knowledge of numerical quantity, and, as a consequence, his numerical ideas are incurably associated with the peculiarities of the figures. When he hears the word seven he does not really think of seven or seven-ness at all, even now, he thinks of a number rather like four and very unlike six. Then again, six and nine are mysteriously and unreasonably linked in his mind, and so are three and five. He confuses numbers like sixty-three and sixty-five, and finds it hard to keep seventy-four distinct from forty-seven. Consequently, when it came to the multiplication table, he learnt each table as an arbitrary arrangement of relationships, and with an extraordinary amount of needless labour and punishment. But obviously with cubes or abacus at hand, it would be the easiest thing in the world for a child to construct and learn its own multiplication table whenever the need arose.] it should be capable of some mental and experimental arithmetic, and I am told that a child of five should be able to give the _sol-fa_ names to notes, and sing these names at their proper pitch. Possibly in social intercourse the child will have picked up names for some of the letters of the alphabet, but there is no great hurry for that before five certainly, or even later. There is still a vast amount of things immediately about the child that need to be thoroughly learnt, and a premature attack on letters divides attention from these more appropriate and educational objects. It should, for the reason given in the footnote, be still ignorant of the Arabic numerals. It should be able to handle a pencil and amuse itself with freehand of this sort:--and its mind should be quite uncontaminated by that imbecile drawing upon squared paper by means of which ignorant teachers destroy both the desire and the capacity to sketch in so many little children. Such sketching could be enormously benefited by a really intelligent teacher who would watch the child’s efforts, and draw with the child just a little above its level. For example, the teacher might stimulate effort by rejoining to such a sketch as the above, something in this vein:-- The child will already be a great student of picture-books at five, something of a critic (after the manner of the realistic school), and it will be easy to egg it almost imperceptibly to a level where copying from simple outline illustrations will become possible. About five, a present of some one of the plastic substitutes for modelling clay now sold by educational dealers, _plasticine_ for example, will be a discreet and acceptable present to the child--if not to its nurse.