so with extravagant notions
and errors.

In the study of the sciences it is an open question whether we ought to
use synthesis or analysis. It is not always necessary to choose
either. In the same process of investigation we can sometimes both
resolve and compound, and while the child thinks he is only analyzing,
we can direct him by the methods teachers usually employ. By thus
using both we make each prove the other. Starting at the same moment
from two opposite points and never imagining that one road connects
them, he will be agreeably surprised to find that what he supposed to
be two paths finally meet as one.

I would, for example, take geography at these two extremes, and add to
the study of the earth's motions the measurement of its parts,
beginning with our own dwelling-place. While the child, studying the
sphere, is transported into the heavens, bring him back to the
measurement of the earth, and first show him his own home.

The two starting-points in his geography shall be the town in which he
lives, and his father's house in the country. Afterward shall come the
places lying between these two; then the neighboring rivers; lastly,
the aspect of the sun, and the manner of finding out where the east is.
This last is the point of union. Let him make himself a map of all
these details; a very simple map, including at first only two objects,
then by degrees the others, as he learns their distance and position.
You see now what an advantage we have gained beforehand, by making his
eyes serve him instead of a compass.

Even with this it may be necessary to direct him a little, but very
little, and without appearing to do so at all. When he makes mistakes,
let him make them; do not correct them. Wait in silence until he can
see and correct them himself. Or, at most, take a good opportunity to
set in motion some thing which will direct his attention to them. If
he were never to make mistakes, he could not learn half so well.
Besides, the important thing is, not that he should know the exact
topography of the country, but that he should learn how to find it out
by himself. It matters little whether he has maps in his mind or not,
so that he understands what they represent, and has a clear idea of how
they are made.

Mark the difference between the learning of your pupils and the
ignorance of mine. They know all about maps, and he can make them.
Our maps will serve as new decorations for our room.