Transfer of training in alphabet arithmetic

• Published in: Memory & cognition 2016-11, Vol.44 (8), p.1288-1300
• Main Authors: Campbell, Jamie I. D., Chen, Yalin, Allen, Kurtis, Beech, Leah
• Format: Article
• Language: English
• Subjects: Addition & subtraction; Adolescent; Adult; Behavioral Science and Psychology; Cognition & reasoning; Cognitive ability; Cognitive Psychology; Experiments; Female; Generalization (Psychology) - physiology; Humans; Male; Mathematical Concepts; Memory; Multiplication & division; Practice (Psychology); Problem Solving - physiology; Psychology; Studies; Transfer (Psychology) - physiology; Young Adult
• ISSN: 0090-502X; 1532-5946
• DOI: 10.3758/s13421-016-0631-x

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 ( N s = 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 = DE F , 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.