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Contrary to a widespread assumption, a recent study suggested that adults do not solve very small additions by directly retrieving their answer from memory, but rely instead on highly automated and fast counting procedures (Barrouillet & Thevenot, 2013). The aim of the present study was to test the hypothesis that these automated compiled procedures are restricted to small quantities that do not exceed the size of the focus of attention (i.e., 4 elements). For this purpose, we analyzed the response times of ninety adult participants when solving the 81 additions with operands from 1 to 9. Even when focusing on small problems (i.e. with sums ⩽10) reported by participants as being solved by direct retrieval, chronometric analyses revealed a strong size effect. Response times increased linearly with the magnitude of the operands testifying for the involvement of a sequential multistep procedure. However, this size effect was restricted to the problems involving operands from 1 to 4, whereas the pattern of response times for other small problems was compatible with a retrieval hypothesis. These findings suggest that very fast responses routinely interpreted as reflecting direct retrieval of the answer from memory actually subsume compiled automated procedures that are faster than retrieval and deliver their answer while the subject remains unaware of their process, mistaking them for direct retrieval from long-term memory. [ABSTRACT FROM AUTHOR]

Abstract: Strategy sequential difficulty effects are the findings that when participants execute strategies, performance is worse after a difficult strategy than after an easy strategy (Uittenhove & Lemaire, 2012). Strategy sequential difficulty effects are hypothesized to result from decreased working-memory resources following difficult strategy execution. In the present study we found a correlation between individuals' working memory and strategy sequential difficulty effects in arithmetic, supporting a working-memory account of these effects. Furthermore, we varied response–stimulus intervals, and we found decreased strategy sequential difficulty effects with increasing response–stimulus intervals. Implications of these findings for further understanding of strategic variations in human cognition are discussed. [Copyright &y& Elsevier]

Objective: Consistent with Uittenhove and Lemaire (2012), we expected that strategy execution would be slower following execution of a difficult strategy than after an easy strategy (strategy sequential difficulty, SSD, effects). Moreover, we expected larger SSD effects in older adults than in young adults, and especially in Alzheimer's disease (AD) patients, a population with marked cognitive impairments. Method: A total of 25 young and older (41 AD and 25 healthy) adults were asked to execute rounding strategies to solve arithmetic problems (e.g., solving 43 + 68 by rounding operands down or up, e.g., 40 + 70 = 110). We measured solution latencies and percentage errors with a strategy as a function of the difficulty of the just-executed strategy. Results: Solution latencies were significantly shorter following the easier rounding-down strategy than following the harder rounding-up strategy, F(2, 156) = 35.8. Moreover, this effect was significantly larger in AD patients, F(1, 78) = 117.4. Conclusions: We found comparable SSD effects in young and healthy older adults but dramatically increased SSD effects in AD patients. This has implications to further our understanding of strategic aspects underlying decreased cognitive functioning in AD patients. [ABSTRACT FROM AUTHOR]

According to associationist models, initial sequential processing of algorithmic steps is replaced through learning by single-step access to a memory instance. In an alphabet-arithmetic task where equations such as C + 3 = F have to be verified, the shift from algorithmic procedures to retrieval would manifest in a transition from steep slopes relating solution times to addends at the beginning of learning to a flat function at the end (e.g., Logan & Klapp, 1991). Nevertheless, we argue that computation of the slopes at the end of training is biased by a systematic drop in solution times for the largest addend in the study set. In this paper, this drop is observed even when the longest training period in alphabet-arithmetic literature is doubled (Experiment 1) and even when the size of the largest addend is increased (Experiment 2). We demonstrate that this drop is partly due to end-term effects but remains observable even when end-term problems are not considered in the analyses. As Logan and Klapp suggested, we conclude that the drop is partly due to deliberate memorization of the problems with the largest addend. In contrast, departing from Logan and Klapp, we demonstrate that, when problems with the largest addend are excluded from the analyses, the possibility that counting is still used after learning cannot be discarded. This conclusion is reached because after this exclusion, the slopes were still significant. To conclude, our results advocate that practicing an algorithm leads to its acceleration and not to a shift from algorithmic procedures to retrieval. [ABSTRACT FROM AUTHOR]