on; taught to play guessing games with marbles in a hand, and the like.
The abacus, the hundred square and the thousand cube, will then in all
probability become its cardinal numerical memories. Playing cards
(without corner indices) and dominoes supply good recognizable
arrangements of numbers, and train a child to grasp a number at a
glance. The child should not be taught the Arabic numerals until it has
counted for a year or more. Experience speaks here. I know one case
only too well of a man who learnt his Arabic numerals prematurely,
before he had acquired any sound experimental 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