e young
engineering students. The difficulty of the situation is increased by
the fact that the young instructor is often led to believe that his
advancement and the appreciation of his services are directly
proportional to his achievements in investigations of a high order.
This belief naturally leads many to begrudge the time and thought
which their teaching duties should normally receive.

The young college teacher of mathematics is thus confronted with a
much more complex situation than that which confronts the mathematics
teachers in secondary school work. Here the success in the classroom
is the one great goal, and the mathematical knowledge required is
comparatively very modest. Possibly the situation of the college
teacher could be materially improved if it were understood that his
first promotion would be mainly dependent upon his success as a
teacher, but that later promotions involved the element of productive
scholarship in an increasing ratio.

The schools of education which have in recent years been established
in most of our leading universities have thus far had only a slight
influence on the preparation of the college teachers, but it seems
likely that this influence will increase as the needs of professional
training become better known. It is probably true that the ratio of
courses on methods to courses on knowledge of the subject will always
be largest for the elementary teacher, in view of the great difference
between the mental maturity of the student and the teacher, somewhat
less for the secondary teacher and least for the college teacher; but
this least should not be zero, as is so frequently the case at present,
since there usually is even here a considerable difference between the
mathematical maturity of the student and that of the teacher.

It may be argued that the future college teacher will probably profit
more by noting the methods employed by his instructors than he would
by the theoretic discussions relating to methods. This is doubtless
true, but it does not prove that the latter discussions are without
value. On the other hand, these discussions will often serve to fix
more attention on the former methods and will lead the student to note
more accurately their import and probable adaptability to the needs of
the younger students.

Among the useful features for the training of the future mathematics
teachers are the mathematical clubs which are connected with most of
the active m