The influence of visual-spatial skills on the association between processing of nonsymbolic numerical magnitude and number word sequence skills.

Nonsymbolic numerical magnitude processing skills are assumed to be fundamental to mathematical learning. Recent findings suggest that visual-spatial skills account for associations between children's performance in visually presented nonsymbolic numerical magnitude comparison tasks and their performance in visually presented arithmetic tasks. The aim of the current study was to examine whether associations between children's performance in visually presented tasks assessing nonsymbolic numerical magnitude processing skills and their performance in tasks assessing early mathematical skills, which do not involve visual stimulation, may also be mediated by visual-spatial skills. This line of reasoning is based on the assumption that children make use of mental visualization processes when working on tasks assessing early mathematical skills, such as knowledge of the sequence of number words, even when these tasks do not involve visual stimulation. We assessed 4- to 6-year-old children's performance in a nonsymbolic numerical magnitude comparison task, in tasks concerning knowledge of the sequence of number words, and in a developmental test to assess visual-spatial skills. Children's nonsymbolic numerical magnitude processing skills were found to be associated with their number word sequence skills. This association was fully mediated by interindividual differences in visual-spatial skills. The effect size of this mediation effect was small. We assume that the ability to construct mental visualizations constitutes the key factor underlying this mediation effect.

Exploring factors underlying children's acquisition and retrieval of sound-symbol association skills.

Letter knowledge is considered an important cognitive foundation for learning to read. The underlying mechanisms of the association between letter knowledge and reading skills are, however, not fully understood. Acquiring letter knowledge depends on the ability to learn and retrieve sound-symbol pairings. In the current study, this process was explored by setting preschool children's (N = 242, mean age = 5.57 years) performance in the acquisition and retrieval of a paired associate learning (PAL) task in relation to their letter knowledge as well as to their performance in tasks assessing precursors of reading skills (i.e., phonological awareness, rapid automatized naming, phonological short-term memory, backward recall, and response inhibition). Multiple regression analyses revealed that performance in the acquisition of the PAL task was significantly associated with phonological awareness and backward recall, whereas performance in the retrieval of the PAL task was significantly associated with rapid automatized naming, phonological awareness, and backward recall. Moreover, PAL proved to be mediating the relation between reading precursors and letter knowledge. Together, these findings indicate that the acquisition of letter knowledge may depend on a visual-verbal associative learning mechanism and that different factors contribute to the acquisition and retrieval of such visual-verbal associations.

Thinking about time and number: An application of the dual-systems approach to numerical cognition.

Based on the notion that time, space, and number are part of a generalized magnitude system, we assume that the dual-systems approach to temporal cognition also applies to numerical cognition. Referring to theoretical models of the development of numerical concepts, we propose that children's early skills in processing numbers can be described analogously to temporal updating and temporal reasoning.

Erratum: Ultrahigh Bandwidth Spin Noise Spectroscopy: Detection of Large g-Factor Fluctuations in Highly-n-Doped GaAs [Phys. Rev. Lett. 111, 186602 (2013)].

This corrects the article DOI: 10.1103/PhysRevLett.111.186602.

The association between gray matter volume and reading proficiency: a longitudinal study of beginning readers.

Neural systems involved in the processing of written language have been identified by a number of functional imaging studies. Structural changes in cortical anatomy that occur in the course of literacy acquisition, however, remain largely unknown. Here, we follow elementary school children over their first 2 years of formal reading instruction and use tensor-based morphometry to relate reading proficiency to cortical volume at baseline and follow-up measurement as well as to intraindividual longitudinal volume development between the two measurement time points. A positive relationship was found between baseline gray matter volume in the left superior temporal gyrus and subsequent changes in reading proficiency. Furthermore, a negative relationship was found between reading proficiency at the second measurement time point and intraindividual cortical volume development in the inferior parietal lobule and the precentral and postcentral gyri of the left hemisphere. These results are interpreted as evidence that reading acquisition is associated with preexisting structural differences as well as with experience-dependent structural changes involving dendritic and synaptic pruning.

Children's understanding of demonstratives: an experimental study with German-speaking children between 5 and 7 years of age.

