hough he may
understand what precedes, is not _familiar_ with it. This is very
strikingly the case with Geometry. The class study the definitions, and
the teacher supposes they fully understand them; in fact, they do
_understand_ them, but the name and the thing are so feebly connected in
their minds that a direct effort and a short pause are necessary to
recall the idea when they hear or see the word. When they come on,
therefore, to the demonstrations, which in themselves would be difficult
enough, they have double duty to perform. The words used do not readily
suggest the idea, and the connection of the ideas requires careful
study. Under this double burden many a young geometrician sinks
discouraged.

A class should go on slowly, and dwell on details so long as to fix
firmly and make perfectly familiar whatever they undertake to learn. In
this manner the knowledge they acquire will become their own. It will be
incorporated, as it were, into their very minds, and they can not
afterward be deprived of it.

The exercises which have for their object this rendering familiar what
has been learned may be so varied as to interest the pupil very much,
instead of being tiresome, as it might at first be supposed.

Suppose, for instance, a teacher has explained to a large class in
grammar the difference between an adjective and an adverb; if he leave
it here, in a fortnight one half of the pupils would have forgotten the
distinction, but by dwelling upon it a few lessons he may fix it
forever. The first lesson might be to require the pupils to write twenty
short sentences containing only adjectives. The second to write twenty
containing only adverbs. The third to write sentences in two forms, one
containing the adjective, and the other expressing the same idea by
means of the adverb, arranging them in two columns, thus:

He writes well. | His writing is good.

Again, they may make out a list of adjectives, with the adverbs derived
from each in another column. Then they may classify adverbs on the
principle of their meaning, or according to their termination. The
exercise may be infinitely varied, and yet the object of the whole may
be to make _perfectly familiar_, and to fix forever in the mind the
distinction explained.

These two points seem to me to be fundamental, so far as assisting
pupils through the difficulties which lie in their way is concerned.
Diminish the difficulties as far as is necessary by shortening