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Institute
Numbers and space are two semantic primitives that interact with each other. Both recruit brain regions along the dorsal pathway, notably parietal cortex. This makes parietal cortex a candidate for the origin of numerical–spatial interaction. The underlying cognitive architecture of the interaction is still under scrutiny. Two classes of explanations can be distinguished. The early interaction approach assumes that numerical and spatial information are integrated into a single representation at a semantic level. A second approach postulates independent semantic representations. Only at the stage of response selection and preparation these two streams interact. In this study we used a numerical landmark task to identify the locus of the interaction between numbers and space. While lying in an MR scanner participants decided on the smaller of two numerical intervals in a visually presented number triplet. The spatial position of the middle number was varied; hence spatial intervals were congruent or incongruent with the numerical intervals. Responses in incongruent trials were slower and less accurate than in congruent trials. By combining across-vertex correlations (micro pattern) with a cluster analysis (macro pattern) we identified large-scale networks that were devoted to number processing, eye movements, and sensory–motor functions. Using support vector classification in different regions of interest along the intraparietal sulcus, the frontal eye fields, and supplementary motor area we were able to distinguish between congruent and incongruent trials in each of the networks. We suggest that the identified networks participate in the integration of numerical and spatial information and that the exclusive assumption of either an early or a late interaction between numerical and spatial information does not do justice to the complex interaction between both dimensions.
In the course of elementary school children start to develop an academic self-concept reflecting their motivation, thoughts, and feelings about a specific domain. For the domain of mathematics, gender differences can emerge which are characterized by a less pronounced math self-concept for girls. However, studies are rather sparse regarding the early years of elementary school education, hence, the point in time when such gender differences emerge yet remains a matter of debate. In our study, we found that the math self-concept of elementary school children (n = 81) declined from first to second grade. While no differences in math achievement were observed between girls and boys, it became apparent that girls’ math self-concept was already less pronounced than the math self-concept of boys in the first years of elementary school. Our findings emphasize the importance of considering such gender differences even at the beginning of school education.
Magnitude processing is one of the most central cognitive mechanisms that underlie persistent mathematics difficulties. No consensus has yet been reached about whether these difficulties can be predominantly attributed to deficits in symbolic or nonsymbolic magnitude processing. To investigate this issue, we assessed symbolic and nonsymbolic magnitude representations in children with low or typical achievement in school mathematics. Response latencies and the distance effect were comparable between groups in both symbolic and nonsymbolic tasks. The results indicated that both typical and low achievers were able to access magnitude representation via symbolic and nonsymbolic processing. However, low achievers presented higher error rates than typical achievers, especially in the nonsymbolic task. Furthermore, measures of nonsymbolic magnitude explained individual differences in school mathematics better than measures of symbolic magnitude when considering all of the children together. When examining the groups separately, symbolic magnitude representation explained differences in school mathematics in low achievers but not in typical achievers. These results suggest that symbolic magnitude is more relevant to solving arithmetic problems when mathematics achievement is particularly low. In contrast, individual differences in nonsymbolic processing appear to be related to mathematics achievement in a more general manner.
The approximate number system (ANS) is assumingly related to mathematical learning but evidence supporting this assumption is mixed. The inconsistent findings might be attributed to the fact that different measures have been used to assess the ANS and mathematical skills. Moreover, associations between the performance on a measure of the ANS and mathematical skills may be discontinuous, i.e., stronger for children with lower math scores than for children with higher math scores, and may change with age. The aim of the present study was to examine the development of the ANS and arithmetic skills in elementary school children and to investigate how the relationship between the ANS and arithmetic skills develops. Individual markers of children's ANS (internal Weber fractions and mean reaction times in a non-symbolic numerical comparison task) and addition skills were assessed in their first year of school and 1 year later. Children showed improvements in addition performance and in the internal Weber fractions, whereas mean reaction times in the non-symbolic numerical comparison task did not change significantly. While children's addition performance was associated with the internal Weber fractions in the first year, it was associated with mean reaction times in the non-symbolic numerical comparison task in the second year. These associations were not found to be discontinuous and could not be explained by individual differences in reasoning, processing speed, or inhibitory control. The present study extends previous findings by demonstrating that addition performance is associated with different markers of the ANS in the course of development.
As demonstrated by the Overlapping Waves Model (Siegler, 1996), children’s strategy use in arithmetic tasks is variable, adaptive, and changes gradually with age and experience. In this study, first grade elementary school children (n = 73), who scored high, middle, or low in a standardized scholastic mathematic achievement test, were confronted with different arithmetic tasks (simple addition, e.g., 3 + 2, simple subtraction, e.g., 7 – 2, and more advanced addition, e.g., 7 + 9) to evoke different calculation strategies. Video analysis and children’s self-report were used to identify individual strategy behavior. In accordance with the Overlapping Waves Model, children in all achievement groups showed variable and multiple strategy usage and adapted their behavior to the tasks of the different categories. We demonstrated that not only low achievers differed from normal achievers but also that high achievers exhibited a unique pattern of strategy behavior in early mathematics.
