Academic journal article Memory & Cognition

Do Multiplication and Division Strategies Rely on Executive and Phonological Working Memory Resources?

Academic journal article Memory & Cognition

Do Multiplication and Division Strategies Rely on Executive and Phonological Working Memory Resources?

Article excerpt

The role of executive and phonological working memory resources in simple arithmetic was investigated in two experiments. Participants had to solve simple multiplication problems (e.g., 4 × 8; Experiment 1) or simple division problems (e.g., 42 ÷ 7; Experiment 2) under no-load, phonological-load, and executive-load conditions. The choice/no-choice method was used to investigate strategy execution and strategy selection independently. Results for strategy execution showed that executive working memory resources were involved in direct memory retrieval of both multiplication and division facts. Executive working memory resources were also involved in the use of nonretrieval strategies. Phonological working memory resources, on the other hand, tended to be involved in nonretrieval strategies only. Results for strategy selection showed no effects of working memory load. Finally, correlation analyses showed that both strategy execution and strategy selection correlated with individual-difference variables, such as gender, math anxiety, associative strength, calculator use, arithmetic skill, and math experience.

Working memory is a system devoted to short-term storage and processing and is used in various cognitive tasks, such as reading, reasoning, and mental arithmetic. Throughout the past decennium, research into the role of working memory in mental arithmetic has flourished (for a review, see DeStefano & LeFevre, 2004) and has shown that solving both simple arithmetic problems (e.g., 8 + 5, 3 × 9) and complex arithmetic problems (e.g., 23 + 98, 12 × 35) relies on working memory resources. The present study further investigates the role of working memory in simple-arithmetic strategies, on the basis of the multicomponent working memory model of Baddeley and Hitch (1974). In this model, there is an attentional system (the central executive) that supervises a phonological subsystem and a visuospatial subsystem. The phonological subsystem guarantees short-term maintenance of phonological information, and the visuospatial subsystem guarantees short-term maintenance of visuospatial information.

The role of executive working memory resources in simple arithmetic has been shown extensively (see, e.g., Ashcraft, 1995; De Rammelaere, Stuyven, & Vandierendonck, 1999, 2001; De Rammelaere & Vandierendonck, 2001; Deschuyteneer & Vandierendonck, 2005a, 2005b; Deschuyteneer, Vandierendonck, & Muyllaert, 2006; Hecht, 2002; Lemaire, Abdi, & Fayol, 1996; Seitz & Schumann-Hengsteler, 2000, 2002). The role of phonological working memory resources in simple arithmetic is less clear. In some studies, an effect of phonological load on simple-arithmetic problem solving was observed (see, e.g., Lee & Kang, 2002; Lemaire et al., 1996; Seite & Schumann-Hengsteier, 2002), whereas, in other studies, it was not (see, e.g., De Rammelaere etal., 1999, 2001; Seite & Schumann-Hengsteler, 2000). Investigations of the role of the visuospatial "sketch pad" in simple arithmetic are scarce (but see Lee & Kang, 2002; Seite & Schumann-Hengsteler, 2000), and the findings in the few studies conducted are equivocal.

A drawback of all the studies mentioned above, however, is that none of them showed any distinction between retrieval and nonretrieval trials. Yet it has been shown that adults use several strategies to solve even the simplest arithmetic problems (see, e.g., Hecht, 1999; LeFevre, Bisanz, et al., 1996; LeFevre, Sadesky, & Bisanz, 1996). For instance, although direct memory retrieval (i.e., knowing that 3 × 4 = 12) is the most frequently used strategy, nonretrieval strategies (or procedural strategies) are used as well. Examples of such procedural strategies are transformation (e.g., 9 × 6 = (10 × 6) - 6 = 60 - 6 = 54) and counting (e.g., 4 × 7 = 7 ... 14 ... 21 ... 28). The studies mentioned above notwithstanding, it is impossible to discern the specific simple-arithmetic strategies in which executive and phonological working memory resources are needed. …

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