and other finger work still practiced in some kindergartens and primary schools.
We have thus seen that there are certain branches of instruction for which the mind of the child from five to ten has ripened, and which may therefore be taught most economically and safely during this period. Concerning the teaching of language I shall speak presently, but thus far we have found that from the psychological standpoint there are at any rate three subjects which are strikingly adapted to this period, namely, natural science, history, and morals, using these terms with the latitude and restriction already explained. Certain branches of Nature study and one branch of what we have called morals—namely, manual training—have in recent years been introduced into our best elementary city schools, and in a few schools history is taught systematically in the lower grades by means of stories. They have not, however, crowded out reading, writing, and arithmetic so much as crowded into them. But if we consider the great mass of schools in city, town, and country throughout the land, the subjects which practically complete the elementary school curriculum—reading, writing, arithmetic, and geography—are, with the exception of the latter, found to be subjects which do not naturally belong to this period at all. Mathematics in every form is a subject conspicuously ill fitted to the child mind. It deals not with real things, but with abstractions. When referred to concrete objects, it concerns not the objects themselves, but their relations to each other. It involves comparison, analysis, abstraction. It calls for a fuller development of the association tracts and fibers of the cerebral hemispheres. The grotesque "number forms" which so many children have, and which originate in this period, are evidence of the necessity which the child feels of giving some kind of bodily shape to these abstractions which he is compelled to study. Under mathematics I do not of course include the mere mentioning or learning a number series, such as in the process called "counting," or the committing to memory of a multiplication table. Furthermore, in this and in all discussions of this kind it must be remembered that there are exceptional children in whom the mathematical faculty, or musical faculty, or literary faculty, develops much earlier than with the average child. If possible, they should have instruction suited to their peculiarities. But it is evident that, so long as children are educated in "schools," there must be a general plan of education, and that it can not be based upon exceptional children.
What we learn from physiology and psychology about the ripening of the child's mind is confirmed by the theory of the "culture epochs." I can not discuss here the doctrine of "recapitulation," with its great truths and its minor exceptions, but it is well known