The subjects thus far discussed, that may be brought into close relation to the central stories, are oral and written language, reading and literature, geography, and the natural sciences. The connection between these branches are numerous and strong at every step. _Drawing_ has a very intimate and important relation to the objects described in history, natural science, arithmetic, and geography; while the _songs_ learned should express in those poetic and rhythmic forms which appeal so strongly to the feelings, many of the noblest ideas suggested by travel, scenery, history, and the experiences of home life.
_Arithmetic_, finally, seems to stand like an odd sheep among the studies. It is certainly the least social of the common school branches. While avoiding all forced connection between arithmetic and other studies, we shall find some points where the relations are simple and clear. Children in the first grade should see numbers in the leaves, flowers, trees, and animals they study. At the beginning of the first grade this would be a good informal way of beginning numbers. The value of _objects_ in first and second grade number is so great that it is only a question as to how far the objects suggested by other lessons may be used.
But we are speaking of concentration in the fourth and fifth grades. In the stories and in geography we deal with journeys up great rivers, with the height of mountains, with the extent of valleys and lakes, with regular forts, mounds, and enclosures, with companies and bodies of men, with railroads, cities, and agricultural products, and with many other topics which suggest excellent practical problems in arithmetic for these grades. All such careful arithmetical computations add clearness and definiteness to historical and geographical ideas. The natural sciences have been so little systematically taught in our common schools, that we are scarcely able to realize what connection may be made between them and arithmetic. We know that in the advanced study and applications of some of the natural sciences, mathematics is an essential part.
A brief retrospect will make it appear that the history stories, natural sciences, and geography, with the more formal studies, such as reading, language, and arithmetic, may be brought into a _close organic harmony_. Each of them depends upon and throws light upon the other; and while the connections are natural, not forced, there is a concentration upon the central historical and literary matter that makes moral character the highest aim of teaching.