Induction Test: Finding A Rule

PROCEDURE. Provide six sheets of thin blank paper, say 81/2 x 11 inches.

Take the first sheet, and telling the subject to watch what you do, fold

it once, and in the middle of the folded edge tear out or cut out a

small notch; then ask the subject to tell you _how many holes there will

be in the paper when it is unfolded_. The correct answer, _one_, is

nearly always given without hesitation. But whatever the answer, unfold
/> the paper and hold it up broadside for the subject's inspection. Next,

take another sheet, fold it once as before and say: "_Now, when we

folded it this way and tore out a piece, you remember it made one hole

in the paper. This time we will give the paper another fold and see how

many holes we shall have._" Then proceed to fold the paper again, this

time in the other direction, and tear out a piece from the folded side

and ask how many holes there will be when the paper is unfolded. After

recording the answer, unfold the paper, hold it up before the subject so

as to let him see the result. The answer is often incorrect and the

unfolded sheet is greeted with an exclamation of surprise. The governing

principle is seldom made out at this stage of the experiment. But

regardless of the correctness or incorrectness of the first and second

answers, proceed with the third sheet. Fold it once and say: "_When we

folded it this way there was one hole._" Then fold it again and say:

"_And when we folded it this way there were two holes._" At this point

fold the paper a third time and say: "_Now, I am folding it again. How

many holes will it have this time when I unfold it?_" Record the answer

and again unfold the paper while the subject looks on.

Continue in the same manner with sheets four, five, and six, adding one

fold each time. In folding each sheet recapitulate the results with the

previous sheets, saying (with the sixth, for example): "_When we folded

it this way there was one hole, when we folded it again there were two,

when we folded it again there were four, when we folded it again there

were eight, when we folded it again there were sixteen; now, tell me

how many holes there will be if we fold it once more._" In the

recapitulation avoid the expression "_When we folded it once, twice,

three times_," etc., as this often leads the subject to double the

numeral heard instead of doubling the number of holes in the previously

folded sheet. After the answer is given, do not fail to unfold the paper

and let the subject view the result.

SCORING. The test is passed _if the rule is grasped by the time the

sixth sheet is reached_; that is, the subject may pass after five

incorrect responses, provided the sixth is correct and the governing

rule can then be given. It is not permissible to ask for the rule until

all six parts of the experiment have been given. Nothing must be said

which could even suggest the operation of a rule. Often, however, the

subject grasps the principle after two or three steps and gives it

spontaneously. In this case it is unnecessary to proceed with the

remaining steps.

REMARKS. This test was first used by the writer in a comparative study

of the intellectual processes of bright and dull boys in 1905, but it

was not standardized until 1914. Rather extensive data indicate that it

is a genuine test of intelligence. Of 14-year-old school children

testing between 96 and 105 I Q, 59 per cent passed this test; of

14-year-olds testing below 96 I Q, 41 per cent passed; of those testing

above 105, 71 per cent passed. That is, the test agrees well with the

results obtained by the scale as a whole. Of "average adults" only

10 per cent fail; and of "superior adults," fewer than 5 per cent. As a

rule, the higher the grade of intelligence, the fewer the steps

necessary for grasping the rule. Of the superior adults, only

35 per cent fail to get the rule as early as the end of the fourth step.

The test is little affected by schooling, and apart from differences in

intelligence it is little influenced by age. Other advantages of the

test are the keen interest it always arouses and its independence of

language ability. It has been used successfully with immigrant subjects

who had been in this country but a few months.

We have named the experiment an "induction test." It might be supposed

that the solution would ordinarily be arrived at by deduction, or by an

_a-priori_ logical analysis of the principle involved. This, however, is

rarely the case. Not one average adult out of ten reasons out the

situation in this purely logical manner. It is ordinarily only after one

or more mistakes have been made and have been exposed by the examiner

holding up the unfolded paper to view that the correct principle is

grasped. In the absence of deductive reasoning the subject must note

that each unfolded sheet contains twice as many holes as the previous

one, and must infer that folding the paper again will again double the

number. The ability tested is the ability to generalize from

particulars where the common element of the particulars can be discerned

only by the selective action of attention, in this case attention to the

fact that each number is the double of its predecessor.