The student may be confronted with an unfamiliar organism or situation
and be given a limited time in which to obtain and record his results.
He may be asked to state and enumerate the problems that are suggested
by the situation; outline a method of solving them; discover as large
a body of facts as possible; arrange them in an order that seems to
him logical, with his reasons; and to make whatever inferences seem to
him sound in the light of facts,--supporting his conclusions at every
point. The ability to make such a total mental reaction promptly and
comprehendingly is the best test of any teaching whatsoever. The
important thing is that we shall not ourselves lose sight of the
essential parts of it in our enthusiasm for one portion of it.
In judging attitude and appreciation I think it is possible for
discriminating teachers to obtain the testimony of the pupil himself
in appraisal of his own progress and attitude. This needs to be done
indirectly, to be sure. The student's self-judgment may not be
accurate; but it is not at all impossible to secure a disposition in
students to measure and estimate their own progress in these various
things with some accuracy and fairness of mind. Besides its incidental
value as a test, I know of no realm of biological observation,
discrimination, and conclusion more likely to prove profitable to the
student than this effort to estimate, without prejudice, his own
growth.
THE LITERATURE OF THE SUBJECT
=Scarcity of authoritative pedagogical literature in biology=
For various reasons very little attention has been given to the
pedagogy of college biology by those in the best position to throw
light upon this vital problem. More information as to the attitude of
teachers of the subject is to be derived from college and university
catalogs than elsewhere,--howbeit of a somewhat stereotyped and
standardized kind. Much more has been written relative to the teaching
of biology in the secondary schools. In my opinion the most effective
teaching of biology in America today is being done in the best high
schools by teachers who have been forced to acquire a pedagogical
background that would enable them to reconstruct completely their
presentation of the subject. Most of these people obtained very little
help in this task from their college courses in biology. For these
reasons every college teacher will greatly profit by studying what has
been written for the secondary teachers. _School Science and
Mathematics_ (Chicago) is the best source for current views in this
field. Its files will show no little of the best thought and
investigation that have been devoted to the principles underlying
instruction in biology. Lloyd and Bigelow, in _The Teaching of
Biology_ (Longmans, Green & Co.), have treated the problems of
secondary biology at length. Ganong's _Teaching Botanist_ (The
Macmillan Company) has high value.
The authors of textbooks of biology, botany, and zoology issued during
the last ten years have ventured to develop, in their prefaces,
appendices, and elsewhere, their pedagogical points of view. The
writer has personal knowledge that teaching suggestions are still
resented by some college teachers of zoology. Illustrations of the
tendency to incorporate pedagogical material in textbooks on
biological subjects can be found in
DODGE, C. W. _Practical Biology._ Harper and Brothers, 1894.
GAGER, C. S. _Fundamentals of Botany._ P. Blakiston's Son & Co., 1916.
GALLOWAY, T. W. _Textbook of Zoology._ P. Blakiston's Son & Co., 1915.
KINGSLEY, J. S. _Textbook of Vertebrate Zoology._ H. Holt & Co.
PETRUNKEVITCH, A. _Morphology of Invertebrate Types._ The Macmillan
Company, 1916.
T. W. GALLOWAY
_Beloit College_
BIBLIOGRAPHY
CRAMER, F. Logical Method in Biology. _Popular Science Monthly_, Vol.
44, page 372. 1894.
FARLOW, W. G. Biological Teaching in Colleges. _Popular Science
Monthly_, Vol. 28, page 581. 1886.
HARVEY, N. A. Pedagogical Content of Zoology. _Proceedings National
Education Association_, 1899; page 1106.
HODGE, C. F. Dynamic Biology. _Pedagogical Seminar_, Vols. 11-12.
HUXLEY, J. H. Educational Value of Natural History Science. Essay II,
_Science and Education_. 1854.
RUSK, R. R. _Introduction to Experimental Education._ Longmans, Green
& Co., 1912.
SAUNDERS, S. J. Value of Research in Education. _School Science and
Mathematics_, Vol. II, March, 1902.
SMALLWOOD, W. M. Biology as a Culture Study. _Journal of Pedagogy_,
Vol. 17, page 231.
WELTON, J. _Psychology of Education_ (chapter on "Character"). The
Macmillan Company, 1911.
Footnotes:
[2] These problems relate particularly to the introductory courses.
V
THE TEACHING OF CHEMISTRY
=Preparation of entering students a determining factor=
Some of the students entering classes in chemistry in college have
already had an elementary course in the subject in the high school or
academy, while others have not. Again, some study chemistry in college
merely for the sake of general information and culture, while many
others pursue the subject because the vocation they are planning to
make their life's work requires a more or less extensive knowledge of
chemistry. Thus, all students in the natural sciences and their
applications--as we have them in medicine, engineering, agriculture,
and home economics--as well as those who are training to become
professional chemists, either in the arts and industries or in
teaching, must devote a considerable amount of time and energy to the
study of chemistry. The teacher of college chemistry consequently must
take into consideration the preparation with which the student enters
his classes and also the end which is to be attained by the pursuit of
the subject in the case of the various groups of students mentioned.
In the larger high schools courses in chemistry are now quite
generally offered, but this is not yet true of the smaller schools. In
some colleges those who have had high school chemistry are at once
placed into advanced work without taking the usual basal course in
general chemistry which is so arranged that students can enter it who
have had no previous knowledge of the subject. In other words, in some
cases the college builds directly upon the high school course in
chemistry. As a rule, however, this does not prove very successful,
for the high school course in chemistry is not primarily designed as a
course upon which advanced college chemistry can be founded. This is
as it should be, for after all, while the high school prepares
students for college, its chief purpose is to act as a finishing
school for those larger numbers of students who never go to college.
The high school course in chemistry is consequently properly designed
to give certain important chemical facts and point out their more
immediate applications in the ordinary walks of life, as far as this
can properly be done in the allotted time with a student of high
school age and maturity. The result is consequently that while such
work can very well be accepted toward satisfying college entrance
requirements, it is only rarely sufficient as a basis for advanced
college courses in the subject. As a rule it is best to ask all
students to take the basal course in general chemistry offered in
college, arranging somewhat more advanced experiments in the
laboratory wherever necessary for those who have had chemistry in
preparatory schools. This has become the writer's practice after
careful trial of other expedients. The scheme has on the whole worked
out fairly well, for it is sufficiently elastic to meet the needs of
the individual students, who naturally come with preparation that is
quite varied. Almost invariably students who, on account of their
course in high school chemistry, are excused from the general basal
course in college chemistry have been handicapped forever afterward in
their advanced work in the subject.
=Organization of first-year course--General chemistry=
The first year's work in college chemistry consists of general
chemistry. It is basal for all work that is to follow, and yet at the
same time it is a finished course, giving a well-rounded survey of the
subject to all who do not care to pursue it further. This basal course
is commonly given in the freshman year, though sometimes it is
deferred to the sophomore year. Its content is now fairly uniform in
different colleges, the first semester being commonly devoted to
general fundamental considerations and the chemistry of the
non-metals, while the metals receive attention in the second semester,
the elements of qualitative analysis being in some cases taught in
connection with the chemistry of the metals.
The work is almost universally conducted by means of lectures,
laboratory work, and recitations. The lectures have the purpose to
unfold the subject, give general orientation as to the most important
fundamental topics and points of view, and furnish impetus, guidance,
and inspiration for laboratory study and reading. To this end the
lectures should be illustrated by means of carefully chosen and
well-prepared experiments. These serve not only to illustrate typical
chemical processes, and fundamental laws, but they also stimulate
interest and teach the student many valuable points of manipulation,
for it is well-nigh impossible to watch an expert manipulator without
absorbing valuable hints on the building up, arranging, and handling
of apparatus. In the lectures the material should be presented slowly,
carefully, and clearly, so that it may readily be followed by the
student. Facts should always be placed in the foreground, and they
should be made the basis of the generalization we call laws, and then
the latter naturally lead to theoretical conceptions. It is a great
mistake to begin with the atomic theory practically the first day and
try to bolster up that theory with facts later on as concrete cases of
chemical action are studied. On the other hand, it is also quite
unwise to defer the introduction of theoretical conceptions too long,
for the atomic theory is a great aid in making rapid progress in the
study of chemistry. At least two or three weeks are well spent in
studying fundamental chemical reactions as facts quite independent of
any theories whatsoever, in order that the student may thoroughly
appreciate the nature of chemical change and become familiar with
enough characteristic and typical cases of chemical action so that the
general laws of chemical combination by weight and by volume may be
logically deduced and the atomic and molecular theories presented as
based upon those laws.
Up to this stage the reactions should be written out in words and all
formulation should be avoided, so that the student will not get the
idea that "chemistry is the science of signs and symbols," or that
"chemistry is a hypothetical science," but that he will feel that
chemistry deals with certain very definite, characteristic, and
fundamental changes of matter in which new substances are formed, and
that these processes always go on in accordance with fixed and
invariable laws, though they are influenced by conditions of
temperature, pressure, light, electricity, and the presence of other
substances in larger or smaller amounts. The theory and formulation
when properly introduced should be an aid to the student, leading him
to see that the expression of chemical facts is simplified thereby.
Thus he will never make the error of regarding the symbol as the
fundamental thing, but he will from the very outset look upon it
simply as a useful form of shorthand expression, as it were, which is
also a great aid in chemical thinking. Facts and theories should ever
be kept distinct and separate in the student's mind, if he is to make
real progress in the science.
A thoroughgoing, logical presentation of the subject, leading the
student slowly and with a sense of perfect comprehension into the
deeper and more difficult phases, should constitute one of the prime
features of the work of the first year. Interest should constantly be
stimulated by references to the historical development of the subject,
to the practical applications in the arts and industries, to
sanitation and the treatment of disease, to the providing of proper
food, clothing, fuel, and shelter, to the problems of transportation
and communication, to the chemical changes that are constantly going
on in the atmosphere, the waters, and the crust of the earth as well
as in all living beings. Nevertheless, all the time the _science_
should be taught as the backbone of the entire course. The allusions
to history and the manifold applications to daily life are indeed very
important, but they must never obscure the science itself, for only
thus can a thorough comprehension of chemistry be imparted and the
benefits of the mental drill and culture be vouchsafed to the student.
=Methods of teaching--The Lecture method=
For the freshman and sophomore, two lectures per week are sufficient
for this type of instruction. In these exercises the student should
give his undivided attention to what is presented by the lecturer. The
taking of notes is to be discouraged rather than encouraged, for it
results in dividing the attention between what is presented and the
mechanical work of writing. To take the place of the usual lecture
notes, students of this grade had better be provided with a suitable
text, definite chapters in which are assigned for reading in
connection with each lecture. The text thus serves for purposes of
review, and also as a means for inculcating additional details which
cannot to advantage be presented in a lecture, but are best studied at
home by perusing a book, the contents of which have been illuminated
by the experimental demonstrations, the explanations on the
blackboard, the charts, lantern slides, and above all the living
development and presentation of the subject by the lecturer. The
lectures should in no case be conducted primarily as an exercise in
dictation and note taking. If the lectures do not give general
orientation, illumination, and inspiration for further study in
laboratory and library, they are an absolute failure and had better be
omitted entirely. On the other hand, when properly conducted the
lectures are the very life of the course.
