The cognitive literature now shows how critically math performance depends on working memory, for any form of arithmetic and math that involves processes beyond simple memory retrieval. The psychometric literature is also very clear on the global consequences of mathematics anxiety. People who are highly math anxious avoid math: They avoid elective coursework in math, both in high school and college, they avoid college majors that emphasize math, and they avoid career paths that involve math. We go beyond these psychometric relationships to examine the cognitive consequences of math anxiety. We show how performance on a standardized math achievement test varies as a function of math anxiety, and that math anxiety compromises the functioning of working memory. High math anxiety works much like a dual task setting: Preoccupation with one's math fears and anxieties functions like a resource-demanding secondary task. We comment on developmental and educational factors related to math and working memory, and on factors that may contribute to the development of math anxiety.

The combined efforts of many fields are advancing our understanding of how number is represented. Researchers studying numerical reasoning in adult humans, developing humans and non-human animals are using a suite of behavioral and neurobiological methods to uncover similarities and differences in how each population enumerates and compares quantities to identify the neural substrates of numerical cognition. An important picture emerging from this research is that adult humans share with non-human animals a system for representing number as language-independent mental magnitudes and that this system emerges early in development.

This review considers the two possible causal directions between mathematics anxiety (MA) and poor mathematics performance. Either poor maths performance may elicit MA (referred to as the Deficit Theory), or MA may reduce future maths performance (referred to as the Debilitating Anxiety Model). The evidence is in conflict: the Deficit Theory is supported by longitudinal studies and studies of children with mathematical learning disabilities, but the Debilitating Anxiety Model is supported by research which manipulates anxiety levels and observes a change in mathematics performance. It is suggested that this mixture of evidence might indicate a bidirectional relationship between MA and mathematics performance (the Reciprocal Theory), in which MA and mathematics performance can influence one another in a vicious cycle.

We have developed a toolbox and graphic user interface, EEGLAB, running under the crossplatform MATLAB environment (The Mathworks, Inc.) for processing collections of single-trial and/or averaged EEG data of any number of channels. Available functions include EEG data, channel and event information importing, data visualization (scrolling, scalp map and dipole model plotting, plus multi-trial ERP-image plots), preprocessing (including artifact rejection, filtering, epoch selection, and averaging), independent component analysis (ICA) and time/frequency decompositions including channel and component cross-coherence supported by bootstrap statistical methods based on data resampling. EEGLAB functions are organized into three layers. Top-layer functions allow users to interact with the data through the graphic interface without needing to use MATLAB syntax. Menu options allow users to tune the behavior of EEGLAB to available memory. Middle-layer functions allow users to customize data processing using command history and interactive 'pop' functions. Experienced MATLAB users can use EEGLAB data structures and stand-alone signal processing functions to write custom and/or batch analysis scripts. Extensive function help and tutorial information are included. A 'plug-in' facility allows easy incorporation of new EEG modules into the main menu. EEGLAB is freely available (http://www.sccn.ucsd.edu/eeglab/) under the GNU public license for noncommercial use and open source development, together with sample data, user tutorial and extensive documentation.

Deficits in basic numerical abilities have been investigated repeatedly as potential risk factors of math anxiety. Previous research suggested that also a deficient approximate number system (ANS), which is discussed as being the foundation for later math abilities, underlies math anxiety. However, these studies examined this hypothesis by investigating ANS acuity using a symbolic number comparison task. Recent evidence questions the view that ANS acuity can be assessed using a symbolic number comparison task. To investigate whether there is an association between math anxiety and ANS acuity, we employed both a symbolic number comparison task and a non-symbolic dot comparison task, which is currently the standard task to assess ANS acuity. We replicated previous findings regarding the association between math anxiety and the symbolic distance effect for response times. High math anxious individuals showed a larger distance effect than less math anxious individuals. However, our results revealed no association between math anxiety and ANS acuity assessed using a non-symbolic dot comparison task. Thus, our results did not provide evidence for the hypothesis that a deficient ANS underlies math anxiety. Therefore, we propose that a deficient ANS does not constitute a risk factor for the development of math anxiety. Moreover, our results suggest that previous interpretations regarding the interaction of math anxiety and the symbolic distance effect have to be updated. We suggest that impaired number comparison processes in high math anxious individuals might account for the results rather than deficient ANS representations. Finally, impaired number comparison processes might constitute a risk factor for the development of math anxiety. Implications for current models regarding the origins of math anxiety are discussed.

