Abstract
Experimental research in cognitive arithmetic frequently relies on participants’ self-reports to discriminate solutions based on direct memory retrieval from use of procedural strategies. Given concerns about the validity and reliability of strategy reports, Thevenot et al. in Mem Cogn 35:1344–1352, (2007) developed the operand-recognition paradigm as an objective measure of arithmetic strategies. Participants performed addition or number comparison on two sequentially presented operands followed by a speeded operand-recognition task. Recognition times increased with problem size following addition but not comparison. Thevenot et al. argued that the complexity of addition strategies increases with problem size. A corresponding increase in operand-recognition time occurs because, as problem size increases, working memory contains more numerical distracters. However, because addition is substantially more difficult than comparison, and difficulty increases with problem size for addition but not comparison, their findings could be due to difficulty-related task-switching costs. We repeated Thevenot et al. (Experiment 1) but added a control condition wherein participants performed a parity (odd or even) task instead of operand recognition. We replicated their findings for operand recognition but found robust, albeit smaller, effects of addition problem size on parity judgements. The results indicate that effects of strategy complexity in the operand-recognition paradigm are confounded with task-switching effects, which complicates its application as a precise measure of strategy complexity in arithmetic.
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Notes
An earlier experiment in our lab found no switch costs using a letter-comparison control task in which participants decided if a presented letter preceded or followed the letter E. This was a poor task-switch control, however, because the numerical task set (i.e., addition or number comparison) would not compete with letter comparison. In contrast, like operand recognition, parity judgments following addition or comparison required participants to switch number-processing task sets.
For the problem pair 7 5, Task 2 trials were always paired with a false comparison due to a coding error; this affected 0.01% of Task 2 trials and had no practical consequences for the recognition or parity tasks. Also, because false Task 2 addition answers were ±1 from the correct sum participants could use addition parity rules to solve Task 2 addition problems (Lemaire and Reder 1999). Future research might wish to avoid this possibility, but the current experiment was designed to be a close replication of Thevenot et al. (2007, Experiment 1) and adopted their rules for false answer stimuli.
We refer to the component stages of addition and comparison as Task 1 and Task 2, but because the Task 2 decision stage necessarily refers to the processes and representations generated during Task 1, it is reasonable to assume that they constitute an integrated task set and that task difficulty is properly indexed by total solution time (i.e., Task 1 + Task 2 RT).
As the parity task did not afford analysis in terms of first versus second operand we did not include this as a factor in our main analysis.
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This research was supported by a grant and scholarship from the Natural Sciences and Engineering Research Council of Canada.
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Metcalfe, A.W.S., Campbell, J.I.D. Switch costs and the operand-recognition paradigm. Psychological Research 74, 491–498 (2010). https://doi.org/10.1007/s00426-009-0272-9
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DOI: https://doi.org/10.1007/s00426-009-0272-9