=The laboratory work=
The laboratory work should be well correlated with the lectures,
especially during the first year. The experiments to be performed by
the student should be carefully chosen and should not be a mere
repetition of the lecture demonstrations. The laboratory experiments
should be both qualitative and quantitative in character. They should
on the one hand illustrate the peculiar properties of the substances
studied and the typical concomitant changes of chemical action, but on
the other hand a sufficient number of quantitative exercises in the
laboratory should be introduced to bring home to the student the laws
of combining weights and volumes, thus giving him the idea that
chemistry is exact and that quantitative relations always obtain when
chemical action takes place. At the same time the quantitative
exercises lay the basis for the proper comprehension of the laws of
combining weights and volumes and the atomic and molecular theories.
At least three periods of two consecutive hours each should be spent
in the laboratory per week, and the laboratory exercises should be
made so interesting and instructive that the student will feel
inclined to work in the laboratory at odd times in addition if his
program of other studies permits. The laboratory should at all times
be, as its name implies, a place where work is done. Order and
neatness should always prevail. Apparatus should be kept neat and
clean, and in no case should slovenly habits of setting up apparatus
be tolerated. The early introduction of a certain amount of
quantitative experimentation in the course makes for habits of order
and neatness in experimentation and guards against bringing up
"sloppy" chemists.
=The student's laboratory record=
The laboratory notebook should be a neat and accurate record of the
work in the laboratory. To this end the entries in the notebook should
be made in the laboratory at the time when the experiment is actually
being performed. The writing of data on loose scratch paper and then
finally writing up the notebook later at home from such sheets is not
to be recommended, for while thus the final appearance of the notebook
may be improved, it is no longer a first-hand record such as every
scientist makes, but rather a transcribed one. The student, in making
up such a transcription, is only too apt to draw upon his inner
consciousness to make the book appear better; indeed, when he has
neglected to transcribe his notes for several days, he is bound to
produce anything but a true and accurate record, to say nothing about
being put to the temptation to "fake" results which he has either not
at all obtained in the laboratory, or has recorded so imperfectly on
the scratch paper that he can no longer interpret his record properly.
The only true way is to have the notes made directly in the
permanently bound notebook at the time when the experiment is actually
in progress. The student ought not to take the laboratory notebook
home at all without the instructor's knowledge and permission. Each
experiment should be entered in the notebook in a brief, businesslike
manner. Long-winded, superfluous discussions should be avoided. As a
rule, drawings of apparatus in the notes are unnecessary, it being
sufficient to indicate that the apparatus was set up according to
Figure so-and-so in the laboratory manual or according to the
directions given on page so-and-so. The student should be made to feel
that the laboratory is the place where careful, purposeful
experimentation is to be done, that this is the main object of the
laboratory work, and that the notebook is merely a reliable record of
what has been accomplished. To this end the data in the notebook
should be complete, yet brief and to the point, so that what has been
done can be looked up again and that the instructor may know that the
experiment has been performed properly, that its purpose was
understood by the student, and that he has made correct observations
and drawn logical conclusions therefrom. While in each case the notes
should indicate the purpose of the experiment, what has actually been
done and observed, and the final conclusions, it is on the whole best
not to have a general cut-and-dried formula according to which each
and every experiment is to be recorded. It is better to encourage a
certain degree of individuality in this matter on the part of each
student. Notebooks should be corrected by the teacher every week, and
the student should be asked to correct all errors which the teacher
has indicated. A businesslike atmosphere should prevail in the
laboratory at all times, and this should be reflected in the
notebooks. Anything that savors of the pedantic is to be strictly
avoided. Small blackboards should be conveniently placed in the
laboratory so that the instructor may use them in explaining any
points that may arise. Usually the same question arises with several
members of the class, and a few moments of explanation before the
blackboard enable the instructor to clear up the points raised. This
not only saves the instructor's time, but it also stimulates interest
in the laboratory when explanations are thus given to small groups
just when the question is hot.
It is, of course, assumed that the necessary amount of apparatus,
chemicals, and other supplies is available, and that the laboratory
desks, proper ventilation of the rooms, and safeguards in the case of
all experiments fraught with danger have received the necessary
painstaking attention on the part of the instructor, who must never
for a moment relax in looking after these matters, which it is not the
purpose to discuss here. At all times the student should work
intelligently and be fully aware of any dangers that are inherent in
what he is doing. It need hardly be said that a beginner should not be
set at experiments that are specially dangerous. Having been given
proper directions, the student should be taught to go ahead with
confidence, for working in constant trepidation that an accident may
occur often creates a nervous state that brings about the accident.
Too much emphasis cannot be laid upon proper, definite laboratory
instructions, especially as to kinds and amounts of materials to be
used. Such directions as "take a _little_ phosphorus," for example,
should be strictly avoided, for the direction as to amount is
absolutely indefinite and may in the case where phosphorus or any
other dangerous substance is used lead to dire accidents. The student
should be given proper and very definite directions, and then he
should be taught to follow these absolutely and not use more of the
materials than is specified, as the beginner is so apt to do, thus
often wasting his time and the reagents as well. Economy and the
correct use of all laboratory supplies should be inculcated indirectly
all the time. A fixed set of printed rules for the laboratory is
generally neither necessary nor desirable when students are properly
directed to work intelligently as they go, and good directions are
given in the laboratory manual. Thus a spirit of doing intelligently
what is right and proper, guarding against accidents, economizing in
time and materials of all kinds will soon become dominant in the
laboratory and will greatly add to the efficiency of the workers.
Minor accidents are almost bound to occur at times in spite of all
precautions, and the instructor should be ready to cope with these
promptly by means of a properly supplied first-aid kit.
=Recitations and quizzes=
For students of the first year quizzes or recitations should be held
at least twice a week. In these exercises the ground covered in the
lectures and laboratory work should be carefully and systematically
reviewed. The quiz classes should not be too large. Twenty-five
students is the upper limit for a quiz section. The laboratory
sections too should not be larger than this, and it is highly
desirable that the same instructor conduct both the recitation and the
immediate laboratory supervision of the student. Lecture classes can,
of course, be very much larger in number. In most colleges the
attendance upon classes in chemistry is so large that it is not
possible for the professor to deliver the lectures and also personally
conduct all of the laboratory work and recitations. It is consequently
necessary to divide the class up into small sections for laboratory
and quiz purposes. It is highly desirable that the student become well
acquainted with his individual instructor in laboratory and quiz work,
and therefore it would be unfortunate to have one instructor in the
laboratory and still another instructor in the quiz. It might be
argued that it is a good thing to have the student become acquainted
with a number of instructors, but in the writer's experience such
practice results to the disadvantage of the student, and is
consequently not to be recommended.
In the recitations the student is to be encouraged to do the talking.
He is to be given an opportunity to ask questions as well as to answer
the queries put by the teacher. Short written exercises of about ten
minutes' duration can be given to advantage in each of these
recitations. In this way the entire class writes upon a well-chosen
question or solves a numerical chemical problem and thus a great deal
of time is saved. The quiz room should be well provided with
blackboards which may be used to great advantage in the writing of
equations and the solution of chemical problems just as in a class in
mathematics. The textbook, from which readings are assigned to the
student in connection with the lectures, should contain questions
which recapitulate the contents of each chapter. When such questions
are not contained in the book, they ought to be provided by the
teacher on printed or mimeographed sheets. When properly conducted,
the recitation aids greatly in clarifying, arranging and fixing the
important points of the course in the mind of the student. Young
instructors are apt to make the mistake of doing too much talking in
the quiz, instead of encouraging the student to express his views. In
these days, when foreign languages and mathematics are more or less on
the wane in colleges, the proper study of chemistry, particularly in
the well-conducted quiz, will go far toward supplying the mental drill
which the older subjects have always afforded.
=Summary of first-year course=
If the work of the first year has been properly conducted, it will
have given the student a general view of the whole field of chemistry,
together with a sufficient amount of detail so securely anchored in
careful laboratory work and practical experience as to form a basis
for either more advanced work in chemical lines or in the pursuance of
the vocations already mentioned in which a knowledge of chemistry is
basal. It is hardly necessary to add that if well taught, the student
will at the end of such a course have a desire for more chemistry.
=Organization of second-year course=
The work of the second year of chemistry in college generally consists
of quantitative analysis, though the more intensive study of the
compounds of carbon, known as organic chemistry, is also frequently
taken up at this time, and there is much to be said in favor of such
practice.
=Content of the course in quantitative analysis=
In the quantitative analysis, habits of neatness and accuracy must be
insisted upon. It is well to give the general orientation and
directions by means of lectures. One or two such exercises per week
will suffice. There should also be recitations. When two lectures per
week are given, it will suffice to review the work with the student in
connection with such lectures, provided the class is not too large for
quiz purposes. Intelligent work should characterize a course in
quantitative analysis. To this end the student should be taught how to
take proper representative samples of the material to be analyzed. He
should then be taught how to weigh or measure out that sample with
proper care. The manipulations of the analytical process should be
carried out so that each step is properly understood and its relations
to the general laws of chemistry are constantly before the mind. In
carrying out the process, the various sources of error must be
thoroughly appreciated and guarded against. The final weighing or
measuring of the form in which the ingredient sought is estimated
should again be carried out with care, and in the calculation of the
percentage content due regard should be had for the limits of error of
experimentation throughout the entire analytical process. The student
feels that a large number of the exercises in quantitative analysis
are virtually cases of making chemical preparations of the highest
possible purity, thus connecting his previous chemical experience with
his quantitative work. The course in quantitative analysis should
cover the determination of the more important basic and acid radicals,
and should consist of both gravimetric and volumetric exercises.
The choice of the exercises is of great importance. It may vary, and
should vary considerably in different cases. Thus a student in
agriculture is naturally interested in the methods of estimating lime,
phosphorus, nitrogen, potash, silica, sulphur, etc., whereas a student
in engineering would be more interested in work with the heavy metals
and the ingredients which the commercial samples of such metals are
apt to contain. Thus, analytical work on solder, bearing metal, iron
and steel, cement, etc., should be introduced as soon as the student
in engineering is ready for it. It is quite possible to inculcate the
principles of quantitative analysis by selecting exercises in which
the individual student is interested, though, to be sure, certain
fundamental things would naturally have to be taken by all students,
whatever be the line for which they are training. A few exercises in
gas analysis and also water analysis should be given in every good
course in quantitative analysis that occupies an entire year. Careful
attention should be given to the notebook in the quantitative work,
and the student should also be made to feel that in modern
quantitative analysis not only balances and burettes are to serve as
the measuring instruments, but that the polariscope and the
refractometer also are very important, and that at times still other
physical instruments like the spectroscope, the electrometer, and the
viscometer may prove very useful indeed.
The quantitative analysis offers a splendid opportunity for bringing
home to the student what he has learned in the work of the first year,
showing him one phase of the application of that knowledge and making
him feel, as it were, the quantitative side of science. This latter
view can be imparted only to a limited degree in the first year's
work, but the quantitative course offers an unusual opportunity for
giving the student an application of the fundamental quantitative laws
which govern all chemical processes. It is not possible to analyze
very many substances during any college course in quantitative
analysis. The wise teacher will choose the substances to be analyzed
so as to keep up the interest of the student and yet at the same time
give him examples of all the fundamental cases that are commonly met
in the practice of analytical work. A careful, painstaking,
intelligent worker should be the result of the course in quantitative
analysis. Toward the end of the course, too, a certain amount of speed
should be insisted upon. The student should be taught to carry on
several processes at the same time, but care should be taken not to
overdo this.
