TABLE 4. Years of study of geometry-Continued. Age. 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 Age.. School year.. Austria: TABLE 6.- Years of study of analytic geometry and the calculus. The calculus. Gymnasium, 2-year.. Realschule, 2-year.. Realgymnasium, 2-year... Belgium: Analytic geometry. 14-15 15-16 16-17 17-18 18-19 14-15 15-16 16-17 17-18 18-19 XVI. CERTAIN IMPORTANT POINTS OF DIFFERENCE BETWEEN THE WORK IN MATHEMATICS ABROAD AND IN THE UNITED STATES. The European schools are doing certain kinds of work that we are not doing, some that we can not hope to do under present conditions, and some that we might not care to do if we could. They are also doing some work that we wish we could do, and some that we shall probably do before many years have elapsed. In every country of Europe the secondary school period extends over at least six years. In most of the countries the majority of the teachers above the primary school have had the advantage of college or university training. The teachers have a margin of scholarship that is not common among teachers in the United States. Abundant provision is made for daily drill in mathematics. The educator of Europe realizes that this daily drill is absolutely necessary in order to give the pupil a real mastery of number facts and relations. A little smattering of the subject will not suffice. The pupil is expected to know thoroughly certain facts and principles, and to this end daily drill is provided. No small part of the thoroughness in detail, which is so characteristic of most of the schools of Europe, may be traced to this drill. The American pupil has some information on a great variety of topics, but much of his knowledge is vague and indefinite, rather than clear-cut notions about definite things. Everywhere algebra is introduced earlier than in the United States. In certain of the German schools some work in algebra is introduced during the sixth school year, and in no country, except the United States, is this introductory work postponed later than the seventh school year. Some instruction in constructional, observational, or intuitive geometry is always offered during the sixth, seventh, and eighth school years. This instruction is always of a propedeutic nature. Much emphasis is placed upon estimates and constructions. In all of the schools of Europe algebra and geometry are studied simultaneously during a considerable number of years. The various mathematical subjects are more closely correlated than in this country. A pupil who is studying geometry can use his arithmetic and his algebra more readily than is the case with the average American boy. The introduction of the trigonometric functions while the pupil is studying similar figures in geometry has the sanction of most of the best teachers abroad. The distinction between plane and solid geometry is much less marked than in this country. This is due, in part at least, to the fact that models are very extensively used in the study of geometry. Everywhere the attempt is being made to find genuine applications of mathematics that are really within the experience of the pupil and to link the subject of mathematics as closely as possible with the activities of real life. Drawing and physics are frequently taught by the same teacher, and the correlation between these subjects is found to be to the advantage of each. European school men believe that a course in mathematics should be planned by those who know some mathematics rather than by educators who are practically ignorant of the subject. The reports do not indicate that the schools of Europe are hearing a demand for weak algebra and anemic geometry, or even for no work in these subjects. If any pressure of this sort exists, it has hitherto produced no modification of the course of study. XVII. BIBLIOGRAPHY. All of the reports submitted to the International Commission on the Teaching of Mathematics were consulted in the preparation of this bulletin. The reports listed below contain material of especial value for such a study as this. They may be secured from Messrs. Georg & Co., Geneva, Switzerland. AUSTRIA. Kraus, K. Volks-und Bürgerschulen. Heft I of the Austrian reports. Bergmann, F. Realschulen. Heft I of the Austrian reports. Dintzl, E. Gymnasien. Heft III of the Austrian reports. Konrath, Th. Mädchenlyzeen. Heft IV of the Austrian reports. Adler, A. Der Unterricht in der darstellenden Geometrie an den Realschulen und Realgymnasien. Heft IX of the Austrian reports. Müller, E. Der Unterricht in der darstellenden Geometrie an den Technischen Hochschulen. Heft IX of the Austrian reports. |