Publications in Mathematics by NOMIS researchers

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Affected people show persistent deficits in number processing, which are associated with aberrant brain activation and structure. Reduced gray matter has been reported in DD for the parietal cortex including the intraparietal sulcus (IPS), but also the frontal and occipito-temporal cortex. Furthermore, dyscalculics show white matter differences for instance in the inferior (ILF) and superior longitudinal fasciculus (SLF). However, the longitudinal development of these structural differences is unknown. Therefore, our goal was to investigate the developmental trajectory of gray and white matter in children with and without DD. In this longitudinal study, neuropsychological measures and T1-weighted structural images were collected twice with an interval of 4 years from 13 children with DD (8.2–10.4 years) and 10 typically developing (TD) children (8.0–10.4 years). Voxel-wise estimation of gray and white matter volumes was assessed using voxel-based morphometry for longitudinal data. The present findings reveal for the first time that DD children show persistently reduced gray and white matter volumes over development. Reduced gray matter was found in the bilateral inferior parietal lobes including the IPS, supramarginal gyri, left precuneus, cuneus, right superior occipital gyrus, bilateral inferior and middle temporal gyri, and insula. White matter volumes were reduced in the bilateral ILF and SLF, inferior fronto-occipital fasciculus (IFOF), corticospinal tracts, and right anterior thalamic radiation (ATR). Behaviorally, children with DD performed significantly worse in various numerical tasks at baseline and follow-up, corroborating persistent deficits in number processing. The present results are in line with the literature showing that children with DD have reduced gray and white matter volumes in the numerical network. Our study further sheds light on the trajectory of brain development, revealing that these known structural differences in the long association fibers and the adjacent regions of the temporal- and frontoparietal cortex persist in dyscalculic children from childhood into adolescence. In conclusion, our results underscore that DD is a persistent learning disorder accompanied by deficits in number processing and reduced gray and white matter volumes in number related brain areas.

The link between number and space has been discussed in the literature for some time, resulting in the theory that number, space and time might be part of a generalized magnitude system. To date, several behavioral and neuroimaging findings support the notion of a generalized magnitude system, although contradictory results showing a partial overlap or separate magnitude systems are also found. The possible existence of a generalized magnitude processing area leads to the question how individuals with developmental dyscalculia (DD), known for deficits in numerical-arithmetical abilities, process magnitudes. By means of neuropsychological tests and functional magnetic resonance imaging (fMRI) we aimed to examine the relationship between number and space in typical and atypical development. Participants were 16 adolescents with DD (14.1 years) and 14 typically developing (TD) peers (13.8 years). In the fMRI paradigm participants had to perform discrete (arrays of dots) and continuous magnitude (angles) comparisons as well as a mental rotation task. In the neuropsychological tests, adolescents with dyscalculia performed significantly worse in numerical and complex visuo-spatial tasks. However, they showed similar results to TD peers when making discrete and continuous magnitude decisions during the neuropsychological tests and the fMRI paradigm. A conjunction analysis of the fMRI data revealed commonly activated higher order visual (inferior and middle occipital gyrus) and parietal (inferior and superior parietal lobe) magnitude areas for the discrete and continuous magnitude tasks. Moreover, no differences were found when contrasting both magnitude processing conditions, favoring the possibility of a generalized magnitude system. Group comparisons further revealed that dyscalculic subjects showed increased activation in domain general regions, whilst TD peers activate domain specific areas to a greater extent. In conclusion, our results point to the existence of a generalized magnitude system in the occipito-parietal stream in typical development. The detailed investigation of spatial and numerical magnitude abilities in DD reveals that the deficits in number processing and arithmetic cannot be explained with a general magnitude deficiency. Our results further indicate that multiple neuro-cognitive components might contribute to the explanation of DD.

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Studies report persistent deficits in number processing and aberrant functional activation of the fronto-parietal numerical network in DD. However, the neural development of numerical abilities has been scarcely investigated. The present paper provides a first attempt to investigate behavioral and neural trajectories of numerical abilities longitudinally in typically developing (TD) and DD children. During a study period of 4 years, 28 children (8–11 years) were evaluated twice by means of neuropsychological tests and a numerical order fMRI paradigm. Over time, TD children improved in numerical abilities and showed a consistent and well-developed fronto-parietal network. In contrast, DD children revealed persistent deficits in number processing and arithmetic. Brain imaging results of the DD group showed an age-related activation increase in parietal regions (intraparietal sulcus), pointing to a delayed development of number processing areas. Besides, an activation increase in frontal areas was observed over time, indicating the use of compensatory mechanisms. In conclusion, results suggest a continuation in neural development of number representation in DD, whereas the neural network for simple ordinal number estimation seems to be stable or show only subtle changes in TD children over time.