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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

factor, which has perhaps not received the attention in the reports that it merits, is that in general the instructors in normal schools are themselves not university trained, and the demand for universitytrained instructors can not become strong until the principles upon which the training of elementary-school teachers is based become broader and more liberal. Finally, it may be that in most countries, and in the United States in particular, the standards in mathematics have been greatly affected by the fact that the great majority of candidates entering the teaching profession are women. It is almost universally the case in European normal schools that in mathematics lower attainments are required from the women than from the men students.

The general problem is, however, receiving considerable attention both in practical administration and in theoretical discussions. At present the European countries are all passing through a transition stage, which finds expression in dissatisfaction with the prevailing arrangements. The tendency generally is in the direction of raising the standards of the academic or cultural training a tendency which reaches its culmination in the admission of certain elementary-school teachers to some university courses in Germany; in the provision of facilities to attract graduates of secondary schools to the elementaryschool service, as in Hesse, England, Italy, and Switzerland; in the gradual separation of professional and academic training by such a provision as the introduction of a fourth year for students in the departments of education of universities in England; and in the United States in the continually increasing opportunities for the improvement of teachers in service. That the best thought in this country has not been backward in formulating the task that lies before those interested in the training of teachers is indicated in the recommendations of the American committees, which are quoted in the section on the United States.

BELGIUM.

The normal schools for men and women in Belgium are organized on the basis of a four-year course. The students are admitted at the age of 15, after an entrance examination on the subjects of the elementary school. Arithmetic is the only mathematical subject included in the examination, and consists of a written test (two questions of general arithmetic and two problems) and an oral test (two questions of general arithmetic and an exercise in mental arithmetic). The students must obtain 50 per cent of the marks to pass. The mathematical subjects in the normal schools consist of arithmetic, algebra (in first and second years), and plane geometry (in second and third years) for men, and only arithmetic for women. The time allotment per week is as follows: