Introduction
Mathematical disability (MD) is a brain-based learning disorder affecting numerical and arithmetic abilities (De Smedt et al.
2019; Kaufmann et al.
2011). MD emerges at the early stages of development, affecting 3–6% of children and continues into adulthood (Kucian and von Aster
2015). It harms the career perspectives, mental health, and economic status of those diagnosed, and also puts a burden on society (Gross et al.
2009; Kaufmann et al.
2013). Surprisingly, we have little knowledge about the neural mechanisms of arithmetic processing in MD and the way these mechanisms change in the face of training. This knowledge will help us to further develop brain-based educational interventions directly derived from research in children with MD, whose brain responses might differ from typically developing (TD) children. Therefore, in the current study, we aim to investigate the neurocognitive mechanisms of arithmetic learning in children with MD.
The neural network of arithmetic processing consists of a widespread fronto-parietal network: the bilateral intraparietal sulcus (related to manipulation of magnitude) and the bilateral superior parietal lobule (related to visuospatial attention) and the left angular gyrus and hippocampus (related to verbal retrieval from long-term memory and attentional demands) and the prefrontal cortex (related to executive functions and cognitive demands) (Arsalidou et al.
2018; Dehaene et al.
2003; Klein et al.
2016). Studies in TD children reported consistent findings within the neural network of arithmetic processing with a rather high similarity across studies (Arsalidou et al.
2018; Peters and De Smedt
2018), whereas neuroimaging studies in children with MD solving arithmetic tasks provide divergent and seemingly contradictory findings.
One group of studies on arithmetic processing in children with MD reported higher activation (Davis et al.
2009; Rosenberg-Lee et al.
2015; Simos et al.
2008) and hyper-functional connectivity (Jolles et al.
2016; Michels et al.
2018; Rosenberg-Lee et al.
2015) in the fronto-parietal network as compared to TD children while solving arithmetic tasks. For instance, Davis et al. (
2009) found higher activation in the bilateral precentral gyri and the right insula during simple addition in children with MD as compared to TD children, suggesting that children with MD rely on less advanced strategies to solve arithmetic problems. In a similar vein, Rosenberg-Lee et al. (
2015) found higher activation in the right intraparietal sulcus, bilateral fusiform gyri, right visual cortex, and the left lingual gyrus during simple addition and subtraction in children with MD as compared to TD children (see also Simos et al.
2008). While showing higher brain activation, children with MD had worse behavioral performance in simple addition and subtraction tasks than that of TD children. Kucian and von Aster (
2015) explain that children with MD overuse counting strategies and finger counting, have limited arithmetic fact retrieval, and experience difficulties with both procedural and conceptual knowledge; therefore, they overuse inefficient and compensatory strategies which leads to higher brain activation than seen in TD children. The conclusion from this group of studies is that children with MD have higher but inefficient brain activation, which is accompanied by poor behavioral performance (i.e., response time and accuracy) on mental arithmetic tasks as compared to TD children.
Another group of studies on the arithmetic abilities of children with MD observed reduced activation (Ashkenazi et al.
2012; Berteletti et al.
2014; Kucian et al.
2006; Peters et al.
2018; Schwartz et al.
2018) and structural connectivity (Rotzer et al.
2008; Rykhlevskaia et al.
2009) in the fronto-parietal network as compared to TD children during arithmetic problem solving. For instance, children with MD had reduced activation in the left inferior frontal gyrus, the left middle and superior temporal gyri, the right intraparietal sulcus, and the superior parietal lobule when completing simple multiplication tasks (Berteletti et al.
2014). The authors suggest impaired arithmetic mechanisms in both numerical- and language-related regions in the brains of children with MD. Ashkenazi et al. (
2012) found reduced activation related to the complexity in addition in several regions, such as the intraparietal sulcus, superior parietal lobule, angular gyrus, and supramarginal gyrus in the right hemisphere, and bilaterally in the temporal and dorsolateral prefrontal cortex for children with MD as compared to TD children. Moreover, children with MD performed worse on the addition tasks than TD children. The conclusion from this group of studies is that arithmetic problem solving does not lead to the recruitment of the relevant neurocognitive resources in children with MD leading to poor behavioral performance.
These contradictory findings are not conclusive. It is unclear whether increased or decreased brain activation during arithmetic problem solving is an advantage or disadvantage in children with MD. More importantly, the question is how children with MD learn arithmetic and whether a behavioral improvement is accompanied by increased or decreased brain activation. While the first group of above-mentioned literature (i.e., higher but inefficient brain activation in children with MD) might suggest reduced but more efficient brain activation after training, the second group of literature (i.e., reduced and non-engaged necessary brain activation in children with MD) might suggest increased brian activation in the fronto-parietal network of mental calculation. By identifying these brain activation changes, the covert strategies that underly arithmetic problem solving will be disclosed to better understand the deficiencies in individuals with MD.
Intervention studies can provide this insight about changes in strategies and brain responses. So far, only very limited information is available about neuronal changes related to intervention (Iuculano et al.
2015; Kucian et al.
2011; Michels et al.
2018) or development (McCaskey et al.
2018,
2020) in children with MD. Of these studies, only one training study investigated neural activation changes during arithmetic learning in children with MD (Iuculano et al.