=The course in organic chemistry=
In the course in organic chemistry, lectures, laboratory work, and
recitations, arranged very much as to time as in the first year, will
be found advantageous. If the intensive work in organic chemistry is
postponed to the third year in college, there are certain advantages.
For example, the student is more mature and has had drill and
experience in the somewhat simpler processes commonly taught in
general and analytical chemistry. On the other hand, the postponing of
organic chemistry to the third year has the disadvantage that the
student goes through his basal training in quantitative analysis
without the help of that larger horizon which can come to him only
through the study of the methods of organic chemistry. The general
work of the first year, to be sure, if well done compensates in part
for what is lost by postponing organic chemistry till the third year,
but it can never entirely remove the loss to the student. Teachers
will differ as to whether the time-honored division of organic
chemistry into the aliphatic and aromatic series should be maintained
pedagogically, but they will doubtless all agree that the methods of
working out the structure of the chemical compound are peculiarly
characteristic of the study of the compounds of carbon, and these
methods must consequently constitute an important point to be
inculcated in organic chemistry. The derivation of the various types
of organic compounds from the fundamental hydrocarbons as well as from
one another, and the characteristic reactions of each of these
fundamental forms which lead to their identification and also often
serve as a means of their purification, should naturally be taught in
a thoroughgoing manner. The numerous practical applications which the
teacher of organic chemistry has at his command will always serve to
make this subject one of the deepest interest, if not the most
fascinating portion of the entire subject of chemistry. No student
should leave the course in organic chemistry without feeling the
beautiful unity and logical relationship which obtains in the case of
the compounds of carbon, the experimental study of which has cast so
much light upon the chemical processes in living plants and animals,
processes upon which life itself depends. The analysis of organic
compounds is probably best taught in connection with the course in
organic chemistry. It is here that the student is introduced to the
use of the combustion furnace and the method of working out the
empirical formulae of the compounds which he has carefully prepared and
purified. The laboratory practice in organic chemistry generally
requires the use of larger pieces of apparatus. Some of the
experiments also are connected with peculiar dangers of their own.
These facts require that the student should not approach the course
without sufficient preliminary training. Furthermore, the teacher
needs to exercise special care in supervising the laboratory work so
as to guard the student against serious accidents.
The historical development of organic chemistry is especially
interesting, and allusions to the history of the important discoveries
and developments of ideas in organic chemistry should be used to
stimulate interest and so enhance the value of the work of the
student. The practical side of organic chemistry should never be lost
sight of for a moment, and under no condition should the course be
allowed to deteriorate into one of mere picturing of structural
formulae on the blackboard. All chemical formulas are merely compact
forms of expression of what we know about chemical compounds. There
are, no doubt, many facts about chemical compounds which their
accepted formulas do not express at all, and the wise teacher should
lead the student to see this. There is peculiar danger in the course
in organic chemistry that the pupil become a mere formula worshiper,
and this must carefully be guarded against.
The applications of organic chemistry to the arts and industries, but
especially to biochemistry, will no doubt interest many members of the
class of a course in organic chemistry if the subject is properly
taught. This will be particularly the case if the teacher always holds
before the mind of the pupil the actual realities in the laboratory
and in nature, using formulation merely as the expression of our
knowledge and not as an end in itself.
=Place of physical chemistry in the college curriculum=
Physical chemistry, commonly regarded as the youngest and by its
adherents the most important and all-pervading branch of chemistry, is
presented very early in the college course by some teachers, and
postponed to the junior and even the senior year by others. Just as a
certain amount of organic chemistry should be taught in the first
year, so a few of the most fundamental principles of physical
chemistry must also find a place in the basal work of the beginner.
However, in the first year's work in chemistry so many phases of the
subject must needs be presented in order to give a good general view,
that many details in either organic, analytical, or physical chemistry
must necessarily be omitted. What is to be taught in that important
basal year must, therefore, be selected with extreme care. Moreover,
so far as physical chemistry is concerned, it is in a way chemical
philosophy or general chemistry in the broadest sense of the word, and
consequently requires for its successful pursuit not only a basal
course, but also proper knowledge of analytical and organic chemistry,
as well as a grounding in physics, crystallography, and mathematics.
At the same time a certain amount of biological study is highly
desirable. A good course in physical chemistry postulates lectures,
laboratory work, and recitations. In general, these should be arranged
much like those in the basal course and the course in organic
chemistry. If anything, more time should be put upon the lectures and
recitations; certainly more time should be devoted to exercises of
this kind than in the course in quantitative analysis, which is best
taught in the laboratory. At the same time it would be a mistake to
teach physical chemistry without laboratory practice. Indeed,
laboratory practice is the very life of physical chemistry, and the
more of such work we can have, the better. However, since physical
chemistry, as already stated, delves into the philosophical field,
discussions in the lecture hall and classroom become of peculiar
importance.
=Courses in applied chemistry=
Many colleges now give additional courses in chemical technology.
These would naturally come after the student has had a sufficient
foundation in general chemistry, chemical analysis, and organic and
physical chemistry. As a rule such applied courses ought not to be
given until the junior or senior year. It is a great mistake to
introduce such courses earlier, for the student cannot do the work in
an intelligent manner.
=Enthusiastic teaching a vital factor=
In all the courses in chemistry, interest and enthusiasm are of vital
importance. These can be instilled only by the teacher himself, and no
amount of laying out courses on paper and giving directions, however
valuable they may be, can possibly take the place of an able, devoted,
enthusiastic teacher. Chemistry deals with things, and hence is always
best taught in the laboratory. The classroom and the library should
create interest and enthusiasm for further laboratory work, and in
turn the laboratory work should yield results that will finally
manifest themselves in the form of good written reports.
=The teacher must continue his researches=
Original work should always be carried on by the college teacher. If
he fails in this, his teaching will soon be dead. There will always be
some bright students who can help him in his research work. These
should be led on and developed along lines of original thought. From
this source there will always spring live workers in the arts and
industries as well as in academic lines. Lack of facilities and time
is often pleaded by the college teacher as an excuse for not doing
original work. There is no doubt that such facilities are often very
meager. Nevertheless, the enthusiastic teacher is bound to find the
time and also the means for doing some original work. A great deal
cannot be expected of him as a rule because of his pedagogical duties,
but a certain amount of productive work is absolutely essential to any
live college teacher.
=Future of chemistry in the college curriculum=
The importance of chemistry in daily life and in the industries has
been increasing and is bound to continue to increase. For this reason
the subject is destined to take a more important place in the college
curriculum. If well taught, college chemistry will not only widen the
horizon of the student, but it will also afford him both manual
training and mental drill and culture of the highest order.
LOUIS KAHLENBERG
_University of Wisconsin_
VI
THE TEACHING OF PHYSICS
The need of giving to physics a prominent place in the college
curriculum of the twentieth century is quite universally admitted. If,
as an eminent medical authority maintains, no man can be said to be
educated who has not the knowledge of trigonometry, how much more true
is this statement with reference to physics? The five human senses are
not more varied in scope than are the five great domains of this
science. In the study of heat, sound, and light we may strive merely
to understand the nature of the external stimuli that come to us
through touch, hearing and sight; but in mechanics, where we examine
critically the simplest ideas of motion and inertia, we acquire the
method of analysis which when applied to the mysteries of molecular
physics and electricity carries us along avenues that lead to the most
profound secrets of nature. Utilitarian aspects dwindle in our
perspective as we face the problem of the structure, origin, and
evolution of matter--as we question the independence of space and
time. Modern physics possesses philosophic stature of heroic size.
=Utilitarian value of the study Of physics=
But with regard to everyday occurrences a study of physics is
necessary. It is trite to mention the development in recent years of
those mechanical and electrical arts that have made modern
civilization. The submarine, vitalized by storage battery and Diesel
engine, the torpedo with its gyroscopic pilot and pneumatic motors,
the wireless transmission of speech over seas and continents--these
things no longer excite wonder nor claim attention as we scan the
morning paper; yet how many understand their mechanism or appreciate
the spirit which has given them to the world?
=Disciplinary value of the study=
If culture means the subjective transformation of information into a
philosophy of life, can culture be complete unless it has included in
its reflections the marvelously simple yet intricate interrelations
of natural phenomena? The value of this intricate simplicity as a
mental discipline is equaled perhaps only in the finely drawn
distinctions of philosophy and in the painstaking statements of
limitations and the rapid generalizations of pure mathematics; and let
us not forget the value of discipline, outgrown and unheeded though it
be in the acquisitive life of the present age.
=Relation of physics to philosophy and the exact sciences=
The professional student, continually increasing in numbers in our
colleges, either of science or in certain branches of law, finds a
broad familiarity with the latest points of view of the physicist not
only helpful but often indispensable. Chemistry can find with
difficulty any artificial basis for a boundary of its domain from that
of physics. Certainly no real one exists. The biologist is heard
asking about the latest idea in atomic evolution and the electrical
theories of matter, hoping to find in these illuminating points of
view, he tells us, some analogy to his almost hopelessly complex
problems of life and heredity. Even those medical men whose interest
is entirely commercial appreciate the convenience of the X-ray and the
importance of correctly interpreting the pathological effects of the
rays of radio-activity and ultra-violet light. One finds a great
geologist in collaboration with his distinguished colleague in
physics, and from the latter comes a contribution on the rigidity of
the earth. Astronomy answers nowadays to the name of astrophysics, and
progressive observatories recognize in the laboratory a tool as
essential as the telescope. In a word, the professional student of
science not only finds that the subject matter of physics has many
fundamental points of contact with his own chosen field, but also
recognizes that the less complex nature of its material allows the
method of study to stand out in bolder relief. Training in the method
and a passion for the method are vital to a successful and an ardent
career.
=Should the teaching of college physics change its aim for different
classes of students?=
In the teaching of physics, then, the aim might at first sight appear
to be quite varied, differing with different classes of students. A
careful analysis of the situation, however, will show, we think, that
this conclusion can with difficulty be justified: that it is necessary
to conduct college instruction in a fashion dictated almost not at all
by the subsequent aims of the students concerned. In the more
elementary work, certainly, adherence to this idea is of great
importance. The character, design, and purpose of an edifice do not
appear in the foundations except that they are massive if the
structure is to be great.
Not infrequently this seems an unnecessary hardship to a professional
student anxious to get into the work of his chosen field. If such is
the case, let him question perhaps whether any study of physics should
be attempted, as this query may have different answers for different
individuals. But if he is to study it at all, there is but one place
where the analysis of physical phenomena can begin, and that is with
fundamentals--space, time, motion, and inertia. How can one who is
ignorant of the existence and characteristics of rotational inertia
understand a galvanometer? How can waves be discussed unless in terms
of period, amplitude, frequency, and the like, that find definition in
simple harmonic motion? How does one visualize the mechanism of a gas,
unless by means of such ideas as momentum interchange, energy
conservation, and forces of attraction?
