Identifying strategies in arithmetic with the operand recognition paradigm: a matter of switch cost?

Determining adults' and children's strategies in mental arithmetic constitutes a central issue in the domain of numerical cognition. However, despite the considerable amount of research on this topic, the conclusions in the literature are not always coherent. Therefore, there is a need to carry on the investigation, and this is the reason why we developed the operand recognition paradigm (ORP). It capitalizes on the fact that, contrary to retrieval, calculation procedures degrade the memory traces of the operands involved in a problem. As a consequence, the use of calculation procedures is inferred from relatively long recognition times of the operands. However, it has been suggested that recognition times within the ORP do not reflect strategies but the difficulty of switching from a difficult task (calculation) to a simpler one (recognition). In order to examine this possibility, in a series of 3 experiments we equalized switch-cost variations in all conditions through the introduction of intermediate tasks between problem solving and recognition. Despite this neutralization, we still obtained the classical effects of the ORP, namely longer recognition times after addition than after comparison. We conclude that the largest part of the ORP effects is related to different strategy use and not to difficulty-related switch costs. The possible applications and promising outcomes of the ORP in and outside the field of numerical cognition are discussed.

Numerical abilities in children with congenital hemiplegia: an investigation of the role of finger use in number processing.

In this study, we assessed basic and more complex non-symbolic and symbolic numerical task abilities in children with hemiplegia and obtained a detailed picture of their strengths and weaknesses in the numerical domain. Those children, who experience difficulties in finger gnosia and spontaneous use of fingers in counting, exhibit difficulties in finger pattern recognition and symbolic numerical tasks. However, their non-symbolic numerical abilities and arithmetic skills are preserved. These original results are discussed in light of the "manumerical cognition" hypothesis, which postulates that the use of fingers in numerical activities during childhood shapes our comprehension of numbers.

The use of the operand-recognition paradigm for the study of mental addition in older adults.

OBJECTIVES: Determining how individuals solve arithmetic problems is crucial for our understanding of human cognitive architecture. Elderly adults are supposed to use memory retrieval more often than younger ones. However, they might backup their retrieval by reconstructive strategies. In order to investigate this issue, we used the operand-recognition paradigm, which capitalizes on the fact that algorithmic procedures degrade the memory traces of the operands. METHOD: Twenty-three older adults (M = 70.4) and 23 younger adults (M = 20.0) solved easy, difficult, and medium-difficulty addition and comparison problems and were then presented with a recognition task of the operands. RESULTS: When one-digit numbers with sums larger than 10 were involved (medium-difficulty problem), it was more difficult for younger adults to recognize the operands after addition than comparison. In contrast, in older adults, recognition times of the operands were the same after addition and comparison. DISCUSSION: Older adults, in contrast with younger adults, are able to retrieve the results of addition problems of medium difficulty. Contrary to what was suggested, older participants do not seem to resort to backup strategies for such problems. Finally, older adults' reliance on the more efficient retrieval strategy allowed them to catch up to younger adults in terms of solution times.