2015) similarly to our current study of arithmetic intervention. Iuculano et al. (
2015) trained 15 children with MD for 8 weeks using one-on-one tutoring focusing on efficient counting strategies and arithmetic fact retrieval. Before training, they observed higher activation in the bilateral dorsolateral prefrontal and the left ventrolateral prefrontal cortex, the left intraparietal sulcus, the right fusiform gyrus, and bilateral insula during simple addition problem solving in children with MD as compared to age-matched TD peers. Thus, this training study supports the first group of literature discussed above in suggesting that there is higher brain activation in children with MD as compared to TD children. Interestingly, there were no differences in brain activation between the two groups of children after training as the over-engagement of the distributed brain activation was reduced in children with MD. This reduced activation over training manifests the existent inefficient widespread activation during simple arithmetic in MD, which is unnecessary, does not lead to appropriate performance on arithmetic tasks and therefore decreases after appropriate training.
The only existing neuroimaging study on arithmetic training in children with MD (Iuculano et al.
2015) is limited to simple calculation. Complex calculation differs from simple calculation in strategy use, and procedural and conceptual knowledge (Soltanlou et al.
2017a,
b). Uncovering the neural mechanisms underlying complex calculation will help us to understand arithmetic learning beyond behavioral improvements in children with MD because these children struggle more with complex calculations. While behavioral training studies mainly support different interventional approaches, they do not answer the question of why children’s performance during arithmetic problem solving improves. Neuroimaging studies of arithmetic training provide more specific information about changes in the covert dysfunctions, which might be related to magnitude, cognitive, or language-related processes. These changes may not be clearly demonstrated in behavioral investigations because of the compensatory, but inefficient strategies that partially cover mathematical weaknesses. This knowledge would help us to develop better interventions that target particular mathematical weaknesses rather than an unspecific improvement in compensatory strategies in a child’s behavioral performance.
Therefore, in the present within-participant study, we investigate neural activation changes before and after 2 weeks of simple and complex multiplication training in children with MD. This study is built upon on our recent multiplication training in TD children (Soltanlou et al.
2018a,
b), with a very similar procedure. We set out to examine whether the same training would lead to similar or different brain responses in children with MD. Moreover, by training both simple and complex arithmetic problems, we can extend the findings by Iuculano et al. (
2015) that trained only simple arithmetic problems, and also test for the difficulty-related modulation of neural activity (Ashkenazi et al.
2012). The difficulty-related modulation of neural activity is expected as distinguishable brain responses to simple and complex calculation. Ashkenazi et al. (
2012) reported no distinguishable neural activation patterns during simple and complex addition in children with MD in a single-session measurement, which is usually observed in TD children (Soltanlou et al.
2017a,
b). Additionally, while simple multiplication is mainly solved via retrieval strategy in TD children, it may not necessarily be true in children with MD. Therefore, simple multiplication (specially larger than 5) may still rely on procedural strategies. Lastly, the task of interest in the current study is complex multiplication because in our previous study in TD children, we observed training-related changes only in complex but not simple multiplication (Soltanlou et al.
2018b). However, we are not sure whether complex multiplication would be too difficult for our children with MD that have the risk of drop-out, insufficient number of trials and corresponding fNIRS data. Therefore, we train both simple and complex multiplication in the current study.
Training-induced changes is evaluated using functional near-infrared spectroscopy (fNIRS), a well-suited technique for children (Soltanlou et al.
2018a,
b; Soltanlou and Artemenko
2020). We predict that children with MD exhibit shorter response times and make fewer errors on both simple and complex multiplication tasks after training. Following Iuculano et al. (
2015), we expect an overall reduced fronto-parietal activation after 2 weeks of training on simple multiplication, particularly in the right hemisphere, which is less engaged in advanced retrieval strategies. This activation reduction is mostly expected in the prefrontal regions that support procedural processes of mental calculation. Training would lead to less demands on these processes that are expected to be more automatized. However, this increased automatization might lead to an activation increase in the temporo-parietal regions such as the left angular gyrus (e.g., Rivera et al.
2005). Additionally, training might improve the capability of mental number manipulation that is associated with activation increase in the parietal regions, especially in the bilateral intraparietal sulcus. Concerning complex multiplication, two predictions can be derived from the two groups of literature discussed above. Based on the first literature group, which argued that children with MD have higher neural activation as compared to TD children, we would expect reduced fronto-parietal activation after training in children with MD, which will be more similar to TD children. This prediction is in line with the findings on complex multiplication tasks for TD children (Soltanlou et al.
2018b). According to the second literature group, which reported lower neural activation in children with MD, we would expect increased fronto-parietal activation after 2 weeks of complex multiplication training in children with MD. However, similar to our predictions in training of simple multiplication, we might observe an activation reduction in the frontal regions, but activation increase in the parietal regions (see Zamarian et al.
2009 for review of findings in adults). Therefore, while we have a directional hypothesis for simple multiplication training (i.e., reduced brain activation after training), there is no directional hypothesis for complex multiplication training.
Additionally, we expect differentiable brain activation between simple and complex multiplication (i.e., the difficulty-related modulation of neural activity) after training, like the complexity-related brain activation seen in TD children. Note that since the current study is a follow-up of our recent multiplication training in TD children (Soltanlou et al.
2018b), we will descriptively compare the current findings with the findings of that study as a control group.
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