Let us emphasize here, lest we be misunderstood, that we are
considering collegiate courses. We do not doubt that descriptive
physics may be given after one fashion to farmers, quite differently
to engineers, and from still a third point of view to medical
students. Unfortunately some collegiate courses never get beyond the
high school method. Our aim is not to discuss descriptive courses, but
those that approach the subject with the spirit of critical analysis,
for these alone do we deem worthy of a place in the college
curriculum.
=The course in college physics differentiated from the high school course=
The problem of the descriptive course is the problem of the high
school. Because of failure there, too often we see at many a
university courses in subfreshman physics. These are made necessary
where entrance requirements do not demand this subject and where
subsequent interest along related lines develops among the students a
tardy necessity of getting it. From the point of view of the
collegiate course it often appears as if the subfreshman course could
be raised to academic rank. This is because familiarity with the
material must precede an analysis of it. Credit for high school
physics on the records of the entrance examiner, unless this credit is
based on entrance examination, is often found to stand for very
little. Consequently the almost continual demand for the high school
work under the direct supervision of a collegiate faculty. The number
of students who should go into this course instead of the college
course is increasing at the present time in the immediate locality of
the writer.
As contributory testimony here, witness the number of colleges that do
not take cognizance at all of high school preparation and admit to the
same college classes those who have never had preparatory physics with
those who have had it. We are told the difference between the two
groups is insignificant. Perhaps it is. If so, this fact reflects as
much on the college as on the high school. If we are looking for a
solution of our problem in this direction, let us be undeceived; we
are looking backwards, not forward.
=Need of adequate high school preparation in physics=
No one will affirm that to a class of whose numbers some have never
had high school physics a course that is really analytical can be
given. Wherever a rigorous analytic course is given those who have
been well trained in descriptive physics do well in it in general. Let
us not beg the question by giving such physics in a college that does
not require high school preparation. The college curriculum is full
enough as it is without duplication of high school work, and any
college physics course that is a first course is essentially a high
school course.
Let us rather put the responsibility squarely where it lies. The high
school will respond if the urgency is made clear. Witness some of them
in our cities already attempting the junior college idea, an idea that
has not been unsuccessful in some of our private schools. If it is
made clear that a thoroughgoing course in descriptive physics is a
paramount necessity in college work and that no effort will be spared
on the part of the university to insure this quality, the men will be
found and the proper courses given.
=Preparatory work in mathematics essential for success in college physics=
We favor a comprehensive examination plan in all cases where the
quality of the high school work is either unknown or open to question.
Familiarity, likewise, with the most elementary uses of mathematics
should be insured. It would be highly desirable that a course of
collegiate grade in trigonometry should immediately precede the
physics. This is not because the details of trigonometry are all
needed in physics. In fact, a few who have never had trigonometry make
a conspicuous success in physics. These, however, are ones who have a
natural facility in analysis. To keep them out because of failure to
have had a prerequisite course in trigonometry often works an
unnecessary hardship. We would argue, therefore, for a formal
prerequisite on this subject, reserving for certain students
exemption, which should be determined in all cases, if not by the
instructor himself, at least by his cooperation with some advisory
administrative officer.
=Need of testing each student's preparation=
Nor is it sufficient with regard to the mathematical preparation or
the knowledge of high school physics in either case to go exclusively
by the official credit record of the student. It is our firm
conviction from several years' experience where widely different aims
in the student body are represented that above and beyond all formal
records attention to the individual case is of prime importance. The
opening week of the course should be so conducted that those who are
obviously unequipped can be located and directed elsewhere into the
proper work. How this may best be accomplished can be determined only
by the circumstances in the individual school, we imagine. Daily tests
covering the simplest descriptive information that should be retained
from high school physics and requiring the intelligent use of
arithmetic, elementary algebra, and geometry will reveal amazing
incapacity in these things. Tuttle, in his little book entitled _An
Introduction to Laboratory Physics_ (Jefferson Laboratory of Physics,
Philadelphia, 1915), gives on pages 15-16 an excellent list of
questions of this sort. Any one with teaching experience in the
subject whatever can make up an equally good one suited for his
special needs and temperament. It should not be assumed that all who
fail in such tests should be dropped. Some undoubtedly should be sent
back to high school work or its equivalent; others may need double the
required work in mathematics to overcome their unreadiness in its use.
Personal contacts will show that some are drifting into a scientific
course who have no aptitude for it and who will be doomed to
disappointment should they continue. In a word, then, we are convinced
that the more carefully one plans the work of the first week or so the
more smoothly does the work of the rest of the year follow. The number
of failures may be reduced to a few per cent without in any way
relaxing the standard of the course.
=Methods of teaching college physics=
With regard to the organization of the college courses in physics
there seems to us to be at least one method that leads to a
considerable degree of success. This is not the lecture method of
instruction; neither is it a wholly unmitigated laboratory method.
=Lecture method vs. laboratory method=
To kindle inspiration and enthusiasm nothing can equal the contact in
lectures with others, preferably leaders in their profession, but at
least men who possess one of these qualities. Such contacts need not
be frequent; indeed, they should not be. The speaker is apt to make
more effort, the student to be more responsive, if such occasions are
relatively rare. Even thus, although real information is imparted at
such a time, it is seldom acquired. However, perspective is furnished,
interest stimulated, and the occasion enjoyed.
=Limitations of exclusive use of each method=
For the real acquisition of scientific information, the great method
is the working out of a laboratory exercise and pertinent problems,
with informal guidance in the atmosphere of active study and
discussion engendered among a small group,--the laboratory method.
Taken alone, it is apt to become mechanical and uninteresting and the
outlook to be obscured by details. Lectures, especially demonstration
lectures, are needed to vitalize and inspire. Moreover, many of the
most vivid illustrations of physical principles that occur on every
hand to focus the popular attention are never met with in the college
course because they are unsuited for inexperienced hands or not
readily amenable to quantitative experimentation. The more informally
such demonstrations can be conducted, the more enthusiastically they
are received.
=Aims of the laboratory method=
With regard to laboratory work, accuracy in moderate degree is
important, but too great insistence upon it is apt to overshadow the
higher aim; namely, that of the analysis of the phenomena themselves.
A determination of the pressure coefficient of a gas to half a per
cent, accompanied by a clear visualization of the mechanism by which a
gas exerts a pressure and a usable identification of temperature with
kinetic agitation, would seem preferable to an experimental error of a
tenth per cent which may be exacted which is unaccompanied by these
inspiring and rather modern points of view. Especially in electricity
is a familiarity with the essentials of the modern theories important.
Here supplementary lectures are of great necessity, for no textbook
keeps pace with progress in this tremendously important field. Problem
solving with class discussion is absolutely essential, and should
occupy at least one third of the entire time. In no other way can one
be convinced that the student is doing anything more than committing
to memory, or blindly following directions with no reaction of his
own.
=Value of the supplementary lecture=
The incorporation recently of this idea into the courses at the
University of Chicago has been very successful. Five sections which
are under different instructors are combined one day a week at an hour
when there are no other university engagements, for a lecture
demonstration. This is given by a senior member of the staff whenever
possible. The other meetings during the week are conducted by the
individual instructors and consist of two two-hour laboratory periods
and two class periods that usually run into somewhat over one hour
each. These sections are limited to twenty-five, and a smaller number
than this would be desirable. The responsibility for the course rests
naturally upon the individual instructors of these small sections.
These men also share in the demonstration work, since each is usually
an enthusiast in some particular field and will make a great effort in
his own specialty to give a successful popular presentation of the
important ideas involved. The enthusiasm which this plan has
engendered is very great. Attendance is crowded and there is always a
row of visitors, teachers of the vicinity, advanced students in other
fields of work, or undergraduates brought in by members of the class.
These latter especially are encouraged, as this does much to offset
current ideas that physics is a subject of unmitigated severity. The
particular topics put into these demonstrations will be discussed in
paragraphs below, which take up in more detail the organization of the
special subdivisions of the material in a general physics course.
=Mechanics a stumbling block--How to meet the difficulty=
Mechanics is a stumbling block at the outset. As we have indicated
above, it must form the beginning of any course that is analytic in
aim. There is no question of sidestepping the difficulty: it must be
surmounted. A judicious weeding during the first week is the initial
part of the plan. Interest may be aroused at once in the demonstration
lectures by mechanical tricks that show apparent violations of
Newton's Laws. These group around the type of experiment which shows a
modification of the natural uniform rectilinear motion of any object
by some hidden force, most often a concealed magnetic field. The
instinctive adherence of every one to Newton's dynamic definition,
that acceleration defies the ratio of force to inertia, is made
obvious by the amusement with which a trick in apparent defiance of
this principle is greeted. Informality of discussion in such
experiments, questions on the part of the instructor that are more
than rhetorical, and volunteer answers and comment from the class
increase the vividness of the impressions. A mechanical adaptation of
the "monkey on the string" problem, using little electric hoists or
clockworks, introduces interesting discussion of the third law in
conjunction with the second. A toy cannon and target mounted on easily
rolling carriages bring in the similar ideas where impulses rather
than forces alone can be measured.
There follow, then, the laboratory experiments of the Atwood machine
and the force table, where quantitative results are demanded. It is
desirable to have these experiments at least worked by the class in
unison. Whatever may be the exigencies of numbers and apparatus
equipment that prevent it later, these introductions should be given
to and discussed by all together. In the nature of things,
fortunately, this is possible. A single Atwood machine will give
traces for all in a short time under the guidance of the instructor.
The force table experiment is nine-tenths calculation, and
verifications may be made for a large number in a short time.
Searching problems and discussion are instigated at once, and the
notion of rotational equilibrium and force moments brought in. Because
of the very great difficulty seeming to attach to force resolutions,
demonstration experiments and problems using a bridge structure, such
as the Harvard experimental truss, will amply repay the time invested.
Another experiment here, which makes analysis of the practice of
weighing, is possible, although there will be divergence almost at
once due to the personality of the instructor and the equipment by
which he finds himself limited. The early introduction of moments is
important, however, because it seems as if a great amount of
unnecessary confusion on this topic is continually cropping out later.
At this point, if limitations of apparatus present a difficulty, a
group of more or less independent experiments may be started. Ideas of
energy may be illustrated in the determination of the efficiency and
the horse power of simple machines, such as water motors, pulleys, and
even small gas or steam engines.
In discussion of power one should not forget that in practical
problems one meets power as force times velocity rather more
frequently than as rate of doing work, and this aspect should be
emphasized in the experiments. Conservation of energy is brought out
in these same experiments with reference to the efficiencies involved.
In sharp contrast here the principle of conservation of momentum may
be brought in by ballistic pendulum experiments involving elastic and
inelastic impacts. Most students are unfamiliar with the application
of these ideas to the determination of projectile velocities, and this
forms an interesting lecture demonstration. Elasticity likewise is a
topic that may be introduced with more or less emphasis according to
the predilection of the instructor. The moduli of Young and of simple
rigidity lend themselves readily to quantitative laboratory
experiments. Any amount of interesting material may be culled here
from recent investigations of Michelson, Bridgman, and others with
regard to elastic limits, departures from the simple relations,
variations with pressure, etc., for a lantern or demonstration talk in
these connections.
