title: 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.
authors.affiliation: Department of Psychology, University of Saskatchewan, 9 Campus Drive, Saskatoon, SK, Canada, S7N 5A5. jamie.campbell@usask.ca.
authors.forename: Jamie I D
authors.initials: JI
authors.lastname: Campbell
authors.affiliation: Department of Psychology, University of Saskatchewan, 9 Campus Drive, Saskatoon, SK, Canada, S7N 5A5.
authors.forename: Yalin
authors.initials: Y
authors.lastname: Chen
authors.affiliation: Department of Psychology, University of Saskatchewan, 9 Campus Drive, Saskatoon, SK, Canada, S7N 5A5.
authors.forename: Kurtis
authors.initials: K
authors.lastname: Allen
authors.affiliation: Department of Psychology, University of Saskatchewan, 9 Campus Drive, Saskatoon, SK, Canada, S7N 5A5.
authors.forename: Leah
authors.initials: L
authors.lastname: Beech
mesh_terms: D000293:Adolescent; D000328:Adult; D005260:Female; D005793:Generalization, Psychological / Q000502:physiology*; D006801:Humans; D008297:Male; D055641:Mathematical Concepts; D011214:Practice, Psychological; D011340:Problem Solving / Q000502:physiology*; D014163:Transfer, Psychology / Q000502:physiology*; D055815:Young Adult
keywords: Addition; Counting; Procedures; Transfer of training