give explanations. Let
the rationale of the various processes through which the child goes,
receive a certain amount of attention. But the extreme into which some
are now going, in primary education, is that of giving too much time to
explanation and to theory, and too little to practice. We reverse, too,
the order of nature in this matter. What it now takes weeks and months
to make clear to the immature understanding, is apprehended at a later
day with ease and delight at the very first statement. There is a clear
and consistent philosophy underlying this whole matter. It is simply
this. In the healthy and natural order of development in educating a
young mind, theory should follow practice, not precede it. Children
learn the practice of arithmetic very young. They take to it naturally,
and learn it easily, and become very rapidly expert practical
accountants. But the science of arithmetic is quite another matter, and
should not be forced upon them until a much later stage in their
advancement.

To have a really correct apprehension of the principle of decimal
notation, for instance, to understand that it is purely arbitrary, and
that we might in the same way take any other number than ten as the base
of a numerical scale,--that we might increase for instance by fives, or
eights, or nines, or twelves, just as well as by tens--all this requires
considerable maturity of intellect, and some subtlety of reasoning.
Indeed I doubt whether many of the pretentious sciolists, who insist so
much on young children giving the rationale of everything, have
themselves ever yet made an ultimate analysis of the first step in
arithmetical notation. Many of them would open their eyes were you to
tell them, for instance, that the number of fingers on your two hands
may be just as correctly expressed by the figures 11, 12, 13, 14, or 15,
as by the figures 10,--a truism perfectly familiar to every one
acquainted with the generalizations of higher arithmetic. Yet it is
up-hill work to make the matter quite clear to a beginner. We may wisely
therefore give our children at first an arbitrary rule for notation. We
give them an equally arbitrary rule for addition. They accept these
rules and work upon them, and learn thereby the practical operations of
arithmetic. The theory will follow in due time. When perfectly familiar
with the practice and the forms of arithmetic, and sufficiently mature
in intellect, they awaken gradually and surely, and