It is desirable, too, that what I have recommended in reference to the whole school should be done in respect to the case of each individual.  When a new pupil comes under your charge, ascertain (by other means, however, than formal examination) to what stage his education has advanced, and deliberately consider what objects you can reasonably expect to effect for him while he remains under your care.  You can not, indeed, always form your plans to suit so exactly your general views in regard to the school and to individuals as you could wish.  But these general views will, in a thousand cases, modify your plans, or affect in a greater or less degree all your arrangements.  They will keep you to a steady purpose, and your work will go on far more systematically and regularly than it would do if, as in fact many teachers do, you were to come headlong into your school, take things just as you find them, and carry them forward at random without end or aim.

This survey of your field being made, you are prepared to commence definite operations, and the great difficulty in carrying your plans into effect is how to act more efficiently on the greatest numbers at a time. The whole business of public instruction, if it goes on at all, must go on by the teacher’s skill in multiplying his power, by acting on numbers at once. In most books on education we are taught, almost exclusively, how to operate on the individual.  It is the error into 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 learning, it is very plain that the process may be explained to the whole at once, so that half an hour spent in that exercise would enable a very large