By this time the student should have found himself sufficiently
prepared to take up problems of rotational motion. The application of
Newton's Laws to pure rotations and combinations of rotation and
translation, such as rolling motions, are very many. We would
emphasize here the dynamic definition of moment of inertia, I = Fh/_a_
rather than the one so frequently given importance for computational
purposes, S_mr_^{2}. Quantitative experiments are furnished
by the rotational counterpart of the Atwood machine. Lecture
demonstrations for several talks abound: stability of spin about the
axis of greatest inertia, Kelvin's famous experiments with eggs and
tops containing liquids, which suggest the gyroscopic ideas, and
finally a discussion of gyroscopes and their multitudinous
applications. The book of Crabtree, _Spinning Tops and the
Gyroscope_, and the several papers by Gray in the _Proceedings of the
Physical Society of London_, summarize a wealth of material. If one
wishes to interject a parenthetical discussion of the Bernouilli
principle, and the simplest laws of pressure distributions on plane
surfaces moving through a resisting medium, a group of striking
demonstrations is possible involving this notion, and by simple
combination of it with the precession of a rotating body the boomerang
may be brought in and its action for the major part given explanation.
Rotational motion leads naturally to a discussion of centripetal
force, and this in turn is simple harmonic motion. This latter finds
most important applications in the pendulum experiments, and no end of
material is here to be found in any of the textbooks. The greatest
refinement of experimentation for elementary purposes will be the
determination of "g" by the method of coincidences between a simple
pendulum and the standard clock. Elementary analysis without use of
calculus reaches its culmination in a discussion of forced vibrations
similar to that used by Magie in his general text. Many will not care
to go as far as this. Others will go farther and discuss Kater's
pendulum and the small corrections needed for precision, for here does
precision find bold expression.
It is not our purpose to give a synopsis of the entire general physics
course. We have made an especially detailed study of mechanics,
because this topic is the one of greatest difficulty by far in the
pedagogy. It is too formally given in the average text, and seems to
have suffered most of all from lack of imagination on the part of
instructors.
=Suggested content for the study of phenomena of heat and molecular
physics=
In the field of heat and molecular physics in general there is much
better textbook material. Experiments here may legitimately be called
precise, for the gas laws, temperature coefficients, and densities of
gases and saturated vapor pressures will readily yield in
comparatively inexperienced hands an accuracy of about one in a
thousand. In the demonstrations emphasis should be given to the
visualization of the kinetic theory points of view. Such models as the
Northrup visible molecule apparatus are very helpful. However, in
absence of funds for such elaboration, slides from imaginative
drawings showing to scale conditions in solids, liquids, and vapors
with average free paths indicated and the history of single molecules
depicted will be found ideal in getting the visualization home to the
student. Where we have a theory so completely established as the
mechanical theory of heat it seems quite fair to have recourse to the
eye of the senses to aid the eye of the mind. Brownian movements have
already yielded up their dances to the motion picture camera. Need the
"movies" be the only ones to profit by the animated cartoon?
Nor should the classical material be forgotten. Boys' experiments in
soap bubbles have been the inspiration of generations of students of
capillarity. And if the physicist will consult with the physiological
chemist he will find a mass of material of which he never dreamed
where these phenomena of surface tension enter in a most direct
fashion to leading questions in the life sciences.
=The teacher of scholarship and understanding is the teacher who uses
sound methods=
Enough has been said to indicate what we consider the methods of
successful teaching of college physics. It is quite obvious, we think,
that physics constitutes no exception to the rule that the teacher
must first of all know and understand his subject. Right here lies
probably nine tenths of the fault with our pedagogy. No amount of
study of method will yield such returns as the study of the subject
itself. The honest student, and every teacher should belong to this
class or he has no claim to the name, is well aware that most of his
deficiency in explaining a topic is in direct ratio to his own lack of
comprehension of it. In physics, as in every other walk of life, we
suffer from lack of thoroughness, from a kind of superficiality that
is characteristically human but especially American. We have yet to
know of any one who really ranks as a scholar in his subject from whom
students do not derive inspiration and enthusiasm. Such a one usually
pays little attention to the methods of others, for the divine fire of
knowledge itself does not need much of tinder to kindle the torches
of others. Our greatest plea is for our teachers to be men of
understanding, for then they will be found to be men of method.
=The method of analysis dominant in physics=
The sequence in which heat, electricity, sound, and light follow
mechanics seems quite immaterial. Several equally logical plans may be
organized. Preference is usually accorded one or the other on the
basis of local conditions of equipment, and needs little reference to
pedagogy. If one gives to mechanics its proper importance, the
difficulty in giving instruction in the other topics seems very much
less. The momentum acquired seems to serve for the balance of the
year. Always must analysis be insisted upon, if our college course is
going to differ from that of the high school. If we are to let
students be content to read current from an ammeter with a calibrated
scale and not have the interest to inquire and the ambition to insist
upon the knowledge of how that calibration was originally made, we
have no right to claim any collegiate rank for our courses. But if we
define electrical current in terms of mechanical force which exhibits
a balanced couple on a system in rotational equilibrium, there can be
no dodging of the issue, for in no other way than by the study of the
mechanics of the situation can the content and the limitations of our
definition be understood. Any college work, so called, that does less
than analyze thus is nothing more than a review and amplification of
the material that should be within the range of the high school
student and in that place presented to him. The first college course
reveals a different method, the method of analysis. Science at the
present time is so far developed that in no branch is progress made by
mere description and classification. The method of analysis is
dominant in the biological and the earth sciences as well as in the
physics and chemistry of today.
=Teaching of advanced courses in physics=
On the more advanced college courses which follow the general physics
course little comment is needed. Problems and questions here also
exist, but they have a strongly local color and are out of place in a
general discussion. The student body is no longer composed of the
rank and file, half of whom are driven, by some requirement or other,
into work in which they have but a passing interest at best. It is no
longer a problem of seeing how much can be made to adhere in spite of
indifference, of how firm a foundation can be prepared for needs as
yet unrecognized in the subject of the effort. A very limited number,
comparatively, enter further work of senior college courses, and these
have either enthusiasm or ability and often both. Of course, a cold
neglect or bored indifference in the attitude of the teacher will be
resented. It will kill enthusiasm and send ability seeking inspiration
elsewhere. But any one who is fond of his subject, and of moderate
ability and industry, should have no difficulty in developing senior
college work. If our instructor in the general course must be a
scholar to be successful, the man in more advanced work must be one _a
fortiori_. If he is not, few who come in contact with him have so
little discernment as to fail to recognize the fact.
=Organization of advanced courses=
Organization of senior college work may be in many ways. One method
where an institution follows the quarter system is the plan of having
eight or ten different and rather unrelated twelve-week major courses
which may be taken in almost any order. Half of these are lecture
courses, the other half exclusively laboratory courses. There should
be a correspondence of material to some extent between the two.
Lectures on the kinetic theory of gases should have a parallel course
in which the classical experiments of the senior heat laboratory are
performed,--such experiments, for example, as vapor density,
resistance and thermocouple pyrometry, bomb calorimetry viscosity,
molecular conductivity, freezing and boiling points, recalescence,
etc. A course of advanced electrical measurements should have a
parallel lecture course in which the theoretical aspects of
electromagnetism, the classical theories, and the equations that
represent transitory and equilibrium conditions in complex circuits
are discussed. In optics, likewise, there is ample material of great
importance: physical, geometrical optics, spectroscopy, photography,
X-ray crystallography, etc. The advanced student in these fields finds
more elasticity and opportunity for cultivating a special interest in
having a large number of limited interest courses from which to choose
than in having such material presented in a completely organized
course covering one or two years of complete work. Instructors who are
specialists have opportunity of working up courses in their own fields
which they do more efficiently under this plan. Research begins at
innumerable places along the way, and the senior college courses so
organized are the feeders of all graduate work.
=Dangers of formalizing methods of instruction=
In all of the above discussion it should be clearly remembered that no
single plan or no one particular method has the final word or ever
will have. As long as a science is growing and unfinished, points of
view will continually be shifting. We are largely orthodox in our
teaching. If brought up on the laboratory method of instruction it may
seem the best one for us, but others may prefer another way which they
have inherited. Let us appeal, then, for a constructive orthodoxy. Let
us be as teachers of a subject to which we are devoted, truly and
sincerely open-minded, quick to recognize and sincere in our efforts
to adopt what is better wherever we meet it: waiting not to meet it,
either, but going out to seek it. From the humblest college to the
greatest university we shall find it here and there. Not alone in
schools but in the legion of human activities about us on every hand
are people who are doing things more efficiently, more thoroughly, and
more skillfully than we do things. If we would be of the number that
lead, we must be among the first to recognize these facts and profit
by them.
First, let our work be organized with respect to that of others--the
high schools; not discounting their labor but having them truly build
for us.
Second, let us be open-minded enough to see that all methods of
instruction have their advantages and make such combinations of the
best elements in each as best suit our purpose.
Above all things, let us know our subject. Here is a task before which
we quail in this generation of vast vistas. But there is no
alternative for us. No amount of method will remove the curse of the
superficially informed. Let us devote ourselves to smaller fields if
we must, but let us not tolerate ignorance among those who bear the
burden of passing on, with its flame ever more consuming, the torch of
knowledge.
HARVEY B. LEMON
_University of Chicago_
VII
THE TEACHING OF GEOLOGY
=Values of the study of geology diverse=
So wide is the scope of the science of the earth, so varied is its
subject matter, and so diverse are the mental activities called forth
in its pursuit, that its function in collegiate training cannot be
summed up in an introductory phrase or two. Geology is so composite
that it is better fitted to serve a related group of educational
purposes than a single one alone. Besides this, these possible
services have not yet become so familiar that they can be brought
vividly to mind by an apt word or phrase; they need elaboration and
exposition to be valued at what they are really worth. Geology is yet
a young science and still growing, and as in the case of a growing
boy, to know what it was a few years ago is not to know what it is
today. Its disciplines take on a realistic phase in the main, but yet
in some aspects appeal powerfully to the imagination. Its subject
matter forms a constitutional history of our planet and its
inhabitants, but yet largely wears a descriptive or a dynamic garb.
=Geology a study of the process of evolution=
Though basally historical, a large part of the literature of geology
is concerned with the description of rocks, structural features,
geologic terrains, surface configurations and their modes of formation
and means of identification. A notable part of the text prepared for
college students relates primarily to phenomena and processes, leaving
the history of the earth to follow later in a seemingly secondary way.
This has its defense in a desire first to make clear the modes of the
geologic processes, to the end that the parts played by these
processes in the complexities of actions that make up the historical
stages may be better realized. This has the effect, however, of giving
the impression that geology is primarily a study of rocks and
rock-forming processes, and this impression is confirmed by the great
mass of descriptive literature that has sprung almost necessarily
from the task of delineating such a multitude of formations before
trying to interpret their modes of origin or to assign them their
places in the history of the earth. The descriptive details are the
indispensable data of a sound history, and they have in addition
specific values independent of their service as historical data. But
into the multiplicity and complexity of the details of structure and
of process, the average college student can wisely enter to a limited
extent only, except as they form types, or appear in the local fields
which he studies, where they serve as concrete examples of
world-forming processes.