Demonstratives ("this"/"that") express a speaker-relative distance contrast and need to be substituted for each other systematically: depending on their relative position, what one speaker refers to by saying "this" another speaker has to refer to by saying "that." This substitution aspect of demonstratives poses additional difficulties for learning demonstratives, because it requires recognizing that two speakers have to refer to the same thing with different words, and might be one reason for the reportedly protracted acquisition of demonstratives. In an online study conducted in German, it was investigated whether children in the estimated upper age range of demonstrative acquisition (5 to 7 years) understand demonstratives' substitution aspect with familiar ("dies"/"das") and novel ("schmi"/"schmu") demonstratives, and whether they understand novel words ("schmi"/"schmu") when used non-demonstratively as labels (N = 73; between-subject). Children's accuracy was compared with adult performance (N = 74). The study shows that children between 5 and 7 years of age perform less accurately than adults in all conditions. While adults' performance was highly accurate in all conditions (between 75% and 92% correct), children performed below chance in both demonstrative conditions and above chance in the labeling condition. This suggests that children do not understand demonstratives in the presented setup. More detailed analyses of children's response patterns indicate that they instead treat words as mutually exclusive labels in any condition.

Rapid scanning of spin noise with two free running ultrafast oscillators.

We combine the scanning temporal ultrafast delay (STUD) technique with spin noise spectroscopy (SNS), which is based upon below band gap Faraday rotation to investigate the full temporal dynamics of stochastically orientated electron spins in slightly n-doped bulk GaAs. The application of STUD-SNS boosts the common technical bandwidth limitation of the electro-optic conversion in cw-SNS into the several hundred GHz regime. Numerical simulations highlight the strengths and examine the limitations of STUD-SNS.

Ultrahigh bandwidth spin noise spectroscopy: detection of large g-factor fluctuations in highly-n-doped GaAs.

We advance all optical spin noise spectroscopy (SNS) in semiconductors to detection bandwidths of several hundred gigahertz by employing a sophisticated scheme of pulse trains from ultrafast laser oscillators as an optical probe. The ultrafast SNS technique avoids the need for optical pumping and enables nearly perturbation free measurements of extremely short spin dephasing times. We apply the technique to highly-n-doped bulk GaAs where magnetic field dependent measurements show unexpected large g-factor fluctuations. Calculations suggest that such large g-factor fluctuations do not necessarily result from extrinsic sample variations but are intrinsically present in every doped semiconductor due to the stochastic nature of the dopant distribution.

Transcoding abilities in typical and atypical mathematics achievers: the role of working memory and procedural and lexical competencies.

Transcoding between numerical systems is one of the most basic abilities acquired by children during their early school years. One important topic that requires further exploration is how mathematics proficiency can affect number transcoding. The aim of the current study was to investigate transcoding abilities (i.e., reading Arabic numerals and writing dictation) in Brazilian children with and without mathematics difficulties, focusing on different school grades. We observed that children with learning difficulties in mathematics demonstrated lower achievement in number transcoding in both early and middle elementary school. In early elementary school, difficulties were observed in both the basic numerical lexicon and the management of numerical syntax. In middle elementary school, difficulties appeared mainly in the transcoding of more complex numbers. An error analysis revealed that the children with mathematics difficulties struggled mainly with the acquisition of transcoding rules. Although we confirmed the previous evidence on the impact of working memory capacity on number transcoding, we found that it did not fully account for the observed group differences. The results are discussed in the context of a maturational lag in number transcoding ability in children with mathematics difficulties.

Investigating the influence of body movements on children's mental arithmetic performance.

Several lines of research have demonstrated spatial-numerical associations in both adults and children, which are thought to be based on a spatial representation of numerical information in the form of a mental number line. The acquisition of increasingly precise mental number line representations is assumed to support arithmetic learning in children. It is further suggested that sensorimotor experiences shape the development of number concepts and arithmetic learning, and that mental arithmetic can be characterized as "motion along a path" and might constitute shifts in attention along the mental number line. The present study investigated whether movements in physical space influence mental arithmetic in primary school children, and whether the expected effect depends on concurrency of body movements and mental arithmetic. After turning their body towards the left or right, 48 children aged 8 to 10 years solved simple subtraction and addition problems. Meanwhile, they either walked or stood still and looked towards the respective direction. We report a congruency effect between body orientation and operation type, i.e., higher performance for the combinations leftward orientation and subtraction and rightward orientation and addition. We found no significant difference between walking and looking conditions. The present results suggest that mental arithmetic in children is influenced by preceding sensorimotor cues and not necessarily by concurrent body movements.

