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Problem Of The Enclosed Boxes

PROCEDURE. Show the subject a cardboard box about one inch on a side.
Say: "_You see this box; it has two smaller boxes inside of it, and each
one of the smaller boxes contains a little tiny box. How many boxes are
there altogether, counting the big one?_" To be sure that the subject
understands repeat the statement of the problem: "_First the large box,
then two smaller ones, and each of the smaller ones contains a little
tiny box._"

Record the response, and, showing another box, say: "_This box has two
smaller boxes inside, and each of the smaller boxes contains two tiny
boxes. How many altogether? Remember, first the large box, then two
smaller ones, and each smaller one contains two tiny boxes._"

The third problem, which is given in the same way, states that there are
_three_ smaller boxes, each of which contains _three_ tiny boxes.

In the fourth problem there are _four_ smaller boxes, each containing
_four_ tiny boxes.

The problem must be given orally, and the solution must be found without
the aid of pencil or paper. Only one half-minute is allowed for each
problem. Note that each problem is stated twice.

A correction is permitted, provided it is offered spontaneously and does
not seem to be the result of guessing. Guessing can be checked up by
asking the subject to explain the solution.

SCORING. _Three of the four_ problems must be solved correctly within
the half-minute allotted to each.

REMARKS. Success depends, in the first place, upon ability to comprehend
the statement of the problem and to hold its conditions in mind.
Subjects much below the 12-year level of intelligence are often unable
to do this.

Granting that the problem has been comprehended, success seems to depend
chiefly upon the facility with which the constructive imagination
manipulates concrete visual imagery. In this respect it resembles the
problem of reversing the hands of a clock. With some subjects, however,
verbal imagery alone is operative. Tactual imagery would, of course,
serve the purpose as well.

This is as good a place as any to emphasize the fact that the
introspective study of mental imagery has little to contribute to the
measurement of intelligence. Intelligence tests are concerned with the
total result of a thought process, rather than with the imagery supports
of that process. Thought may be carried on almost equally well by
various kinds of imagery. As Galton showed, a person can be taught to
carry on arithmetical processes by the use of smell imagery. The kind of
imagery employed is the product of slight, innate preferences
complicated by the more or less accidental effects of habit.

We may say that imagery is to thinking what scaffolding is to
architecture. The important thing is the completed building rather than
the nature of the scaffolding employed in erecting it. No one thinks of
blaming the ill construction of a building upon the kind of scaffolding
used, for if the architect and builder are competent satisfactory
scaffolding will be found. Just as little are deficiencies or
peculiarities of imagery the real cause of low-order intelligence. We
cannot increase intelligence by formal drill in the use of supposedly
important kinds of mental imagery, any more than we can transform a
plain carpenter into a Michael Angelo by instructing him in the use of
scaffolding materials such as were employed in the construction of St.
Peter's Cathedral.

This test is of our own invention and has been brought to its present
form only after a good deal of preliminary experimentation. It
correlates fairly well with mental age as determined by the scale as a
whole. It was passed by 55 per cent of high-school pupils and by
65 per cent of unschooled business men. Success in it is thus seen not
to depend upon schooling.

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Previous: Differences Between Abstract Terms

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