RESUMEN
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.
Asunto(s)
Generalización Psicológica/fisiología , Conceptos Matemáticos , Práctica Psicológica , Solución de Problemas/fisiología , Transferencia de Experiencia en Psicología/fisiología , Adolescente , Adulto , Femenino , Humanos , Masculino , Adulto JovenRESUMEN
Several types of converging evidence have suggested recently that skilled adults solve very simple addition problems (e.g., 2 + 1, 4 + 2) using a fast, unconscious counting algorithm. These results stand in opposition to the long-held assumption in the cognitive arithmetic literature that such simple addition problems normally are solved by fact retrieval from declarative memory. Here we tested a large sample of diversely skilled and culturally diverse men and women at the University of Saskatchewan and examined multiple categories of simple (1 digit plus 1 digit) addition problems for evidence of generalization of practice, a signature of procedure use. The procedure-based 0 + N = N problems presented clear evidence of generalization (i.e., practicing a subset of 0 + N problems lead to speed-up for a different subset of 0 + N problems), but there was no evidence of such generalization of practice for the nonzero problems, although the experiment had good power to detect small effects. Given that generalization of practice is a basic marker of procedure-based processing, its absence for the nonzero addition problems casts doubt on the compacted counting theory.