Factors Influencing the Recall of Compound Numbers

Contributions to the Study of Psycho-physiological Induction (44)

Abstract

The purpose of the present investigation was to explain a nature of error which occures when subjects are required to repeat the multiplication table, on the basis of the reproduction law underlying the recall of a single number. The experimental procedure was as follows : Subjects were requested to write any digit between 0 and 9 in response to a stimulus digit (digits used as stimuli ranged from 0 to 9). Instruction was given to avoid mere repetition of a presented digit and foreward or backward sequence responses.
The intervals between the stimulus digit and the response digit was examined with special attention to the frequency of occurence of each interval.
Many years ago, Obonai and Ito, analized the causes of errors in the repetition of the multiplication table. It was demonstrated that the majority of errors were caused by replacing one of the component numbers. For instance 2×6=14, in this case the 6 was replaced by 7 yielding an erroneous answer, 14.
In the present study, we proceeded a step further and investigated the relation between the tendency to reproduce an associated digit when the stimulus digit was a single unit and when the stimulus digits were composed of compounds as in the multiplication table. The results were as follow; (1) Subjects were requested to respond freely with a digit between 0-9, when a stimulus digit was given. Inspection of Fig. 1 in Jap. text shows that there is a considerable tendency for subjects to reproduce an adjoining digit in their response when the stimulus digit is a single unit. Only a small percentage gave responses which were as much as 4, 5, 6, …… intervals removed from stimulus digit.
(2) Inspection of Figs. 3 and 4 shows that in multiplication error the strength of replacement of digit declines with the increasing degree of remoteness of two digits. Therefore, it is clear that the cause of error in multiplication results from remote association, i.e. induced reproduction, of a single digit.
(3) Fig. 5 shows the various degree to which the latter factor effects error in each stimulus digit. Different digits show different reproductive tendencies. Digit 7, for instance, shows the most marked tendency to induce an adjoining digit, digits 8, 9, 6, and 2 follow in that order as regards strength of their induction tendencies. The similarity in pronounciation of 4 and of 7 in the Japanese language makes the former a special case.
(4) Number replacement occurs more often in the multiplicand than in the multiplier. (Fig. 3) This, to the writer's belief, is due to the retroactive inhibitory effect of the multiplier which results in a failure to reproduce the multiplicand.
(5) As regards the size of the reproductive error, a larger number error occures among small digits, and the reverse holds true for larger digits (Fig. 8). The same phenomenon is also seen in the free reproduction experiment when single digits are used as stimuli (Fig. 2). Thus, we can say safely that a source of error in the multiplication table is the reproductive tendency associated with use of single digits as stimuli. The phenomenon we have described here resembles a central tendency that is seen in the process of perception and judgement and seems to have the same underlying mechanism.