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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.
The role of space in numerical processing has been discussed since the very beginning of the numerical and arithmetical scientific history. Galton’s investigation about the spatial orientation of numbers revealed that subjects have internal representations with various visuo-spatial properties (
Further evidence for the ATOM theory is found in animal studies.
In adults, several behavioral studies report that different magnitude dimensions influence each other.
The ATOM theory was also investigated by means of neuroimaging methods. Functional Magnetic Resonance Imaging (fMRI) studies revealed an activation overlap in the IPS irrespective of the processed magnitude [size/luminance/numbers (
In summary, behavioral and neuroimaging studies offer a broad variety of hints about the relationship of space and number. Several findings support the theory of a generalized magnitude system, although contradictory results speaking for a partial overlap or separate magnitude systems are also found (
In the context of the evidence for and against the existence of a generalized magnitude system, it would be interesting to investigate the relationship between number and space in subjects with specific deficits in number processing, as it is the case in developmental dyscalculia (DD). This disorder is defined as a specific learning disability affecting the acquisition of basic numerical-arithmetical skills that is not explicable on the basis of general mental retardation or of inadequate schooling (
Concerning the visuo-spatial deficits, several behavioral studies investigated the relationship between number and space in children with DD (
To our knowledge, only one neuroimaging study looked at numerical and spatial abilities in children with DD (
To date, several behavioral studies point to deficiencies in visuo-spatial abilities in dyscalculic children (
The main goal in our study was to evaluate the theory of a generalized magnitude system by looking at space and number processing using behavioral as well as neuroimaging measures. We aimed to develop a fMRI task that measures discrete quantity processing (non-symbolic numerosity comparison), continuous quantity/visuo-spatial processing (angles comparison) and complex visuo-spatial processing (mental rotation). The second research question intended to examine if there are behavioral and neuronal differences in adolescents with and without DD regarding generalized magnitude processing. We specifically chose to examine adolescents with DD as there is very little literature regarding this age range.
Based on the previous literature, we hypothesize that the numerical as well as the visuo-spatial task containing a magnitude judgment activates a core region for magnitude processing in the IPS (
Twenty adolescents with DD and 17 TD adolescents between 11.6 and 16.5 years were recruited into this study. Most of the participants were part of a longitudinal project about dyscalculia, 10 participants were additionally recruited for the purpose of this study. The adolescents were either approached in the school setting, School Psychological Services (DD subjects) or applied through our homepage for the participation in the study. Inclusion criteria for all participants were no history of neurological disorders and an Intelligence Quotient (IQ) ≥ 85, measured by the fourth edition of the WISC (Similarities, Block Design, Matrix Reasoning;
Demographic characteristics and scores of numerical abilities, visuo-spatial abilities, domain general cognitive abilities, memory, attention, and reading.
Behavioral measure | DD ( |
TD ( |
Test-statistic | |
---|---|---|---|---|
Age | 14.1 (1.2) | 13.8 (1.3) | 0.705a | 0.487 |
Gender m/f | 4/12 | 4/10 | 0.049b | 0.999 |
Handedness l/a/r | 2/2/12 | 1/4/9 | 1.367b | 0.515 |
Pubertal status | 2.8 (0.8) | 2.8 (0.7) | 0.610c | 0.737 |
BASIS-MATH 4-8 | 50.8 (11.3) | 75.1 (4.2) | -7.971a | <0.001 |
KFT 4-12+R quantity comparison | 40.2 (4.6) | 53.6 (4.9) | -6.395a | <0.001 |
Length estimation (accuracy) | 91.9 (7.6) | 92.2 (6.0) | 0.567c | 0.715 |
Size estimation (accuracy) | 98.4 (2.1) | 97.4 (3.1) | 0.567c | 0.596 |
Position estimation (accuracy) | 63.0 (10.8) | 65.0 (11.0) | -0.485a | 0.632 |
