able, are incidental to more important matters.

Naturally before one is prepared to use mathematical forms of thought
in considering the many social and vocational problems, he must have
mastered the fundamentals. The elementary school, at as early an
age as practicable, should certainly give the necessary preliminary
knowledge of and practice in the fundamental operations of arithmetic.
This should be done with a high degree of thoroughness, but it should
always be kept in mind that this is only a preliminary mastery of the
alphabet of mathematical thinking. The other part of our problem is a
development of the quantitative aspects of the vocational, economic,
and civic subjects. One finds clear recognition of this in Cleveland
in the new arithmetic manual. The following quotations are typical:

"The important problem of the seventh and eighth grades is to
enable the pupils to understand and deal intelligently with the most
important social institutions with which arithmetical processes are
associated."

In discussing the teaching of the mathematical aspect of insurance, we
find this statement: "Owing to the important place this subject holds
in life, we should emphasize its informational value rather than its
mathematical content."

Under taxation and revenue: "If the general features of this subject
are presented from the standpoint of civics, the pupils should have no
difficulty in solving the problems as no new principle is introduced."

Under stocks and bonds: "Pupils should be taught to know what a
corporation is, its chief officers, how it is organized, what stocks
and bonds are, and how dividends are declared and paid, in so far as
such knowledge is needed by the 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