Mental multiplication and working memory

Quarterly Journal of Experimental Psychology

Brauwer³

et al. 2012

Section: Discussionmentioning

confidence: 99%

Error Adaptation in Mental Arithmetic

Desmet

Quarterly Journal of Experimental Psychology

Brauwer³

et al. 2012

“…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;Seitz & Schumann-Hengsteler, 2002), whereas, in other studies, it was not (see, e.g., De Rammelaere et al, 1999Seitz & Schumann-Hengsteler, 2000). Investigations of the role of the visuospatial "sketch pad" in simple arithmetic are scarce (but see Lee & Kang, 2002;Seitz & 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;.…”

mentioning

confidence: 91%

“…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, 1999Deschuyteneer & Vandierendonck, 2005a, 2005bDeschuyteneer, Vandierendonck, & Muyllaert, 2006;Hecht, 2002;Lemaire, Abdi, & Fayol, 1996;Seitz & Schumann-Hengsteler, 2000. The role of phonological working memory resources in simple arithmetic is less clear.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Do multiplication and division strategies rely on executive and phonological working memory resources?

Vandierendonck

2007

Memory & Cognition

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, 1999Deschuyteneer & Vandierendonck, 2005a, 2005bDeschuyteneer, Vandierendonck, & Muyllaert, 2006;Hecht, 2002;Lemaire, Abdi, & Fayol, 1996;Seitz & Schumann-Hengsteler, 2000. 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;Seitz & Schumann-Hengsteler, 2002), whereas, in other studies, it was not (see, e.g., De Rammelaere et al., 1999Seitz & Schumann-Hengsteler, 2000). Investigations of the role of the visuospatial "sketch pad" in simple arithmetic are scarce (but see Lee & Kang, 2002;Seitz & 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;. 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., 96 (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.Investigations of the roles of executive and phonological working memory across different simple-arithmetic strategies have only very recently been conducted, beginning with Hecht (2002). In his study, simple addition equa- 1759Copyright 2007 Psychonomic Society, Inc. Do multiplication and division strategies rely on executive and phonological working memory...

“…Other studies that used more complex arithmetic tasks (e.g., 358 þ 261 ¼ ? ), however, showed an increased problem-difficulty effect with increased workingmemory load, suggesting that working-memory resources may be at stake in mental calculation processing (e.g., Fürst & Hitch, 2000;Seitz & Schumann-Hengsteler, 2000. Following Hecht (2002), a multiple-strategy use approach might shed light on this discrepancy.…”

mentioning

confidence: 99%

Working Memory, Strategy Execution, and Strategy Selection in Mental Arithmetic

Quarterly Journal of Experimental Psychology

Duverne²,

Lemaire

2007

A total of 72 participants estimated products of complex multiplications of two-digit operands (e.g., 63 × 78), using two strategies that differed in complexity. The simple strategy involved rounding both operands down to the closest decades (e.g., 60 × 70), whereas the complex strategy required rounding both operands up to the closest decades (e.g., 70 × 80). Participants accomplished this estimation task in two conditions: a no-load condition and a working-memory load condition in which executive components of working memory were taxed. The choice/no-choice method was used to obtain unbiased strategy execution and strategy selection data. Results showed that loading working-memory resources led participants to poorer strategy execution. Additionally, participants selected the simple strategy more often under working-memory load. We discuss the implications of the results to further our understanding of variations in strategy selection and execution, as well as our understanding of the impact of working-memory load on arithmetic performance and other cognitive domains.