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A long-standing debate concerns whether developmental dyscalculia is characterized by core deficits in processing nonsymbolic or symbolic numerical information as well as the role of domain-general difficulties. Heterogeneity in recruitment and diagnostic criteria make it difficult to disentangle this issue. Here, we selected children ( n = 58) with severely compromised mathematical skills (2 SD below average) but average domain-general skills from a large sample referred for clinical assessment of learning disabilities. From the same sample, we selected a control group of children ( n = 42) matched for IQ, age, and visuospatial memory but with average mathematical skills. Children with dyscalculia showed deficits in both symbolic and nonsymbolic number sense assessed with simple computerized tasks. Performance in the digit-comparison task and the numerosity match-to-sample task reliably separated children with developmental dyscalculia from controls in cross-validated logistic regression (area under the curve = .84). These results support a number-sense-deficit theory and highlight basic numerical abilities that could be targeted for early identification of at-risk children as well as for intervention.

Math anxiety results in a drop in performance on various math-related tasks, including the symbolic number ordering task in which participants decide whether a triplet of digits is presented in order (e.g. 3-5-7) or not (e.g. 3-7-5). We investigated whether the strategy repertoire and reaction times during a symbolic ordering task were affected by math anxiety. In study 1, participants performed an untimed symbolic number ordering task and indicated the strategy they used on a trial-by-trial basis. The use of the memory retrieval strategy, based on the immediate recognition of the triplet, decreased with high math anxiety, but disappeared when controlling for general anxiety. In the study 2, participants completed a timed version of the number order task. High math-anxious participants used the decomposition strategy (e.g. 5 is larger than 3 and 7 is larger than 5 to decide whether 3-5-7 is in the correct order) more often, and were slower in responding when both memory- and other decomposition strategies were used. Altogether, both studies demonstrate that high-math anxious participants are not only slower to decide whether a number triplet is in the correct order, but also rely more on procedural strategies.

The increased prevalence of test anxiety in our competitive society makes it a health issue of public concern. However, its neurobiological basis, especially during the years of formal education, is currently scant. Previous research has highlighted the association between neural excitation/inhibition balance and psychopathology and disease. We examined whether the glutamate/GABA profile tracks test anxiety levels in development, using a cross-sectional and longitudinal design in a cohort spanning from early childhood to early adulthood (N = 289), reassessed approximately 21 months later (N = 194). We used magnetic resonance spectroscopy to noninvasively quantify glutamate and gamma-Aminobutyric acid (GABA) levels in the intraparietal sulcus (IPS) and the middle frontal gyrus. We show that the glutamate/GABA balance within the IPS relates to current individual variation in test anxiety levels and predict future test anxiety approximately 21 months later. Critically, this relationship was observed during early childhood but not during the later developmental stages. Our results extend the use of the excitation/inhibition balance framework to characterize the psychopathology mechanisms of test anxiety, an underexplored yet widespread and debilitating condition that can impact early child development. Our findings provide a better understanding of the neurotransmitter basis underlying the emergence of anxiety disorders during development.

Previous research has highlighted the role of glutamate and gamma-aminobutyric acid (GABA) in perceptual, cognitive, and motor tasks. However, the exact involvement of these neurochemical mechanisms in the chain of information processing, and across human development, are unclear. In a cross-sectional longitudinal design, we used a computational approach to dissociate cognitive, decision, and visuomotor processing in 293 individuals spanning early childhood to adulthood. We found that glutamate and GABA within the intraparietal sulcus (IPS) explained unique variance in visuomotor processing, with higher glutamate predicting poorer visuomotor processing in younger participants but better visuomotor processing in mature participants, while GABA showed the opposite pattern. These findings were functionally, neuroanatomically, and neurochemically specific, and were replicated ~1.5 years later and were generalized in two further different behavioral tasks. Using resting fMRI, we revealed that the relationship between IPS neurochemicals and visuomotor processing is mediated by functional connectivity in the visuomotor network. We then extended our findings to high-level cognitive behavior by predicting fluid intelligence performance. We showed that fluid intelligence performance is explained by IPS GABA and glutamate and is mediated by visuomotor processing, and moderated by the developmental stage. These results provide an integrative biological and psychological mechanistic explanation that links cognitive processes and neurotransmitters across human development and establishes their involvement in intelligent behavior.

