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.