This study aimed to characterize the neural generators of the early components of the visual evoked potential (VEP) to isoluminant checkerboard stimuli. Multichannel scalp recordings, retinotopic mapping and dipole modeling techniques were used to estimate the locations of the cortical sources giving rise to the early C1, P1, and N1 components. Dipole locations were matched to anatomical brain regions visualized in structural magnetic resonance imaging (MRI) and to functional MRI (fMRI) activations elicited by the same stimuli. These converging methods confirmed previous reports that the C1 component (onset latency 55 msec; peak latency 90-92 msec) was generated in the primary visual area (striate cortex; area 17). The early phase of the P1 component (onset latency 72-80 msec; peak latency 98-110 msec) was localized to sources in dorsal extrastriate cortex of the middle occipital gyrus, while the late phase of the P1 component (onset latency 110-120 msec; peak latency 136-146 msec) was localized to ventral extrastriate cortex of the fusiform gyrus. Among the N1 subcomponents, the posterior N150 could be accounted for by the same dipolar source as the early P1, while the anterior N155 was localized to a deep source in the parietal lobe. These findings clarify the anatomical origin of these VEP components, which have been studied extensively in relation to visual-perceptual processes.

Classical theories of sensory processing view the brain as a passive, stimulus-driven device. By contrast, more recent approaches emphasize the constructive nature of perception, viewing it as an active and highly selective process. Indeed, there is ample evidence that the processing of stimuli is controlled by top-down influences that strongly shape the intrinsic dynamics of thalamocortical networks and constantly create predictions about forthcoming sensory events. We discuss recent experiments indicating that such predictions might be embodied in the temporal structure of both stimulus-evoked and ongoing activity, and that synchronous oscillations are particularly important in this process. Coherence among subthreshold membrane potential fluctuations could be exploited to express selective functional relationships during states of expectancy or attention, and these dynamic patterns could allow the grouping and selection of distributed neuronal responses for further processing.

In this review, we consider the potential functional role of beta-band oscillations, which at present is not yet well understood. We discuss evidence from recent studies on top-down mechanisms involved in cognitive processing, on the motor system and on the pathophysiology of movement disorders that suggest a unifying hypothesis: beta-band activity seems related to the maintenance of the current sensorimotor or cognitive state. We hypothesize that beta oscillations and/or coupling in the beta-band are expressed more strongly if the maintenance of the status quo is intended or predicted, than if a change is expected. Moreover, we suggest that pathological enhancement of beta-band activity is likely to result in an abnormal persistence of the status quo and a deterioration of flexible behavioural and cognitive control.

t, F, and χ2 test families. In addition, it includes power analyses forz tests and some exact tests. G*Power 3 provides improved effect size calculators and graphic options, supports both distribution-based and design-based input modes, and offers all types of power analyses in which users might be interested. Like its predecessors, G*Power 3 is free.]]>

While parietal cortex is thought to be critical for representing numerical magnitudes, we recently reported an event-related potential (ERP) study demonstrating selective neural sensitivity to numerosity over midline occipital sites very early in the time course, suggesting the involvement of early visual cortex in numerosity processing. However, which specific brain area underlies such early activation is not known. Here, we tested whether numerosity-sensitive neural signatures arise specifically from the initial stages of visual cortex, aiming to localize the generator of these signals by taking advantage of the distinctive folding pattern of early occipital cortices around the calcarine sulcus, which predicts an inversion of polarity of ERPs arising from these areas when stimuli are presented in the upper versus lower visual field. Dot arrays, including 8-32dots constructed systematically across various numerical and non-numerical visual attributes, were presented randomly in either the upper or lower visual hemifields. Our results show that neural responses at about 90ms post-stimulus were robustly sensitive to numerosity. Moreover, the peculiar pattern of polarity inversion of numerosity-sensitive activity at this stage suggested its generation primarily in V2 and V3. In contrast, numerosity-sensitive ERP activity at occipito-parietal channels later in the time course (210-230ms) did not show polarity inversion, indicating a subsequent processing stage in the dorsal stream. Overall, these results demonstrate that numerosity processing begins in one of the earliest stages of the cortical visual stream.

