e will
discover who will take the trouble to work a simple addition sum,
involving hundreds, in Roman figures. Children are always taught the
number of the house they live in, which makes a starting-point. If, for
instance, 35 is compared with XXXV a meaning is given to the 3.

Many teachers make formal sums of numbers which could quite well be
added without any writing at all. By using any kind of material by which
ten can be made plain as a higher unit--bundles of sticks or tickets,
Sonnenschein's apparatus, Miss Punnett's number scheme, or the new
Montessori apparatus with its chains of beads: the material used is of
no great consequence--children should be able to deal as easily with
tens as with ones, and there is no need for little formal sums which
have no meaning.

Everything in daily life should be used before formal work is attempted.
"Measure, reckon, weigh, compare," said Rousseau. Children love to
measure, whether by lineal or liquid measure, or by learning to tell the
time or to use a pair of scales.

There are a few occasions when interest is in actual number relations,
as when a child for himself discovers that two sixes is six twos. One
boy on his own account compared a shilling and an hour, and said that he
could set out a shilling in five parts by the clock. He looked at the
clock and chose out a sixpence, a threepence, and 3 pennies. But usually
what is abstract belongs to a stage farther on.

So we can end where we began, by letting Froebel once more define the
Kindergarten.

"Creches and Infant Schools must be raised into Kindergartens wherein
the child is treated and trained according to his whole nature, so that
the claims of his body, his heart and his head, his active, moral and
intellectual powers, are all satisfied and developed.

"Not the training of the memory, not learning by rote, not familiarity
with the appearances of things, but culture by means of action,
realities and life itself, bring a blessing upon the individual, and
thereby a blessing upon the whole community; since each one, be he the
highest or the humblest, is a member of the community."

PART II

THE CHILD IN THE STATE SCHOOL

I. THINGS AS THEY ARE

CHAPTER XIV

CERTAIN CHARACTERISTICS OF GROWTH

Early in the nineteenth century two men, moved by very different
impulses, founded what might be considered the beginnings of the Infant
School. For nearly fifty years their work grew separately,