KFT 4-12+R paper folding | 40.4 (10.5) | 52.4 (9.0) | -3.234a | 0.003 |
DTVP-A form constancy | 71.3 (21.7) | 83.6 (14.8) | 1.415c | 0.014 |
DTVP-A copying | 40.0 (25.2) | 58.8 (29.3) | -1.887a | 0.070 |
Block design | 97 (14.8) | 113 (12.1) | -3.075a | 0.005 |
Similarities | 104 (7.6) | 112 (4.7) | -3.562a | 0.001 |
Matrix reasoning | 101 (8.5) | 113 (11.7) | -3.395a | 0.002 |
Estimated general IQ | 101 (6.5) | 113 (5.7) | -5.421a | <0.001 |
Visuo-spatial working memory | 6.0 (1.8) | 7.1 (1.9) | 0.833c | 0.235 |
Verbal memory span | 5.6 (1.3) | 5.7 (1.2) | -0.335a | 0.740 |
Verbal working memory | 4.4 (1.1) | 5.1 (1.3) | 0.659c | 0.407 |
Alertness | 48.8 (21.5) | 52.0 (15.3) | -0.457a | 0.651 |
Go-nogo | 40.1 (16.1) | 40.1 (15.0) | 0.659c | 0.668 |
Words | 19.5 (24.8) | 25.6 (23.7) | 15.088b | 0.213 |
Pseudowords | 23.3 (20.7) | 33.0 (29.5) | 15.088b | 0.326 |
The adolescents visited us twice at the Center for MR-Research of the University Children’s Hospital Zurich. First they completed a neuropsychological session (duration about 2 h) and then underwent the MRI measurement (duration 45 min).
The order of the neuropsychological tests was varied in to ways to avoid order effects. Half of the participants were randomly assigned to the first, the remainder to the second order version of the tests.
Numerical achievement was assessed using the BASIS-MATH 4–8 (
Additionally, the subtest Quantity Comparison of the Cognitive Abilities Test (KFT 4-12+R;
Because of the multifarious nature of visuo-spatial abilities, the tasks are subdivided into visuo-perceptive, visuo-cognitive and visuo-constructive tasks (
Firstly, visuo-perceptive abilities include amongst others the perception of position in space, length, and distance discrimination (
Secondly, visuo-cognitive abilities include in addition to the mere perception of visual stimuli an operation in space, such as mental rotation or change of perspective (
Lastly, visuo-constructive skills indicate the ability to combine elements to a whole, such as drawing a geometrical figure or assembling cubes to one figure (
Regarding the theory of a generalized magnitude system it is important to note, that visuo-perceptive tasks include magnitude processing (because the tasks contain prosthetic dimensions), whilst visuo-cognitive and visuo-constructive tasks do not.
The 1-Minute-Reading-Task from the Salzburg Reading and Orthography Test (
In order to control for memory effects, verbal memory span and working memory were assessed using the subtest Digit Span of the WISC-IV (
Levels of attention and inhibition were measured by means of the subtests Alertness and Go-Nogo of the Testbattery for Attentional Performance (TAP;
Behavioral data was statistically analyzed with SPSS (Version 20). To assess group differences parametric
The fMRI paradigm was newly designed for this study and consist of three experimental and one control condition. In order to avoid strong engagement of executive functions, needed if switching between the four tasks, a block design was chosen rather than an event-related design. Because we aimed to have an optimal signal in terms of high pass filtering (see also
The fMRI paradigm intends to measure perceptive and cognitive spatial as well as magnitude processing. In the task a green and a blue Pacman with varying arrays of dots, mouth size, and rotation angles were presented simultaneously (
A single stimulus consisted of a Pacman with a diameter of 13.2 cm created in Adobe Photoshop. The dot arrays were controlled for dot size, total surface and density. Dots varied between 0.25 and 1 cm in diameter, had a total surface of 5.9 cm2 and were either spread on a small (5 × 6 cm) or al large area (6 × 7 cm; see also
Magnetic resonance imaging data were acquired on a 3T General Electric Discovery 750 Scanner (GE Medical Systems, USA) using an 8-channel head coil. Whole brain functional images were acquired sequentially with a gradient echo EPI sequence [38 slices, 3 mm slice thickness (ST), 0.3 mm interslice gap, 64 × 64 matrix size (MS), field of view (FOV) = 240 mm, flip angle (FA) = 74°, echo time (TE) = 32 ms, repetition time (TR) = 1900 ms]. Additionally, a T1-weighted structural image was obtained with a spoiled gradient echo sequence (3D SPGR, ST = 1 mm, no interslice gap, MS = 256 × 256, FOV = 256 mm, FA = 8°, TE = 5 ms, TR = 11 ms).