Human mathematical competence emerges from two representational systems. Competence in some domains of mathematics, such as calculus, relies on symbolic representations that are unique to humans who have undergone explicit teaching. More basic numerical intuitions are supported by an evolutionarily ancient approximate number system that is shared by adults, infants and non-human animals-these groups can all represent the approximate number of items in visual or auditory arrays without verbally counting, and use this capacity to guide everyday behaviour such as foraging. Despite the widespread nature of the approximate number system both across species and across development, it is not known whether some individuals have a more precise non-verbal 'number sense' than others. Furthermore, the extent to which this system interfaces with the formal, symbolic maths abilities that humans acquire by explicit instruction remains unknown. Here we show that there are large individual differences in the non-verbal approximation abilities of 14-year-old children, and that these individual differences in the present correlate with children's past scores on standardized maths achievement tests, extending all the way back to kindergarten. Moreover, this correlation remains significant when controlling for individual differences in other cognitive and performance factors. Our results show that individual differences in achievement in school mathematics are related to individual differences in the acuity of an evolutionarily ancient, unlearned approximate number sense. Further research will determine whether early differences in number sense acuity affect later maths learning, whether maths education enhances number sense acuity, and the extent to which tertiary factors can affect both.

Behavioral and brain imaging research indicates that human infants, humans adults, and many nonhuman animals represent large nonsymbolic numbers approximately, discriminating between sets with a ratio limit on accuracy. Some behavioral evidence, especially with human infants, suggests that these representations differ from representations of small numbers of objects. To investigate neural signatures of this distinction, event-related potentials were recorded as adult humans passively viewed the sequential presentation of dot arrays in an adaptation paradigm. In two studies, subjects viewed successive arrays of a single number of dots interspersed with test arrays presenting the same or a different number; numerical range (small numerical quantities 1-3 vs. large numerical quantities 8-24) and ratio difference varied across blocks as continuous variables were controlled. An early-evoked component (N1), observed over widespread posterior scalp locations, was modulated by absolute number with small, but not large, number arrays. In contrast, a later component (P2p), observed over the same scalp locations, was modulated by the ratio difference between arrays for large, but not small, numbers. Despite many years of experience with symbolic systems that apply equally to all numbers, adults spontaneously process small and large numbers differently. They appear to treat small-number arrays as individual objects to be tracked through space and time, and large-number arrays as cardinal values to be compared and manipulated.

Coordinated studies with adults, infants, and nonhuman animals provide evidence for two distinct systems of nonverbal number representation. The parallel individuation (PI) system selects and retains information about one to three individual entities and the numerical magnitude system establishes representations of the approximate cardinal value of a group. Recent event-related potential (ERP) work has demonstrated that these systems reliably evoke functionally and temporally distinct patterns of brain response that correspond to established behavioral signatures. However, relatively little is known about the neural generators of these ERP signatures. To address this question, we targeted known ERP signatures of these systems, by contrasting processing of small versus large nonsymbolic numbers, and used a source localization algorithm (LORETA) to identify their cortical origins. Early processing of small numbers, showing the signature effects of PI on the N1 (similar to 150 ms), was localized primarily to extrastriate visual regions. In contrast, qualitatively and temporally distinct processing of large numbers, showing the signatures of approximate number representation on the mid-latency P2p (similar to 200-250 ms), was localized primarily to right intraparietal regions. In comparison, mid-latency small number processing was localized to the right temporalparietal junction and left-lateralized intraparietal regions. These results add spatial information to the emerging ERP literature documenting the process by which we represent number. Furthermore, these results substantiate recent claims that early attentional processes determine whether a collection of objects will be represented through PI or as an approximate numerical magnitude by providing evidence that downstream processing diverges to distinct cortical regions. Hum Brain Mapp 33:2189-2203, 2012. (c) 2011 Wiley Periodicals, Inc.

