e radical mistake of treating number as if it were an end in
itself, instead of the means of accomplishing some end. Let the child
get a consciousness of what is the use of number, of what it really is
for, and half the battle is won. Now this consciousness of the use of
reason implies some end which is implicitly social.

One of the absurd things in the more advanced study of arithmetic is the
extent to which the child is introduced to numerical operations which
have no distinctive mathematical principles characterizing them, but
which represent certain general principles found in business
relationships. To train the child in these operations, while paying no
attention to the business realities in which they are of use, or to the
conditions of social life which make these business activities
necessary, is neither arithmetic nor common sense. The child is called
upon to do examples in interest, partnership, banking, brokerage, and so
on through a long string, and no pains are taken to see that, in
connection with the arithmetic, he has any sense of the social realities
involved. This part of arithmetic is essentially sociological in its
nature. It ought either to be omitted entirely, or else be taught in
connection with a study of the relevant social realities. As we now
manage the study, it is the old case of learning to swim apart from the
water over again, with correspondingly bad results on the practical
side.

In concluding this portion of the discussion, we may say that our
conceptions of moral education have been too narrow, too formal, and too
pathological. We have associated the term ethical with certain special
acts which are labeled virtues and are set off from the mass of other
acts, and are still more divorced from the habitual images and motives
of the children performing them. Moral instruction is thus associated
with teaching about these particular virtues, or with instilling certain
sentiments in regard to them. The moral has been conceived in too
goody-goody a way. Ultimate moral motives and forces are nothing more or
less than social intelligence--the power of observing and comprehending
social situations,--and social power--trained capacities of control--at
work in the service of social interest and aims. There is no fact which
throws light upon the constitution of society, there is no power whose
training adds to social resourcefulness that is not moral.

I sum up, then, this part of the discussio