Involvement of short-term memory in complex mental calculation

Abstract

The aim of this study was to examine the involvement of the short-term memory system in complex mental addition by manipulating the phonological and visual similarity of two numbers to be added. The phonological similarity of the problems appeared to have a major effect on both speed and accuracy. However, the manipulation of visual similarity failed to have any measurable impact. This suggests that the phonological loop, rather than the visual-spatial sketch pad, would be used preferably for temporary storage of addends. An interpretation of these results in terms of the nature of the internal code underlying this task is discussed.

The role of working memory in the carry operation of mental arithmetic: Number and value of the carry

“…Decomposition of this interaction showed that this interaction completely bears on the presence of an executive load. These findings are consistent with previous research that also found that the central executive contributes to handling carries (e.g., Fürst & Hitch, 2000;Seitz & SchumannHengsteler, 2002), but they do not confirm previous findings that found a role for phonological effects in carrying (e.g., Ashcraft & Kirk, 2001;Noël et al, 2001;Seitz & SchumannHengsteler, 2002), and research that found no role for working memory in carrying (Logie et al, 1994).…”

“…Logie et al (1994) did not observe differential effects of load on carry versus no-carry problems for either a phonological or a visuo-spatial load. In contrast, Noël, Désert, Aubrun, and Seron (2001) provided evidence for a mediation of the phonological loop in solving carry problems. They manipulated visual and phonological similarity of the digits to be added in additions of two three-digit numbers.…”

“…A few exceptions notwithstanding (Fürst & Hitch, 2000;Noël et al, 2001), most studies compared no-carry versus one-carry problems, so that there is no clear evidence whether the number of carries in a problem is of importance. Furthermore, all studies were restricted to sums of two numbers so that the value of the carry never exceeded one (an exception must be made for Logie et al, 1994).…”

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

“…More specifically, the recruitment of executive and phonological working memory increases as a function of the number of carry operations (Fürst & Hitch, 2000;Imbo, Vandierendonck, & De Rammelaere, 2007;Imbo, Vandierendonck, & Vergauwe, 2007;Noël et al, 2001). In the present experiment, we investigated whether the carry effect (i.e., the relative inefficiency on carry problems as compared to no-carry problems) differed across cultures.…”

“…As for the relative frequency of strategy use, the efficiency of complex arithmetic strategies depends greatly on the presence of carry operations. Efficiency decreases when carry operations have to be performed (Hitch, 1978;Fürst & Hitch, 2000;Imbo, Vandierendonck, & De Rammelaere, 2007;Imbo, Vandierendonck, & Vergauwe, 2007;Logie, Gilhooly, & Wynn, 1994;Noël, Désert, Aubrun, & Seron, 2001). Interestingly, cultural differences in strategy efficiency have been shown in the domain of simple arithmetic.…”