ispartof: COGNITIVE DEVELOPMENT vol:64 status: accepted

Randomised assignment of individuals to treatment and controls groups is often considered the gold standard to draw valid conclusions about the efficacy of an intervention. In practice, randomisation can lead to accidental differences due to chance. Researchers have offered alternatives to reduce such differences, but these methods are not used frequently due to the requirement of advanced statistical methods. Here, we recommend a simple assignment procedure based on variance minimisation (VM), which assigns incoming participants automatically to the condition that minimises differences between groups in relevant measures. As an example of its application in the research context, we simulated an intervention study whereby a researcher used the VM procedure on a covariate to assign participants to a control and intervention group rather than controlling for the covariate at the analysis stage. Among other features of the simulated study, such as effect size and sample size, we manipulated the correlation between the matching covariate and the outcome variable and the presence of imbalance between groups in the covariate. Our results highlighted the advantages of VM over prevalent random assignment procedure in terms of reducing the Type I error rate and providing accurate estimates of the effect of the group on the outcome variable. The VM procedure is valuable in situations whereby the intervention to an individual begins before the recruitment of the entire sample size is completed. We provide an Excel spreadsheet, as well as scripts in R, MATLAB, and Python to ease and foster the implementation of the VM procedure. Supplementary Information The online version contains supplementary material available at 10.3758/s13423-021-01970-5.

Previous research has highlighted the role of the excitation/inhibition ratio (E/I) for typical and atypical development, mental health, cognition, and learning. Other research has highlighted the benefits of high-frequency random noise stimulation (tRNS)—an excitatory form of neurostimulation—on learning. We examined the E/I as a potential mechanism and studied whether tRNS effect on learning depends on E/I as measured by the aperiodic exponent. In addition to manipulating E/I using tRNS, we also manipulated the level of learning (learning/overlearning) that has been shown to influence E/I. Participants (n=102) received either sham stimulation or 20 min tRNS over the dorsolateral prefrontal cortex (DLPFC) during a mathematical learning task. We showed that tRNS increased E/I, as reflected by the aperiodic exponent, and that lower E/I predicted greater benefit from tRNS specifically for the learning task. In contrast to previous Magnetic Resonance Spectroscopy-based E/I studies, we found no effect of the level of learning on E/I. A further analysis using a different data set suggest that both measures of E/I (EEG vs MRS) may reflect, at least partly, different biological mechanisms. Our results highlight the role of E/I as a marker for neurostimulation efficacy and learning. This mechanistic understanding provides better opportunities for augmented learning and personalized interventions.

The socioeconomic attainment gap in mathematical ability is evident before children begin school and widens over time. Little is known about why this early attainment gap emerges. Two studies were conducted in 3- and 4-year-olds, to explore four possible factors that may explain why attainment gaps arise: working memory, inhibitory control, verbal ability, and frequency of home mathematical activities (N = 304, 54% female from a range of ethnic backgrounds but predominantly White British [76%]). Inhibitory control and verbal ability emerged as indirect factors in the relation between socioeconomic status and early mathematical ability, but neither working memory nor home mathematical activities did. These studies provide important insights about how the early attainment gap in mathematical ability may arise.

The ability to place numbers on a visual "number line" is a hallmark of the understanding of numerical magnitude and it is a strong predictor of mathematical achievement.We examined whether the performance in the number line estimation task is more driven by mental age or experience with numbers in a sample of Italian children with Down syndrome (DS).Sixty-three children with DS (MNo significant differences emerged between the two groups in terms of accuracy of positioning numbers on the 1-10 and 1-20 interval. In addition, the accuracy on the 1-10 interval was related to the ability to recognize numbers, while the accuracy on the 1-20 line was related to the ability to compare magnitudes.Results suggest that in individuals with DS the linear mapping of numbers is driven by mental age, but the accuracy of positioning numbers is also shaped by the experience with symbolic numbers. Therefore, the improvement of numerical estimation abilities should be a target of intervention programs.

Several scientific, engineering, and medical advancements are based on breakthroughs made by people who excel in mathematics. Our current understanding of the underlying brain networks stems primarily from anatomical and functional investigations, but our knowledge of how neurotransmitters subserve numerical skills, the building block of mathematics, is scarce. Using 1H magnetic resonance spectroscopy (N = 54, 3T, semi-LASER sequence, TE = 32 ms, TR = 3.5 s), the study examined the relation between numerical skills and the brain’s major inhibitory (GABA) and excitatory (glutamate) neurotransmitters. A negative association was found between the performance in a number sequences task and the resting concentration of GABA within the left intraparietal sulcus (IPS), a key region supporting numeracy. The relation between GABA in the IPS and number sequences was specific to (1) parietal but not frontal regions and to (2) GABA but not glutamate. It was additionally found that the resting functional connectivity of the left IPS and the left superior frontal gyrus was positively associated with number sequences performance. However, resting GABA concentration within the IPS explained number sequences performance above and beyond the resting frontoparietal connectivity measure. Our findings further motivate the study of inhibition mechanisms in the human brain and significantly contribute to our current understanding of numerical cognition's biological bases.

