CHAPTER XVIII
INSTRUCTIONS FOR YEAR XIV.
XIV, 1. Vocabulary (fifty definitions, 9000 words)
Procedure and Scoring, as in [VIII], [X], and [XII]. At year XIV fifty words must be correctly defined.
XIV, 2. Induction test: finding a rule
Procedure. Provide six sheets of thin blank paper, say 8½ × 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.