Speed of adding and comparing numbers.

Abstract

College students were presented a series of problems consisting of two numbers to be added (A + IB) and a comparison number (C) ranging 13-153. They were to choose the larger, A 4- B or C, as rapidly as possible. Errors and latency increased with size of numbers, except when A + B and C were on opposite sides of 100. Speed and accuracy increased with the difference between A and B, but were also high when A = B. Errors and latency increased when the absolute difference between A + B and C was relatively small, requiring high accuracy on the part of 6". The results were interpreted in terms of an analog operation in which 5s place the magnitudes symbolized by numbers on the number line (an imaginary analog) for manipulating and judging. College students can add two numbers rapidly and accurately. The process is in-teresting in that it accomplishes a genuine mathematical act rapidly and unconsciously. Despite the contrast between elementary cal-culation and "real mathematics, " it is still true, from a psychologist's point of view, that adding is complex problem solving. To measure the speed of adding, one method would be to present a problem and record the time at which 5 " verbally supplies the answer. The difficulties are that: (a) such verbal responses are difficult to time, for they require a "voice-key " which is al-ways subject to extraneous noises, and (b) Ss often stretch out complex numerical re-sponses, saying, e.g., "one hundred and-uh-fifty-fifty-three. " It is difficult to know just when S can be said to have added the terms. These difficulties were avoided in the present study by complicating the task slightly. On each trial, S was presented the two numbers to be added and a third num-ber somewhere of the order of magnitude of the sum. He was required to judge and indicate by a button press which was larger, the sum of the two terms or the alternative number. In this way, the process of adding