Verifying simple arithmetic sums and products: Are the phonological loop and the central executive involved?

Abstract

In two experiments, we investigated the role of the phonological loop and the central executive in the verification of the complete set of one-digit addition (Experiment 1) and multiplication (Experiment 2) problems. The focus of the present study was on the contradictory results concerning the contribution of the phonological loop in the verification of true problems (e.g., 8 + 4 = 12 or 4 3 6 = 24) reported until now. The results revealed that this slave system is not involved in verifying simple arithmetic problems, in contrast to the central executive. Furthermore, our results indicated that the split effect is due to the use of two different arithmetic strategies.

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

“…Similar relationships with early individual differences in the phonological component of working memory have also been reported for math achievement (Berg, 2008;Rasmussen & Bisanz, 2005;Hecht, Torgesen, Wagner, & Rashotte, 2001; but see Lee, Ng, Ng, & Lim, 2004;Swanson, 2006). Here, effects of the central executive seem particularly strong (Bull, Espy, & Wiebe, 2008;Geary, Brown, & Samaranayake, 1991;Geary & Hoard, 2001;Gersten, Jordan, & Flojo, 2005;Leather & Henry, 1994;Lee, Ng, Ng, & Lim, 2004;Lemaire, Abdi, & Fayol, 1996;Logie, Gilhooly, & Wynn, 1994;Passolunghi, & Siegel, 2004;Passolunghi, Vercelloni, & Schadee, 2007;Rammelaere, Stuyven, & Vandierendonck, 2001;Swanson, 2006;Swanson & Beebe-Frankenberger, 2004;Thomas, Zoelch, Seitz-Stein, & Schumann-Hengsteler, 2006). In a recent study by Geary, Hoard, Byrd-Graven, Nugent, and Numtee (2007) it was shown that all components of working memory, including the visual-spatial sketch pad, are related to math performance in school.…”

Short-Term Memory, Working Memory, and Executive Functioning in Preschoolers: Longitudinal Predictors of Mathematical Achievement at Age 7 Years

“…They argued that verbal short-term memory may be used on simple auditorily presented arithmetic questions where children used subvocal rehearsal processes to support the retention of problem information and direct retrieval of arithmetic facts from long-term memory. Other findings from adults using dual-task paradigms have suggested that the phonological loop is involved in temporary storage of partial solutions whereas the central executive controls access to and execution of computational algorithms (e.g., Logie, Gilhooly, & Wynn, 1994), but is not involved in the verification of either simple addition or multiplication problems (De Rammelaere, Stuyven, & Vandierendonck, 2001). Geary et al, (2007) argue that while the central executive is a core component to learning difficulties in mathematics, the phonological loop and visual-spatial sketch pad may contribute to more specific math cognition deficits, dependent on what aspects of mathematical skill are being assessed.…”

Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm

“…For addition problems, this erroneous answer was constructed by adding 1 to or subtracting 1 from the correct answer. Indeed, we know that when a proposed answer is too distant from the correct answer, participants are able to solve that kind of problem by approximation, rather than by calculation (Ashcraft & Battaglia, 1978;Ashcraft & Stazyk, 1981;De Rammelaere, Stuyven, & Vandierendonck, 2001; El Yagoubi, Lemaire, & Besson, 2003;Pesenti, Thioux, Seron, & De Volder, 2000). For comparisons, this number was, in half of the cases, superior to the first operand, which was always the largest one, and, in the other half, inferior to the second operand, the smallest.…”