essary for the right understanding of the economic and commercial conditions of our own and other countries. For the localization of a people and the distribution of their industries within any one country and throughout the world generally can be made thoroughly intelligible only when our geography teaching has clearly realized this as its ultimate aim, and when the knowledge has been imparted to the pupil according to a sound. method. As the final result of our teaching of geography, we should have made our pupils realize not merely that a certain city or town is placed here or there, but why this is so; not merely that it has such and such industries, but why these industries are located here and not elsewhere; and lastly, they must understand the use and function the particular city plays in the economic and social life of the nation and of the world. generally. Only in so far as we have done this can we be said. to have taught the subject at all. Further, while the economic and commercial aspect of this subject is so important for a country such as ours, from the narrow utilitarian point of view, that the knowledge and training is necessary for all those who intend in after life to enter upon a commercial career, yet it is also important from the fact that it is only by a method which endeavors to attain the end of showing the value of Geography for the understanding and interpretation of the economic and social life of a people that we can really educate the child and train his reason. The best method of imparting geographical knowledge is to go direct to nature and learn from direct observation the causal interaction of a physical fact, and how the natural and physical features of a country or district determine the social and economic life of the people. This was the method of Rousseau; still more was it the method of that much greater educationalist, Pestalozzi, in the teaching of Geography. The cardinal principle of the educational method of Pestalozzi was that the symbol should never be given to the child until he had comprehended the thing signified by the symbol, and we are told that once when his own child used a term without a knowledge of the thing signified by it, he wept from sorrow at finding such an example of educational depravity in his own offspring. In his teaching of Geography Pestalozzi carried out thoroughly the maxim of presenting the symbol only after the thing itself was comprehended. In the once famous school at Burgdorf, the children along with their teacher explored the country in the neighborhood of the school, collecting clay in baskets from the river banks, and on their return modeled day by day what they had learned of the physical nature of their environment and of the interconnection of physical feature to physical feature. Only after this had been thoroughly comprehended from the clay model was a flat map introduced and the relation of model to map explained. In our present-day teaching of Geography this method of going direct to nature should be employed wherever possible, and especially in the earlier stages, and any other method must be judged good or bad according as it approximates or falls short of the direct method. But under the altered conditions of our time and especially ir our large towns, the method of going direct to nature can be followed only to a limited extent, and, further, the method has limitations in itself which make its consistent use inapplicable under existing conditions, for it is obvious that the direct method. is always limited by the narrow range of the child's environment. Again, the best method of teaching here, as in so many other subjects, cannot be employed in its entirety even if it were possible on account of the limited time in which the knowledge must be imparted. Hence the direct method must be supplemented by others, and all these subsidary methods must have for their aim the endeavor to make Geography a real, a concrete, and a living subject of instruction. If the Geography teaching of our schools has only for its results the memorizing of lists of names extracted from a book or gleaned from the unintelligent and premature use of a map, then whatever we may be doing we are not educating the child. Nay, more, by such methods we not only kill the child's present interest in the subject, but also fail to foster any future or later interest; and in many cases such teaching tends to make the child grow up dull, stupid, and un-· imaginative, and with reason dormant about the world in which he lives. But we must also remember that the mere picturing of a district or of a country is not sufficient; the child at a later stage must be trained to employ his reason in the perception of the causal interrelations at work. But if we limited our teaching of Geography to the mere understanding of the child's own district and his own country; if our only aim were to make him realize how many factors have to be taken into account in the thorough interpretation of any one region, then we should not attain the highest results, and we should fail to realize all that we should endeavor to do in our Geography teaching. In addition to this we must further endeavor to lead our pupils to a knowledge and understanding -imperfect it may be of the world as a whole and of the relation, position, and place of his own country to the whole. It is not sufficient that we should know how to lead our pupil to understand and interpret his immediate physical environment, nor