Individuals with Down syndrome (DS) present reduced basic numerical skills, which have a negative impact on everyday numeracy and mathematical learning. Here, we evaluated the efficacy of the adaptive (non-commercial) computerized game “The Number Race” in improving basic numerical skills in children with DS. The experimental group (EG; N = 30, Mage-in-months 118, range 70–149) completed a training playing with “The Number Race”, whereas children in the control group (CG; N = 31, Mage-in-months 138, range 76–207) worked with software aiming at improving their reading skills. The training lasted 10 weeks with two weekly sessions of 20–30 min each. We assessed both groups’ numerical and reading skills before and immediately after the end of the training, as well as at a 3-months follow-up. We found weak evidence for post-training groups differences in terms of overall numeracy score. However, the EG displayed substantial improvements in specific numerical skills and in mental calculation, which were maintained over time, and no improvement in reading. Conversely, the CG showed improvements in their reading skills as well as in number skills but to a lesser extent compared to the EG. Overall, “The Number Race” appears as a suitable tool to improve some aspects of numeracy in DS.

Despite the relevance of basic numerical skills to later mathematical outcomes, there remains little consensus on which skills comprise the construct of early numeracy.Here, we evaluate recent studies that investigated this construct using various approaches.Findings from these studies indicated broad consensus in considering skills such as counting, number relations, and basic arithmetic, as central aspects of early numeracy. However, both the number and contents of identified factors varied considerably across studies.Although this review substantiated the critical relevance of certain basic numerical skills, it also highlights a need for future research to evaluate the structure of early numeracy in a more systematic and coordinated way to increase comparability and coherence across studies.

Significance Our knowledge of the effect of a specific lack of education on the brain and cognitive development is currently poor but is highly relevant given differences between countries in their educational curricula and the differences in opportunities to access education. We show that within the same society, adolescent students who specifically lack mathematical education exhibited reduced brain inhibition levels in a key brain area involved in reasoning and cognitive learning. Importantly, these brain inhibition levels predicted mathematical attainment ∼19 mo later, suggesting they play a role in neuroplasticity. Our study provides biological understanding of the impact of the lack of mathematical education on the developing brain and the mutual play between biology and education., Formal education has a long-term impact on an individual’s life. However, our knowledge of the effect of a specific lack of education, such as in mathematics, is currently poor but is highly relevant given the extant differences between countries in their educational curricula and the differences in opportunities to access education. Here we examined whether neurotransmitter concentrations in the adolescent brain could classify whether a student is lacking mathematical education. Decreased γ-aminobutyric acid (GABA) concentration within the middle frontal gyrus (MFG) successfully classified whether an adolescent studies math and was negatively associated with frontoparietal connectivity. In a second experiment, we uncovered that our findings were not due to preexisting differences before a mathematical education ceased. Furthermore, we showed that MFG GABA not only classifies whether an adolescent is studying math or not, but it also predicts the changes in mathematical reasoning ∼19 mo later. The present results extend previous work in animals that has emphasized the role of GABA neurotransmission in synaptic and network plasticity and highlight the effect of a specific lack of education on MFG GABA concentration and learning-dependent plasticity. Our findings reveal the reciprocal effect between brain development and education and demonstrate the negative consequences of a specific lack of education during adolescence on brain plasticity and cognitive functions.

