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The stand together with the cylinders belonging to it, looks,
rather like the ordinary receptacle for weights belonging to a

Within the cylinders embedded in their supports there exists a
regularly graduated difference:

1.    In the first stand, the cylinders are all of the same dia-
meter, but differ in height.   The shortest is 4 cm. high, and others-
increase each by half a centimetre, up to the tenth, which is 5 cms.

2.   In the second stand, the cylinders are all of equal height,
but the circular section decreases regularly.   Whilst the diameter
of the section of the smallest cylinder is i cm., the diameters of
the other sections increase by half a centimetre up to a diameter
of 5 cms.

3.   In the third stand, the cylinders diminish in all three*
dimensions, combining the differences met with in the two other

4.    Finally, in the fourth stand, the cylinders differ in three
dimensions, but height and section in opposite directions.

At first, the children take only one of the stands, hence four
children can find occupation with them at the same tone. The
exercise is the same with all four insets. After being placed on
the table, they are used by removing all the pieces, mixing them
up and then replacing them, fitting each piece into its appropriate
hole. In this exact correspondence between the cylinder and the
hole in the stand there exists the * control of error'.

If, for example, in the case of the first inset the child makes-
a mistake in putting it back, one cylinder will disappear within a
hole which is too deep, and another will project because one is
not deep enough. The irregularity which results, apparent to sight
and touch, affords an absolute, material control of the mistake
made. It follows that the objects must be put back into their
places with care, that the replacement of them must be repeat-
edly tested, so that all may be in place at the same level in the