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 coöperation 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, Σmr2. 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