Children's use of egocentric reference frames in spatial language is related to their numerical magnitude understanding.

Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind, to the right/left) have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old's spatial language skills in tasks that allow responses in egocentric and allocentric frames of reference, as well as their relative understanding of numerical magnitude (assessed by a number word comparison task). In addition, we evaluated influences of children's absolute understanding of numerical magnitude assessed by their number word comprehension (montring different numbers using their fingers) and of their knowledge on numerical sequences (determining predecessors and successors as well as identifying missing dice patterns of a series). Results indicated that when considering responses that corresponded to the egocentric perspective, children's spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children's SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers' relative understanding of numerical magnitude.

Children's spatial language skills predict their verbal number skills: A longitudinal study.

The process of number symbolization is assumed to be critically influenced by the acquisition of so-called verbal number skills (e.g., verbally reciting the number chain and naming Arabic numerals). For the acquisition of these verbal number skills, verbal and visuospatial skills are discussed as contributing factors. In this context, children's verbal number skills have been found to be associated with their concurrent spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind). In a longitudinal study with three measurement times (T1, T2, T3) at an interval of about 6 months, we evaluated the predictive role of preschool children's (mean age at T1: 3 years and 10 months) spatial language skills for the acquisition of verbal number skills. Children's spatial language skills at T2 significantly predicted their verbal number skills at T3, when controlling for influences of important covariates such as vocabulary knowledge. In addition, further analyses replicated previous results indicating that children's spatial language skills at T2 were associated with their verbal number skills at T2. Exploratory analyses further revealed that children's verbal number skills at T1 predict their spatial language at T2. Results suggests that better spatial language skills at the age of 4 years facilitate the future acquisition of verbal number skills.

Why Not Just Features? Reconsidering Infants' Behavior in Individuation Tasks.

It counts as empirically proven that infants can individuate objects. Object individuation is assumed to be fundamental in the development of infants' ontology within the object-first account. It crucially relies on an object-file (OF) system, representing both spatiotemporal ("where") and categorical ("what") information about objects as solid, cohesive bodies moving continuously in space and time. However, infants' performance in tasks requiring them to use featural information to detect individuation violations appears to be at odds with the object-first account. In such cases, infants do not appear to be able to develop correct expectations about the numerosity of objects. Recently, proponents of the object-first account proposed that these individuation failures result from integration errors between the OF system and an additional physical reasoning system. We are going to argue that the predictions of a feature-based physical-reasoning (PR) system are sufficient for explaining infants' behavior. The striking predictive power of the PR system calls into question the relevance of the OF system and, thereby, challenges the assumption that infants can individuate objects early on.

Hierarchical Development of Early Visual-Spatial Abilities - A Taxonomy Based Assessment Using the MaGrid App.

Visual-spatial abilities (VSA) are considered a building block of early numerical development. They are intuitively acquired in early childhood and differentiate in further development. However, when children enter school, there already are considerable individual differences in children's visual-spatial and numerical abilities. To better understand this diversity, it is necessary to empirically evaluate the development as well as the latent structure of early VSA as proposed by the 2 by 2 taxonomy of Newcombe and Shipley (2015). In the present study, we report on a tablet-based assessment of VSA using the digital application (app) MaGrid in kindergarten children aged 4-6 years. We investigated whether the visual-spatial tasks implemented in MaGrid are sensitive to replicate previously observed age differences in VSA and thus a hierarchical development of VSA. Additionally, we evaluated whether the selected tasks conform to the taxonomy of VSA by Newcombe and Shipley (2015) applying a confirmatory factor analysis (CFA) approach. Our results indicated that the hierarchical development of VSA can be measured using MaGrid. Furthermore, the CFA substantiated the hypothesized factor structure of VSA in line with the dimensions proposed in the taxonomy of Newcombe and Shipley (2015). Taken together, the present results advance our knowledge to the (hierarchical) development as well as the latent structure of early VSA in kindergarten children.

