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THIS subject refers directly to the time element in education. It does not, however, present a problem in mathematics. Any solution, therefore, which is obtained by transposition will be a partial one only. There are two sets of conditions involved, each of which demands careful consideration with little or no emphasis upon the terms in which the desired answer will be stated.

The first set refers to the organization and relation of the school sections under consideration. It may be of interest and value in this discussion to review the manner in which the colleges and professional schools in this country have handled the questions of organization and relation which confronted them. The specific aim of the college and that of the professional school had been emphasized until it seemed as if college education and preparation for a profession or for specialization in science were antagonistic. A man or woman looking forward to becoming a self-supporting member of society found the beginning of apprenticeship in practical affairs deferred too long, if an effort was made to get something from both the college and the professional course. Progress in the solution of the time problem was made by the recognition of the fact that its conditions lay in both the common means and special aims of the college and the professional school.

To the general public and the conservative educationalists the 1A paper read before the National Council of Education, Boston, Mass., July 6, 1903.

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reorganization of higher education has seemed to be directed largely in the interest of the short-term degree. This is a misconception of a movement which corrects a waste in time and effort, and thereby increases the efficiency of the schools concerned. With a fairly clear idea as to the general culture which should be the possession of a man or woman intending to specialize, and also of the knowledge essential in preparation for specialization, it was not difficult for the college and the professional school to determine their common means and so organize them that the responsibility in the common territory was properly placed, thus preventing repetition and correcting some tendencies toward indifferent work. On the other hand, with a clear idea as to the special aims of each, their relation to each other was sharply defined so that neither now attempts to do the intensive work that is the special function of the other. This concentration upon the organization and relation of the college and the professional school has rendered it possible for a student to secure the foundations of general culture, and out of them to develop specialized knowledge in less time and with better preparation than formerly, when subject-matter was indiscriminately appropriated by each section.

Turning to the elementary and secondary schools, we find a situation analogous to that which obtained formerly in the college and the professional school. With the development of the high school, the differentiation between it and the grammar school has been made sharper and sharper, until the time spent upon covering the work offered by the two combined has become excessive. The high school views its work, in comparison with that of the grammar school, very much as the professional school viewed its in comparison with that of the college. The treatment of subjects in the elementary school seems to fit the pupils in very slight degree for the work planned in the secondary school.

It is not unusual for high-school teachers to recommend, with great fervor and seriousness, limiting the elementary school to its special subjects, namely, reading, writing, spelling, arithmetic,

and grammar. The efforts to introduce more general culture into the lower grades through the reading of literary classics are often frowned upon by the teachers of literature in the high school. Some teachers of mathematics have an attitude of disapproval toward algebra in the eighth grade. Within the last year there has come under my notice a marked illustration of this general tendency. A class of eighth-grade children that had been studying Latin two years, upon entering a high school was advised and urged to renounce all pretensions to any acquaintance with Latin, and to begin the subject as if it had never learned a Latin word. The teacher is a college graduate and a fine drill mistress. She based her advice upon experience with classes from the same elementary schools in which the members of this class had been taught; and also upon her preconceived ideas as to the impossibility of elementary-school teachers successfully and intelligently teaching subjects which were in charge of the highschool faculty especially. A readjustment in the arrangement of the school necessitated sending this class to another building, and to a teacher who had no well-developed ideas about the limitations and weaknesses of elementary-school teachers when instructing in a high-school subject. The second teacher has an undoubted standing as an excellent instructor. The previous work of the class was accepted without comment, and the study of Cæsar was begun. The class proved unusually strong. This instance might be construed as indicating the complications often introduced into the school situation by personal peculiarities. To some extent that construction would be correct, but it would not include all of the conditions.

In many cities the marked distinction between the two schools has come to be felt so keenly that within the last few years conferences have been held, in which the high-school teachers have told the eighth-grade teachers wherein their work was poor, and the eighth-grade teachers have reciprocated the courtesy by telling the high schools wherein they have failed. As an outcome of these interchanges of opinion, some high-school principals have expressed a willingness to take the seventh and eighth grades

under their care; and, on the other hand, some elementary-school principals have expressed an equal willingness to keep their pupils a year or two longer, and instruct them in the subjects assigned to the ninth and tenth grades. These conferences are straws which indicate the direction of the general trend of thought.

It is usually said that the elementary pupils spend too many years in acquiring a slight acquaintance with the school arts; and yet, no one in touch with the best elementary schools believes their work is restricted to reading, writing, and ciphering. The facts in the case are that many subjects are taken up, but the heavy stress throughout the eight-year course is laid on rudimentary work which is not so developed as to lead into advanced work later on. It is the limitation to short reaches of experience in mental development and subject-matter that induces the strong teachers in the upper grades to emphasize the traditional in education with such stifling thoroughness. Those teachers sometimes doubt the efficiency of a school that enables its pupils to fit for the high school in less than eight years. They would be certain that a school which accomplishes what I saw done within the last fifteen years was radically wrong. A boy eight years old, unable to read, but with a method of his own in calculating, entered a school which covered the field of elementary and secondary education, and in seven years and ten months was admitted to Yale without a condition. Though he was not brilliant, he was a lad of good parts. As he was not delayed at any point in Yale, it is evident that his period of preparation was not too brief.

There are two points in the management of the school just referred to which are worthy of consideration: (1) the principal's daily experience ranged from the kindergarten to the college; (2) each teacher above the third-year classes taught the same subjects through the course for several years, thus giving continuity to those subjects and to the children's efforts with them. It is safe to assume that the arts of reading and writing were acquired in order that the children might use them in learning things; not that they might perform on a trapeze, devised

for reading and writing gymnastics. The principal with valuable subject-matter developing in his higher classes had no interest in playing at the school arts in the lower ones. The teachers also knew what development of a subject meant.

It is doubtless true that many elementary schools enable the more highly endowed boys and girls to prepare for the high school in seven, and sometimes six, years. The secondary schools, however, have not made it possible for even the most brilliant children to graduate in less than the four prescribed years, their general attitude being in favor of giving the children entering at twelve or thirteen years of age "time to grow."

A young girl who was unusually proficient in arithmetic entered a high-school class in algebra that had finished the fundamental operations, factoring, the greatest common divisor, and the least common multiple. She made up that work in three days, without assistance; and yet, neither the teacher nor the principal of the school thought it wrong to keep her sauntering in algebra through the remainder of the year. Each dwelt upon her proficiency in algebra and her having "time to grow." The attitude of both was in no way in advance of that of the strong teachers who devote the eighth grade to reviewing and polishing. The high-school teacher was beating around on a year's horizontal plane in algebra. Without doubt he and the principal supposed they were working on the departmental plan. The great majority of elementary-school teachers and principals are opposed to departmental instruction. They labor under the same delusion that limited the teacher of algebra. They think that teaching five classes a day, in the same subject, and at the same stage of advancement, is departmental instruction. It is horizontal repetition. This self-imitation and the general lawlessness met in the many classes are not attractive, are not stimulating to mental activity in a high degree.

The elementary and secondary schools should be organized on the vertical departmental plan. Soon after entering school a child should be taught mathematics three or four years by the same teacher. If he has marked ability, the teacher will know

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