readily classifiable under those already listed in the questionnaire. We are probably justified in concluding that those listed, in addition to what is implied in the next paragraph, comprehend all that these teachers aim to make the results of their courses in the modern languages.

Differentiation of purpose to meet future vocational needs of students is recognized by some schools, as will be seen in Table XXI. The kinds of differentiation reported are commercial, scientific,

TABLE XXI

NUMBER OF SCHOOLS DIFFERENTIATING COURSES IN MODERN LANGUAGES ALONG COMMERCIAL, SCIENTIFIC, AND INDUSTRIAL LINES

and industrial. The small proportion of schools recognizing such differentiation in the work in German and French is at once apparent. This situation contrasts strikingly with that in Spanish, in which all but a single school recognize the desirability urged by the campaign for commerce with the South American countries of effecting a commercial differentiation.

The year or years of the language sequence in which the differentiations appear, in so far as they are reported, are recorded in Table XXII. Such differentiation does not appear in a large proportion of the schools reporting it until the second year. This is true even of Spanish, the most markedly vocational of these languages.

V. SUMMARY

1. Courses of study in the modern languages extend through two, three, or four years, more commonly two than three or four in German and French. The course in Spanish is frequently four years in length.

2. The length of the school year determines the length of the year-course in modern languages, and this is almost without exception 36 or more weeks. There are usually five recitation periods

of 40 or 45 minutes per week. A small proportion of schools also provide time for supervised study in addition to the recitation period proper.

TABLE XXII

NUMBER OF SCHOOLS REPORTING DIFFERENTIATION ALONG VOCATIONAL LINES IN THE VARIOUS YEARS OF THE MODERN-LANGuage SEQUENCE

3. Work in German and French, especially the former, is reported in the elementary schools. In almost all cases high-school recognition is given for it.

4. Sixty per cent of the schools grant credit toward graduation for a single year of modern language.

5. The first year of a modern language has found no standard place in the high-school program. Only a small proportion of schools provide special sections for students two years or more apart in their high-school classification.

6. The direct method and a combination of the direct and grammar-translation methods are in most common use in beginning classes in modern languages. The grammar-translation and natural methods are also reported.

7. Teachers avail themselves of such materials, devices, and special activities as songbooks, stereopticons, postals, phonographs, maps, phonetic charts, wall pictures, illustrated books and magazines, newspapers, German or French clubs, plays, and games to add interest and value to the work.

8. (a) There is general agreement as to the aims that should dominate the courses in the modern languages.

b) A small proportion of schools recognize, by differentiation of the courses after the first year along commercial, scientific, and industrial lines, the future vocational needs of their students of German and French. Some differentiation along commercial lines is almost universal in the courses in Spanish.

CHAPTER III

MATHEMATICS

I. DISTRIBUTION OF RESPONSES TO THE INQUIRY

The distribution of the schools from which responses have come to the inquiry in mathematics is as follows:

TABLE XXIII

DISTRIBUTION, BY STATES, OF THE RESPONSES TO THE INQUIRIES IN

The small number of responses in the more advanced courses must be due to a considerable extent to their decreasing importance in the high-school students' curricula. This has been brought about largely by, among other causes, the recent democratization of the high-school programs of study through the introduction of a wider range of work and of subjects not formerly offered, and by the resulting marked tendency on the part of the higher institutions to drop advanced algebra and solid geometry as entrance requirements. Two reports on courses in algebra of college caliber have

been received, but such a small number of reports would give facts of too little significance to justify reproduction here.

II. EXTENT OF THE OFFERING AND REQUIREMENT

EXTENT OF THE OFFERING

The divisions of mathematics which are being taught in the high schools of the North Central states may be implied from the foregoing to be elementary algebra, advanced (sometimes called "intermediate") algebra, plane geometry, solid geometry, trigonometry, and college (sometimes called "advanced") algebra. To what extent each high school is offering all this work was not investigated, but it may be implied to some extent from the number of responses received in each of the subjects, i.e., we may say that, although all schools both offer and teach elementary algebra and plane geometry, a smaller proportion both offer and teach advanced algebra, and even fewer both offer and teach solid geometry and trigonometry. A very few schools are offering and teaching algebra of college grade. It would be easy, however, to place too much faith in these implications.

YEARS IN WHICH COURSES IN MATHEMATICS APPEAR

The years in which the subdivisions of mathematics appear are presented in Table XXIV. The essential facts as to years in which such courses appear are as follows: (1) elementary algebra is almost without exception a first-year high-school subject; (2) plane geometry is markedly a second-year subject, but appears in the latter half of the second and the first half of the third year in 10 schools in which it follows both elementary and advanced algebra, and in the third year in 20 schools; (3) advanced algebra is primarily a third- and fourth-year subject, with more schools offering it in the former year; (4) solid geometry is a third- or fourth-year subject; (5) trigonometry is always reported for the last year of the high school.

The reasons most commonly given for placing elementary algebra in the first year are: (1) its necessity as a basis for higher mathematics and for the sciences, (2) its close connection with the

' Commercial arithmetic is treated in the chapter on commercial subjects.

arithmetic of the elementary schools, and (3) its simple, elementary, and, therefore, suitable nature. The reasons most commonly given for placing plane geometry in the second year are: (1) its sequential relation to algebra, (2) its necessity in this year as preparation for physics, and (3) the maturity of the students. This last reason is the one most commonly given for its place by teachers who report plane geometry as a third-year subject. The usual reasons given for placing advanced algebra in the third or the fourth year are: (1) the suitable maturity of the students, (2) their prev

TABLE XXIV

NUMBER OF SCHOOLS REPORTING VARIOUS YEARS IN WHICH THE SEVERAL COURSES IN MATHEMATICS APPEAR

* In the last half of the second year and the first half of the third. † May be taken in either year.

ious experience with geometry, and (3) the proximity to college. The few schools that report this subject in the second year do so in order to make the work in algebra continuous. Solid geometry is placed in the third year in some schools because of its sequential relation to the mathematics of the preceding years, and in the fourth year because of the maturity necessary to the visualization of threedimensional figures and because of proximity to college. The place of trigonometry in the fourth year is determined automatically by the prerequisite work in algebra and geometry.

THE TIME ELEMENT

Weeks in the course. With two exceptions, one of 18 weeks and the other of 48, a school year of 36 or more weeks is devoted to elementary algebra. With one exception of 34 weeks a school year of 36 or more weeks is devoted to plane geometry. The course in advanced algebra usually extends through a half-year of 18-20