tional force teaching the mathematics to engineering students should be made up of men that have themselves taken a technical course. However, when we come to apply this principle under existing circumstances, we find the greatest difficulty in its practical application. In order to be competent to carry on instructional work of this kind, an engineering graduate should have had at least three years of graduate work in mathematics. Under existing conditions the graduates of technical schools are unwilling to give this amount of time to their preparation for instructional work. In fact, it is exceedingly difficult to attract any of the graduates of the technical schools to instructional work of any kind. The opportunities for a successful career in technical work have been so great that the appeal is almost entirely to the professional ambition of the young man. On this account it seems hopeless to secure technical graduates as instructors who have made adequate preparation in mathematics.

I have myself experimented to some extent with engineering graduates as instructors in mathematics, and I think I can say that the best work of teaching that I have ever had done has been by graduates of an engineering course. These men had very little preparation beyond the regular work of their course in engineering, but they were especially selected on account of their all around ability and their interest in scientific subjects. I find, however, that it is no easy matter to retain such men on the instructional force. As soon as good professional opportunities open before them they feel obliged to accept them, and under present conditions instructors who have taken the engineering course prove decidedly unsatis

factory on account of the temporary tenure of their office.

When we come to consider candidates for instructional work from the other class of students, namely, those who have made a specialty of the course in pure mathematics, and have taken their master's and doctor's degree, we find almost equally unsatisfactory conditions. In the first place there is a great dearth of active men in the graduate schools of mathematics at our large universities. Even those that take their major work in mathematics too generally neglect advanced laboratory work in physics, chemistry and other sciences, which should form an essential part of their work if they expect to prepare themselves to do adequate work as instructors in technical schools.

I had hoped that these conditions would show some change in the near future, so that we could attract a reasonable number of engineering graduates to advanced work in mathematics and later provide them with places as instructors in the technical schools. In order to aid in securing men of this kind I believe it would be a great advantage if the men who give instruction in mathematics could be given some work in the more technical part of the undergraduate course. I see no reason why a combination of this sort is not practicable. If an instructor, for example, could give two thirds of his time to the work in mathematics and the remainder to work in the hydraulic laboratory, or in the testing laboratory, or to instruction in mechanics or any other of the courses of this kind, he would feel that he had not cut himself off from technical work and from advancing in the engineering profession. A great many will undoubtedly believe that a

proposition of this kind is too radical; that it is not practicable to make a division of labor in the way in which I have indicated, and that the tendency of the time is in favor of specialization and not in line with a proposal of this sort. To this I can only reply that outside of administrative difficulties I can see no reason why the work of the instructor cannot be thoroughly well done, even though a part of his time be spent in the laboratory. There is undoubtedly a danger that the principal interest of the instructor will be in the technical work and laboratory work, rather than in his mathematical instruction. I fear this less, however, if we require for this purpose students who have taken at least two years of graduate work in mathematics. In any case, it seems to me to be necessary to accept this as a fundamental requirement in the selection of the instructors.

I desire to say a few words concerning the conference system which we are trying to introduce at Wisconsin in the instructional work in mathematics for freshmen and sophomores. For the purpose of conferences with the students we have divided the instructional force for the current year into three groups. These men are present in the office of the department on Tuesdays and Thursdays from 4.00 to 5.30 P. M., and on Saturdays from 9.00 to 10.30 A. M. At these conference hours any students in any of the courses are at liberty to appear for any assistance or additional explanation of the classroom work that they may desire. In the instructions which I have given to the various members of the teaching force, I emphasized the need of not only inviting all of the students that so desire to attend the conferences, but also that students that are behind in their work, or

doing poorly for any cause, shall be urged by the instructor to attend. I have also suggested that these invitations should not be confined to the weak students that need help, but should be extended to the brighter students as well, who might profit by encouragement and suggestions which would lead to more enthusiasm and better work on their part.

We have been very much pleased thus far with the success of the conference system. Each instructor keeps a diary or record of his work with the students. Another year we expect to develop the conference system still further. The work of the instructors in the conferences will hereafter be a principal consideration in determining their promotion. The campus at the University of Wisconsin is not adequately lighted in the evening at the present time, so that we are unable to put the conferences in the evening. As soon as provided with adequate light, we shall hold these conferences every evening from 7.00 to 9.00 o'clock, except Fridays and Saturdays, but shall undoubtedly continue our conference on Saturday morning. Work of this kind we find supplements the instructional work in the very best way and brings the instructors and students into intimate contact. The conference system not only does this, but it brings the students in contact also with all members of the instructional force in the department.

DISCUSSION.

PROFESSOR WALDO: Most of our engineering colleges require both plane and solid geometry of their students for admission. I think that the teaching of these subjects at the present time in the preparatory schools needs improvement, not so much in the amount

covered as in the manner in which it is covered. The trouble in the high schools comes from the teachers having studied very little mathematics, if any, beyond the subjects they teach. Not having a good knowledge of the mathematical work which their students will be later required to study, they do not properly appreciate the importance of a thorough grounding in the mathematics of the high school.

But the most serious difficulty is to teach students how to study. Few of them seem to know how to study mathematics. They set about it as something to be memorized. On account of the increase in the number of subjects taught in our preparatory schools, and the covering of too much ground with a very thin layer of knowledge, the same is probably true of several other subjects. Students seem to get the idea that superficial knowledge is adequate, and that this is true of mathematics. They fail to grasp and retain the fundamental principles and to appreciate the fundamental facts.

PROFESSOR NORRIS: The question is raised, "How are we to influence work at the preparatory schools?"

PROFESSOR MARVIN: I would like to know how much is done by other states in regard to bringing the secondary school people into touch with the university. In my own state we have a conference with the high school people, which is usually held at the university in the spring.

We make it worth their while by furnishing an attractive program, which includes papers from the university people and from the high school people themselves; also something in the way of a lecture by some outside party. Each year some subject is taken up for discussion-one year mathematics, one