Coordinated studies of adults, infants, and nonhuman animals provide evidence for two systems of nonverbal number representation: a

Approximate number discrimination in adult human and nonhuman animals is governed by Weber's Law: The ratio between the values determines discriminability. Here, we review recent evidence from behavioral and neuroimaging studies that suggests that number sense in human infancy shares the same hallmark feature of Weber's Law and may rely on the same neural substrates as previously found in adults, children, and nonhuman animals. These findings support the notion of ontogenetic and phylogenetic continuity in number sense. New methods described here may help uncover how infants' early number sense supports the development of a mature number sense. Moreover, they may aid in understanding how children learn to map nonsymbolic number representations onto symbols for number by providing dependent measures that capture individual variability.

Anxiety about math can lead to long-term negative consequences related to academic achievement and professional success. However, it remains unclear how elevated math-anxiety modulates brain activity while solving arithmetic problems. In the current study, we recorded electrophysiological responses throughout arithmetic problem solving, both at the period of anticipating an upcoming arithmetic problem and solving an arithmetic problem. Results showed that, after controlling for mathematical performance, people with higher math anxiety tended to show stronger beta band oscillation and P300 amplitude while expecting the arithmetic problems, as well as stronger gamma band activity while solving the arithmetic problems. These results suggest that individuals highly anxious about math might use more attentional resources during the course of anticipating the upcoming arithmetic problems, and showed greater attentional bias toward arithmetic problems during solving arithmetic problems.

Anxiety about math is tied to low math grades and standardized test scores, yet not all math-anxious individuals perform equally poorly in math. We used functional magnetic resonance imaging to separate neural activity during the anticipation of doing math from activity during math performance itself. For higher (but not lower) math-anxious individuals, increased activity in frontoparietal regions when simply anticipating doing math mitigated math-specific performance deficits. This network included bilateral inferior frontal junction, a region involved in cognitive control and reappraisal of negative emotional responses. Furthermore, the relation between frontoparietal anticipatory activity and highly math-anxious individuals' math deficits was fully mediated (or accounted for) by activity in caudate, nucleus accumbens, and hippocampus during math performance. These subcortical regions are important for coordinating task demands and motivational factors during skill execution. Individual differences in how math-anxious individuals recruit cognitive control resources prior to doing math and motivational resources during math performance predict the extent of their math deficits. This work suggests that educational interventions emphasizing control of negative emotional responses to math stimuli (rather than merely additional math training) will be most effective in revealing a population of mathematically competent individuals, who might otherwise go undiscovered.

Individuals with mathematics anxiety have been found to differ from their non-anxious peers on measures of higher-level mathematical processes, but not simple arithmetic. The current paper examines differences between mathematics anxious and non-mathematics anxious individuals in more basic numerical processing using a visual enumeration task. This task allows for the assessment of two systems of basic number processing: subitizing and counting. Mathematics anxious individuals, relative to non-mathematics anxious individuals, showed a deficit in the counting but not in the subitizing range. Furthermore, working memory was found to mediate this group difference. These findings demonstrate that the problems associated with mathematics anxiety exist at a level more basic than would be predicted from the extant literature.

In this paper, we show how ElectroEncephaloGraphic (EEG) and MagnetoEncephaloGraphic (MEG) data can be analyzed statistically using nonparametric techniques. Nonparametric statistical tests offer complete freedom to the user with respect to the test statistic by means of which the experimental conditions are compared. This freedom provides a straightforward way to solve the multiple comparisons problem (MCP) and it allows to incorporate biophysically motivated constraints in the test statistic, which may drastically increase the sensitivity of the statistical test. The paper is written for two audiences: (1) empirical neuroscientists looking for the most appropriate data analysis method, and (2) methodologists interested in the theoretical concepts behind nonparametric statistical tests. For the empirical neuroscientist, a large part of the paper is written in a tutorial-like fashion, enabling neuroscientists to construct their own statistical test, maximizing the sensitivity to the expected effect. And for the methodologist, it is explained why the nonparametric test is formally correct. This means that we formulate a null hypothesis (identical probability distribution in the different experimental conditions) and show that the nonparametric test controls the false alarm rate under this null hypothesis.

