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.
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