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

Abstract

Adult's simple-arithmetic strategy use depends on problem-related characteristics, such as problem size and operation, and on individual-diVerence variables, such as working-memory span. The current study investigates (a) whether the eVects of problem size, operation, and working-memory span on children's simple-arithmetic strategy use are equal to those observed in adults, and (b) how these eVects emerge and change across age. To this end, simple-arithmetic performance measures and a working-memory span measure were obtained from 8-year-old, 10-year-old, and 12-year-old children. Results showed that the problem-size eVect in children results from the same strategic performance diVerences as in adults (i.e., sizerelated diVerences in strategy selection, retrieval eYciency, and procedural eYciency). Operation-related eVects in children were equal to those observed in adults as well, with more frequent retrieval use on multiplication, more eYcient strategy execution in addition, and more pronounced changes in multiplication. Finally, the advantage of having a large working-memory span was also present in children. The diVerences and similarities across children's and adult's strategic performance and the relevance of arithmetic models are discussed.

Touch Arithmetic: A process-based Computer-Aided Assessment approach for capture of problem solving steps in the context of elementary mathematics

“…The test revealed significant differences between the mean time of the place-value strategy (p=0.01) and the aspresented (p=0.13) and other (p=0.58) strategies. This agrees with Imbo and Vandierendonck (2008) who argued that computational strategies are more efficient than procedural strategies. Therefore the MuTAT application can detect the relative efficiency of strategies…”

“…Overall, the literature suggests that conceptual understanding plays an important role in strategy adoption and generation. Imbo (2008) described three classes of strategies that can be used to solve mental arithmetic problems. These are; direct memory retrieval, procedural strategies such as counting (e.g., 8+5=9...10...11...12...13; 9 x 6 = 9...18...27...36...45...54) and transformational strategies (e.g., 8 + 5 = 8 + 2 + 3; 9 x 6 = 10 x 6 -6).…”

“…Performance on such problem-solving tasks is dependent on both strategy selection and strategy efficiency (Mayer & Wittrock, 1996). According to the definitions provided by Imbo (2008), strategy selection is the choice of a strategy among several alternatives while strategy efficiency refers to how fast and how accurately a strategy leads to the solution.…”

Fast automated counting procedures in addition problem solving: When are they used and why are they mistaken for retrieval?

“…This model has received strong support from several studies (Barrouillet & Fayol, 1998;Campbell & Timm, 2000;Geary & Brown, 1991;Geary & Burlingham-Dubree, 1989;Hamann & Ashcraft, 1986;Imbo & Vandierendonck, 2007;Imbo & Vandierendonck, 2008;Reder, 1988) and has provided a theoretical basis to the recurrent observation that adults retrieve from memory the answer of small additions instead of having to calculate it (Ashcraft, 1982;Ashcraft, 1987;Ashcraft & Battaglia, 1978;Ashcraft & Stazyk, 1981;Barrouillet & Fayol, 1998;Campbell, 1987a;Campbell, 1987b;LeFevre, Sadesky, & Bisanz, 1996;Miller, Perlmutter, & Keating, 1984). Thus, it is almost universally admitted that small additions have so often been encountered that their answer is necessarily retrieved from memory in adults (see Zbrodoff & Logan, 2005, for a review).…”

The Effect of Strategy on Problem Solving: An fMRI Study

“…While only a few studies have examined the effect of working memory on arithmetic strategy selection, it has been found that working memory does have an impact (Imbo & Vandierendonck, 2008a, 2008bHecht, 2002;Seyler, Kirk, & Ashcraft, 2003). For example, during arithmetic problem solving, higher working memory capacity participants used a retrieval strategy more often than low-span participants (Imbo & Vandierendonck, 2008b).…”