Participants were carefully instructed and supplied with hearing protection before entering the scanner. To minimize head motion, the head was stabilized with padding.
The fMRI data were analyzed by means of Statistical Parametric Mapping (SPM8, Wellcome Trust Centre for NeuroImaging, UK) running under Matlab (Release 2012b, The MathWorks Inc., USA).
Three dummy scans, acquired to stabilize magnetization at the beginning of the scan, were excluded from the analysis. Afterward, the subjects’ functional scans were realigned with rigid body transformations using the mean image as a reference scan. Six motion parameters (translation in
The first level analysis was performed using a mass-univariate approach based on the GLM (General Linear Model). The time series from each subject were modeled with an event related design for the experimental and control condition using a canonical HRF (hemodynamic response function). The six subjects’ motion parameters were entered as additional regressors. Slow signal drifts and serial correlations were accounted for by using a high-pass filter of 128 s and a first level autoregressive model during maximum-likelihood estimation of the GLM parameters.
At the second level, a full factorial analysis with the factors group (DD, TD) and task (Numerical, Perceptive Spatial, Mental Rotation) was conducted for the contrast images experimental > control condition.
Statistical results are shown with a threshold of
Anatomical localization of the fMRI results was attained through the SPM Anatomy Toolbox v2.0 (
The neuropsychological results and the demographic data for all participants are summarized in
Regarding the comorbid disorders such as attention deficit and hyperactivity disorder, dyslexia and working memory deficits, groups did not differ significantly in any measurement of attention, reading or memory performance (all
Numerical abilities, assessed by the Basis-Math, differed highly between the TD and the DD group (
In the visuo-perceptive tasks, accuracy was measured by calculating the ratio of the correctly solved items compared to the total number of items. The results revealed that both groups were able to solve the length and size estimation task well. The position estimation task was more difficult for the adolescents as seen by the lower accuracy values. All participants solved the task with an accuracy level of over 50%, except for two DD and two TD subjects. However, no significant differences could be found between the groups in any of the visuo-perceptive tasks (all
In the visuo-cognitive abilities, significant differences between groups could be found in both tests. Adolescents with DD performed worse than the TD adolescents in the Form Constancy subtest of the DTVP-A (
Finally, in the visuo-constructive tasks, no significant difference in performance was observed in the Copying subtest of the DTVP-A, although, a trend-level difference in performance was detected, with dyscalculic adolescents reaching a mean PR of 40, whereby TD adolescents score at PR 59 (
As the fMRI paradigm was newly designed for this study and adolescents solved it in a self-paced mode, we first looked at some general features of the paradigm before looking at group differences. Hence, the number of solved items was quantified and entered into a mixed-model ANOVA with experimental condition as a within-subject factor and group as a between-subject factor. Results showed a significant effect of condition [
Accuracy and RT were calculated for each condition, excluding trials in which RT was smaller than 300 ms and misses (
Mean accuracies and RT of the fMRI paradigm conditions for DD and TD adolescents as well as the total mean.