Seven experiments conducted in India and the United States (N ∼7,000; 5 preregistered) examined the effects of wealth on warmth and competence, 2 fundamental dimensions of social impressions. Wealth causally influenced perceptions of a target's competence: high wealth increased perceived competence and low wealth decreased perceived competence (Experiments 1-3). Furthermore, both high and low wealth reduced perceived warmth compared with control conditions that provided no wealth-related information (Experiments 2 and 3). Attributing prosocial tendencies to the target in the form of charitable donations reversed wealth-induced reductions in warmth, while low levels of charitable donations lowered both perceived warmth and competence (Experiment 3). Reciprocally, information about the target's competence or warmth influenced how wealthy they were perceived to be (Experiment 4). Knowing the source of wealth (e.g., entrepreneurship, corporate fraud, inheritance) also affected perceptions of competence and warmth (Experiments 5 and 6). Moreover, participants expressed greater willingness to hire wealthier targets compared with poorer targets in hypothetical employment scenarios, a relationship mediated by perceived competence, suggesting that an individual's wealth may influence consequential assessments and decisions (Experiment 7). With rising economic inequality, it is crucial to understand how wealthy and poor individuals are perceived and the implications of these perceptions. The present experiments offer insight in this direction. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

The ability to choose the larger between two numbers reflects a mature understanding of the magnitude associated with numerical symbols. The present study explores how the knowledge of the number sequence and memory capacity (verbal and visuospatial) relate to number comparison skills while controlling for cardinal knowledge. Preschool children’s (N = 140, Mage‐in‐months = 58.9, range = 41–75) knowledge of the directional property of the counting list as well as the spatial mapping of digits on the visual line were assessed. The ability to order digits on the visual line mediated the relation between memory capacity and number comparison skills while controlling for cardinal knowledge. Beyond cardinality, the knowledge of the (spatial) order of numbers marks the understanding of the magnitude associated with numbers.

Random noise has been shown to improve the detection of suboptimal signals in humans and machines. Based on that, transcranial random noise stimulation (tRNS) has aimed to improve human behaviour by targeting neuronal activity. To uncover the poorly understood mechanistic underpinnings of tRNS, we recorded electroencephalography data during arithmetic training while delivering active or sham tRNS above the dorsolateral prefrontal cortex (dlPFC). By successfully removing the tRNS artefact in the time and frequency domains, we examined the mechanisms that underlie its behavioural improvement. We found that active tRNS improved arithmetic performance and impacts specific ERPs components that are associated with attentional mechanisms. Furthermore, the tRNS effect was maximal in individuals with suboptimal arithmetic ability and neurophysiological measures of top-down control and excitation/inhibition ratio. These results providing a novel mechanistic explanation for the effect of tRNS on human behaviour and highlight how suboptimal task-specific behaviour and neurophysiology predicts its effect.

There is an ongoing debate concerning how numbers acquire numerical meaning. On the one hand, it has been argued that symbols acquire meaning via a mapping to external numerosities as represented by the approximate number system (ANS). On the other hand, it has been proposed that the initial mapping of small numerosities to the corresponding number words and the knowledge of the properties of counting list, especially the order relation between symbols, lead to the understanding of the exact numerical magnitude associated with numerical symbols. In the present study, we directly compared these two hypotheses in a group of preschool children who could proficiently count (most of the children were cardinal principle knowers). We used a numerosity estimation task to assess whether children have created a mapping between the ANS and the counting list (i.e., ANS-to-word mapping). Children also completed a direction task to assess their knowledge of the directional property of the counting list. That is, adding one item to a set leads to he next number word in the sequence (i.e., successor knowledge) whereas removing one item leads to the preceding number word (i.e., predecessor knowledge). Similarly, we used a visual order task to assess the knowledge that successive and preceding numbers occupy specific spatial positions on the visual number line (i.e., preceding: [?], [13], [14]; successive: [12], [13], [?]). Finally, children's performance in comparing the magnitude of number words and Arabic numbers indexed the knowledge of exact symbolic numerical magnitude. Approximately half of the children in our sample have created a mapping between the ANS and the counting list. Most of the children mastered the successor knowledge whereas few of them could master the predecessor knowledge. Children revealed a strong tendency to respond with the successive number in the counting list even when an item was removed from a set or the name of the preceding number on the number line was asked. Crucially, we found evidence that both the mastering of the predecessor knowledge and the ability to name the preceding number in the number line relate to the performance in number comparison tasks. Conversely, there was moderate/anecdotal evidence for a relation between the ANS-to-word mapping and number comparison skills. Non-rote access to the number sequence relates to knowledge of the exact magnitude associated with numerical symbols, beyond the mastering of the cardinality principle and domain-general factors.

