Instruction and load effects on high-skill and low-skill individuals: A study in the domain of mental arithmetic

Abstract

What happens when people are asked to respond as quickly or as accurately as possible? This study tested the effects of speed/accuracy instructions and working-memory load on people's strategy efficiency and strategy selection. Adult participants solved simple addition problems (Experiment 1) and simple multiplication problems (Experiment 2) under load and no-load conditions and provided trial-by-trial strategy reports. High-skill participants were more efficient than low-skill participants, but the underlying causes of these skill-related effects differed across experiments. In the addition experiment, high-skill participants responded adaptively to the changing situations by changing their strategy choices, which resulted in smaller effects on their actual performance. Low-skill participants in contrast, did not change their strategy choices as adaptively, which resulted in less efficient performance—and especially so under load conditions. In the multiplication experiment, high-skill and low-skill participants differed in strategy efficiencies rather than in strategy choices. In the discussion, the results are further interpreted and future adaptations for the adaptive strategy choice model (ASCM; Siegler & Jenkins, 1989) are suggested.

Keywords:

• Working memory
• Mental arithmetic
• Strategy adaptivity
• Strategy efficiency
• Arithmetic skill

Acknowledgements

Support for this research was provided by the Research Foundation Flanders (FWO Flanders) with a postdoctoral fellowship to II. Thanks are extended to the reviewers for their helpful comments on previous drafts of this paper.

Notes

¹For Experiment 1 (addition), independent sample t-tests showed that high-skill and low-skill participants did not differ in male/female ratio, math anxiety, or math experience, each t(38) < 1.0. High-skill and low-skill participants did differ in calculator use, however, t(38) = 2.25. Low-skill participants reported more frequent calculator use (3.3) than did high-skill participants (2.5). For Experiment 2 (multiplication), independent sample t-tests showed that high-skill and low-skill participants did not differ in male/female ratio, maths anxiety, or calculator use, each t(39) < 1.8. High-skill and low-skill participants did differ in maths experience, however, t(39) = 2.80. The amount of maths experience was higher in high-skill participants (5.16) than in low-skill (3.86) participants.

²We acknowledge that the only method to achieve 100% unbiased strategy efficiency data is the choice/no-choice method (Siegler & Lemaire, 1997). In this method, there is not only a choice condition, in which participants are allowed to choose among several solution strategies; this method includes several no-choice conditions as well, in which participants are asked to use one single strategy to solve all problems. The accuracy and speed data obtained in these no-choice conditions then provide unbiased strategy efficiency data. The reason why the choice/no-choice method was not applied in the present experiment is its incompatibility with accuracy and speed instructions. It makes little sense to ask participants to respond “as fast as possible” while requesting them to use—for example—a counting strategy. Such incompatible requirements may cause discrepancies between the used strategy (e.g., retrieval), on the one hand, and the reported strategy (e.g., counting), on the other. These inconsistencies may then, in turn, bias the results (see also Kirk & Ashcraft, 2001).