Switch costs and the operand-recognition paradigm

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.

Efficiency of Arithmetic Procedures Modulates the Problem-Size Effect in Subtraction

“…In any case, this alternative explanation complicates the application of the operand recognition paradigm as a precise measure of strategy selection in arithmetic, because it may not distinguish between efficient (fast) retrieval and equally efficient (fast) procedures. This criticism of the interpretation of the operand recognition paradigm can be added to those put forward by Metcalfe and Campbell (2010, 2011), who indicated that findings for performance in the operand recognition paradigm may also be modulated by task-switching and difficulty-related carryover effects.…”

Adults' strategies for simple addition and multiplication: Verbal self-reports and the operand recognition paradigm.

“…Operation X Size effect on parity RT (-H62 ms). Metcalfe and Campbell (2010) interpreted this result as evidence that operand recognition RT was directly affected by the difficulty of the preceding problem. Indeed, much research has demonstrated RT and accuracy costs to switch between tasks (Monsell, 2003).…”

“…This raised the possibility that effects of arithmetic problem size in the ORP reflected difficulty-related switch costs rather than strategy use. Metcalfe and Campbell (2010) subsequently investigated the possibility that difficulty-related switch-costs were responsible for the Operation X Size interaction observed by Thevenot et al (2007). Participants received the standard ORP (Thevenot et al, 2007; Experiment 1) with one critical change: In addition to the operand recognition probe following one third of addition and comparison trials, participants also received a parity control task on another one third of trials following addition or comparison.…”

Cognitive Switching Affects Arithmetic Strategy Selection: Evidence from Eye-gaze and Behavioral Measures

“…Mao (2012) also found that the reaction time of switching task was higher than repetition task. Moreover, the study of Metcalfe and Campbell (2010) suggested that adults' performance of arithmetic cognitive strategy in mental arithmetic task was influenced by cognitive switching function. Moreover, Bull (2001) found that children with poor inhibitory ability and working memory had difficulty shifting between and choosing strategies for specific tasks.…”