It is debated whether cognitive training of specific executive functions leads to far transfer effects, such as improvements in fluid intelligence (Gf). Within this context, transcranial direct current stimulation and recently also novel protocols such as transcranial random noise and alternating current stimulation are being investigated with regards to their ability to enhance cognitive training outcomes. We compared the effects of four different transcranial electrical brain stimulation protocols in combination with nine daily computerized training sessions on Gf. 82 participants were randomly assigned to receive transcranial direct current stimulation (tDCS), random noise stimulation (tRNS), multifocal alternating current stimulation at 40 Hz (mftACS), or multifocal tDCS (mftDCS) in combination with an adaptive and synergistic executive function (EF) training, or to a no-contact control group. EF training consisted of gamified tasks drawing on isolated as well as integrated executive functions (working memory, inhibition, cognitive flexibility). Transfer was assessed with a combined measure of Gf including three established tests (Bochumer Matrizentest - BOMAT, Raven's Advanced Progressive Matrices - RAPM, and Sandia Matrices). We found significant improvements in Gf for the tDCS, mftDCS, and tRNS groups when compared with the no-contact group. In contrast, the mftACS group did not improve significantly and showed a similar pattern as the no-contact group. Mediation analyses indicated that the improvement in Gf was mediated through game progression in the mftDCS and tRNS group. Electrical brain stimulation in combination with sustained EF training can lead to transfer effects in Gf, which are mediated by training progression.

Attraverso una rielaborazione di appunti vengono raccontate le giornate formative della VI Conferenza del Network Italiano per la ricerca empirica sui gruppi psicodinamici avvenuta a Torino alla fine di marzo 2017.

A series of effects characterises the processing of symbolic numbers (i.e., distance effect, size effect, SNARC effect, size congruency effect). The combination of these effects supports the view that numbers are represented on a compressed and spatially oriented mental number line (MNL) as well as the presence of an interaction between numerical and other magnitude representations. However, when individuals process the order of digits, response times are faster when the distance between digits is small (e.g., 1-2-3) compared to large (e.g., 1-3-5; i.e., reversed distance effect), suggesting that the processing of magnitude and order may be distinct. Here, we investigated whether the effects related to the MNL also emerge in the processing of symbolic number ordering. In Experiment 1, participants judged whether three digits were presented in order while spatial distance, numerical distance, numerical size, and the side of presentation were manipulated. Participants were faster in determining the ascending order of small triplets compared to large ones (i.e., size effect) and faster when the numerical distance between digits was small (i.e., reversed distance effect). In Experiment 2, we explored the size effect across all possible consecutive triplets between 1 and 9 and the effect that physical size has on order processing. Participants showed faster reactions times only for the triplet 1-2-3 compared to the other triplets, and the effect of physical magnitude was negligible. Symbolic order processing lacks the signatures of the MNL and suggests the presence of a familiarity effect related to well-known consecutive triplets in the long-term memory. ispartof: Acta Psychologica vol:204 ispartof: location:Netherlands status: published

Background Numeracy is an area of difficulty for children with Down syndrome (DS). It has been demonstrated that The Number Race, a non-commercial adaptive computer game designed to foster basic mathematical abilities, represents a promising instrument to enhance these skills in children with DS when delivered by an expert in a clinical setting. Aims In the present study, we assessed the efficacy of The Number Race when administered at home by properly instructed and remotely supervised parents. Methods and procedures Basic numerical skills were assessed before and after training, as well as at three-months follow-up. Performance of children with DS who worked at home with the parent (PG) was compared with that of children who received the training by an expert (EG). For both groups, the training lasted ten weeks, with two weekly sessions of 20−30 min. Outcomes and results Results show that both groups improved across various measures of numerical proficiency, including the overall score of the numeracy assessment battery, while only the EG showed an improvement in a measure of mental calculation. The improvements were maintained three months after the end of the training. Conclusions and implications These findings confirm the efficacy of The Number Race and extend it to an home-based setting, whereby parents administer the training with external supervision.

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record

The ability to map numbers onto space has been widely investigated with the number line (NL) task. Accurate (linear) placement is typically preceded by a developmental phase in which children assign more space to small numbers and compress large numbers to the right part of the line, thereby resembling a biased log-like mapping. Here, we exploited a task that separately assesses direction, order and accuracy of spatial mapping (DOS task) to investigate the origin of the biased NL mapping in a sample of first and second graders. Children with reduced ordinal knowledge in the DOS task showed a more biased NL mapping, which was formally assessed using the leading mathematical models of the NL task. However, the log-like biased mapping did not emerge in the DOS task, thereby showing a lack of generalisation across different number-space mapping tasks. Both ordinal knowledge in the DOS task and linearity in the NL task related to arithmetic fluency beyond domain-general cognitive factors. We conclude that the NL task is a meter of children’s arithmetic skills rather than an expression of the mental representation of numbers.