=Disciplinary worth of study of geology=
The study of these structures, formations, configurations, and
processes yields each its own special phase of discipline and its own
measure of information. The work takes on various chemical,
mechanical, and biological aspects. As a means of discipline it calls
for keenness and diligence in observation, circumspection in
inference, a judicial balancing of factors in interpretation. An
active use of the scientific imagination is called forth in following
formations to inaccessible depths or beneath areas where they are
concealed from view.
While thus the study of structures, formations and configurations
constitutes the most obtrusive phase of geologic study and has given
trend to pedagogical opinion respecting its place in a college course,
such study is not, in the opinion of the writer, the foremost function
of the subject in a college curriculum that is designed to be really
broad, basal, and free, in contradistinction to one that is tied to a
specific vocational purpose.
=This study concerned primarily with the typical college course, not
with vocational courses=
While we recognize, with full sympathy, that the subject matter of
geology enters vitally into certain vocational and prevocational
courses, and, in such relations, calls for special selections of
material and an appropriate handling, if it is to fulfill these
purposes effectively, this seems to us aside from the purpose of this
discussion, which centers on typical college training--training which
is liberal in the cosmic sense, not merely from the homocentric point
of view.
=Knowledge of geology contributes to a truly liberal education=
To subserve these broader purposes, geology is to be studied
comprehensively as the evolution of the earth and its inhabitants. The
earth in itself is to be regarded as an organism and as the
foster-parent of a great series of organisms that sprang into being
and pursued their careers in the contact zones between its rigid body
and its fluidal envelopes. These contact zones are, in a special
sense, the province of geography in both its physical and its biotic
aspects. The evolution of the biotic and the psychic worlds in these
horizons is an essential part of the history of the whole, for each
factor has reacted powerfully on the others. An appreciative grasp of
these great evolutions, and of their relations to one another, is
essential to a really broad view of the world of which we are a part;
it is scarcely less than an essential factor in a modern liberal
education.
=Geology embraces all the great evolutions=
Let us agree, then, at the outset, that a true study of the career of
the earth is not adequately compassed by a mere tracing of its
inorganic history or an elucidation of its physical structure and
mineral content, but that it embraces as well all the great evolutions
fostered within the earth's mantles in the course of its career.
Greatest among these fostered evolutions, from the homocentric point
of view, are the living, the sentient, and the thinking kingdoms that
have grown up with the later phases of the physical evolution. It does
not militate against this view that each of these kingdoms is, in
itself, the subject of special sciences, and that these, in turn,
envelop a multitude of sub-sciences, for that is true of every
comprehensive unit. Nor is it inconsistent with this larger view of
the scope of geology that it is, itself, often given a much narrower
definition, as already implied. In its broader sense, geology is an
enveloping science, surveying, in a broad historical way, many
subjects that call for intensive study under more special sciences,
just as human history sweeps comprehensively over a broad field
cultivated more intensively by special humanistic sciences. In a
comprehensive study of the earth as an organism, it is essential that
there be embraced a sufficient consideration of all the vital factors
that entered into its history to give these their due place and their
true value among the agencies that contributed to its evolution. A
true biography of the earth can no more be regarded as complete
without the biotic and psychic elements that sprang forth from it, or
were fostered within its mantles, than can the biography of a human
being be complete with a mere sketch of his physical frame and bodily
growth. The physical and biological evolutions are well recognized as
essential parts of earth history. Although the mental evolutions have
emerged gradually with the biological evolutions, and have run more or
less nearly parallel with them--have, indeed, been a working part of
them--they have been less fully and frankly recognized as elements of
geological history. They have been rather scantily treated in the
literature of the subject; but they are, none the less, a vital part
of the great history. They have found some recognition, though much
too meager, in the more comprehensive and philosophical treatises on
earth-science. It may be safely prophesied that the later and higher
evolutions that grace our planet will be more adequately emphasized as
the science grows into its full maturity and comes into its true place
among the sciences. It is important to emphasize this here, since it
is preeminently the function of a liberal college course to give
precedence to the comprehensive and the essential, both in its
selection of its subject matter and in its treatment of what it
selects. It is the function of a liberal course of study to bring that
which is broad and basal and vital into relief, and to set it over
against that which is limited, special, and technical, however
valuable the latter may be in vocational training and in economic
application.
=Physical and dynamic boundaries of geology--Implications for teaching=
In view of these considerations--and frankly recognizing the
inadequacies of current treatment--let us note, before we go further,
what are the physical and dynamic boundaries of the geologic field,
that we may the better see how that field merges into the domains of
other sciences. This will the better prepare us to realize the nature
of the disciplines for which earth-science forms a suitable basis, as
well as the types of intellectual furniture it yields to the mind.
Obviously these disciplines and this substance of thought should
determine the place of the science in the curriculum of any course
that assumes the task of giving a broad and liberal education.
Earth-science is the domestic chapter of celestial science. Our planet
is but a modest unit among the great celestial assemblage of worlds;
but, modest as it is, it is that unit about which we have by far the
fullest and most reliable knowledge. The earth not only furnishes the
physical baseline of celestial observation, but supplies all the
appliances by which inquiry penetrates the depths of the heavens. Not
alone earth-science, as such, but several of the intensive sciences
brought into being through the intellectual evolutions that have
attended the later history of the earth, have been prerequisites to
the development of the broad science of the outer heavens. The science
of the lower heavens is a factor of earth-science in the definition we
are just about to give. At the same time, the whole earth, including
the lower heavens, is enveloped by the more comprehensive domain of
celestial science.
If we seek the most logical limit that may be assigned the realm of
earth-science, as distinguished from that of celestial science, of
which it is the home unit, it may be found at that borderline _within
which_ any passive body obeys the call of the earth, as against the
call of the outer worlds, and _without which_ such a passive body
obeys the call of the outer worlds, the call of the sun in particular.
This limit is the _dynamic dividing line_ between the kingdom of the
earth and the kingdom of the outer heavens. This boundary, according
to Moulton, incloses a spheroid whose minimum radius is about 620,000
miles, and whose maximum radius is about 930,000 miles. We may, then,
conveniently say that the earth's sphere of control stretches out a
million kilometers from its center and that this defines its true
realm. At the same time, this defines the logical limit of the earth's
ultra-atmosphere and appears to mark a zone of exchange between the
ultra-atmosphere of the earth and the ultra-atmosphere of the sun. It
thus appears to imply the place and the mode of an exchange of vital
elements upon which probably hangs the wonderful maintenance of the
earth's atmosphere for many millions of years and the equally
wonderful regulation of the essential qualities of the atmosphere so
that these have always remained within the narrow range subservient to
terrestrial life. It is needless to add that this regulation also
conditions the present intellectual status of the thinking factor
among the inhabitants of the earth out of which--may I be pardoned for
saying?--has grown the present educational discussion.
If this last shall seem to squint toward special pleading, let it be
considered that, as we see things, it is precisely those views that
take hold of the issues upon which our very being and all its
activities depend, that serve best to train youth to broad views and
penetrating thought. Such thinking seems to me to form the very
essence of a really liberal education.
Not only is this definition of the sphere of geology comprehensive,
but it has the special merit of being _dynamic_, rather than material.
Such a dynamic definition comports with the view that earth-study
should center on the forces and energies that actuated its evolution,
since these are the most vital feature of the evolution itself. It is
important to form adequate concepts of the energies that have
maintained the past ongoings of the earth not only, but that still
maintain its present activities and predetermine its future. It is the
study of the forces and the processes of past and of present
evolutions that constitute the soul of the science, rather than the
apparently fixed and passive aspects of the earth's formations and
configurations which are but the products of the processes that have
gone before. Even the apparent passiveness of the geologic products is
illusive, for they are in reality expressions of continued internal
activities of an intense, though occult, order. These escape notice
largely because they are balanced against one another in a system of
equilibrium which pervades them and gives them the appearance of
fixity. To serve their proper functions as sources of higher
education, the concepts of the constitution of the earth should
penetrate even to these refined aspects of physical organization and
should bring the whole into harmony with the most advanced views of
the real nature of physical organisms. This removes from the whole
terrestrial organism every similitude of inertness and gives it a
fundamental refinement, activity, and potency of the highest order. To
form a true and consistent concept, the enveloping earth-science must
be assumed to embrace, potentially at least, the essentials of all
that was evolved within it and from it, with, of course, due
recognition of what was added from without.
_The history of the earth should therefore be taught in college
courses as a succession of complex dynamic events, great in the past
and great in future potentialities._
The formations and configurations left by the successive phases of
action are to be studied primarily as the vestiges of the processes
that gave them birth, and hence as their historic credentials. They
are to be looked upon less as the vital things in themselves, than as
the _record_ of the events of the time and as the forerunners of the
subsequent events that may be potential in them. And so, primarily,
the geologic records are to be scrutinized to find _the deeper
meanings which they embody_, whether such meanings lie in the
physical, the biological, or the psychological world.
=Geology the means of developing scientific imagination of time and space=
Turning to specific phases of the subject, it may first be noted that
geology is singularly suited to develop clear visions of vast
stretches of time; it opens broad visions of the panorama of world
events, a panorama still passing before us. While the celestial order
of things no doubt involves greater lapses of time, these are not so
easily realized, for they are not so well filled in with a succession
of records of the passing stages that make up the whole. But even the
lapses of geologic time are greater than immature minds can readily
grasp; however, their _powers of realization_ are greatly strengthened
by studying so protracted a record, built up stage upon stage. The
very slowness with which the geologic record was made, as well as the
evidences of slowness in each part of the record, help to draw out an
appreciation of the immensity of the whole. The round period covered
by the more legible range of the geologic record rises to the order of
a hundred million years, perhaps to several hundred million years. The
large view of history which this implies has already come to form the
ample background on which are projected the concepts of the broader
class of thinkers; such largeness of view will quite surely be held to
be an indispensable prerequisite to the still broader thinking of the
future for which the better order of students are now preparing.
While this is preeminently true of the concept of time, the concept of
space is fairly well cultivated by geologic study, though far less
effectively than is done by astronomical study. Astronomy and geology
work happily together in contributing to largeness of thought.
The study of the origin and early history of the earth brings the
student into touch with the most far-reaching problems that have thus
far called forth the intellectual efforts of man. If rightly handled,
these great themes may be made to teach the true method of inquiry
into past natural events whose vastness puts them quite beyond the
resources of the laboratory. This method finds its key in a search for
the history of such vast and remote events by a scrutiny of the
vestiges these events have left as their own automatic record. This
method stands in sharp contradistinction to simple speculation without
such search for talismanic vestiges, a discredited method which is too
often supposed to be the only way of dealing with such themes. To be
really competent in the field of larger and deeper thinking, every
courageous mind should be able to cross the threshold of any of the
profound problems of the universe with safe and circumspect steps,
however certain it may be that only a slight measure of penetration of
the problem may be attainable. A well-ordered mind will remain at once
complacent and wholesome when brought to the limit of its effort by
the limit of evidence. The problem of the origin of celestial worlds,
of which the genesis of the earth is the theme of largest human
interest, is admirably suited to give college students at once a
modest sense of their limitations and a wholesome attitude toward
problems of the vaster type. Without having acquired the power to make
prudent and duly controlled excursions into the vaster fields of
thought, the mind can scarcely be said to have been liberalized.
