In addition the child should be able to count, [Footnote: There can be
little doubt that many of us were taught to count very badly, and that
we were hampered in our arithmetic throughout life by this defect.
Counting should be taught be means of small cubes, which the child can
arrange and rearrange in groups. It should have at least over a hundred
of these cubes--if possible a thousand; they will be useful as toy
bricks, and for innumerable purposes. Our civilization is now wedded to
a decimal system of counting, and, to begin with, it will be well to
teach the child to count up to ten and to stop there for a time. It is
suggested by Mrs. Mary Everest Boole that it is very confusing to have
distinctive names for eleven and twelve, which the child is apt to
class with the single numbers and contrast with the teens, and she
proposes at the beginning (_The Cultivation of the Mathematical
Imagination_, Colchester: Benham & Co.) to use the words "one-ten,"
"two-ten," thirteen, fourteen, etc., for the second decade in counting.
Her proposal is entirely in harmony with the general drift of the
admirably suggestive diagrams of number order collected by Mr. Francis
Gallon. Diagram after diagram displays the same hitch at twelve, the
predominance in the mind of an individualized series over
quantitatively equal spaces until the twenties are attained. Many
diagrams also display the mental scar of the clock face, the early
counting is overmuch associated with a dial. One might perhaps head off
the establishment of that image, and supply a more serviceable
foundation for memories by equipping the nursery with a vertical scale
of numbers divided into equal parts up to two or three hundred, with
each decade tinted. When the child has learnt to count up to a hundred
with cubes, it should be given an abacus, and it should also be
encouraged to count and check quantities with all sorts of things,
marbles, apples, bricks in a wall, pebbles, spots on dominoes, and so