Behavioral measure | DD ( |
TD ( |
Total |
---|---|---|---|
Numerical condition | 73.9 (9.1) | 84.1 (9.1) | 78.7 (10.3) |
Perceptive Spatial condition | 70.9 (9.9) | 71.2 (8.9) | 71.0 (9.3) |
Mental Rotation condition | 86.4 (18.4) | 93.1 (7.6) | 98.5 (14.6) |
Control condition | 98.0 (2.6) | 99.0 (1.5) | 98.0 (2.2) |
Numerical condition | 1190 (350) | 1239 (267) | 1213 (299) |
Perceptive Spatial condition | 1320 (254) | 1313 (313) | 1316 (282) |
Mental Rotation condition | 1312 (383) | 1333 (361) | 1322 (367) |
Control condition | 571 (124) | 582 (91) | 577 (106) |
The analysis of the RT revealed a significant effect of condition [
Motion determined by the total displacement of the motion fingerprint (
Firstly, conjunction analyses were conducted to examine jointly used regions over all experimental conditions (experimental > control condition; FWE corrected at
Brain areas that showed significant activation in the conjunction analyses for all experimental conditions, magnitude conditions and visuo-spatial conditions, respectively (
Region | Cluster size | Peak |
Peak MNI coordinates | ||
---|---|---|---|---|---|
R middle occipital gyrus | 249 | 6.59 | 28 | -71 | 33 |
R inferior occipital gyrus (assigned to fusiform gyrus) | 6.57 | 43 | -65 | -12 | |
R calcarine gyrus (assigned to V1) | 144 | 7.79 | 13 | -86 | 6 |
N/A (assigned to V1) | 119 | 6.80 | -14 | -86 | 3 |
L inferior occipital gyrus | 38 | 6.34 | -35 | -77 | -9 |
R insula | 10 | 5.27 | 34 | 22 | 3 |
L superior parietal lobe (assigned to area 7A) | 6 | 5.21 | -20 | -71 | 48 |
L middle occipital gyrus | 6 | 5.42 | -29 | -89 | 15 |
L middle occipital gyrus | 1850 | 9.60 | -29 | -89 | 15 |
R middle occipital gyrus | 8.03 | 31 | -86 | 15 | |
R calcarine gyrus (assigned to V1) | 7.79 | 13 | -86 | 6 | |
R insula | 10 | 5.27 | 34 | 22 | 3 |
L superior parietal lobe (assigned to area 7A) | 9 | 5.21 | -20 | -71 | 48 |
Cerebellar vermis | 7 | 5.22 | 4 | -71 | -27 |
R inferior temporal gyrus (assigned to fusiform gyrus) | 402 | 7.24 | 46 | -68 | -12 |
R superior parietal lobe (assigned to area 7A) | 6.74 | 22 | -68 | 57 | |
R calcarine gyrus (assigned to V1) | 147 | 8.09 | 13 | -89 | 6 |
N/A (assigned to V1) | 119 | 6.80 | -14 | -86 | 3 |
L inferior occipital gyrus | 87 | 6.34 | -35 | -77 | -9 |
R precentral gyrus | 31 | 5.90 | 49 | 4 | 30 |
L superior parietal lobe (assigned to area 7A) | 12 | 5.21 | -20 | -71 | 48 |
R insula | 10 | 5.27 | 34 | 22 | 3 |
L inferior parietal lobe (assigned to intraparietal sulcus) | 8 | 5.06 | -29 | -56 | 48 |
L middle occipital gyrus | 6 | 5.42 | -29 | -86 | 15 |
Secondly, comparisons between the conditions were conducted to examine regions used specifically for the single conditions (
Brain areas that showed significant activation for the different task comparisons in typically developing adolescents (
Region | Cluster size | Peak |
Peak MNI coordinates | ||
---|---|---|---|---|---|
N/A (adjacent to the R superior frontal gyrus) | 301 | 4.33 | 31 | 1 | 45 |
R superior frontal gyrus | 4.29 | 25 | -8 | 60 | |
R inferior parietal lobe (assigned to intraparietal sulcus) | 217 | 4.70 | 40 | -50 | 54 |
R superior parietal lobe (assigned to intraparietal sulcus) | 3.94 | 28 | -56 | 63 | |
R middle occipital gyrus | 29 | 3.87 | 40 | -74 | 30 |
L inferior parietal lobe | 28 | 4.27 | -44 | -56 | 60 |
L superior frontal gyrus (assigned to frontal pole) | 215 | 4.87 | -14 | 64 | 21 |
L superior medial gyrus | 4.07 | -2 | 61 | 18 | |
R inferior occipital gyrus (assigned to V3) | 213 | 6.05 | 22 | -92 | -6 |
R middle occipital gyrus | 5.22 | 31 | -92 | 3 | |
R insula/rolandic operculum | 129 | 5.13 | 49 | -5 | 9 |
L calcarine gyrus | 129 | 5.03 | -17 | -98 | -3 |
L insula | 36 | 4.32 | -41 | -11 | 9 |
R superior frontal gyrus | 405 | 4.79 | 22 | 1 | 66 |
R middle frontal gyrus | 4.52 | 25 | 10 | 45 | |
R inferior parietal lobe (assigned to intraparietal sulcus) | 146 | 4.05 | 40 | -50 | 54 |
L middle frontal gyrus | 44 | 3.71 | -26 | -2 | 54 |
R supramarginal gyrus (assigned to inferior parietal lobe) | 40 | 3.96 | 58 | -29 | 45 |
R middle occipital gyrus | 26 | 4.44 | 40 | -71 | 30 |
L superior frontal gyrus (assigned to frontal pole) | 119 | 4.43 | -5 | 61 | 18 |
L middle occipital gyrus (assigned to V3) | 27 | 3.76 | -29 | -95 | 12 |
L middle temporal gyrus | 24 | 4.49 | -62 | -35 | 0 |
Numerical versus Perceptive Spatial: The contrast Numerical versus Perceptive Spatial condition revealed no significant differences.
