l processes. But for making expert practical
accountants, which is generally quoted as its distinguishing benefit, I
confess I am partial to the slate and pencil, and to that venerable
parallelogram, the old-fashioned Multiplication Table, in the shape it
came down to us from Pythagoras.

The reader will not, of course, understand me as wishing to discard
Mental arithmetic. All that I mean to suggest is the inquiry, whether
its advantages are not looked for in the wrong direction, whether they
are not sometimes over-estimated, and whether this mode of teaching
arithmetic, especially when pursued as a hobby, is not sometimes pushed
too far, and made the means of curious display, rather than of solid and
lasting benefit. In teaching mental arithmetic, too, for I would
certainly teach it to some extent, I would suggest the expediency of
teaching children, in performing these mental operations, to think in
figures, in other words, to form conceptions of the arithmetical figures
and signs, which are visible objects, rather than of quantities and
relations, which are mere abstractions. Multiplication is a mere
metaphysical entity. The sign of multiplication is a simple, visible
symbol, addressed to the eye, and capable of being conceived by the mind
with unmistakable clearness and precision. A child counting its fingers
in the first steps of learning to add and to take away, is a pretty
sight, doubtless. But it is painful to see a person grown to man's
estate, and in other respects well educated, as I have very often seen,
still dependent upon the same infantile contrivance,--still counting
fingers when required to add long columns of figures. Count the fingers,
if necessary, in order to get the child under way. But the sooner the
leading-string can be dropped, and the child can be made to picture in
his mind the pure figures and signs, their combinations and results,
without reference to fingers, or apples, or cakes, or tops, the better
for his arithmetic, and the better for his mental cultivation.

The subject has a painful interest for the Sabbath-School Teacher. The
teacher of the infant school, indeed, has some opportunity for employing
this principle of pictorial representation, in teaching the little ones
of his charge. The infant school-room usually has conveniences for maps
and picture cards and diagrams, and even blackboards; and most infant
school teachers wisely avail themselves of the opportunity afforded. But
g