The approximate number system (ANS) has been consistently found to be associated with math achievement. However, little is known about the interactions between the different instantiations of the ANS and in how many ways they are related to exact calculation. In a cross-sectional design, we investigated the relationship between three measures of ANS acuity (non-symbolic comparison, non-symbolic estimation and non-symbolic addition), their cross-sectional trajectories and specific contributions to exact calculation. Children with mathematical difficulties (MD) and typically achieving (TA) controls attending the first six years of formal schooling participated in the study. The MD group exhibited impairments in multiple instantiations of the ANS compared to their TA peers. The ANS acuity measured by all three tasks positively correlated with age in TA children, while no correlation was found between non-symbolic comparison and age in the MD group. The measures of ANS acuity significantly correlated with each other, reflecting at least in part a common numerosity code. Crucially, we found that non-symbolic estimation partially and non-symbolic addition fully mediated the effects of non-symbolic comparison in exact calculation.
Human beings are assumed to possess an approximate number system (ANS) dedicated to extracting and representing approximate numerical magnitude information. The ANS is assumed to be fundamental to arithmetic learning and has been shown to be associated with arithmetic performance. It is, however, still a matter of debate whether better arithmetic skills are reflected in the ANS. To address this issue, Chinese and German adults were compared regarding their performance in simple arithmetic tasks and in a non-symbolic numerical magnitude comparison task. Chinese participants showed a better performance in solving simple arithmetic tasks and faster reaction times in the non-symbolic numerical magnitude comparison task without making more errors than their German peers. These differences in performance could not be ascribed to differences in general cognitive abilities. Better arithmetic skills were thus found to be accompanied by a higher speed of retrieving non-symbolic numerical magnitude knowledge but not by a higher precision of non-symbolic numerical magnitude representations. The group difference in the speed of retrieving non-symbolic numerical magnitude knowledge was fully mediated by the performance in arithmetic tasks, suggesting that arithmetic skills shape non-symbolic numerical magnitude processing skills.
The neural correlates of developmental dyslexia have been investigated intensively over the last two decades and reliable evidence for a dysfunction of left-hemispheric reading systems in dyslexic readers has been found in functional neuroimaging studies. In addition, structural imaging studies using voxel-based morphometry (VBM) demonstrated grey matter reductions in dyslexics in several brain regions. To objectively assess the consistency of these findings, we performed activation likelihood estimation (ALE) meta-analysis on nine published VBM studies reporting 62 foci of grey matter reduction in dyslexic readers. We found six significant clusters of convergence in bilateral temporo-parietal and left occipito-temporal cortical regions and in the cerebellum bilaterally. To identify possible overlaps between structural and functional deviations in dyslexic readers, we conducted additional ALE meta-analyses of imaging studies reporting functional underactivations (125 foci from 24 studies) or overactivations (95 foci from 11 studies ) in dyslexics. Subsequent conjunction analyses revealed overlaps between the results of the VBM meta-analysis and the meta-analysis of functional underactivations in the fusiform and supramarginal gyri of the left hemisphere. An overlap between VBM results and the meta-analysis of functional overactivations was found in the left cerebellum. The results of our study provide evidence for consistent grey matter variations bilaterally in the dyslexic brain and substantial overlap of these structural variations with functional abnormalities in left hemispheric regions.
Different lines of evidence suggest that children's mental representations of numbers are spatially organized in form of a mental number line. It is, however, still unclear whether a spatial organization is specific for the numerical domain or also applies to other ordinal sequences in children. In the present study, children (n = 129) aged 8–9 years were asked to indicate the midpoint of lines flanked by task-irrelevant digits or letters. We found that the localization of the midpoint was systematically biased toward the larger digit. A similar, but less pronounced, effect was detected for letters with spatial biases toward the letter succeeding in the alphabet. Instead of assuming domain-specific forms of spatial representations, we suggest that ordinal information expressing relations between different items of a sequence might be spatially coded in children, whereby numbers seem to convey this kind of information in the most salient way.
Human beings are supposed to possess an approximate number system (ANS) dedicated to extracting and representing approximate numerical magnitude information as well as an object tracking system (OTS) for the rapid and accurate enumeration of small sets. It is assumed that the OTS and the ANS independently contribute to the acquisition of more elaborate numerical concepts. Chinese children have been shown to exhibit more elaborate numerical concepts than their non-Chinese peers, but it is still an open question whether similar cross-national differences exist with regard to the underlying systems, namely the ANS and the OTS. In the present study, we investigated this question by comparing Chinese and German preschool children with regard to their performance in a non-symbolic numerical magnitude comparison task (assessing the ANS) and in an enumeration task (assessing the OTS). In addition, we compared children’s counting skills. To ensure that possible between-group differences could not be explained by differences in more general performance factors, we also assessed children’s reasoning ability and processing speed. Chinese children showed a better counting performance and a more accurate performance in the non-symbolic numerical magnitude comparison task. These differences in performance could not be ascribed to differences in reasoning abilities and processing speed. In contrast, Chinese and German children did not differ significantly in the enumeration of small sets. The superior counting performance of Chinese children was thus found to be reflected in the ANS but not in the OTS.
