UNITED STATES BUREAU OF EDUCATION BULLETIN, 1915, NO. 39 WHOLE NUMBER 666 THE TRAINING OF ELEMENTARYSCHOOL TEACHERS IN MATHEMATICS IN THE COUNTRIES REPRESENTED IN saac By Leon ASSOCIATE IN EDUCATIONAL ADMINISTRATION, TEACHERS COLLEGE, COLUMBIA UNIVERSITY, AND SPECIALIST IN EDUCATION, CARNEGIE FOUNDATION FOR THE ADVANCEMENT OF TEACHING With the Editorial Cooperation of DAVID EUGENE SMITH, WILLIAM F. OSGOOD, r. w. A. YOUNG MEMBERS OF THE COMMISSION FROM THE UNITED STATES ADDITIONAL COPIES OF THIS PUBLICATION MAY BE PROCURED FROM THE SUPERINTENDENT OF DOCUMENTS GOVERNMENT PRINTING OFFICE WASHINGTON, D. C. AT 10 CENTS PER COPY CONTENTS. General career of candidates for teaching profession. Elementary school mathematics.. 3 THE TRAINING OF ELEMENTARY-SCHOOL TEACHERS IN MATHEMATICS IN THE COUNTRIES REPRESENTED IN THE INTERNATIONAL COMMISSION ON THE TEACHING OF MATHEMATICS. INTRODUCTION. The accompanying report deals with the mathematical training of prospective teachers in elementary schools as described in the reports submitted by the International Commission on the Teaching of Mathematics to the Fifth International Congress of Mathematicians, held at Cambridge, England, in August, 1912. A comparative study of the facts presented in these reports is of interest for those engaged in the training of teachers in this country, if only because they indicate that the standards elsewhere are as chaotic as they are here. The requirements of the normal schools, or corresponding institutions, vary from a review of the elementary-school arithmetic to the mathematics required for entrance to colleges and universities; or, from another point of view, from an emphasis on the purely professional needs, limited to the immediate requirements of the elementary schools, to academic and cultural aims founded on the principle that the more a teacher knows about the subject, in addition to the purely professional training, the more successful will be his teaching. But, great as is the variety of standards and aims in Europe, almost every standard finds a parallel in this country, owing to the absence of uniformity—a condition almost paralleled in England and Switzerland. But, if a generalization may be permitted, it would be true to say that the academic standards in the best systems are higher in the more advanced countries of Europe than they are in the United States. Several reasons may be adduced to account for the condition here described. The training of elementary-school teachers is still obsessed with the traditions that are associated with a system of training by apprenticeship. More emphasis has always been placed on professional knowledge and technical ability than on general academic training; so that while the secondary-school teacher has been expected to be a master of subject matter, the elementaryschool teacher has been narrowly trained in methods of instruction. Hence the candidate for the elementary-school branch has been considered to be sufficiently equipped if his knowledge of subject matter is equivalent to that given in a secondary school. Another important |