to develop the matters both within the arithmetic classes and
in the other classes. Neither being complete at present, each will
tend to complete the other.

On the side of the preliminary training in the fundamental operations,
the present arithmetic course of study is on the whole of a superior
character. It provides for much drill, and for a great variety of
drill. It emphasizes rapidity, accuracy, and the confidence that
comes to pupils from checking up their results. It holds fast to
fundamentals, dispensing with most of the things of little practical
use. It provides easy advances from the simple to the complicated. The
field of number is explored in a great variety of directions so that
pupils are made to feel at home in the subject. One large defect is
the lack of printed exercise materials, the use of which would result
in greatly increased effectiveness. Such printed materials ought to be
furnished in great abundance.

ALGEBRA

In the report of the Educational Commission of Cleveland, 1906, we
find the following very significant sentences relative to the course
of study for the proposed high school of commerce:

"An entirely new course of study should be made out for this school.
Subjects which have been considered necessary in a high school,
because they tend to develop the mind, should not for this reason only
be placed in a commercial course. Subjects should not be given because
they strengthen the mind, but the subjects which are necessary in this
course should be given in such a way as to strengthen the mind. The
mathematics in this school should consist of business arithmetic and
mensuration. We can see no reason for giving these students either
algebra or geometry. But they should be taught short and practical
methods of working business problems."

We find here a recommendation since carried out that indicates a clear
recognition of the principle of adaptation of the course of study to
actual needs. Carried out to its logical conclusion, and applied to
the entire city system, it raises questions as to the advisability of
requiring algebra of girls in any of the high school courses; or of
requiring it of that large number of boys looking forward to vocations
that do not involve the generalized mathematics of algebra. Now either
the commercial students do need algebra or a large proportion of these
others do not need it. It seems advisable here to do nothing more than
to present the question as