Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability

Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: differences between children and adults?

“…High-span second graders used retrieval more frequently than did low-span second graders, but this eVect disappeared in fourth and sixth graders. Up until now, the relevance of working memory in children's strategy selection process was equivocal, since some studies observed a correlation between working-memory span and retrieval use (e.g., Barrouillet & Lépine, 2005), whereas others did not (e.g., Geary et al, 2004). The current study suggests that strategy selection processes tend to rely on working-memory resources in young children only.…”

“…Working memory in children has been studied in relation to mathematical disabilities (see Geary, 2004, for a review); rather than in relation to its role in normally developing children. As respects strategy selection, higher working-memory spans have been linked with less frequent use of procedural strategies and more frequent use of retrieval strategies (e.g., Barrouillet & Lépine, 2005;Geary, Bow-Thomas, Liu, & Siegler, 1996;Geary, Hoard, Byrd-Craven, &, DeSoto, 2004;Noël, Seron, & Trovarelli, 2004;Steel & Funnel, 2001). Working memory has also been related to strategy eYciency.…”

Exploring the impact of phonological awareness, visual–spatial working memory, and preschool quantity–number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study

“…Moreover, in studies focusing on children with mathematical learning disabilities, school children showed deficits in these quantity-number competencies (Gaupp, Zoelch, & Schumann-Hengsteler, 2004;Geary, Hamson, & Hoard, 2000;Geary, Hoard, Byrd-Craven, & DeSoto, 2004;Landerl, Bevan, & Butterworth, 2004). Confirming the special importance of the quantity to number-word linkage, for instance, the 7-year-olds with Williams Syndrome in the study by Ansari, Donlan, Thomas, Ewing, Peen, and Karmiloff-Smith (2003) demonstrated an extremely delay in the understanding of the cardinality principle (Level II), despite the fact that they could recite the number-word sequence (Level I) in the assessed number range almost without errors.…”

Working memory in children with reading disabilities

“…More complex addition computations require memory-based problem solving involving either the direct retrieval of facts or problem decomposition, leading to eventual automatic retrieval of facts (Geary 2004). Working memory appears to play an important role at the earliest stage of counting: children with low scores on complex memory tasks are more likely to use primitive fingerbased counting strategies than those with high scores, possibly due to the relatively low working memory demands of the activities (Geary, Hoard, Byrd, Craven, & DeSoto, 2004). …”

“…As a result, the normal incremental process of acquiring knowledge and skills in these domains is impaired (Gathercole, 2004). In a more specific account of the association between working memory and mathematical abilities, Geary et al (2004) proposed that poor working memory capacity impairs the process of acquiring mathematical facts that arises from successful counting strategies.…”