general public."
These statements indicate a recognition of the most important principle that
should control in the development of all of the mathematics, elementary and
secondary, beyond the preliminary training needed for accuracy and rapidity in
the fundamental operations.
When this principle is carried through to its logical conclusion, it will be
observed that most of these developments will not take place within the
arithmetic class, but in the various other subjects. Arithmetic teaching, like the
teaching of penmanship, etc., is for the purpose of giving tools that are to be
used in matters that lie beyond. The full development will take place within
these various other fields. For the present, it probably will be well for the schools
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