Standardized Assessment of Strategy Use and Working Memory in Early Mental Arithmetic Performance

Abstract

Although children's use of a variety of strategies to solve arithmetic problems has been well documented, there is no agreed upon standardized and validated method for assessing this mix. We examined the convergent validity of typically achieving (TA, n = 39) and low achieving (LA, n = 20) 2 nd and 3 rd grade children's strategy choices in simple addition using three different methods: child self-report, observer-report, and response time (RT). The high concordance between child and observer reports (Kappa = .948) in both groups suggests that the participants were aware of, and could accurately report, the strategies they used. The Receiver-Operator Characteristic (ROC) analysis showed that RT accurately differentiated between retrieval and counting (AUC = 82%). The specificity and sensitivity of the ROC profiles were significantly greater for the TA group than for LA group, even though the groups did not differ in the overall strategy mix. Our findings suggest that ROC analysis is more sensitive to group differences in the mechanisms governing strategy choice than observation or child report. Children's use of retrieval strategies as well as accuracy during both retrieval and counting trials were all related to the central executive, but not the phonological and visuospatial sketchpad, component of working memory. We discuss the implication of these findings for early mathematical learning.

Microgenetic patterns of children’s multiplication learning: Confirming the overlapping waves model by latent growth modeling

“…Although relationships have often been found between working memory and strategy selection (e.g., Barouillet & Lépine, 2005;Geary et al, 2004;Wu et al, 2008), and between working memory and accuracy (for a review, see Raghubar et al, 2010) we incorporated both analyses simultaneously and longitudinally by means of a microgenetic design. We found indications for a twofold role of working memory, which was significantly related to both strategy choice and accuracy.…”

“…Children of this age are capable of reporting their strategies (Wu et al, 2008). The procedure lasted approximately 20 minutes per child per session.…”

“…In second to fourth grade, children with high working memory used the retrieval strategy more often than children with lower working memory when solving addition problems (Barouillet & Lépine, 2005;Wu et al, 2008). In first and third grade, high working memory skills were also associated with less finger counting, and in third and fifth grade with more frequent use of more advanced decomposition strategies (Geary, Hoard, Byrd-Craven, & DeSoto, 2004;Noël et al, 2004).…”

“…Success in these early stages likely enables transitions to more mature strategies, which require fewer steps and are therefore faster and less error-prone, and eventually enable relying on retrieval. Retrieval requires few working memory resources (Imbo & Vandierendonck, 2007; but see Wu et al, 2008).…”

Contribución de los Componentes de la Memoria de Trabajo a la Eficiencia en Aritmética Básica Durante la Edad Escola

“…Algunos autores encuentran que solo la MT visuo-espacial está vinculada al desempeño en matemáticas, pero no la MT verbal (Amor Díaz & Torres Díaz, 2016;Dumontheil & Klingberg, 2012), mientras que otros reportan que las tareas de MT verbal se vinculan al desempeño matemático solo si involucran números (Wu et al, 2008). A pesar de lo anterior, Friso-van den Bos, van der Ven, Kroesbergen y van Luit (2013), en su meta-análisis sobre estudios que exploran la relación entre el desempeño matemático y los componentes de la MT en niños de entre 4 y 12 años de edad, mostraron que, de manera general, todos estos componentes aportan una contribución única a la varianza en el desempeño matemático, independientemente de otras variables de dominio general, como la inteligencia, la habilidad lectora, la edad y la memoria a corto plazo.…”