Rehabilitation of arithmetic fact retrieval via extensive practice: a combined fMRI and behavioural case-study.

The present study investigates the effects of a training of arithmetic fact retrieval in a patient suffering from particular difficulties with multiplication facts. Over a period of four weeks simple multiplication facts were trained extensively. The outcome of the training was assessed behaviourally and changes in cerebral activation patterns were investigated using fMRI. The training led to a change in calculation strategies: Prior to training, the patient used predominantly time-consuming back-up strategies, after training he relied increasingly on the direct retrieval of arithmetic facts from long-term memory. Regarding the fMRI results, prefrontal activations were observed for untrained problems, which can be attributed to the application of back-up strategies strongly relying on fronto-executive functions. Interestingly, significant foci of activation for both trained and untrained items were found in the angular gyrus of the right hemisphere, which, however, differed in their exact localisation. For the trained condition, activations were observed in anterior parts of the angular gyrus which may be related to the training-based automatisation in fact retrieval. Activations in the untrained condition were found in a more posterior portion of the angular gyrus, that might be attributable to one of the patient's back-up strategies, namely to recite a whole multiplication row to get to the correct answer.

Mental Number Representations in 2D Space.

There is evidence both for mental number representations along a horizontal mental number line with larger numbers to the right of smaller numbers (for Western cultures) and a physically grounded, vertical representation where "more is up." Few studies have compared effects in the horizontal and vertical dimension and none so far have combined both dimensions within a single paradigm where numerical magnitude was task-irrelevant and none of the dimensions was primed by a response dimension. We now investigated number representations over both dimensions, building on findings that mental representations of numbers and space co-activate each other. In a Go/No-go experiment, participants were auditorily primed with a relatively small or large number and then visually presented with quasi-randomly distributed distractor symbols and one Arabic target number (in Go trials only). Participants pressed a central button whenever they detected the target number and elsewise refrained from responding. Responses were not more efficient when small numbers were presented to the left and large numbers to the right. However, results indicated that large numbers were associated with upper space more strongly than small numbers. This suggests that in two-dimensional space when no response dimension is given, numbers are conceptually associated with vertical, but not horizontal space.

Spatial representations of numbers in children and their connection with calculation abilities.

Evidence for a connection between number and space processing comes from behavioural, patient, and brain imaging data, but only a few studies have addressed this issue in children. We asked children (n=118) at the age of 8-9 years to decide which one of the two numerical distances in a visually presented number triplet was numerically larger. Numerical and spatial distances were manipulated independently, resulting in congruent, neutral, and incongruent conditions. The spatial distances between the numbers clearly affected the comparison of numerical distances: reactions times were faster and error rates smaller for congruent than for incongruent trials. These findings are in line with the assumption of a spatial layout of mental number representations in third graders. Correlations between the size of the congruity effect and calculation abilities were found to be differently marked for girls and boys: a positive correlation was found for boys, while a marginally negative correlation was obtained for girls.

Differences in Counting Skills Between Chinese and German Children Are Accompanied by Differences in Processing of Approximate Numerical Magnitude Information.

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.

Differences in arithmetic performance between Chinese and German adults are accompanied by differences in processing of non-symbolic numerical magnitude.

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.

Differences in Arithmetic Performance between Chinese and German Children Are Accompanied by Differences in Processing of Symbolic Numerical Magnitude.

Symbolic numerical magnitude processing skills are assumed to be fundamental to arithmetic learning. It is, however, still an open question whether better arithmetic skills are reflected in symbolic numerical magnitude processing skills. To address this issue, Chinese and German third graders were compared regarding their performance in arithmetic tasks and in a symbolic numerical magnitude comparison task. Chinese children performed better in the arithmetic tasks and were faster in deciding which one of two Arabic numbers was numerically larger. The group difference in symbolic numerical magnitude processing was fully mediated by the performance in arithmetic tasks. We assume that a higher degree of familiarity with arithmetic in Chinese compared to German children leads to a higher speed of retrieving symbolic numerical magnitude knowledge.