The present study was aimed at investigating the neural underpinnings of developmental dyscalculia in schoolchildren using functional magnetic resonance imaging (fMRI).
Specific disorders of numerical skills are neither widely recognized nor well understood. Children can exhibit low math performance in many different ways . Some may have particular difficulties with arithmetical facts , others with procedures and strategies , while most disabled children seem to have difficulties across the whole spectrum of numerical tasks . Just as diverse as the manifestation of specific math learning disabilities is the wide range of terms referring to these developmental math disabilities (developmental dyscalculia, mathematical disability, arithmetical learning disability, number fact disorder, psychological difficulties in mathematics). The term 'developmental dyscalculia' (DD) will be used here, which is defined as a significant discrepancy between specific math performance and performance in other domains (i.e. reading) and/or general intelligence that cannot be explained by mental retardation, inappropriate schooling or poor social environment according to the International Classification of Diseases, 10th revision (ICD-10, F81.2, ). Prevalence studies using different definitions of DD have been carried out in various countries. In spite of the lack of definitional consistency, the prevalence of DD across countries is relatively uniform, ranging from 3–6% in the normal population, which is similar to that of developmental dyslexia and attention deficit hyperactivity disorder (ADHD) . Unlike these other learning disabilities, girls and boys seem to be affected by DD equally [6, 7]. Furthermore, DD seems to be an enduring specific learning difficulty, persisting into late adolescence . While it is clearly the case that DD is frequently co-morbid with a variety of disorders, like dyslexia, ADHD, poor hand-eye coordination, poor working memory span, epilepsy, fragile X syndrome, Williams syndrome and Turner syndrome, causal relationships between these disorders have not been established [1, 9–13]. For illustration, about one quarter of dyscalculics show comorbidity with ADHD and dyslexia [10, 13]. Over the past two decades sufficient genetic, neurobiological, and epidemiologic evidence has accumulated to indicate that learning disabilities, including DD, are in fact expressions of brain dysfunction [12–18].
Functional neuroimaging has revealed that parietal and prefrontal cortices are involved in arithmetic tasks [19–24]. In particular, the intraparietal sulcus (IPS) seems to play a major role in number processing . While in adults the IPS seems to be mainly involved in the processing of numerical quantities, number comparison and simple quantity manipulations, including approximation, the left angular gyrus and left prefrontal regions are mainly implicated in exact, verbal memory based, language-dependent calculation [20, 26, 27]. According to this functional dissociation, circumscribed lesions should cause different patterns of dysfunction depending on whether the lesion affects the quantity or the verbal system of numerical representation . Indeed, patients with IPS lesions particularly fail to comprehend numerical quantities that are required in approximation, numerical comparison tasks or solving subtraction trials, whereas simple multiplication might be unaffected, presumably because it can still be retrieved from intact verbal memory [29–31]. Conversely, patients with acalculia following a perisylvian lesion exhibited greater impairment in the verbal processing of numbers needed for multiplication tables rather than for quantity-based operations [29, 32]. Although several imaging as well as lesion studies corroborate the existence of a dissociated processing for exact and approximate calculation [24, 29, 31], this dissociation could not be systematically replicated in normal and disabled calculators [33, 34]. Moreover, studies testing fact retrieval based on multiplication or addition and quantity processing by using subtraction or number comparison tasks could also not identify a neuronal dissociation. In contrast, they found close activation patterns for verbal and quantity based processing of numbers [22, 35].
Do children and adults with DD exhibit the same neuronal networks reported in typically achieving subjects? Can dissociation between the verbal and the quantity-based system be observed in children and adults with DD? Is one of these systems more affected by DD? These are only a few of the open questions in dyscalculia research. Answers to these questions would enable us to specify the neuronal underpinnings of this learning disability and provide new possibilities to develop and evaluate therapeutic interventions.
Thus far, a few MRI studies have begun to elucidate the correlation of dyscalculia with neuronal processing, morphology and metabolism in patients with dyscalculia. Functional [34, 36–38], spectroscopic  and morphometric [39, 40] MRI techniques have been conducted on dyscalculia.
FMRI has been used to study neural activity in a subject with dyscalculia secondary to a right temporal lobe hemorrhage endured during infancy [37, 38], and in samples of patients with Turner's  and fragile X syndrome . All these fMRI studies provide evidence for an abnormality in the parietal cortices with overall diminished as well as abnormally modulated IPS activity, correlating to number size or task difficulty [34, 36, 37]. Investigating verbal and quantity based number processing, Molko et al.  used an experimental design that included exact and approximate addition tasks in subjects with Turner's syndrome. In contrast to controls, these subjects failed to show any difference in brain activation between trials of exact and approximate calculation, although they performed the calculations as well as the controls. Molko and colleagues concluded that Turner's syndrome subjects might have used quantity manipulation strategies during both tasks .
By means of magnetic resonance spectroscopy a defect in the left parieto-temporal area was indicated in one patient with DD without any known structural abnormality .
Voxel-based morphometry indicated a decrease in grey matter density in the left IPS in premature children with DD  and in a symmetrical location in the right IPS of Turner syndrome subjects . In addition, morphometric analysis revealed atypical anatomy of the right IPS in Turner syndrome subjects .
In summary, the data derived from findings in patients with dyscalculia suggest that defects in parietal areas seem to be particularly responsible for arithmetic problems. However, the potentially distinct roles of the left and right IPS remain to be clarified. Finally, the question remains open whether observed structural abnormalities in IPS are the cause or consequence of poor arithmetic ability .
The present fMRI study investigated brain activation in 18 children with DD and 20 typically achieving schoolchildren during different numerical tasks. We used exact and approximate addition tasks that examine the verbal and the quantity based system in cerebral representations of numbers. The comparison of exact and approximate calculation is expected to assess a dissociation of these processes and afford a more specialized delineation of possible functional deficits in children with DD. Additionally, non-symbolic magnitude comparison was used to investigate basic number representations independent of the Arabic notation system. The present study represents the first examination of brain activation in a non-clinical sample of children with DD. Therefore, it is difficult to pose clear hypotheses. However, according to previous findings and the important role of the parietal lobe in number processing, we expect that children with DD would show deviations in parietal activation patterns compared to typically achieving children. In particular, differences in IPS activation during approximate calculation are anticipated since the IPS is supposed to represent the neuronal correlate of the mental number line in typical calculators. Moreover, an existing fMRI study in dyscalculic patients provided evidence for an abnormal activation of this region during approximate calculation . With respect to neuropsychological theory of verbal and quantity based representations , we predict that children with DD might show a disorganization of the functional patterns and stronger impairments of quantity based representations compared to verbal representations. However, whether such a dissociation could really be expected is still unclear, as the literature reports divergent findings.