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which theoretic writers almost always fall. We meet in every periodical,
and in every treatise, and, in fact, in almost every conversation on the
subject, with remarks which sound very well by the fireside, but they
are totally inefficient and useless in school, from their being
apparently based upon the supposition that the teacher has but _one_
pupil to attend to at a time. The great question in the management of
schools is not how you can take _one_ scholar, and lead him forward most
rapidly in a prescribed course, but how you can classify and arrange
_numbers_, comprising every possible variety both as to knowledge and
capacity, so as to carry them all forward effectually together.

The extent to which a teacher may multiply his power by acting on
numbers at a time is very great. In order to estimate it, we must
consider carefully what it is when carried to the greatest extent to
which it is capable of being carried under the most favorable
circumstances. Now it is possible for a teacher to speak so as to be
easily heard by three hundred persons, and three hundred pupils can be
easily so seated as to see his illustrations or diagrams. Now suppose
that three hundred pupils, all ignorant of the method of reducing
fractions to a common denominator, and yet all old enough to learn, are
collected in one room. Suppose they are all attentive and desirous of


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