Transfer of training in alphabet arithmetic.

Abstract

In recent years, several researchers have proposed that skilled adults may solve single-digit addition problems (e.g., 3 + 1 = 4, 4 + 3 = 7) using a fast counting procedure. Practicing a procedure, however, often leads to transfer of learning to unpracticed items; consequently, the fast counting theory was potentially challenged by subsequent studies that found no generalization of practice for simple addition. In two experiments reported here (Ns = 48), we examined generalization in an alphabet arithmetic task (e.g., B + 5 = C D E F G) to determine that counting-based procedures do produce generalization. Both experiments showed robust generalization (i.e., faster response times relative to control problems) when a test problem's letter augend and answer letter sequence overlapped with practiced problems (e.g., practice B + 5 = C D E F G, test B + 3 = C D E ). In Experiment 2, test items with an unpracticed letter but whose answer was in a practiced letter sequence (e.g., practice C + 3 = DEF, test D + 2 = E F) also displayed generalization. Reanalysis of previously published addition generalization experiments (combined n = 172) found no evidence of facilitation when problems were preceded by problems with a matching augend and counting sequence. The clear presence of generalization in counting-based alphabet arithmetic, and the absence of generalization of practice effects in genuine addition, represent a challenge to fast counting theories of skilled adults' simple addition.