We investigated the time course of neural processing of multi-digit additions in high- (HMA) and low-math anxious (LMA) individuals. Seventeen HMA and 17 LMA individuals were presented with two-digit additions and were asked to perform a verification task. Behavioral data showed that HMA individuals were slower and more error prone than their LMA peers, and that incorrect solutions were solved more slowly and less accurately than correct ones. Moreover, HMA individuals tended to need more time and commit more errors when having to verify incorrect solutions than correct ones. ERPs time-locked to the presentation of the addends (calculation phase) and to the presentation of the proposed solution (verification phase) were also analyzed. In both phases, a P2 component of larger amplitude was found for HMA individuals than for their LMA peers. Because the P2 component is considered to be a biomarker of the mobilization of attentional resources toward emotionally negative stimuli, these results suggest that HMA individuals may have invested more attentional resources both when processing the addends (calculation phase) and when they had to report whether the proposed solution was correct or not (verification phase), as compared to their LMA peers. Moreover, in the verification phase, LMA individuals showed a larger late positive component (LPC) for incorrect solutions at parietal electrodes than their HMA counterparts. The smaller LPC shown by HMA individuals when verifying incorrect solutions suggests that these solutions may have been appeared more plausible to them than to their LMA counterparts.

While recent studies in adults have demonstrated the existence of a neural mechanism for a visual sense of number, little is known about its development and whether such a mechanism exists at young ages. In the current study, I introduce a novel steady-state visual evoked potential (SSVEP) technique to objectively quantify early visual cortical sensitivity to numerical and non-numerical magnitudes of a dot array. I then examine this neural sensitivity to numerical magnitude in children between three and ten years of age and in college students. Children overall exhibit strong SSVEP sensitivity to numerical magnitude in the right occipital sites with negligible SSVEP sensitivity to non-numerical magnitudes, the pattern similar to what is observed in adults. However, a closer examination of age differences reveals that this selective neural sensitivity to numerical magnitude, which is close to absent in three-year-olds, increases steadily as a function of age, while there is virtually no neural sensitivity to other non-numerical magnitudes across these ages. These results demonstrate the emergence of a neural mechanism underlying direct perception of numerosity across early and middle childhood and provide a potential neural mechanistic explanation for the development of humans' primitive, non-verbal ability to comprehend number.

Humans are endowed with an intuitive number sense that allows us to perceive and estimate numerosity without relying on language. It is controversial, however, as to whether there is a neural mechanism for direct perception of numerosity or whether numerosity is perceived indirectly via other perceptual properties. In this study, we used a novel regression-based analytic method, which allowed an assessment of the unique contributions of visual properties, including numerosity, to explain visual evoked potentials of participants passively viewing dot arrays. We found that the human brain is uniquely sensitive to numerosity and more sensitive to changes in numerosity than to changes in other visual properties, starting extremely early in the visual stream: 75 ms over a medial occipital site and 180 ms over bilateral occipitoparietal sites. These findings provide strong evidence for the existence of a neural mechanism for rapidly and directly extracting numerosity information in the human visual pathway.

BACKGROUND: Emerging work suggests that academic achievement may be influenced by the management of affect as well as through efficient information processing of task demands. In particular, mathematical anxiety has attracted recent attention because of its damaging psychological effects and potential associations with mathematical problem solving and achievement. This study investigated the genetic and environmental factors contributing to the observed differences in the anxiety people feel when confronted with mathematical tasks. In addition, the genetic and environmental mechanisms that link mathematical anxiety with math cognition and general anxiety were also explored. METHODS: Univariate and multivariate quantitative genetic models were conducted in a sample of 514 12-year-old twin siblings. RESULTS: Genetic factors accounted for roughly 40% of the variation in mathematical anxiety, with the remaining being accounted for by child-specific environmental factors. Multivariate genetic analyses suggested that mathematical anxiety was influenced by the genetic and nonfamilial environmental risk factors associated with general anxiety and additional independent genetic influences associated with math-based problem solving. CONCLUSIONS: The development of mathematical anxiety may involve not only exposure to negative experiences with mathematics, but also likely involves genetic risks related to both anxiety and math cognition. These results suggest that integrating cognitive and affective domains may be particularly important for mathematics and may extend to other areas of academic achievement.

