me, it should not be severely reproved, because nine
children in ten honestly think, that if the lesson was learned so that
it could be recited any where, their duty is discharged. But it should
be kindly, though distinctly explained to them, that, in the business of
life, they must have their knowledge so much at command, that they can
use it, at all times, and in all circumstances, or it will do them
little good.

One of the most common causes of difficulty in pursuing mathematical
studies, or studies of any kind, where the succeeding lessons depend
upon those which precede, is the fact that the pupil, though 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 connexion 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 cannot
afterwards 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 would have forgotten the distinction,
but by dwelling upon it, a few lessons, he may fix it for ever. The
first lesson might be 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 wel