Pupils usually enter school at the age of 6 or 7, and attendance is compulsory up to the age of 14. The school year is 34 weeks in length. Both the church and the school are under the supervision of the same department of the Government.

The primary school has a six years' course. The parish is usually the school district, and instruction is carried on under the supervision of local inspection and of inspectors appointed by the Government. Coeducation is common in the primary schools of the rural districts. From five to seven periods per week are devoted to mathematics in the primary school.

The higher school is divided into the Realschule and the Gymnasium. The aim of the Realschule is to provide a general practical education beyond the primary school. The course of six years is concluded without an examination. In all Realschulen four or five periods per week are devoted to mathematics.

After completing the first five years of the Realschule, a pupil may enter the first year of the Realgymnasium or of the Latin Gymnasium, instead of taking the sixth year of the Realschule. In the Gymnasium pupils are urged to take subjects for which they have special talent, and considerable freedom to discontinue a subject is permitted.

The school day for secondary schools begins at 7.45 in the morning and must not be longer than six periods of 45 minutes each.

With the exception of a few of the public Realschulen, all of the secondary schools are for boys only, and a small fee is charged. Most of the higher schools for girls are private, and they are taught almost exclusively by women.

Any pupil who is successful in passing the examinations at the close of the last year in the Gymnasium is permitted to enter the university.

The Cantons differ greatly in the number of periods per week devoted to mathematics. In the primary school one period daily is the general rule.

The following table shows the number of periods per week devoted to mathematics, including bookkeeping, in the literary Gymnasium, Realgymnasium, and Realschule of Zurich.

Although each of the 25 Cantons of Switzerland is autonomous in all matters pertaining to education, there are some similar features in the various school systems. In most of the Cantons the legislature appoints a general director of education, but in some Cantons this authority is vested in an educational council. Most of the Cantons have special inspectors for each type of school.

The chief characteristic of education might be said to be its variability. This is caused by the great geographical, economic, and religious differences prevailing in the various Cantons. There is considerable dissatisfaction in Switzerland because of the great variety in educational systems, and there is a tendency toward centralization of authority in education. The school year varies from 38 to 48 weeks.

The primary schools are said to be unusually efficient in the training they give. The entering age varies from 6 to 7 years in the different Cantons, and the course is six years in length. All primary schools are free, and coeducation predominates except in the large cities.

In many Cantons a pupil who has completed the fourth year of the primary school may enter an advanced school called the lower middle school or the Sekundarschule. In this school one or more foreign languages and algebra are taught. In some Cantons a pupil enters this type of school after completing the sixth year of the primary school. The course is then from three to five years in length. These schools correspond to the Bürgerschulen in Germany and Austria and to the upper primary schools in France. A pupil who has completed the six-year course of the primary school may enter the higher middle school. There are many names used in the various Cantons for the

different types of schools of secondary grade, but most of these schools may be called either Gymnasia or Realschulen. The Realschulen of Switzerland correspond to the Oberrealschulen of Germany. In French Switzerland there is even more differentiation of courses than in German Switzerland, and many of the secondary schools resemble the French lycées.

Zurich is the largest of the Cantons, and the system there may be taken as roughly typical. There are three types of secondary schools in Zurich: (a) Literary Gymnasium, (b) Realgymnasium, (c) Realschule. A pupil who has completed a six-year course in the primary school may enter either type of Gymnasium. To enter the Realschule a pupil must have completed not only a six-year course in the primary school, but he must have had two additional years in some secondary school.

[For arrangement of school courses in the United States, see note on page 6.]

TABLE 1.

Table 1 is a graphic representation of the arrangement of the school years in different countries. A heavily dotted line indicates that in some cases the type of school under consideration extends over the period represented.

The table portrays general conditions and not exceptional cases.

Age...

TABLE 1.-Arrangement of school years-Continued.

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

II. THE WORK IN MATHEMATICS IN THE FIRST SCHOOL

YEAR.

AUSTRIA. The pupils are taught to read and write numbers from 1 to 10, and the four fundamental operations are usually taught within these limits. In some schools the pupils learn to read and write numbers from 1 to 100 during the first school year. Simple problems involving denominate numbers familiar to the children are given. Most of the work is oral.

BELGIUM.-Pupils are taught to count and to read and write numbers from 1 to 20. Simple exercises involving numbers within these limits are given. The reading and writing of numbers is often extended to 100. Objects are freely used to develop the number concepts. From four to five periods a week are usually devoted to arithmetic.

DENMARK.-The first year's work includes the reading and writing of numbers from 1 to 10. and the four fundamental operations involving numbers within these limits. In a few schools the limit is extended to 20. The concepts.}, and are taught. Almost all the work is oral and objects are freely used. Arithmetic is taught five periods a week to boys and four to girls.

ENGLAND. The third grade of the infant department corresponds to the first school year in the United States. Pupils are taught to count from 1 to 10 and from 10 to 1. The various numbers from 1 to 10 are factored. No formal addition or subtraction is taught. Only the simplest exercises are given. The pupils play store, dominos, and various other games. Measurement, using the foot, inch, and halfinch is taught, and pupils learn to estimate small distances. The terms half and quarter are taught by means of paper folding and by the use of numerous objects. FINLAND. In the city schools the pupils are taught to count and to read and write numbers from 1 to 100. The most common measures are taught.

In the country schools the reading and writing of numbers from 1 to 100 are taught and addition and substraction involving numbers less than 20 are studied. The meaning and use of the terms meter, liter, kilogram, and mark are also taught.

FRANCE. The course includes the reading and writing of numbers from 1 to 100, and the four operations involving the numbers to 10. The terms meter, liter, and franc are taught and extensively used. The fractions,, and are taught. Almost all of the work is oral.

GERMANY. The number scale from 1 to 20 is taught, and addition and subtraction of numbers within this limit.

In some of the German States the multiplication table of twos is taught during the first school year. The terms meter, decimeter, pound, and mark are usually taught. In a few of the States the number scale is taught only from 1 to 10, but all four operations are taught within these limits.

From three to four periods a week are devoted to arithmetic.

HOLLAND.—The course is practically the same as in Belgium. The numbers from 1 to 20 are studied synthetically. From 20 to 100 the tens are studied before the intermediate numbers. Four to five periods a week are given to the subject. HUNGARY. The course is practically the same as in Austria. The simple number relations involved in the activities of the home and the school are emphasized. ITALY.-The pupils are taught to read and write numbers from 1 to 100 and to perform the four operations on numbers from 1 to 20. Most of the work is oral. JAPAN. The course includes the reading and writing of numbers from 1 to 100 and the four operations on numbers less than 20. Most of the exercises are in addition and subtraction. A few simple exercises with numbers between 20 and 100 are given.

Five periods a week for 40 weeks are usually devoted to arithmetic.
NORWAY.—(No report is available.)

ROUMANIA. (The report does not include the work of this school year.)

RUSSIA. (Details of the work of the first school year are not available; see the third school year.)

SPAIN. (There is no report on the work of the elementary school.)

SWEDEN.-The pupils are taught to read and write numbers from 1 to 100, and to solve simple oral problems involving numbers of one digit.

SWITZERLAND.-The pupils are taught to read and write numbers to 100, and to perform the four operations on small numbers.