Doing as they are told and telling it like it is: Self-reports in mental arithmetic

Abstract

Adults (n = 64) solved single-digit multiplication problems under both speed and accuracy instructions. Half also provided self-reports of their solutions to the problems. The participants with relatively low levels of arithmetic fluency were most influenced by instructional requirements. They responded more slowly and accurately when asked to provide descriptions of their solution procedures, whereas the performance of the participants with high and average levels of arithmetic fluency did not change. Furthermore, the performance of the low-fluency participants was more affected by speed and accuracy demands than was that of the other individuals, but only when the low-fluency participants were also required to provide self-reports. Accordingly, models of mental arithmetic will need to include roles for individual differences and situational factors.

Simple arithmetic processing: The question of automaticity

“…Additionally, such an explanation fits well with the 120 ms SOA findings in that it does not predict an advantage in response times to congruent targets. Furthermore, the notion of an obligatory self-regulatory mechanism operating toward exactness in arithmetic performance is compatible with the importance that is placed on accuracy in computation both in learning environments and in every day life (Smith-Chant & LeFevre, 2003). Certainly, the workings of such a mechanism, even at a voluntary level, could be seen to complement explanations of arithmetic performance such as Siegler and Jenkins (1989) Distribution of Associations model.…”

“…Additionally, individual differences and instructional demands may bias verbal reports and the solution procedures that are reported (Kirk & Ashcraft, 2001;Smith-Chant & LeFevre, 2003). Indeed, a recent study by Smith-Chant and LeFevre (2003) showed that low skill participants responded more slowly and accurately when asked to describe their solution procedures for large and very large problems. Furthermore, low skill participants exhibited greater variation in procedures and were more likely to alter their selection of retrieval method, with changes in instructional emphasis between speed and accuracy.…”

“…The self-report methodology has nonetheless been criticised on the grounds that, when asked to describe mental processing, people may change or be unable to accurately describe their behaviours (Kirk & Ashcraft, 2001;Smith-Chant & LeFevre, 2003). Additionally, individual differences and instructional demands may bias verbal reports and the solution procedures that are reported (Kirk & Ashcraft, 2001;Smith-Chant & LeFevre, 2003).…”

Error Adaptation in Mental Arithmetic

“…For example, in a multiplication production task under time pressure, adults make between 1% and 35% errors (De Brauwer, Verguts & Fias, 2006;Imbo & Vandierendonck, 2010;Smith-Chant & LeFevre, 2003;Verguts & Fias, 2005). Future studies in the field of mental arithmetic need to be aware of post error effects.…”

“…Traditionally, researchers in this domain focus on RTs of correct responses and on percentages of errors (e.g., Campbell & Xue, 2001;Imbo & Vandierendonck, 2007a,b;LeFevre et al, 1996;Seitz & Schumann-Hengsteler, 2000;Siegler & Lemaire, 1997;Smith-Chant & LeFevre, 2003;etc.). Mostly, response times after errors are not discarded from the analyses.…”