heated controversy as to the "transfer of training," a very large proportion of teachers of mathematics hold to the opinion of the pervasive nature of the training in their courses. Only in the case of trigonometry does content seem to be recognized as making the essential contribution to the educational value of the subject. Nevertheless, we cannot pass without notice the fact that with a far from negligible proportion of teachers content is elevated to the superior position, while another considerable proportion deems the two of equal value.

TABLE XXXV

OPINIONS OF TEACHERS ON RELATIVE VALUES OF CONTENT AND DISCIPLINE IN COURSES IN MATHEMATICS

1. Elementary algebra is almost always a first-year high-school subject. Plane geometry is markedly a second-year subject, but is reported in some schools in the third year, or in the latter half of the second year and the first half of the third. Advanced algebra appears most commonly in the third and fourth years, but in a few schools in the second. Solid geometry appears in the third or fourth years and trigonometry in the fourth year.

2. Elementary algebra and plane geometry extend almost without exception through a full school year of 36 weeks or more. The three advanced courses named are almost always a half-year in length. Each week is usually constituted of five 40- or 45minute periods. Some schools report periods of greater length.

3. Supervised study is reported in a few schools for elementary algebra or plane geometry, or both.

4. Most schools require two years of mathematics for graduation, while a small proportion each require none, two and one-half years, or three years. Still others vary the requirement with the high-school course taken.

5. Textbooks dominate content and organization of courses in mathematics.

6. There is no standard practice in the disposition of the class period as to recitation, study, teaching, and lesson assignment, except that a very large number of schools allow no class time, or a very small proportion of class time, for study.

7. The deductive, inductive, and analytic methods are most commonly used in class instruction.

8. Historical notes are introduced into courses in elementary algebra and plane geometry in somewhat more than half the schools and into the advanced courses in mathematics in approximately a third of the schools. They are reported as "humanizing," i.e., adding interest to, the work.

9. More than 60 per cent of the replies report efforts to correlate algebra and geometry. The values of such correlation are said to be: (1) making the subjects easier of comprehension, (2) teaching the unity of mathematics, and (3) increasing the interest in it.

10. Approximately 60 per cent of the replies report efforts to meet current criticisms of high-school mathematics. Such efforts are usually constituted of the introduction of "practical" problems, problems drawn from the vocations, or problems within the students' experiences.

II. The aims in the teaching of mathematics usually classify under (1) the development of a working knowledge of the subject, (2) preparation for subsequent academic work, (3) a stressing of the practical values, and (4) free play for the disciplinary values of the subject.

12. Except in the case of trigonometry, most teachers believe that the discipline of courses in mathematics is more valuable than the content. However, a considerable number of teachers place the content value on a level with or superior to the disciplinary value.

CHAPTER IV

SCIENCE

A. SCIENCES OTHER THAN AGRICULTURE

I. DISTRIBUTION OF RESPONSES TO THE INQUIRY

The distribution, by states, of the schools from which responses to the inquiry in the teaching of the various sciences have come is shown in Table XXXVI. The number of responses in physiology

TABLE XXXVI

DISTRIBUTION, BY STATES, OF THE SCHOOLS FROM WHICH RESPONSES TO THE INQUIRY IN THE VARIOUS COURSES IN SCIENCE HAVE COME

is so small as to forbid drawing from them any far-reaching conclusions. As has been stated in chapter i, this small number is probably in large part attributable to the small holding this science has in high-school programs of study, and this in itself is due to the

Total

opinions of the school authorities that it is not of sufficient educational value, either in itself or as it is usually taught, to justify a place for it in the programs. While the number of responses for some of the other sciences is not large, they are sufficient to constitute a fair sample or representation and to support such conclusions as are drawn from them.

II. THE OFFERING

YEARS IN WHICH SCIENCE COURSES APPEAR

The years in which the various high-school science courses appear are shown in Tables XXXVII and XXXVIII. In the former they are represented in gross numbers and in the latter in percentages of schools listing the subjects in the different years. From these tables the following facts are evident: (1) general science is almost always listed in first year; (2) physiography is most commonly a first-year subject, although in some schools it appears in the second year, and in a few in years beyond the second; (3) the biological sciences are more commonly reported for the second year, but are reported by some schools in the first year, and in a smaller proportion of schools beyond the second year; (4) chemistry is a third- or fourth-year subject with some preponderance of practice for the fourth year; (5) physics is also a third- and fourth-year subject, but in practice is more markedly a fourth-year subject than is chemistry.

RANGE OF YEARS IN WHICH STUDENTS MAY TAKE THE VARIOUS
HIGH-SCHOOL SCIENCES

The facts just presented as to the years in which the study of the various high-school sciences appears do not tell all the truth as to their place in students' curricula. Some interesting and pertinent information as to the range of years during which a student may take the several sciences is to be found in the teachers' responses to the question, "From what other years may the student elect the subject?" These responses have been compiled and are reproduced in Table XXXIX. The method of compilation for the purposes of this table may be illustrated as follows: if, e.g., a teacher listed botany for the second year and stated that it might

also be elected in the third or the fourth year, the answer was classified as signifying that the student may take botany in any one of three years. Again, if physics was listed in the fourth year and the

TABLE XXXVII

NUMBER OF THE SCHOOLS IN WHICH THE HIGH-SCHOOL SCIENCES APPEAR IN THE

PERCENTAGES OF THE SCHOOLS IN WHICH THE HIGH-SCHOOL SCIENCES APPEAR IN

teacher reported that the student might also take the subject in the third year, the answer was understood to signify that the student may take physics in that school in either of two years. From the