is it sufficient to know how to make him best realize the place and function of his own country on this terrestrial globe. We must further endeavor to make him comprehend the nature of the Universe as a whole and how this planet on which he lives is related to the solar system of which it froms a part and to other systems which the starry heavens reveal to our gaze. We may thus lead him to understand the vastness. the complexity, the grandeur, and the mystery of this Universe in which man at times seems to play but a poor and sorry part. -Extracted from the Scottish Geographical Magazine, September, 1906. THE AGRICULTURAL HIGH SCHOOL. Bainbridge, N. Y. Although it is true that we have but three leading types of high schools, "literary," "commercial," and "manual training," there is still a fourth that is attracting some attention, and which is likely to come in for a somewhat general consideration. I refer to the agricultural high school. The agricultural school can hardly be classed with the manual training school, for it has so many distinct features. Like those schools, however, it is not to be considered industrial, but chiefly educational. A prominent representative of the Educational Department of one of our great states said recently in a public address that "the scholarship of agriculture is a scholarship that stands with that of Greek or Latin." It is undoubtedly true, however, as was remarked by an official of the Agricultural Department of that same state only the day before the utterance just quoted, that, "in the estimation of the so-called scholarly world, the agricultural college graduate does not rank with the graduate of the literary college." And he added, "To my mind, this is wrong." Whatever may be regarded as the truth respecting the scholarship of the two college courses mentioned, the fact remains that we have the two courses, both requiring, practically, the same degree of preparation, and the same length of time for graduation. The agricultural high school is also an accomplished fact, with as complete a curriculum as the literary school, and requiring as highly trained a teacher, at least, in point of time spent. Various state educational departments have been active in some degree in promoting agricultural high schools. In New England, one state, New Hampshire, seems to stand out more prominently than the rest in this respect. In those schools an agricultural college graduate is in charge. The schools are not large and the principal has immediate charge of the work, not only of the agricultural curriculum, but of the literary and commercial as well, all three courses being taught by competent teachers. English is taught in every year in each course, algebra the first year and geometry the second. The agricultural course has a year of botany, one year of zoology and physiology, one of physics, and one of chemistry. There is the equivalent of one year in agronomy, rural engineering and horticulture, a half year in plant pathology and another half in a study of insects. and insecticides. There are four credits, out of a possible five for a year in one study, in animal industry and dairying, and two credits for a study of farm management. Two years are given to the study of French. THE TEACHER OF MATHEMATICS.* BY HENRY L. COAR, PH.D. Marietta, Ohio. One of the marked advances in the educational field in recent years is the recognition of the advantage of having teachers in charge of the various departments of our high schools, who have had some special training in their respective branches and who know a good deal more of the subject than they are expected to teach. This is particularly marked in the case of the so-called natural sciences. For some reason, however, this advantage has not been as much recognized in the field of mathematics, and we still find school authorities who seem to labor under the impression that anyone who has studied any algebra, is perfectly capable of teaching the subject, if he is capable of teaching at all. In the case of the higher institutions of learning much greater demands are being made of the teacher than were made even a few years ago, and a man must have had considerable training in mathematics to become the head of such a department, even in our smaller colleges. One reason for this is that the study of mathematics is being pursued by an ever increasing number of young men, and as a result, there are usually several well prepared candidates for every vacancy of this kind. For similar positions in the high school, however, we do not find the same number of similarly prepared candidates. In order that the last statement may not be misunderstood, it is necessary to define the status of a well prepared teacher of mathematics for the high school. The question has been more or less discussed by mathematicians, and they now seem fairly well agreed as to what shall constitute a reasonable minimum of special training for a man to take charge of the department of mathematics in a high school. This minimum embraces the following subjects: College Algebra, Trigonometry, Analytic Geometry, Calculus, Advanced Algebra (Theory of Equations and Determinants), History and Pedagogy of Mathematics, Physics (i. e., some applied work), Modern language, preferably German. This minimum requirement may seem somewhat high, but *Read before the Mathematics Section of the Central Association of Science and Mathematics Teachers on December 1, 1906, at the University of Chicago. |