Four experiments used a preferential looking method to investigate 6-month-old infants' capacity to represent numerosity in visual-spatial displays. Building on previous findings that such infants discriminate between arrays of eight versus 16 discs, but not eight versus 12 discs (Xu & Spelke, 2000), Experiments 1 and 2 investigated whether infants' numerosity discrimination depends on the ratio of the two set sizes with even larger numerosities. Infants successfully discriminated between arrays of 16 versus 32 discs, but not 16 versus 24 discs, providing evidence that their discrimination shows the set-size ratio signature of numerosity discrimination in human adults, children and many non-human animals. Experiments 3 and 4 addressed a controversy concerning infants' ability to discriminate large numerosities (observed under conditions that control for total filled area, array size and density, item size and correlated properties such as brightness: Brannon, 2002; Xu, 2003b; Xu & Spelke, 2000) versus small numerosities (not observed under conditions that control for total contour length: Clearfield & Mix, 1999). To investigate the sources of these differing findings, Experiment 3 tested infants' large-number discrimination with controls for contour length, and Experiment 4 tested small-number discrimination with controls for total filled area. Infants successfully discriminated the large-number displays but showed no evidence of discriminating the small-number displays. These findings provide evidence that infants have robust abilities to represent large numerosities. In contrast, infants may fail to represent small numerosities in visual-spatial arrays with continuous quantity controls, consistent with the thesis that separate systems serve to represent large versus small numerosities.

Math anxiety is a negative emotional reaction to situations involving mathematical problem solving. Math anxiety has a detrimental impact on an individual's long-term professional success, but its neurodevelopmental origins are unknown. In a functional MRI study on 7- to 9-year-old children, we showed that math anxiety was associated with hyperactivity in right amygdala regions that are important for processing negative emotions. In addition, we found that math anxiety was associated with reduced activity in posterior parietal and dorsolateral prefrontal cortex regions involved in mathematical reasoning. Multivariate classification analysis revealed distinct multivoxel activity patterns, which were independent of overall activation levels in the right amygdala. Furthermore, effective connectivity between the amygdala and ventromedial prefrontal cortex regions that regulate negative emotions was elevated in children with math anxiety. These effects were specific to math anxiety and unrelated to general anxiety, intelligence, working memory, or reading ability. Our study identified the neural correlates of math anxiety for the first time, and our findings have significant implications for its early identification and treatment.

Electroencephalographic gamma band oscillations (GBOs) induced over the human primary somatosensory cortex (SI) by nociceptive stimuli have been hypothesized to reflect cortical processing involved directly in pain perception, because their magnitude correlates with pain intensity. However, as stimuli perceived as more painful are also more salient, an alternative interpretation of this correlation is that GBOs reflect unspecific stimulus-triggered attentional processing. In fact, this is suggested by recent observations that other features of the electroencephalographic (EEG) response correlate with pain perception when stimuli are presented in isolation, but not when their saliency is reduced by repetition. Here, by delivering trains of three nociceptive stimuli at a constant 1 s interval, and using different energies to elicit graded pain intensities, we demonstrate that GBOs recorded over SI always predict the subjective pain intensity, even when saliency is reduced by repetition. These results provide evidence for a close relationship between GBOs and the cortical activity subserving pain perception.

Studies have shown that numerosity processing (e.g., comparison of numbers of dots in two dot arrays) is significantly correlated with arithmetic performance. Researchers have attributed this association to the fact that both tasks share magnitude processing. The current investigation tested an alternative hypothesis, which states that visual perceptual ability (as measured by a figure-matching task) can account for the close relation between numerosity processing and arithmetic performance (computational fluency). Four hundred and twenty four third- to fifth-grade children (220 boys and 204 girls, 8.0-11.0 years old; 120 third graders, 146 fourth graders, and 158 fifth graders) were recruited from two schools (one urban and one suburban) in Beijing, China. Six classes were randomly selected from each school, and all students in each selected class participated in the study. All children were given a series of cognitive and mathematical tests, including numerosity comparison, figure matching, forward verbal working memory, visual tracing, non-verbal matrices reasoning, mental rotation, choice reaction time, arithmetic tests and curriculum-based mathematical achievement test. Results showed that figure-matching ability had higher correlations with numerosity processing and computational fluency than did other cognitive factors (e.g., forward verbal working memory, visual tracing, non-verbal matrix reasoning, mental rotation, and choice reaction time). More important, hierarchical multiple regression showed that figure matching ability accounted for the well-established association between numerosity processing and computational fluency. In support of the visual perception hypothesis, the results suggest that visual perceptual ability, rather than magnitude processing, may be the shared component of numerosity processing and arithmetic performance.