I take one more illustration, namely, mathematics. This does, or does not, accomplish its full purpose according as it is, or is not, presented as a social tool. The prevailing divorce between information and character, between knowledge and social action, stalks upon the scene here. The moment mathematical study is severed from the place which it occupies with reference to use in social life, it becomes unduly abstract, even upon the purely intellectual side. It is presented as a matter of technical relations and formulae apart from any end or use. What the study of number suffers from in elementary education is lack of motivation. Back of this and that and the other particular bad method is the 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.