ith objects, in handling which he may
associate the number facts with certain acts of grouping objects. It is
in this way that a child should approach such problems as:

How many fours are there in twelve?
How many feet in a yard?
How many quarts in a peck? etc.

The teaching of fractions by means of scissors and cardboard; the
teaching of board measure by having boards actually measured; the
teaching of primary geography by means of the sand-table; the teaching
of nature study by excursions to fields and woods; these are all easy
because we are working in harmony with the child's natural tendency to
be physically active. The more closely the lesson problem adjusts itself
to these tendencies, the greater will be the pupil's activity and hence
the more rapid his progress.

2. Through Constructive Instinct.--The child's delight in motor
expression is closely associated with his instinctive tendency to
construct. When, therefore, new knowledge can be presented to the child
in and through constructive exercises, he is more likely to feel its
value. Thus it is possible, by means of such occupations as paper
folding or stick-laying, to provide interesting problems for teaching
number and geometric forms. In folding the check-board, for example, the
child will master necessary problems relating to the numbers, 2, 4, 8,
and 16. In learning colour, it is more interesting for the child to
study different colours through painting leaves, flowers, and fruits,
than to learn them through mere sense impressions, or even through
comparing coloured objects, as in the Montessori chromatic exercises. A
study of the various kindergarten games and occupations would give an
abundance of examples illustrative of the possibility of presenting
knowledge in direct association with various types of constructive
work.

=A. Activity must be Directly Connected with Problem.=--It may be noted,
however, that certain dangers associate themselves with these methods.
One danger consists in the fact that, if care is not taken, the physical
activity may not really involve the knowledge to be conveyed, but may be
only very indirectly associated with it. Such a danger might occur in
the use of the Montessori colour tablets for teaching tints and shades.
In handling those, kindergarten children show a strong inclination to
build flat forms with the tablets. Now unless these building exercises
involve the distinguishing of the various tints an