What is the meaning of it all? What is its relation to life? There is no doubt that much of this mathematics has its application to life's needs, and that these successive subjects of mathematics are thoroughly interdependent. But nothing in the mode of instruction leads the student to see either the application or the interrelation of all this higher mathematics. Would it not be better to give a single course called mathematics rather than these successive subjects? Would it not be more enlightening if each new mathematical principle were taught through a situation in building, engineering, or mechanics so that the student would at all times see the intimate relation between mathematical law and physical forces? Would not the disciplinary values of mathematics be intensified for the student by teaching it in a way that presents a quantitative interpretation of the daily phenomena in his experience?
Teachers of philosophy and psychology too often fall into a formalism that robs their subject of all its vitalizing influences. Many a student enters his course in logic with high hopes. At last he is to learn the laws of thought which will render him keen in detection of fallacies and potent in the presentation of argument. How bitter is his disappointment when he finds his course dissipated in definitions and classifications. His logic gives itself to the discussion of such patent fallacies as, "A good teacher knows his subject; Williams knows his subject, therefore he is a good teacher." Day after day he proves the error in every form of stupidity or the truth of what is axiomatic. He tires of "Gold is a metal" and "Socrates is mortal." Few courses in logic have the courage to break away from the traditional formalism and to begin each new principle or fundamental concept of logic by analyzing editorials, arguments, contentions in newspapers, magazines, campaign literature, or the actual textbooks. Few students complete their course in logic with a keener insight into thought and with a maturer or more aggressive mental attitude.
Beginning at the point of contact relates the subject to the life of the student
It was pointed out in a previous illustration that the college student "taking philosophy" is seldom made to feel that the subject he studies is related to the problems that arise in his own life. Too frequently introductory courses in philosophy are historical and extensive in scope, striving to develop mastery of facts rather than to give new viewpoints. The student learns names of philosophers, and attempts to memorize the philosophic system developed by each thinker. Such a course imposes a heavy burden on retentive power, for no little effort is required to remember the distinctive philosophical systems advocated by the respective writers. To the students these philosophers represent a group of peculiar people differing one from the other in their degrees of "queerness." One system is as far removed as another from the life that the student experiences; no system helps him to find himself. An introductory course in philosophy should begin with the problems of philosophy; it should have its origin in the reflective and speculative problems of the student himself. As the course progresses, the student should feel a growing sense of power, an increasing ability to formulate more clearly, to himself at least, the questions of religion and ethics that arise in the life of a normal thinking person. So, too, courses in ethics and psychology lose the vital touch unless they begin in the life of the student and apply their lessons to his social and intellectual environment.
It must be pointed out, however, that the social sciences lend themselves more readily to this intimate treatment than do languages, or the physical sciences, but at all points possible in the study of a subject, the experience of the student must be introduced as a means of giving the subject real meaning. In teaching composition and rhetoric illustrations of the canons of good form need not be restricted to the past. Current magazines and newspapers are not devoid of effective illustrations. When the older literary forms are used exclusively as models of language, the student ends his course with the erroneous notion that contemporary writing is cheap and sensational and devoid of artistic craftsmanship.
Courses in physics and chemistry frequently devote themselves to a development of principles rather than to the applications of the studies to every sphere of life. Introductory college courses in zoölogy spend the year in the minutiæ of the lowest animal forms and rarely reach any animal higher in the scale than the crayfish. We still find students in botany learning the various margins of leaves, the system of venation, the scientific classifications, but at the end of the course, unable to recognize ordinary leaves and just as blind to nature as they were before. Zoölogy and botany do not always—as they should—give a new view of life, a new attitude towards living phenomena, a new contact with nature.
Careful inquiry among college students will reveal an amazing ignorance of common chemical and physical phenomena after full-year courses in chemistry and physics. We find a student giving two semesters to work in each of these subjects. He spends most of his time learning the chemical elements, their characteristics and the modes of testing for them. The major portion of the time is spent in the laboratory, where he must discover for himself the elementary practices of the subject and test the validity of well-established truths. At the end of his second semester he has not developed sufficient laboratory technique for significant work in chemistry; he is ignorant of the chemical explanation of the most common phenomena in life.
Pedagogical vs. logical organization
There is much to be said for the position taken by the "older teachers," who may not possess the scholarship of the "younger investigators" but who argue for a general course in which laboratory work shall be reduced, technique minimized, and attention focused on giving an extensive view of chemical forces. The simple chemical facts in digestion, metabolism, industry, war, medicine, etc., would be presented in such a way as to make life a more intelligent process and to give an insight into the method of science. In the courses that follow the introductory one, there would be a marked change in aim; the student would be taught the laboratory technique and would be given a more intensive study of the important aspects of chemistry. Similar changes in the introductory courses in physics are urged by these same teachers.
Beginning at the point of contact may frequently interfere with the logical arrangement of the course of study; it may wrench many a topic out of its accustomed place in the textbook; it will demand that the applications, which come last in most logically arranged courses, be given first and that definitions and principles which come first be given last. This logical arrangement, it was pointed out, is usually the expression of the matured mind that is thoroughly conversant with every aspect of a subject; it may mean little, however, to the beginner—so little that he does not even slightly appreciate its significance. The loss in logical sequence entailed by beginning at the point of contact is often more than compensated for by the advantages which are derived from a psychological presentation.