*"Domestic Science" applies to the Girls' columns only; for the Boys' columns it should be replaced by "Manual Training".

CHAPTER XI

Mathematical Curricula in Foreign Countries'

BY

JOSEPH CLIFTON BROWN,

State Teachers College, St. Cloud, Minnesota.

TABLE OF CONTENTS

I. General Arrangement of Courses in Typical Schools of the Various

II. Summaries of the Work in Mathematics by Years....

III. Graphic Representation of Work in Mathematics...

IV. Certain Important Points of Difference between the Work in Mathematics Abroad and in the United States...

V. Bibliography

.131

154

..165

.....172

.173

No one believes in the bodily transplantation of a course of study or of methods of work from one nation to another; yet every nation can profit from a careful comparative study of the work of other nations.

Administrators and teachers are now forced by events to consider eliminations, additions, and modifications of the courses of study

For a more detailed discussion of courses in mathematics given in foreign countries, the reader is referred to Curricula in Mathematics, or comparison of courses in the countries represented by the International Commission on the Teaching of Mathematics, by J. C. Brown (U. S. Bureau of Education, Bulletin, 1914, No. 45, Washington, 1915.) It should be noted that the present chapter describes conditions as they were before the It appears that changes since then have not as yet been extensive or far reaching.

war.

and the methods of instruction. A study of conditions in other countries should be very profitable as a basis for readjustment of our

own courses.

The curricula in mathematics of the leading nations of Europe have much more in common with each other than with those of the United States. European nations will therefore sometimes find in the practice of their sister nations encouraging confirmation of their own customs, whereas the United States will be confronted by the question as to whether she alone has found the path that is best, at least for herself. Some lines of divergence between the general practice in Europe and that of the United States are mentioned in the concluding remarks of this chapter (p. 172). Historical and other reasons for the existence of the divergencies are easily found. Reasons, sometimes of a theoretical and sometimes of a practical nature, may doubtless also be found sufficient to warrant the present continuance of some of these divergencies. At the same time the possession of authoritative statements of the practice of the world's leading nations, as contained in the reports from which the material that follows is taken, can but prove helpful and stimulating to the educators of the United States.

All of the statements of fact in the chapter are based upon reports of the International Commission to the congress at Cambridge. A complete bibliography of the reports used is given on page 173-176. The data for the various nations have perforce been given with varying degrees of completeness, depending upon the information available in the reports. The reports from all of the countries indicate conditions at the time that the reports were submitted (1912-1914). As the age at which pupils enter school varies somewhat in different countries, the age of the pupil, rather than the school year, was chosen as the basis of comparison.

Unless otherwise stated, it is to be understood that the European schools are for boys only. Relatively little is as yet done in most of the European countries for the mathematical education of girls beyond the fundamentals of arithmetic. The scanty information that is available is given in appropriate connections.

I. General Arrangement of the Courses in Typical Schools of the Various Countries.

Compulsory education extends from the sixth to the fourteenth year. Coeducation is the rule in the rural districts and the exception. in the cities.

All schools, whether public or private, are subject to the same regulations as the State schools. Most of the secondary schools are maintained by the State.

There are two kinds of elementary schools: (a) The common primary, usually called the Volksschule, and (b) the superior elementary school, called the Bürgerschule. Many of the Bürgerschulen in the rural communities are ungraded. In the cities the course in these schools comprises from two to eight grades. The Bürgerschulen usually consist of three classes, which follow the fifth year of the primary school. Pupils may enter directly from the primary school. Different courses are offered for boys and girls, and as far as possible the sexes are instructed in different schools.

Sometimes an intermediate course of one year follows the Bürgerschule. The nature of the course which a pupil follows during this year depends largely upon the type of school for which he is preparing. It is now proposed to make the intermediate course an additional class of the Bürgerschule.

There are three general types of secondary schools: (a) The Gymnasium, (b) the Realschule, and (c) the Realgymnasium. The first has a course of eight, the second of seven, and the third of eight years, thus differing from the custom in Germany. The minimum