Abstract
The triple-code model (TCM) of number processing suggests the involvement of distinct parietal cortex areas in arithmetic operations: the bilateral horizontal segment of the intraparietal sulcus (hIPS) for arithmetic operations that require the manipulation of numerical quantities (e.g., subtraction) and the left angular gyrus (AG) for arithmetic operations that require the retrieval of answers from long-term memory (e.g., multiplication). Although neuropsychological, neuroimaging, and brain stimulation studies suggest the dissociation of these operations into distinct parietal cortex areas, the role of strategy (online calculation vs. retrieval) is not yet fully established. In the present study, we further explored the causal involvement of the left AG for multiplication and left hIPS for subtraction using a neuronavigated repetitive transcranial magnetic stimulation (rTMS) paradigm. Stimulation sites were determined based on an fMRI experiment using the same tasks. To account for the effect of strategy, participants were asked whether they used retrieval or calculation for each individual problem. We predicted that the stimulation of the left AG would selectively disrupt the retrieval of the solution to multiplication problems. On the other hand, stimulation of the left hIPS should selectively disrupt subtraction. Our results revealed that left AG stimulation was detrimental to the retrieval and online calculation of solutions for multiplication problems, as well as, the retrieval (but not online calculation) of the solutions to subtraction problems. In contrast, left hIPS stimulation had no detrimental effect on both operations regardless of strategy.
Highlights
The ability to attend to numbers is innate to some degree in human beings
The strategy questionnaires alone revealed that multiplication compared to subtraction problems were more often solved using a retrieval strategy. Functional Magnetic Resonance Imaging (fMRI) data analysis revealed significant recruitment of the left angular gyrus (AG) during retrieval, even though we did not observe a significant increase in activity at the left AG during multiplication
We would like to emphasize that great care must be taken in correlating our results with previous repetitive transcranial magnetic stimulation (rTMS) studies because none of them took into account the strategy used by the participants
Summary
The ability to attend to numbers is innate to some degree in human beings. Discrimination of small numerosities begins during the first weeks of life (Antell and Keating, 1983). By about 5 months after birth, children already attend to the addition or subtraction of one or two items (Wynn, 1992). Direct retrieval of solutions from long-term memory is efficient when solving simple addition and multiplication problems that were taught by rote learning. Procedural strategies such as counting (‘‘online calculation’’) are often used for subtraction, which is often taught by quantity-based counting or other strategies (e.g., inverse addition; Siegler, 1988; Dehaene et al, 2003). Depends on several problem-related variables, such as problem size, and individualrelated variables, such as working memory span (Imbo and Vandierendonck, 2008). A high working-memory span has been linked to the frequent use of retrieval strategies (Imbo and Vandierendonck, 2008)
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