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between two others of smaller size—all strike the eye, which is
also drawn to them by the bright colours. And this striking whole
calls upon the eye to recognize the error and the hand to remedy
it by rearrangement.

A fact which accompanies the eye exercise is motor activity,
sometimes as the manipulation of the small objects to be moved
about (the cylinders of the solid insets), sometimes as carrying and
placing heavy blocks of wood. The work of the senses is then
carried out by movements which are co-ordinated round some
intelligent purpose to be achieved.

By observations made, it is seen that this movement helps
to concentrate the attention with constant fixity on a repetitive

If we consider the relative differences present in the three series
of blocks, we find them to be of mathematical proportions.

The ten rods are, individually, in agreement with the numbers

The ten prisms of the same length which, however, vary in
cross section, correspond with the squares of the numbers—

IS 22, 32,4S 52, 6s, 7S &S 92,10s.

Finally, the ten cubes, having three varying dimensions, stand
in relationship to the cubes of the numbers—

1s, 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s, 10s.

It is true that these proportions appeal to the child only
through the senses, but the mind is working on exact foundations
fitted to prepare it for mathematical operations.

The child finds easiest of all the exercises those with the cubes
(maximum differences) and most difficult those with the rods
(minimum differences).

When, however, in the elementary classes he begins to be
interested in arithmetic and geometry, he takes up again the cubes
of his early childhood and studies them over again in their relative
proportions, applying the science of numbers,