nd 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.

Since real concentration is practically a new educational undertaking,
it involves a number of _unsolved subordinate problems_; for instance,
how far shall science lessons, grammar, and geography follow their own
principles of selection, based on the nature and scientific arrangement
of their materials, while keeping up the dependence upon and
connections with the central subject. But if concentration is a true
principle of education, it is evident that none of these problems can
be solved until concentration has been agreed upon and made
fundamental. In this case those teachers who are trying to lay out
courses of study in geography, natural science, or history, without
regard to the relation of studies to each other, will have most of
their work to do over again.

A little reflection will convince us, perhaps, that a year's work thus
concentrated will produce a much more powerful and lasting impression
upon children than the loose aggregation of facts which is usually
collected during a year's work. Not