=Geology a means of training in thinking in scientific experiences=
From the very outset, the tracing of the earth history forces a
comprehensive study of the co-workings of the three dominant states of
matter massively embodied in the atmosphere, the hydrosphere, and the
lithosphere, the great terrestrial triumvirate. The strata of the
earth are the joint products of these three elements and constitute
their lithographic record. These three cooperating and contending
elements not only bring into view the three typical phases of physical
action, but they present this action in such titanic aspects as to
force the young mind to think along large lines, with the great
advantage that these actions are controlled by determinate laws, while
the causes and the results are both tangible and impressive.
While there is a large class of tangible and determinate problems of
this kind, embracing shiftings of matter on the earth's surface,
distortions of strata, and changes of bodily form, there are also
problems of a more hidden nature such as internal mutations. These
give rise to mathematical, physical, and chemical inquiries while at
the same time they call into play the use of the scientific
imagination and are thus rich in the possibilities of training. Thus
in varied ways geological work joins hands with chemical, physical,
mechanical, and mathematical work.
When life first appears in the record, there is occasion to raise the
profound question of its origin, and with this arises a closely
related question as to the nature of the conditions that invited life,
which leads on to the further question, what fostered the development
of life throughout its long history? While the obscurity of the
earliest record leaves the question of origin indeterminate for the
present, duly guarded thought upon the subject should foster a
wholesome spirit toward inquiry in this vital line as well as a
hospitable attitude toward whatever solution may finally await us. In
all such studies the student should be invited to look to _the
vestiges left automatically by the process itself_ for the answer, and
he should learn to accept the teachings of evidence precisely as it
presents itself. So also when a problem is, for the present,
indeterminate, it is peculiarly wholesome for the inquirer to learn to
rest the case where the light of evidence fails, and to be complacent
in such suspension of judgment and to wait further light patiently in
serene confidence that the vestiges left by the actuating agencies in
their constructive processes are the surest index of the ultimate
truth and are likely to be sooner or later detected and read truly.
=Relation of geology to botany, zoology, psychology, and sociology=
In the successive records of past life impressed on strata piled one
upon another until they form the great paleontologic register, there
is an ample and a solid basis for the study of the historic evolution
of life. With this also go evidences of the conditions that attended
this life progress and that gave trend to it. This record of the
relations of life to the environing physical conditions forms one of
the most stimulating fields of study that can engage the student who
seeks light on the great problems of biological progress. Here geology
joins hands with botany and zoology in a mutual helpfulness that is
scarcely less than indispensable to each.
Following, or perhaps immediately attending, the introduction of
physiological life, there appeared signs of sentient life. The
preservation of certain of the sense organs, taken together with the
collateral evidences of sense action, as early as Cambrian times,
furnish the groundwork for a historical study of the progress of
sentient life, eventuating in the higher forms of mental life. Here
the problems of geology run hand in hand with the problems of
psychology. The limitations of the evidence bearing on psychological
phenomena, while regrettable, are not without some compensation in
that they center the attention on the simpler aspects of the
protracted deployment of the psychological functions.
In addition to the clear evidences of psychic action, in at least its
elementary forms, there appeared early in the stratigraphic records
intimations of some of the relationships that sentient beings then
bore to one another; and this relationship gives occasion to study the
primitive aspects of sociological phenomena. If nothing more is
learned than the important lesson that sociology is not a thing of
today, not an untried realm inviting all kinds of ill-digested
projects, but on the contrary is a field of vast and instructive
history, the gain will not be inconsiderable. There are intimations of
the early existence and effective activity of those affections that
precede and that cluster about the parental relationship, the nucleus
of the most vital of all the sociological relationships. In contrast
to the affections, there are distinct evidences of antagonistic
relations, of pursuit and capture, of attack and defense; there were
tools of warfare and devices for protection. In time, a wide-ranging
series of experiments, so to speak, were tried to secure advantage, to
avoid suffering, to escape death, and to preserve the species. There
were even suggestions of the cruder forms of government. The many
stages in the evolution of the various devices, as well as the stages
of their abandonment, that followed one another in the course of the
ages recorded the results of a multitude of efforts at sociological
adjustment. They raise the question whether a common set of guiding
principles does not underlie all such relationships, earlier and
later, whatever their rank in our scale of valuation. And so this
great field of inquiry--too narrowly regarded as merely
humanistic--comes into view early in the history of the earth. The
geological and the sociological sciences find in it common working
ground. If the geologic and the humanistic sciences are given each
their widest interpretation and their freest application, the
advantage cannot be other than mutual.
It is perhaps not too much to say that studies in the physiological,
the psychological, the sociological, and the allied fields necessarily
lack completeness if they do not bring into their purview the data of
their common historical record traced as far back as it is found to
contain intimations of their actual extension.
It is customary to speak of the geologic ages as though they were
wholly past; they are, indeed, chiefly past as the record now stands,
but time runs on and earth history continues; the processes of the
past are still active, and they are likely to work on far into the
future. And so geologic study links itself fundamentally into all such
present terrestrial interests as take hold of the distant future. The
forecast of the earth's endurance, attended by conditions congenial to
life and to the mental and moral activities, hinges on a sound insight
into the great actuating forces inherent in the earth, together with
those likely to come into play from the celestial environment. All
human interests, in so far as they are dependent on a protracted
future, center in the prognosis of the earth based on its present and
its past. The latest phases of geologic doctrine prophesy a long
future habitability of the earth. They thus give meaning and emphasis
to the deeper purposes sought in all the higher endeavors, not the
least of which is education, particularly those phases of education
that lead to effects which may be handed down from age to age.
=Standard for selecting subject matter for the general college course:
select fundamentals or that which bears on fundamentals=
Out of all this vast physical, biological, and psychological history,
the things to be selected for substance of thought and for service in
mental training in a college course are, first of all, those that are
either fundamental in themselves, or that have vital bearings on what
is fundamental. These are chiefly the great dynamic factors, the
agencies that gave trend to the master events, the forces that
actuated the basal processes by which the vast results were attained.
The material formations and the surficial configurations that resulted
are to be duly considered, to be sure, for they form the basis of
interpretation and they are, besides, the repositories of economic
values of indispensable worth; but, as already urged, in a course of
intellectual training, these are to be regarded rather as the relics
of the great agencies and the proofs of their actions, than as the
most vital subjects of study, which are the agencies themselves. As
already remarked, the geologic formations are to be treated rather as
the credentials of the potencies that reside in the earth organism,
than as the vital things themselves. The vestiges of creation and the
footprints of historical progress embody the soul of the subject; they
constitute the chief source of inspiration to those who aspire to
think in large, deep ways of really great things. It is of little
value, from the viewpoint of liberal culture, to know that there is a
certain succession of sandstones, shales, and limestones; that
professional convention has given them certain names, more or less
infelicitous in derivation and in phonic quality; but it is of vital
consequence to learn how and why these relics of former processes came
to be left as they were left, and thus came to be witnesses to the
history of the far past. It was a wise thing, no doubt, that the
fathers of geology strongly insisted that there should be a rigorous
and rather literal adhesion to the terrestrial record in all earth
studies, because in those times of transition from the loose, more or
less fantastic thought that marked the adolescent stage of the human
race, it was imperative that students should stick close to the
immediate evidence of what had transpired, and should withhold
themselves from much enlargement of view based on the less tangible
evidences; but at the present stage, when the general nature of the
earth's history has been firmly established, it would be an error on
the part of those who seek for the most liberalizing and broadening
values of the science, to treat the record merely as a material
register of immediate import only, to the neglect of the less tangible
but more vital teachings immanent in its great forces and processes.
The seeker of liberal culture should direct his attention to the great
events, and, above all, to the larger and deeper meanings implied by
these events.
And so--may I be pardoned for reemphasizing?--the teacher of geology
whose essential purpose is liberal training, leading to broad and firm
knowledge and to sound processes of thought, will critically observe
the distinction between geology taught appropriately from the
collegiate point of view, and geology taught specifically from the
professional and technical points of view. In these latter, specific
details in specific lines are important, and may even be essential,
but it is the function of the college teacher of geology _to select_
from the great mass of material of the science such factors as are
basal, vital, and talismanic. He will give these emphasis, while he
neglects the multitude of details that lack significance as working
elements or as landmarks of progress, whatever their value in other
relations. This selection is equally important, whether applied to the
great physical processes that have shaped the earth into its present
configuration, or to the great chemical and mineralogical processes
that have determined its texture and its structure, or to the great
biological and psychological processes that have given trend to the
development of its inhabitants.
Even if the undergraduate course in geology is pursued less for the
purpose of liberal culture than as a means of preparing for a
professional career as an economic geologist, no essential departure
from an effort to master first the basal features and the broader
aspects of the science, especially the dynamic aspects, is to be
advised. The shortest road to _declared success_ in professional and
economic geology lies through the early mastery of its fundamentals.
No doubt immediate and apparent success may often be sooner reached by
a narrower and shallower study of such special phases of the subject
as happen just now to be most obviously related to the existing state
of the industries; but industrial demands are constantly
changing--indeed, at present, rather rapidly--and new aspects follow
one another in close succession. These new aspects almost inevitably
spring from the more basal factors as these rise into function with
the progress of experience or the stress of new demands. Those who
have sought only the immediate and the superficial, at the expense of
the basal, and especially those who have neglected to acquire _the
power and the disposition to search out the fundamentals_, are quite
sure to be left among the unfortunates who trail behind; they are
little likely to be found among those who lead at the times when
leadership counts. In the judgment of those master minds that lead in
affairs and that take large and penetrating views, the lines along
which the most vital contributions to economic interests are being
made connect closely with basal studies of the actuating agencies that
condition great enterprises. In the judgment of the writer, it is a
false view to suppose that any short, superficial study of so vast a
subject as the constitution and history of the earth can result in
economic competency. In so far as time for study is limited, it should
be concentrated on the great underlying factors that constitute the
essentials of the science. It is here assumed that men who care to
take a college course at all are seeking for a large success and are
ambitious for a high personal career. If they look ultimately to
professional work in economic lines, they may safely be advised that
the straight road to declared success lies in a search for the vital
forces, the critical agencies, and the profound principles that make
for great results, not along the by-paths whose winding, superficial
courses are turned hither and thither by adventitious conditions whose
very nature invites distrust rather than confidence.
=Evaluations of methods of teaching=
Turning to some of the more formal phases of treatment, three types of
work are presented: (1) the use of nature's laboratory, the world
itself, (2) the use of the college collections and laboratories, and
(3) the use of the literature of the subject.
