Strategy over operation: neural activation in subtraction and multiplication during fact retrieval and procedural strategy use in children.

Arithmetic development is characterized by strategy shifts between procedural strategy use and fact retrieval. This study is the first to explicitly investigate children's neural activation associated with the use of these different strategies. Participants were 26 typically developing 4th graders (9- to 10-year-olds), who, in a behavioral session, were asked to verbally report on a trial-by-trial basis how they had solved 100 subtraction and multiplication items. These items were subsequently presented during functional magnetic resonance imaging. An event-related design allowed us to analyze the brain responses during retrieval and procedural trials, based on the children's verbal reports. During procedural strategy use, and more specifically for the decomposition of operands strategy, activation increases were observed in the inferior and superior parietal lobes (intraparietal sulci), inferior to superior frontal gyri, bilateral areas in the occipital lobe, and insular cortex. For retrieval, in comparison to procedural strategy use, we observed increased activity in the bilateral angular and supramarginal gyri, left middle to inferior temporal gyrus, right superior temporal gyrus, and superior medial frontal gyrus. No neural differences were found between the two operations under study. These results are the first in children to provide direct evidence for alternate neural activation when different arithmetic strategies are used and further unravel that previously found effects of operation on brain activity reflect differences in arithmetic strategy use. Hum Brain Mapp 38:4657-4670, 2017. © 2017 Wiley Periodicals, Inc.

The value of structural brain imaging in explaining individual differences in children's arithmetic fluency.

How do different measures of brain structure correlate with individual differences in arithmetic fluency? This paper builds on two previously published studies in which individual differences in children's arithmetic fluency were correlated with measures of white (Polspoel et al., 2019) and grey matter (Polspoel et al., 2020) in one sample of children. We combined the brain imaging data of these two studies with measures of cognitive abilities that have been shown to be predictive of arithmetic fluency, i.e., numerical magnitude processing, working memory and rapid automatized naming (RAN). This allowed us to investigate to which extend the observed structural brain imaging measures uniquely correlated with children's arithmetic fluency, on top of each other as well as on top of the abovementioned cognitive variables. Participants were 43 typically developing 9-10-year-olds. All measures were added to a hierarchical multiple regression model. This regression model showed that the white matter integrity of the right inferior longitudinal fasciculus and the cortical complexity of the left postcentral gyrus remained unique predictors of individual differences in arithmetic when the abovementioned cognitive variables were taken into account. This indicates that structural neuroimaging measures can explain individual differences in arithmetic performance that are not merely accounted for by relevant cognitive predictors.

The association of grey matter volume and cortical complexity with individual differences in children's arithmetic fluency.

Only a small amount of studies have looked at the structural neural correlates of children's arithmetic. Furthermore, these studies mainly implemented voxel-based morphometry, which only takes the volume of regions into account, without looking at other structural properties. The current study aimed to contribute knowledge on which brain regions are important for children's arithmetic on a structural level, by not only implementing voxel-based morphometry, but also cortical complexity analyses, based on the fractal dimension index. This complexity measure describes a characteristic of surface shape. Data of 43 typically developing 9-10 year-olds were analyzed. All children were asked to take part in two test sessions: behavioral data collection and MRI data acquisition. For data analysis, mean values for volume and cortical complexity were estimated within regions of interest (ROIs) and extracted for further analysis. The selected ROIs were based on regions found to be related to children's mathematical abilities in previous research. Results point towards associations between arithmetic fluency and the volume of the right fusiform gyrus, as well as the cortical complexity of the left postcentral gyrus, right insular sulcus, and left lateral orbital sulcus. Remarkably, no significant associations were observed between the children's arithmetic fluency and the volume or cortical complexity of typically arithmetic-associated parietal regions, such as the superior parietal lobe, intraparietal sulcus, or angular gyrus. Accordingly, the current study highlights the importance of structural characteristics of brain regions other than these typically arithmetic-associated parietal regions for children's arithmetic fluency.

Relating individual differences in white matter pathways to children's arithmetic fluency: a spherical deconvolution study.

Connectivity between brain regions is integral to efficient complex cognitive processing, making the study of white matter pathways in clarifying the neural mechanisms of individual differences in arithmetic abilities critical. This white matter connectivity underlying arithmetic has only been investigated through classic diffusion tensor imaging, which, due to methodological limitations, might lead to an oversimplification of the underlying anatomy. More complex non-tensor models, such as spherical deconvolution, however, allow a much more fine-grained delineation of the underlying brain anatomy. Against this background, the current study is the first to use spherical deconvolution to investigate white matter tracts and their relation to individual differences in arithmetic fluency in typically developing children. Participants were 48 typically developing 9-10-year-olds, who were all in grade 4, and who underwent structural diffusion-weighted magnetic resonance imaging scanning. Theoretically relevant white matter tracts were manually delineated with a region of interest approach, after which the hindrance modulated orientational anisotropy (HMOA) index, which provides information on the structural integrity of the tract at hand, was derived for each tract. These HMOA indices were correlated with measures of arithmetic fluency, using frequentist and Bayesian approaches. Our results point towards an association between the HMOA of the right inferior longitudinal fasciculus and individual differences in arithmetic fluency. This might reflect the efficiency with which children process Arabic numerals. Other previously found associations between white matter and individual differences in arithmetic fluency were not observed.

The neural substrates of the problem size and interference effect in children's multiplication: An fMRI study.

Within children's multiplication fact retrieval, performance can be influenced by various effects, such as the well-known problem size effect (i.e., smaller problems are solved faster and more accurately) and the more recent interference effect (i.e., the quality of memory representations of problems depends on previously learned problems; the more similar a problem is to a previously learned one, the more proactive interference impacts on storing in long-term-memory). This interference effect has been observed in behavioral studies, and determines a substantial part of performance beyond problem size. Unlike the problem size effect, the neural basis of the interference effect in children has not been studied. To better understand the underpinning mechanisms behind children's arithmetic fact retrieval, we aimed to investigate the neural basis of both effects in typically developing children. Twenty-four healthy 9- to 10-year-olds took part in a behavioral and fMRI scanning session, during which multiplication items had to be solved. Data were analyzed by manipulating problem size and interference level in a 2 × 2 factorial design. Concurring with previous studies, our results reveal clear behavioral effects of problem size and interference, with larger and high interfering items being solved significantly slower. On the neural level, a clear problem size effect was observed in a fronto-parietal and temporal network. The interference effect, however, was not detected; no clear neural distinctions were observed between low and high interfering items.

Brain activity during arithmetic in symbolic and non-symbolic formats in 9-12 year old children.

People process numbers in different formats, such as dot arrays (non-symbolic), Arabic digits and number words (symbolic), and use these representations when performing arithmetic calculations. It remains, however, unclear if and how these various presentation formats affect brain activity during arithmetic. We conducted an fMRI study in 23 typically developing children aged 9-12. The children were asked to subtract numbers up to 10 and had to compare the result to a reference number. Numbers were presented in non-symbolic (dot arrays), as well as symbolic formats (Arabic digits and number words). Our findings suggest that similar brain networks are recruited during arithmetic with different symbolic formats, i.e. Arabic digits and number words. On the other hand, there are clear differences between calculating with symbolic and non-symbolic formats. Specifically, calculating in symbolic formats showed increased activity in angular and supramarginal gyri, whereas arithmetic in the non-symbolic format showed increased activity in middle occipital and superior parietal lobes, as well as in superior frontal gyrus and insula. These differences in brain activity might be explained by differences in the strategies used to solve these arithmetic problems.