These findings have important implications regarding mechanisms underlying age-related differences in using rule-violation checking strategies to verify arithmetic problems and in combining two strategies into a single, more efficient one.

Multiplication is thought to be primarily solved via direct retrieval from memory. Two of the main factors known to influence the retrieval of multiplication facts are problem size and interference. Because these factors are often intertwined, we sought to investigate the unique influences of problem size and interference on both performance and neural responses during multiplication fact retrieval in healthy adults. Behavioral results showed that both problem size and interference explained separate unique portions of RT variance, but with significantly stronger contribution from problem size, which contrasts with previous work in children. Whole-brain fMRI results relying on a paradigm that isolated multiplication fact retrieval from response selection showed highly overlapping brain areas parametrically modulated by both problem size and interference in a large network of frontal, parietal, and subcortical brain areas. Subsequent analysis within these regions revealed problem size to be the stronger and more consistent “unique” modulating factor in overlapping regions as well as those that appeared to respond only to problem size or interference at the whole-brain level, thus underscoring the need to look beyond anatomical overlap using arbitrary thresholds. Additional unique contributions of interference (beyond problem size) were identified in right angular gyrus and subcortical regions associated with procedural processing. Together, our results suggest that problem size, relative to interference, tends to be the more dominant factor in driving behavioral and neural responses during multiplication fact retrieval in adults. Nevertheless, unique contributions of both factors demonstrate the importance of considering the overlapping and unique contributions of each in explaining the cognitive and neural bases of mental multiplication.

Individual differences in arithmetic have been explained by differences in cognitive processes and by arithmetic strategy use and selection. In the present study, we investigated the involvement of reactive and proactive control processes. We explored how variation in proactive and reactive control was related to individual differences in strategy selection. We correlated proactive and reactive measures obtained from the AX-CPT and an adjusted N-back task with a measure of strategy adaptiveness during a numerosity judgment task. The results showed that both measures of reactive control (of the AX-CPT and N-back task) correlated positively with strategy adaptiveness, while proactive control was not. This suggests that both cognitive control modes might have a different effect on adaptive strategy selection, where adaptive strategy selection seems to benefit from a transient (late) control mode, reactive control. We discuss these results in the light of the Dual Mechanisms Framework. The last decade has witnessed an increased interest in individual differences in arithmetic (see Cappelletti & Fias, 2016or De Smedt, Noël, Gilmore, & Ansari, 2013 for an overview). Generally, the selection and use of appropriate arithmetical strategies explain part of this variability Imbo, Vandierendonck, & Rosseel, 2007). In the present study, we investigated the involvement of reactive and proactive control processes in this selection of appropriate strategies. Recently, the involvement of cognitive control processes in arithmetic strategy use has been investigated (for a review, see and sometimes interpreted as reflecting either reactive or proactive control. However, the specific involvement of these control processes was never explicitly investigated, which was the aim of the current study. Because strategy selection involves a decision-making process (i.e., choosing between the different strategies), cognitive control is involved to make an adaptive strategy selection. Investigating how proactive and reactive control are involved in the process of strategy selection, furthers our understanding on arithmetic strategy use.To adequately perform mental arithmetic, a variety of cognitive processes are needed. Among these processes, we consider attention (e.g., focus on the arithmetic problem; Menon, 2010), working memory (e.g., holding and manipulating information in mind; Andersson, 2008;Raghubar, Barnes, & Hecht, 2010), response selection, Journal of Numerical Cognition jnc.psychopen.eu | 2363-8761 and executive functions. Miyake et al. (2000) identified three different functions in executive control and all three are known to contribute to individual differences in arithmetic: (a) shifting between tasks or mental sets (Yeniad, Malda, Mesman, van IJzendoorn, & Pieper, 2013), (b) information updating and monitoring of working memory representations (Raghubar, Barnes, & Hecht, 2010), and (c) inhibition of prepotent or dominant responses (Bull & Scerif, 2001;Gilmore et al., 2013;Kroesbergen, Van Luit, Van Lieshout, Van Loos...

Not all researchers interested in human behavior remain convinced that modern neuroimaging techniques have much to contribute to distinguishing between competing cognitive models for explaining human behavior, especially if one removes reverse inference from the table. Here, we took up this challenge in an attempt to distinguish between two competing accounts of the problem size effect (PSE), a robust finding in investigations of mathematical cognition. The PSE occurs when people solve arithmetic problems and indicates that numerically large problems are solved more slowly and erroneously than small problems. Neurocognitive explanations for the PSE can be categorized into representation-based and process-based views. Behavioral and traditional univariate neural measures have struggled to distinguish between these accounts. By contrast, a representational similarity analysis (RSA) approach with fMRI data provides competing hypotheses that can distinguish between accounts without recourse to reverse inference. To that end, our RSA (but not univariate) results provided clear evidence in favor of the representation-based over the process-based account of the Highlights •The problem-size effect (PSE) is a common and robust behavioral effect in arithmetic •Univariate fMRI does not but RSA does differentiate cognitive accounts of the PSE •RSA data show problems are stored as memory traces sensitive to input frequency •Data were inconsistent with a strictly magnitude-based account of memory encoding •Human fMRI data can directly inform cognitive explanations of behavioral phenomena