, but the development of pure appreciation and interest. There
can hardly be a regular place on the time-table for such irregular work,
comprising excursions, gardening, handwork, and literature at least, and
depending on the weather and the seasons. There should always be a
regular morning time for attending to plants and animals and for the
Nature Calendar, but no "living" teacher will be a slave to mere
time-table thraldom.

CHAPTER XXIII

EXPERIENCES OF MATHEMATICAL TRUTHS

By means of toys, handwork and games, as well as various private
individual experiments, a child touches on most sides of mathematics in
the nursery class. In experimenting with bricks he must of necessity
have considered relative size, balance and adjustment, form and
symmetry; in fitting them back into their boxes some of the most
difficult problems of cubic content; in weighing out "pretence" sugar
and butter by means of sand and clay new problems are there for
consideration; in making a paper-house questions of measurement evolve.
This is all in the incidental play of the Nursery School, and yet we
might say that a child thus occupied is learning mathematics more than
anything else. Here, if he remained till six, he did a certain amount of
necessary counting, and he may have acquired skill in recognising
groups, he may have unconsciously and incidentally performed
achievements in the four rules, but never, of course, in any shortened
or technical form. Probably he knows some figures. It is best to give
these to a child when he asks for or needs them, as in the case of
records of games. On the other hand he may be content with strokes.
Various mathematical relationships are made clear in his games or trials
of strength, such as distance in relation to time or strength, weight in
relation to power and to balance, length and breadth in relation to
materials, value of material in relation to money or work. By means of
many of his toys the properties of solids have become working knowledge
to him. Here, then, is our starting-point for the transition period.

AFTER THE NURSERY STAGE

Undoubtedly the aim of the transition class is partly to continue by
means of games and dramatic play the kind of knowledge gained in the
Nursery School; but it has also the task of beginning to organise such
knowledge, as the grouping into tens and hundreds. This organisation of
raw material and the presenting of shortened processes, as occur in the
f