One accepts, for the most part, the studies of the
existing course and then assigns values to them as a sufficient
reason for their being taught. Mathematics is said to have, for
example, disciplinary value in habituating the pupil to accuracy
of statement and closeness of reasoning; it has utilitarian value
in giving command of the arts of calculation involved in trade
and the arts; culture value in its enlargement of the imagination
in dealing with the most general relations of things; even
religious value in its concept of the infinite and allied ideas.
But clearly mathematics does not accomplish such results, because
it is endowed with miraculous potencies called values; it has
these values if and when it accomplishes these results, and not
otherwise. The statements may help a teacher to a larger vision
of the possible results to be effected by instruction in
mathematical topics. But unfortunately, the tendency is to treat
the statement as indicating powers inherently residing in the
subject, whether they operate or not, and thus to give it a rigid
justification. If they do not operate, the blame is put not on
the subject as taught, but on the indifference and recalcitrancy
of pupils.
This attitude toward subjects is the obverse side of the
conception of experience or life as a patchwork of independent
interests which exist side by side and limit one another.
Students of politics are familiar with a check and balance theory
of the powers of government.
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