Perceptive Spatial versus Numerical: The contrast Perceptive Spatial versus Numerical condition revealed no significant differences.
Mental Rotation versus Numerical: The Mental Rotation task elicited greater activation compared to the Numerical task in the right IPS, the right MOG reaching into IPL, left IPL and the right superior frontal gyrus (SFG) (
Numerical versus Mental Rotation: The opposite contrast revealed higher activation in the bilateral IOG/MOG, bilateral insula, left superior medial gyrus and SFG (
Mental Rotation versus Perceptive Spatial: For the Mental Rotation task activation increase was found in the right IPS (extending into the angular gyrus), the supramarginal gyrus, the MOG, and bilateral SFG/superior medial gyrus compared to the Perceptive Spatial task (
Perceptive Spatial versus Mental Rotation: The Perceptive Spatial condition, however, revealed higher activation in the left MOG, the medial temporal gyrus and the SFG (
In the Numerical condition, adolescents with DD showed increased activation in the left inferior frontal gyrus (IFG; pars triangularis) compared to TD adolescents (
Brain areas that showed significant activation in the different conditions when contrasting DD adolescents and TD adolescents (
Region | Cluster size | Peak |
Peak MNI coordinates | ||
---|---|---|---|---|---|
L inferior frontal gyrus | 37 | 4.26 | -41 | 19 | 21 |
L inferior frontal gyrus | 27 | 4.35 | -35 | 31 | 15 |
L middle occipital gyrus | 24 | 4.12 | -29 | -86 | 15 |
In the Perceptive Spatial condition dyscalculic adolescents showed increased activation in the left IFG (pars triangularis), whereas TD adolescents had higher activation in the left MOG (
Finally, in the Mental Rotation task neither the DD nor the TD adolescents showed activation differences when comparing them against each other.
The link between space and number has been discussed and investigated in the literature for some time, leading to the theory that time, space, and number might be part of a generalized magnitude system located in the parietal cortex (
The main goal of this study was to elaborate the theory of a generalized magnitude system looking at number and visuo-spatial processing. In our fMRI task, we therefore aimed to measure discrete quantity processing (Numerical condition), continuous quantity/simple visuo-spatial processing (Perceptive Spatial condition) and complex visuo-spatial processing, the latter without an explicit magnitude decision (Mental Rotation).
