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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