory work introducing the student to
the technique of bacteriology and to the more important facts about
the structure and function of bacteria. Special applications of
bacteriology to agriculture and the industries are discussed, and
brief references are made to the activities of allied microbes, the
yeasts and molds. The general relations of bacteria to disease and the
principles of immunity and its control are included.
One lecture, one recitation and four laboratory hours a week; counts 3.
42. _Bacteriology of Foods._
This includes the bacteriologic examination of water, sewage, air,
milk, the various food products together with the methods used in the
standardization of disinfectants, a detailed study of yeast and
bacterial fermentation and their application to the industries.
Numerous trips to industrial plants will be made.
Prerequisite: Hygiene 41.
Fall term, one lecture and six laboratory hours a week; counts 3.
43. _Bacteriology of Pathogenic Micro-organisms._
This subject is devoted to the laboratory methods of biology as
applied in the state and municipal boards of health. Practice will be
given in the methods used for the diagnosis of diphtheria,
tuberculosis, malaria, rabies, and other diseases caused by
micro-organisms, together with a detailed study of the groups to which
they belong.
Prerequisite: Hygiene 41.
Spring term, one lecture and six laboratory hours a week; counts 3.
44. _Potable and Industrial Water._
Very few industries are independent of a water supply. No one is
independent of the source of his drinking water. Water varies in its
usefulness for definite purposes.
This subject differentiates between various waters, takes them up from
industrial and hygienic standpoints, considers softening, filtering,
purifying and water analysis.
Work is divided into three groups.
A. Industrial Water )
} given in the Chemistry Department.
B. Potable Water )
C. Water Bacteriology )
} given in the Department of Hygiene.
(microscopy of water) )
Municipal students may elect any or all of the three groups.
Prerequisite: Chemistry 4 and Hygiene 41. Chemistry 9 is desirable.
Spring term, seven hours a week; counts 3.
48. _Municipal Sanitation._
Lectures, discussions and visits to public works of special
importance. The principles which underlie a pure water supply and the
means by which the wastes of the city, its sewage and garbage may be
successfully disposed of, and the problems of pure milk and pure food
supplies, the housing question with its special phase of ventilation
and plumbing, and the methods by which a municipal board of health is
organized to fight tuberculosis and other specific diseases will be
studied.
Fall term, two lectures and one field trip a week; counts 3.
49. _Municipal Sanitary Inspection._
_Professor B---- and Bureau of Foods and Drugs, New York City
Department of Health._
The seminar work of this subject is done in the College and the field
work in company with and under the direct supervision of an Inspector
of the Department of Health of the City. The subject is limited to six
students each semester, and is intended for those planning to go into
this branch of the City's service. The qualifications will be based
upon individuality, personality playing an important part.
Prerequisite: Hygiene 41 and 48 and Chemistry 19.
Spring term, two seminar hours, one recitation and one inspection tour
a week; counts 3.
50. _Research._
Seniors who have completed satisfactorily a sufficient amount of work
in the Department may be assigned some topic to serve as a basis for a
thesis which will be submitted as credit for the work at its
completion. The student will receive the advice of the instructor in
the subject in which the research falls, but as much independent work
as possible will be insisted upon. The purpose is to introduce the
student into research methods, and also to foster independence.
DIVISION OF HEALTH EXAMINATION
I. _Individual Instruction in Hygiene._
This instruction is of a personal confidential character, and
is given in the form of advice based upon medical history supplied
by the individual, and upon medical and hygienic examinations
and inspections of the individual.
(_a_) Medical and hygienic history and examination.
In this relationship with the student the Department attempts to secure
such information concerning environmental and habit influences in the
life of the student as may be used as a basis for supplying him with
helpful advice concerning the organization of his policy of personal
health control. The medical examinations are utilized for the purpose of
finding remediable physical defects whose proper treatment may be added
to the physiological efficiency and therefore to the health
possibilities of the student.
Prescribed: freshman, sophomore, junior, senior and special students.
Once each term. No credits.
(_b_) Hygiene inspections.
These inspections are applied in the mutual interest of personal,
departmental and institutional hygiene.
Prescribed: freshman and sophomore.
(_c_) Conferences.
All students who have been given personal hygienic or medical advice are
required to report in conference by appointment in order that the advice
may be followed up.
All individuals found with communicable diseases are debarred from all
classes until it is shown in conference that they are receiving proper
medical treatment, and that they may return to class attendance with
safety to their comrades.
All individuals found with remediable physical or hygienic defects are
required to report in conference with evidence that the abnormal
condition has been brought to the serious attention of the parent,
guardian or family medical or hygienic adviser. Students failing to
report as directed may be denied admission to all classes.
II. _Medical and Sanitary Supervision._
(_a_) Sanitary supervision.
An "Advisory Committee on Hygiene and Sanitation" with the Professor of
Hygiene as Chairman, has been appointed by the President. This committee
has been instructed to "inquire from time to time into all our
institutional influences which are likely to affect the health of the
student and instructor, and to make such reports with recommendations to
the President as may seem wise and expedient."
(_b_) A medical examination is required of all applicants for admission
to the College. Approval of the Medical Examiner must be secured before
registration is permitted.
(_c_) Medical consultation.
Open to all students. (Optional.)
(_d_) Medical examination of Athletes.
Required of all students before admission to athletic training and
repeated at intervals during the training season.
(_e_) Treatment.
Emergency treatment is the only treatment attempted by the Department.
Such treatment will be applied only for the purpose of protecting the
individual until he can secure the services he selects for that purpose.
(_f_) Conferences.
(See "c" under I.)
(_g_) Laboratory: The Department Laboratories are equipped for
bacteriological and other analyses. The water in the swimming pool is
examined daily. The laboratory service is utilized to identify disease
carriers, and in every other reasonable way to assist in the protection
of student health.
DIVISION OF RECREATIONAL INSTRUCTION
Liberal provision is made by the College for voluntary recreational
activities indoors and outdoors during six days of the week and
throughout vacation periods. Emphasis is laid on recreation as a
health habit and a means of social training.
DIVISION OF ATHLETICS
(1) _Athletic Supervision._
Three organizations are concerned:
(_a_) The Faculty Athletic Committee, which has to do with all
athletic activities that involve academic relationships.
(_b_) The Athletic Council, a committee of the Department of Hygiene,
charged with the supervision of all business activities connected with
student athletic enterprises.
(_c_) The Athletic Association of the Student Body.
(2) _Athletic Instruction._
The Department utilizes various intramural and extramural athletic
activities for the purpose of securing a further influence on the
promotion of health habits, the development of physical power, and the
establishment and maintenance of high standards of sportsmanly conduct
on part of the individual and the group.
At present the schedule includes the following sports: baseball,
basket ball, track and field, swimming and water polo, tennis, soccer
foot ball, and hand ball.
THOMAS ANDREW STOREY, M.D.
_College of the City of New York_