(1) Fortunately, there is no place on the face of the earth where
there is not some natural material for geologic study, for even in the
most artificialized locations geological processes are active. In
crowded cities these processes may be easily overlooked, but yet they
are susceptible of effective use. Within easy access from almost every
college site there are serviceable fields of study, and these, in any
live course, will be assiduously cultivated. They may be relatively
modest in their phenomena; they may seem to lack that impressiveness
which has played so large a part in the popular notion of the content
of geology, but they may nevertheless serve as most excellent training
grounds for young geologists. If students are so situated as to be
brought at the beginning of study under the influence of very
impressive displays of geologic phenomena--precipitous mountains,
rugged cliffs, deep canyons, and the like--there is danger that their
mental habits may become diffusive rather than close and keen; the
emotions may be called forth in wonder rather than turned into zest in
the search for evidence. If students are to be trained to diligence in
inquiry and to the highest virility in inference and interpretation,
it is perhaps fortunate for them if they are located where only modest
records of geological processes are presented for study. In such
regions they are more likely to be led to scrutinize the field keenly,
sharply, and diligently for data on which to build their
interpretations. The scientific use of their imaginations is all the
better trained if, in their endeavor to build up a consistent concept
of the whole structure that underlies their field, they are forced to
project their inferences from a few out-crops far beneath the cover of
the adjacent mantle that shuts off direct vision. Few teachers have,
therefore, any real occasion to long for richer fields than those
accessible to them, if they have the tact to render these fertile in
stimulus and suggestion.
(2) Laboratory work upon the material collected in the field work, as
well as laboratory work upon the college collections, are essential
adjuncts. Ample provisions for this supplementary work, however modest
the appointments, are important and can usually be secured by
ingenuity and diligence in spite of financial limitations.
Both field and laboratory work should be well correlated with one
another and with the systematic work on the text that guides the
study, so that each shall whet the edge of the other and all together
accomplish what neither could alone.
(3) The text selected should be such as lends itself, in some notable
degree at least, to the general purposes set forth above. It should be
supplemented, so far as may be, by judicious assignments for reading
and for special study. Lectures may be made a valuable aid to the
discussions of the classroom, but with college classes they can rarely
be made an advantageous substitute for the discussions. Lecturing, so
far as used, is best woven informally into the classroom discussions.
Supplementary lecturettes may be advised if they are of such an
informal sort that they may almost unconsciously take their start from
any vital point encountered in the course of discussion, may run on as
far as the occasion invites, and may then give way again to the
discussion with the utmost informality. Such little participations in
the work of the classroom, on the part of the teacher, are likely to
be cordially welcomed. At the same time, if well done, they will set
an excellent example in the presentative art as also in an apt
organization of thought.
=Organization of courses=
If the stated course in earth-science is limited to the junior and
senior year by the existing requirements of the curriculum of the
institution or by the rulings of its officers--as is not uncommonly
the case at present--it is relatively immaterial whether the sections
of the course are marshaled under the single name "geology" or whether
they are given separate titles as sub-sciences, provided the special
subjects are arranged in logical sequence and in consecutive order.
If, on the other hand, the teacher's choice of time and relations is
freer, the more accessible phases of earth study, now well organized
under the name of "physiography," form an excellent course for either
freshmen or sophomores. It opens their minds to a world of interesting
activities about them which have probably been largely overlooked in
previous years. It gives them substance of thought that will be of
much service in the pursuit of other sciences. It has been found that
it is not without rather notable service to young students as the
basis of efforts in the art of literary presentation, a felicity to
which teachers of this important art frequently give emphatic
testimony. The secret seems to lie in the fact that physiography gives
varied and vivid material susceptible of literary presentation, while
the fixed qualities of the subject matter control the choice of terms
and the mode of expression.
If geography and physiography are given in the earlier years, the
course in historical geology, as well as the study of the more
difficult phases of geological processes, of the principles of dynamic
geology, together with mineralogy, petrology, and paleontology, may
best fall into the later years, even if some interval separates them
from the geography and physiography.
One hundred and twenty classroom hours, or their equivalent in
laboratory and field work, are perhaps to be regarded as the
irreducible minimum in a well-balanced undergraduate course, while
twice that time or more is required to give a notably strong college
course in earth-science.
A consideration of the sequences among the geological sub-subjects, as
also among the subjects that are held to be preliminary to the
earth-sciences, is important, but it would lead us too far into
details which depend more or less on local conditions. In the
experience of American teachers it appears to have been found
advisable to put geological processes and typical phenomena to the
front and to take up geological history afterwards. The earlier method
of taking up the history first, beginning with recent stages and
working backward down the ages,--once in vogue abroad,--has been
abandoned in this country. It was the order in which the science was
developed and it had the advantage of starting with the living present
and with the most accessible formations, but this latter advantage is
secured by studying the living processes, as such, first, and turning
to the history later. This permits the study of the history in its
natural order, which seems better to call forth the relations of
cause and effect and to give emphasis to the influence of inherited
conditions.
Respecting antecedents to the study, the more knowledge of physics,
chemistry, zoology, and botany, the better, but it is easy to
over-stress the necessity for such preparation, however logical it may
seem, for in reality all the natural sciences are so interwoven that,
in strict logic, a complete knowledge of all the others should be had
before any one is begun, a _reductio ad absurdum_. The sciences have
been developed more or less contemporaneously and progressively, each
helping on the others. They may be pursued much in the same way, or by
alternations in which each prior study favors the sequent one. They
may even be taken in a seemingly illogical order without serious
disadvantage, for the alternative advantages and other considerations
may outweigh the force of the logical order, which is at best only
partially logical. It is of prime importance to stimulate in students
a habit of observing natural phenomena at an early age. It may be wise
for a student to take up physiography, or its equivalent, early in the
college course, irrespective of an ideal preparation in the related
sciences. It is unfortunate to defer such study to a stage when the
student's natural aptitude for observation and inference has become
dulled by neglect or by confinement to subjects devoid of naturalistic
stimulus. To permit students to take up earth-science in the freshman
and sophomore years, even without the ideal preparation, is therefore
probably wiser than to defer the study beyond the age of
responsiveness to the touch of the natural environment. The geographic
and geologic environment conditioned the mental evolution of the race.
It left an inherited impress on the perceptive and emotional nature,
only to be awakened most felicitously, it would seem, at about the age
at which the naturalistic phases of the youth's mentality were
originally called into their most intense exercise.
T. C. CHAMBERLIN
_The University of Chicago_
VIII
THE TEACHING OF MATHEMATICS
=Recent changes and some of their sources=
In recent years the teaching of mathematics has undergone remarkable
changes in many countries, both as regards method and as regards
content. With respect to college mathematics these changes have been
evidenced by a growing emphasis on applications and on the historic
setting of the various questions. To understand one direct source of
these changes it is only necessary to recall the fact that in about
1880 there began a steady stream of American mathematical students to
Europe, especially to Germany. Most of these students entered the
faculties of our colleges and universities on their return to America
It is therefore of great importance to inquire what mathematical
situation served to inspire these students.
The German mathematical developments of the greater part of the
nineteenth century exhibited a growing tendency to disregard
applications. It was not until about 1890 that a strong movement was
inaugurated to lay more stress on applied mathematics in Germany.[3]
Our early American students therefore brought with them from Germany a
decided tendency toward investigations in mathematical fields remote
from direct contact with applications to other scientific subjects,
such as physics and astronomy, which had so largely dominated
mathematical investigations in earlier years.
This picture would, however, be very incomplete without exhibiting
another factor of a similar type working in our own midst. J. J.
Sylvester was selected as the first professor of mathematics at Johns
Hopkins University, which opened its doors in 1876 and began at once
to wield a powerful influence in starting young men in higher
research. Sylvester's own investigations related mainly to the formal
and abstract side of mathematics. Moreover, "he was a poor teacher
with an imperfect knowledge of mathematical literature. He possessed,
however, an extraordinary personality; and had in remarkable degree
the gift of imparting enthusiasm, a quality of no small value in
pioneer days such as these were with us."[4]
=Influence of researches in mathematics on methods of teaching=
Mathematical research was practically introduced into the American
colleges during the last quarter of the nineteenth century, and the
wave of enthusiasm which attended this introduction was unfortunately
not sufficiently tempered by emphasis on good teaching and breadth of
knowledge, especially as regards applications. In fact, the leading
mathematician in America during the early part of this period was
glaringly weak along these lines. By means of his bountiful enthusiasm
he was able to do a large amount of good for the selected band of
gifted students who attended his lectures, but some of these were not
so fortunate in securing the type of students who are helped more by
the direct enthusiasm of their teacher than by the indirect enthusiasm
resulting from good teaching.
The need of good mathematical teaching in our colleges and
universities began to become more pronounced at about the time that
the wave of research enthusiasm set in, as a result of the growing
emphasis on technical education which exhibited itself most
emphatically in the development of the schools of engineering. While
the student who is specially interested in mathematics may be willing
to get along with a teacher whose enthusiasm for the new and general
leads him to neglect to emphasize essential details in the
presentation, the average engineering student insists on clearness in
presentation and usability of the results. As the latter student does
not expect to become a mathematical specialist, he is naturally much
more interested in good teaching than in the mathematical reputation
of his teacher, even if his reputation is not an entirely
insignificant factor for him.
During the last decade of the nineteenth century and the first decade
of the present century the mathematical departments of our colleges
and universities faced an unusually serious situation as a result of
the conditions just noted. The new wave of research enthusiasm was
still in its youthful vigor and in its youthful mood of
inconsiderateness as regards some of the most important factors. On
the other hand, many of the departments of engineering had become
strong and were therefore able to secure the type of teaching suited
to their needs. In a number of institutions this led to the breaking
up of the mathematical department into two or more separate
departments aiming to meet special needs.
In view of the fact that the mathematical needs of these various
classes of students have so much in common, leading mathematicians
viewed with much concern this tendency to disrupt many of the stronger
departments. Hence the question of good teaching forced itself rapidly
to the front. It was commonly recognized that the students of pure
mathematics profit by a study of various applications of the theories
under consideration, and that the students who expect to work along
special technical lines gain by getting broad and comprehensive views
of the fundamental mathematical questions involved. Moreover, it was
also recognized that the investigational work of the instructors would
gain by the broader scholarship secured through greater emphasis on
applications and the historic setting of the various problems under
consideration.
To these fundamental elements relating to the improvement of college
teaching there should perhaps be added one arising from the
recognition of the fact that the number of men possessing excellent
mathematical research ability was much smaller than the number of
positions in the mathematical departments of our colleges and
universities. The publication of inferior research results is of
questionable value. On the other hand, many who could have done
excellent work as teachers by devoting most of their energies to this
work became partial failures both as teachers and as investigators
through their ambition to excel in the latter direction.
=Range of subjects and preparation of students=
It should be emphasized that the college and university teachers of
mathematics have to deal with a wide range of subjects and conditions,
especially where graduate work is carried on. Advanced graduate
students have needs which differ widely from those of the freshmen who
aim to become engineers. This wide range of conditions calls for
unusual adaptability on the part of the college and university
teacher. This range is much wider than that which confronts the
teachers in the high school, and the lack of sufficient adaptability
on the part of some of the college teachers is probably responsible
for the common impression that some of the poorest mathematical
teaching is done in the colleges. It is doubtless equally true that
some of the very best mathematical teaching is to be found in these
institutions.
In some of the colleges there has been a tendency to diminish the
individual range of mathematical teaching by explicitly separating the
undergraduate work and the more advanced work. For instance, in Johns
Hopkins University, L. S. Hulburt was appointed "Professor of
Collegiate Mathematics" in 1897, with the understanding that he should
devote himself to the interests of the undergraduates. In many of the
larger universities the younger members of the department usually
teach only undergraduate courses, while some of the older members
devote either all or most of their time to the advanced work; but
there is no uniformity in this direction, and the present conditions
are often unsatisfactory.