Elementary subtraction.

Abstract

Four experiments examined performance on the 100 "basic facts" of subtraction and found a discontinuous "stair step" function for reaction times and errors beginning with 11 - n facts. Participants' immediate retrospective reports of nonretrieval showed the same pattern in Experiment 3. The degree to which elementary subtraction depends on working memory (WM) was examined in a dual-task paradigm in Experiment 4. The reconstructive processing used with larger basic facts was strongly associated with greater WM disruption, as evidenced by errors in the secondary task: this was especially the case for participants with lower WM spans. The results support the R. S. Siegler and E. Jenkins (1989) distribution of associations model, although discriminating among the alternative solution processes appears to be a serious challenge.

Strategies in subtraction problem solving in children

“…Half of the resulting 40 problems were presented during the first session, and the other half were presented during the second session. In line with Barrouillet and Lépine, who observed a dramatic difference in response times and use of retrieval for additive problems with a sum greater than 10, on the one hand, and problems with a sum less than or equal to 10, on the other, we considered the corresponding subtractive problems with a minuend greater than 10 as large problems and those with a minuend less than or equal to 10 as small problems (see also Seyler et al, 2003).…”

“…For sake of comparison, LeFevre, Sadesky, and Bisanz (1996) reported a retrieval rate of 71% in adults solving the 100 additions with operands from 0 to 9. Seyler, Kirk, and Ashcraft (2003) reported higher rates, with 97% of the easy problems and 67% of the hard problems being solved through retrieval, but it should be noted that these authors grouped genuine retrieval of subtractive answers and the use of the basic corresponding additive fact (e.g., solving 7 -3 by retrieving the additive fact 3 + 4 = 7) within the same category. Thus, LeFevre and colleagues (2006) concluded that ''subtraction appears to be the most procedural of the single-digit arithmetic operations" (p. 214).…”

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

“…Low-span adults have been shown to perform worse on arithmetic tasks than high-span adults (e.g., Jurden, 1995;Seyler, Kirk, & Ashcraft, 2003), but it is not known whether this eVect is due to individual diVerences in strategy selection, strategy eYciency, or both. 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.…”

“…Consequently, it is less demanding to increase multiplication eYciencies than to increase addition eYciencies. Strategy selection and strategy eYciency processes in other arithmetic operations (such as subtraction and division) have been investigated less frequently (but see Campbell & Xue, 2001;Imbo & Vandierendonck, 2007b, c;Robinson et al, 2006;Seyler et al, 2003) and are an issue for further research.…”

Cultural differences in complex addition: Efficient Chinese versus adaptive Belgians and Canadians.

“…The phonological loop, in contrast, is needed for complex arithmetic but is only applied to simple arithmetic when non-retrieval strategies, such as counting are used (e.g., Hecht, 2002;Imbo & Vandierendonck, 2007a,b,c;Seyler, Kirk, & Ashcraft, 2003). The possible roles of the visuospatial sketchpad and the episodic buffer in mental arithmetic are theoretically less established and will not be considered in the current research.…”