The investigation of mathematical expertise can shape numerical and mathematical cognition theories by providing insights about the modifications that the neurocognitive system undergoes when mastering mathematical knowledge. In particular, both qualitative and quantitative methods should be combined within a developmental perspective to identify those promoting factors that lead some individuals to focus their interests on mathematics and possibly become experts in the field. The behavioral and neural differences in math experts constitute valuable information to study the limits of the mastering of mathematical knowledge, which ultimately represents a powerful form of formal human reasoning.

Interacting to reach a shared decision is an omnipresent component of human collaboration. We explored the interaction between dyads of individuals with different levels of expertise. The members of the dyads completed a number line task privately, jointly and privately again. In the joint condition, dyad members shared their private estimates and then negotiated a joint estimate. Both dyad members averaged their private individual estimates to determine joint estimates, thereby showing a strong equality bias. Their performance in the joint condition exceeded the performance of the dyad's best estimator, demonstrating interaction benefit, only when the dyad members had similar levels of expertise and when the averaged dyad performance was sufficiently accurate. At the end of the task, participants rated their level and their partner's level of competence. Participants were accurate in classifying themselves as the expert or the novice within the dyad. Nevertheless, novices tended to overestimate their ability as they admitted to being less competent but only slightly worse than their expert partner. Experts, instead, believed themselves to be more competent but were humble and considered their performance only marginally better than their partner's. Overall, these results have important implications for settings in which people with different levels of expertise interact. (PsycINFO Database Record

Math Anxiety (MA) is characterized by a negative emotional response when facing math-related situations. MA is distinct from general anxiety and can emerge during primary education. Prior studies typically comprise adults and comparisons between high- versus low-MA, where neuroimaging work has focused on differences in network activation between groups when completing numerical tasks. The present study used voxel-based morphometry (VBM) to identify the structural brain correlates of MA in a sample of 79 healthy children aged 7–12 years. Given that MA is thought to develop in later primary education, the study focused on the level of MA, rather than categorically defining its presence. Using a battery of cognitive- and numerical-function tasks, we identified that increased MA was associated with reduced attention, working memory and math achievement. VBM highlighted that increased MA was associated with reduced grey matter in the left anterior intraparietal sulcus. This region was also associated with attention, suggesting that baseline differences in morphology may underpin attentional differences. Future studies should clarify whether poorer attentional capacity due to reduced grey matter density results in the later emergence of MA. Further, our data highlight the role of working memory in propagating reduced math achievement in children with higher MA.

The ability to compare the numerical magnitude of symbolic numbers represents a milestone in the development of numerical skills. However, it remains unclear how basic numerical abilities contribute to the understanding of symbolic magnitude and whether the impact of these abilities may vary when symbolic numbers are presented as number words (e.g., "six vs. eight") vs. Arabic numbers (e.g., 6 vs. 8). In the present study on preschool children, we show that comparison of number words is related to cardinality knowledge whereas the comparison of Arabic digits is related to both cardinality knowledge and the ability to spatially map numbers. We conclude that comparison of symbolic numbers in preschool children relies on multiple numerical skills and representations, which can be differentially weighted depending on the presentation format. In particular, the spatial arrangement of digits on the number line seems to scaffold the development of a "spatial route" to understanding the exact magnitude of numerals.

Numerical cognition describes the processes that one uses to assimilate, ascribe, and manipulate numerical information. This chapter is organized into two sections. The first draws heavily on data from developmental and cognitive psychology. We use this to outline core findings related to numerical‐information processing in humans. In particular, we describe the trajectory of the acquisition of basic numerical skills. Starting in early infancy, we outline the processes that are believed to underlie nonsymbolic representation. Next, we summarize core studies that examine the representation of symbolic quantities (Arabic system). Lastly, we briefly report on the relationship between basic numerical processing and mathematical achievement. The second part of the chapter explores evidence from neuropsychology and neuroscience. The core methodological approaches used are briefly outlined with signposting to relevant literature. Next, we examine data from early lesion studies, followed by a short review of one of the most influential models in the study of numerical cognition, the triple‐code model. Lastly, we look at the neurocognitive features of number, such as different modes of representation and the processing of quantity. Throughout, the core literature plus recent advances are summarized, giving the reader a thorough grounding in the neurocognitive bases of numerical cognition.