At first, the neuronal and behavioral analyses of the tasks containing magnitude processing (prosthetic dimensions) were of interest. The conjunction analysis with the tasks involving magnitude processing revealed a network with a prominent activation cluster in the occipital and the IPL/SPL (
Additional clusters of activation were revealed in the bilateral higher order visual areas MOG/IOG as well as in the visual cortex (V1). This was not the case in the aforementioned studies (
Regarding the behavioral data, the adolescents performed better in the Numerical task than the Perceptive Spatial task. However, previous results showed that comparison of continuous stimuli (Perceptive Spatial task) is easier than discrete magnitude comparisons (Numerical task;
To summarize, our findings about magnitude processing argue for a common network irrespective of whether discrete or continuous magnitude judgment is used, in agreement with several studies (
In a next step, comparisons between the magnitude and visuo-spatial conditions were drawn. Not surprisingly, task specific differences between the Mental Rotation task and the Perceptive Spatial or Numerical tasks were found in similar regions, namely right IPS, right MOG, and right/bilateral SFG. Activations in these regions are widely discussed in mental rotation studies and have been associated with visuo-spatial image transformation, working memory, motor simulation, motor planning/execution, and monitoring (
Taken together, differences in task specific activation is mainly explained by the extent to which domain-general functions are involved in the single conditions. On the other hand, similar activation patterns in the occipito-parietal lobe were observed in the tasks containing magnitude processing, indicating a comparable involvement of the domain-specific areas for the magnitude conditions. Hence, the results from our first research question would support the notion of a generalized magnitude system.
In our second research question, we intended to investigate differences regarding the general magnitude system in adolescents with and without dyscalculia. If a shared magnitude system exists, it would be reasonable to find deficits in tasks containing spatial magnitude processing in adolescents with DD, taking into account their deficits in numerical processing. Alternatively, dissociation in these two abilities could possibly argue for partially overlapping or even separate systems.
Our DD group performed significantly worse than the control group in all numerical tasks, showing difficulties in basic arithmetical skills. According to our hypothesis, we further found significantly lower performances in a variety of behavioral visuo-spatial tasks. More precisely, DD participants performed significantly worse in the visuo-cognitive and visuo-constructive tasks, but reached similar levels in all visuo-perceptive tasks compared to the TD group. Several other studies have also reported deficits in visuo-spatial abilities in DD, although most of them examined only one of the various spatial components (
In the Numerical condition of the fMRI task, adolescents with DD did not show a deficient performance. Previous findings about non-symbolic magnitude processing are inconclusive (
Regarding brain activation, only tasks containing magnitude decisions elicited neuronal differences between the groups (
In summary, DD adolescents show in addition to the known deficits in numerical-arithmetical processing difficulties in cognitive and constructive visuo-spatial processing. Abilities to process non-symbolic (discrete) and perceptive visuo-spatial (continuous) magnitudes seem not to be affected in adolescents with DD. On the neuronal level, the increase in frontal activation might hint to the use of compensatory domain-general regions, revealing possible difficulties in dyscalculic adolescents. TD peers have increased activation in task relevant areas probably using a more efficient way of processing magnitudes. In this context, the deficits in number processing and arithmetic cannot be explained with a general magnitude deficit. This challenges the conclusion of previous studies that DD results from a deficit in the approximate magnitude representation (e.g.,
In summary, adolescents with DD seem to have a well-developed magnitude system for discrete and continuous sizes favoring the proposed theory of a generalized magnitude system (
In the present study some limitations regarding group differences, paradigm design and interpretation of the data have to be taken into account.
Firstly, the revealed differences in the estimated IQ between adolescents with and without dyscalculia might limit the interpretation of the results. However, IQ tests are known to be not completely independent from numerical skills, and differences in IQ measures between a group of children with learning disabilities and a control group are often reported (
Secondly, although carefully planned and developed, the paradigm did not control for eye movements. This is important to consider, as studies show that saccades activate bilateral areas of the SPL and parts of the IPS (
Finally, our results point to the existence of a generalized magnitude system. However, it is important to note that in addition to providing a key region for number processing, the parietal lobe is reported to show activation in various tasks of spatial, motor, and attentional functions (
The results obtained in the present study favor the possibility of a generalized magnitude system in the occipito-parietal lobe. It might be further assumed, that with development more refined and specific neuronal functions form in order to process magnitudes with increasing difficulty (
All authors have contributed and have approved the final manuscript. UM contributed to the design of the study, the acquisition, analysis and interpretation of the data, and writing the manuscript. MvA and RO contributed to data interpretation and revised the manuscript. KK contributed to the design of the study, data interpretation, editing and revising the manuscript.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
We would like to thank all subjects and their parents for participation in this study. The present manuscript is partially based on the thesis of the UM (
The Supplementary Material for this article can be found online at: