Less precise representation of numerical magnitude in high math-anxious individuals: An ERP study of the size and distance effects

Cognitive, affective and sociological predictors of school performance in mathematics

Mathematics is a key school subject for some of the most lucrative and economically important careers. Low mathematics performance in school is associated with low psychometric intelligence, family socioeconomic status (SES), specific mathematical abilities, and high mathematics anxiety. We used a sample of Hungarian schoolchildren (N = 102, mean age = 12.3 years) to directly compare the predictive power of general intelligence, specific mathematical abilities measured by the Pedagogical Examination of Dyscalculia (DPV), mathematics anxiety, and socioeconomic status for mathematics grades. Mathematics grades correlated with IQ, specific mathematic ability, mathematics anxiety, and a composite measure of family SES. The WISC-IV showcased a manifest correlation of 0.62 and a latent correlation of 0.78 with the DPV and high manifest (r=-0.53) and latent (r=-0.59) correlations with mathematics anxiety. IQ alone accounted for 52% of the variance in mathematics grades. IQ, specific mathematical ability, family SES and mathematics anxiety jointly accounted for 56% of the variance in grades, with a non-significant contribution of specific mathematical ability and family SES over IQ and a marginal contribution of mathematics anxiety. Our results show that psychometric intelligence is the most important predictor of mathematics grades, while family SES and specific mathematical abilities are only associated with grades to the extent they reflect psychometric intelligence. The results, however, confirmed a small role of mathematics anxiety over intelligence in predicting grades.

Mathematics anxiety and math achievement in primary school children: Testing different theoretical accounts

Some students suffer from math anxiety and experience negative emotions in mathematics education. Children's math anxiety is negatively related to their math achievement, suggesting that math anxiety puts their math learning at risk. Several theoretical accounts have been proposed that help to explain this association between math anxiety and achievement. In the current study, we aimed to test predictions of two prominent theories, namely the disruption account and the reduced competency account, using a comprehensive and unifying approach. A sample of 6- to 8-year-olds (N = 163) answered a math anxiety questionnaire, solved a spatial task (mental rotation), and solved several arithmetic problems. After each arithmetic problem, they were asked how they solved the problem. Strategies were then classified into counting and higher-level mental strategies (including decomposition and retrieval), with higher-level strategies loading strongly on working memory resources. Analyses revealed a negative, albeit small, association between children's math anxiety and accuracy in solving arithmetic problems. In line with the disruption account, children's frequency of using higher-level mental strategies mediated this relation between math anxiety and arithmetic performance. Moreover, our results support the reduced competency account given that arithmetic performance was related to math anxiety, whereas mental rotation was only indirectly related to math anxiety. Overall, our findings corroborate both accounts, lending further support to the notion that these accounts might not be mutually exclusive. Our findings imply that interventions might be most effective when focusing on emotion regulation strategies and improving mathematical and spatial performance.

Response inhibition deficits in math-anxious individuals

We examined whether math anxiety is related to a response inhibition deficit and, if so, whether it is a domain-specific inhibition deficit in numerical tasks or a general inhibition deficit. Behavioral performance and electroencephalogram activity were recorded while 28 highly math-anxious (HMA) and 28 low math-anxious (LMA) individuals performed both a numerical and a non-numerical Go/Nogo task. In the numerical task, single-digit numbers were presented, and participants were asked to press a button if the number was even. In the non-numerical task, letters were presented, and the button had to be pressed if the letter was a vowel. Nogo trials were answered less accurately and elicited larger Nogo-N2 and Nogo-P3 than Go trials in both tasks and both groups. Importantly, behavioral and brain response differences between tasks were only found in the HMA group. First, they were more error-prone in numerical Nogo than in non-numerical Nogo trials; and second, their Nogo-N2 and N2d (Nogo-Go difference) were smaller in the numerical task than in the non-numerical task. No differences were found in the LMA group. These results suggest that HMA individuals' response inhibition is impaired specifically when dealing with numbers, which could contribute to their low achievement in math tasks.

The relationship between numerical magnitude processing and math anxiety, and their joint effect on adult math performance, varied by indicators of numerical tasks

According to the hypothesis of Maloney et al. (Cognition 114(2):293-297, 2010. https://doi.org/10.1016/j.cognition.2009.09.013), math anxiety is related to deficits in numerical magnitude processing, which in turn compromises the development of advanced math skills. Because previous studies on this topic are contradictory, which may be due to methodological differences in the measurement of numerical magnitude processing, we tested Maloney et al.'s hypothesis using different tasks and their indicators: numerical magnitude processing (symbolic and non-symbolic comparison tasks: accuracy, reaction time, numerical ratio, distance and size effects, and Weber fraction; number line estimation task: estimation error), math anxiety (combined scores of learning, testing, math problem solving, and general math anxiety), and math performance. The results of our study conducted on 119 young adults mostly support the hypothesis proposed by Maloney et al. that deficiency in symbolic magnitude processing is related to math anxiety, but the relationship between non-symbolic processes and math anxiety was opposite to the assumptions. Moreover, the results indicate that estimation processes (but not comparison processes) and math anxiety are related to math performance in adults. Finally, high math anxiety moderated the relationship between reaction time in the symbolic comparison task, reaction time in the non-symbolic comparison task, numerical ratio effect in the symbolic comparison task, and math performance. Because the results of the joint effect of numerical magnitude processing and math anxiety on math performance were inconsistent, this part of the hypothesis is called into question.

Understanding the social-emotional components of our "number sense": insights from a novel non-symbolic numerical comparison task

Introduction

A large body of work has identified a core sense of number supported by the Approximate Number System (ANS) that is present in infancy and across species. Although it is commonly assumed that the ANS directly processes perceptual input and is relatively independent from affective factors, some evidence points at a correlation between ANS performance and math anxiety. However, the evidence is mixed. We tested whether giving participants active control in completing a numerical task would change the relationship between math anxiety on performance.

Methods

Adult participants (N = 103) completed a novel four-alternative-forced-choice non-symbolic numerical comparison task. In a repeated-measures design, participants either passively viewed different dot arrays or actively chose to view each array (i.e., active information-seeking) before deciding on the largest quantity. Participants also provided confidence judgments during the passive version of the task.

Results

We replicated the ratio-dependent signature in participants' accuracy in both the passive and active versions of the task using this novel paradigm, as well as in trial-level confidence judgments and information-seeking behavior. Participants' self-reported math anxiety significantly correlated with their accuracy on the passive version of the task. Critically, the correlation disappeared in the active version of the task. Gender also emerged as a predictor of confidence judgments and a moderator of the effect of task on overall accuracy and the effect of active information seeking on accuracy in the active version of the task. Exploratory analysis of estimated Weber Fraction suggests that these results may be driven by auxiliary factors instead of changes in ANS acuity.

Conclusion

These findings have implications for understanding the relationship between math anxiety and performance on numerical tasks.

A neural network model of mathematics anxiety: The role of attention

Anxiety about performing numerical calculations is becoming an increasingly important issue. Termed mathematics anxiety, this condition negatively impacts performance in numerical tasks which can affect education outcomes and future employment. The disruption account proposes poor performance is due to anxiety disrupting limited attentional and inhibitory resources leaving fewer cognitive resources for the current task. This study provides the first neural network model of math anxiety. The model simulates performance in two commonly-used tasks related to math anxiety: the numerical Stroop and symbolic number comparison. Different model modifications were used to simulate high and low math-anxious conditions by modifying attentional processes and learning; these model modifications address different theories of math anxiety. The model simulations suggest that math anxiety is associated with reduced attention to numerical stimuli. These results are consistent with the disruption account and the attentional control theory where anxiety decreases goal-directed attention and increases stimulus-driven attention.

Foundations for future math achievement: Early numeracy, home learning environment, and the absence of math anxiety

BACKGROUND

Mathematics achievement is pivotal in shaping children's future prospects. Cognitive skills (numeracy), feelings (anxiety), and the social environment (home learning environment) influence early math development.

METHOD

A longitudinal study involved 85 children (mean age T1 = 6.4 years; T2 = 7.9) to explore these predictors holistically. Data were collected on early numeracy skills, home learning environment, math anxiety, and their impact on various aspects of math.

RESULTS

The study found that early numeracy skills, home learning environment, and math anxiety significantly influenced math school achievement. However, they affected written computation, sequences, and comparisons differently. Early numeracy skills strongly predicted overall achievement and comparison subtest performance.

CONCLUSION

These findings underscore the substantial role of math anxiety and home learning environment in children's math achievement. The study emphasizes the need to consider the selective impacts of these factors in future research, shedding light on the multifaceted nature of mathematics achievement determinants.

The neuroscience basis and educational interventions of mathematical cognitive impairment and anxiety: a systematic literature review

Introduction

Mathematics is a fundamental subject with significant implications in education and neuroscience. Understanding the cognitive processes underlying mathematical cognition is crucial for enhancing educational practices. However, mathematical cognitive impairment and anxiety significantly hinder learning and application in this field. This systematic literature review aims to investigate the neuroscience basis and effective educational interventions for these challenges.

Methods

The review involved a comprehensive screening of 62 research articles that meet the ESSA evidence levels from multiple databases. The selection criteria focused on studies employing various methodologies, including behavioral experiments and neuroimaging techniques, to explore the neuroscience underpinnings and educational interventions related to mathematical cognitive impairment and anxiety.

Results

The review identified key themes and insights into the neuroscience basis of mathematical cognitive impairment and anxiety. It also examined their impact on educational practices, highlighting the interplay between cognitive processes and educational outcomes. The analysis of these studies revealed significant findings on how these impairments and anxieties manifest and can be addressed in educational settings.

Discussion

The review critically analyzes the shortcomings of existing research, noting gaps and limitations in current understanding and methodologies. It emphasizes the need for more comprehensive and diverse studies to better understand these phenomena. The discussion also suggests new directions and potential improvement strategies for future research, aiming to contribute to more effective educational interventions and enhanced learning experiences in mathematics.

Conclusion

This systematic review provides valuable insights into the neuroscience basis of mathematical cognitive impairment and anxiety, offering a foundation for developing more effective educational strategies. It underscores the importance of continued research in this area to improve educational outcomes and support learners facing these challenges.

Basic Symbolic Number Skills, but Not Formal Mathematics Performance, Longitudinally Predict Mathematics Anxiety in the First Years of Primary School

Mathematical anxiety (MA) and mathematics performance typically correlate negatively in studies of adolescents and adults, but not always amongst young children, with some theorists questioning the relevance of MA to mathematics performance in this age group. Evidence is also limited in relation to the developmental origins of MA and whether MA in young children can be linked to their earlier mathematics performance. To address these questions, the current study investigated whether basic and formal mathematics skills around 4 and 5 years of age were predictive of MA around the age of 7-8. Additionally, we also examined the cross-sectional relationships between MA and mathematics performance in 7-8-year-old children. Specifically, children in our study were assessed in their first (T1; aged 4-5), second (T2; aged 5-6), and fourth years of school (T3; aged 7-8). At T1 and T2, children completed measures of basic numerical skills, IQ, and working memory, as well as curriculum-based mathematics tests. At T3, children completed two self-reported MA questionnaires, together with a curriculum-based mathematics test. The results showed that MA could be reliably measured in a sample of 7-8-year-olds and demonstrated the typical negative correlation between MA and mathematical performance (although the strength of this relationship was dependent on the specific content domain). Importantly, although early formal mathematical skills were unrelated to later MA, there was evidence of a longitudinal relationship between basic early symbolic number skills and later MA, supporting the idea that poorer basic numerical skills relate to the development of MA.

Meta-analysis of skill-based and therapeutic interventions to address math anxiety

The purpose of this meta-analysis was to examine the impact of school-based therapeutic and math skill interventions on math anxiety symptoms and math achievement among K-12 students. Potential moderators included treatment type and study quality. A systematic search yielded 17 included studies representing 1786 primary and secondary students. The results suggested that therapeutic interventions reduced math anxiety symptoms (gav = -0.51) better than math skill interventions (gav = -0.32) and math skill interventions improved math achievement (gav = 0.76) more than therapeutic interventions (gav = 0.12). Moderator analysis indicated that when accounting for study quality, the differences between intervention type were not significant for either of the outcome measures (i.e., achievement and math anxiety). Theoretical and practical implications of these findings are discussed.

Assessment of math anxiety as a potential tool to identify students at risk of poor acquisition of new math skills: longitudinal study of grade 9 Italian students

Introduction

Numerous international educational institutions have sounded the alarm about the gradual increase in the number of students failing to achieve a sufficient level of proficiency in mathematical abilities. Thus, the growing interest in identifying possible solutions and factors interfering with learning seems justified. In recent years, special attention has accrued to the possible role played by emotional factors.

Methods

In the present investigation, students in the first grade of a technical vocational secondary school are followed to assess the influence of math anxiety (MA) on the development of skill acquisition in calculus. A math skills assessment test is administered on two occasions, at the beginning and end of the school year.

Results

Results highlighted that the score on the anxiety scale, administered at the beginning of the year, negatively correlated with the score obtained on the mathematics test, administered at the end of the school year: the higher the level of anxiety, the worse the performance. Furthermore, the score obtained in the second administration makes it possible to divide the students tested into two groups: students who improved their performance and students who did not benefit at all from repeating the test. In these two groups, an analysis of the relationships between the outcome of the end-of-year mathematics test and the level of MA at the beginning of the year showed that MA correlates negatively with performance only in students who will fail to acquire new expertise in mathematics over the course of the school year.

Discussion

The results suggest that MA may interfere with the smooth development of math skills. Assessing the level of MA at the beginning of the school year could prove to be a useful tool in identifying which and how many students are at risk of failing to achieve the skills expected from the usual course of instruction. A consideration of anxiety as one of the variables at play in the genesis of learning difficulties may prompt educators to modify teaching methodology and strategies by increasing focus on the impact of the emotional dimension on learning.

The relationship between math anxiety and math performance: The moderating role of visuospatial working memory

According to the processing efficiency theory (PET), math anxiety would interfere with working memory resources, negatively affecting mathematical abilities. To date, few studies have explored how the interaction between math anxiety and working memory would affect different types of math tasks, especially in primary school children. Therefore, the purpose of this study was to explore whether the interplay between math anxiety and working memory would influence performance in numerical operations (i.e., math fluency task) and mathematical reasoning (i.e., math reasoning task) in a group of primary school children (N = 202). Results showed that visuospatial working memory appeared to moderate the relationship between math anxiety and math performance when the math fluency task was considered, indicating that participants with higher levels of working memory were more negatively affected by math anxiety. No interaction effect was found for the math reasoning task in which students' scores were explained only by visuospatial working memory. The findings suggest that math anxiety and visuospatial working memory interact to influence performance in the math fluency task and that this effect may vary depending on the strategies used to complete the task. On the other hand, results on the math reasoning task showed that visuospatial working memory continues to have a positive effect on the math performance independently of math anxiety. The implications in the educational setting are discussed, pointing to the importance of monitoring and intervention studies on affective factors.

EXPRESS: Arithmetic operations without symbols are unimpaired in adults with math anxiety

This study characterizes a previously unstudied facet of a major causal model of math anxiety. The model posits that impaired "basic number abilities" can lead to math anxiety, but what constitutes a basic number ability remains underdefined. Previous work has raised the idea that our perceptual ability to represent quantities approximately without using symbols constitutes one of the basic number abilities. Indeed, several recent studies tested how participants with math anxiety estimate and compare non-symbolic quantities. However, little is known about how participants with math anxiety perform arithmetic operations (addition and subtraction) on non-symbolic quantities. This is an important question because poor arithmetic performance on symbolic numbers is one of the primary signatures of high math anxiety. To test the question, we recruited 92 participants and asked them to complete a math anxiety survey, two measures of working memory, a timed symbolic arithmetic test, and a non-symbolic "approximate arithmetic" task. We hypothesized that if impaired ability to perform operations was a potential causal factor to math anxiety, we should see relationships between math anxiety and both symbolic and approximate arithmetic. However, if math anxiety relates to precise or symbolic representation, only a relationship between math anxiety and symbolic arithmetic should appear. Our results show no relationship between math anxiety and the ability to perform operations with approximate quantities, suggesting that difficulties performing perceptually based arithmetic operations does not constitute a basic number ability linked to math anxiety.

Relationships Between Mathematics Performance and Attitude to Mathematics: Influences of Gender, Test Anxiety, and Working Memory

Many studies have indicated that mathematics anxiety, and other negative attitudes and emotions toward mathematics, are pervasive and are associated with lower mathematical performance. Some previous research has suggested that working memory is related to both mathematics anxiety and mathematics. Moreover, both gender and chosen course of study (sciences vs. humanities) appeared likely to influence students’ attitudes to mathematics. In the present study, 40 university undergraduates completed a battery of assessments investigating working memory, attitude to mathematics, test anxiety. and mental and written arithmetic. Attitudes to mathematics were significantly associated with the other variables: working memory, test anxiety, and both measures of mathematical performance. The other variables were not strongly associated with one another. There were no gender differences in mathematical performance, but females exhibited more negative attitudes to mathematics and higher test anxiety than males. After controlling for test anxiety, there ceased to be significant gender differences in attitudes to mathematics. Science students had more positive attitudes to mathematics than humanities students, but the groups did not differ in test anxiety, Science students were better at written but not mental arithmetic. They were also better at working memory, but this was not a significant covariate when the groups were compared on mathematical performance and attitudes to mathematics The results are discussed, with particular focus on implications for future research on influences on mathematics anxiety.

Math anxiety differentially impairs symbolic, but not nonsymbolic, fraction skills across development

Although important for the acquisition of later math skills, fractions are notoriously difficult. Previous studies have shown that higher math anxiety (MA) is associated with lower performance in symbolic fraction tasks in adults and have suggested that MA may negatively impact the acquisition of fractions in children. However, the effects of MA on fraction skills in school-aged children remain underexplored. We, therefore, investigated the impact of MA on the performance of younger (second and third graders) and older (fifth and sixth graders) children in math fluency (MF), written calculation, fraction knowledge (FK), and symbolic fraction and nonsymbolic ratio processing. On the basis of our prior work suggesting a perceptual foundation for fraction processing, we predicted that symbolic, but not nonsymbolic, math skills (especially fractions) would be impaired by MA. As predicted, higher MA was associated with lower performance in general mathematics achievement and symbolic fraction tasks, but nonsymbolic ratio processing was not affected by MA in either age group. Furthermore, working memory capacity partially mediated the effects of MA on general mathematics achievement, FK, and symbolic fraction processing. These results suggest that understanding the bidirectional interactions between MA and fractions may be important for helping children acquire these critical skills.

Developmental relations between mathematics anxiety, symbolic numerical magnitude processing and arithmetic skills from first to second grade

We investigated the levels of and changes in mathematics anxiety (MA), symbolic numerical magnitude processing (SNMP) and arithmetic skills, and how those changes are linked to each other. Children's (n = 264) MA, SNMP and arithmetic skills were measured in Grade 1, and again in Grade 2, also including a mathematics performance test. All three constructs correlated significantly within each time point, and the rank-order stability over time was high, particularly in SNMP and arithmetic skills. By means of latent change score modelling, we found overall increases in SNMP and arithmetic skills over time, but not in MA. Most interestingly, changes in arithmetic skills and MA were correlated (i.e. steeper increase in arithmetic skills was linked with less steep increase in MA), as were changes in SNMP and arithmetic skills (i.e. improvement in SNMP was associated with improvement in arithmetic skills). Only the initial level of arithmetic skills and change in it predicted mathematics performance. The only gender difference, in favour of boys, was found in SNMP skills. The differential effects associated with MA (developmentally only linked with arithmetic skills) and gender (predicting only changes in SNMP) call for further longitudinal research on the different domains of mathematical skills.

ERP Characteristics of Inducing Rule Validity in Number Series Under Time Pressure

A great deal of research has been devoted to examining the neural mechanisms of inductive reasoning. However, the influences of rule validity and time pressure on numerical inductive reasoning remain unclear. In the current study, we aimed to examine the effects of these variables on the time course of rule identification in numerical inductive reasoning. We designed a 3 (task type: valid, invalid, and anomalous) × 2 (time pressure: with time pressure and without time pressure) within-subject experiment based on electroencephalographic event-related potentials (ERP). Behaviorally, we found significant effects of rule validity and time pressure on rule identification. Neurologically, we considered the elicited N200 ERP to reflect conflict detection and found it to be modulated by rule validity but not time pressure. We considered the induced P300 ERP to be primarily related to updating working memory, affected by both rule validity and time pressure. These findings have new implications for better understanding dynamic information processing within numerical inductive reasoning.

Emerging neurodevelopmental perspectives on mathematical learning

Strong foundational skills in mathematical problem solving, acquired in early childhood, are critical not only for success in the science, technology, engineering, and mathematical (STEM) fields but also for quantitative reasoning in everyday life. The acquisition of mathematical skills relies on protracted interactive specialization of functional brain networks across development. Using a systems neuroscience approach, this review synthesizes emerging perspectives on neurodevelopmental pathways of mathematical learning, highlighting the functional brain architecture that supports these processes and sources of heterogeneity in mathematical skill acquisition. We identify the core neural building blocks of numerical cognition, anchored in the posterior parietal and ventral temporal-occipital cortices, and describe how memory and cognitive control systems, anchored in the medial temporal lobe and prefrontal cortex, help scaffold mathematical skill development. We highlight how interactive specialization of functional circuits influences mathematical learning across different stages of development. Functional and structural brain integrity and plasticity associated with math learning can be examined using an individual differences approach to better understand sources of heterogeneity in learning, including cognitive, affective, motivational, and sociocultural factors. Our review emphasizes the dynamic role of neurodevelopmental processes in mathematical learning and cognitive development more generally.

The Spatial-Numerical Association of Response Codes (SNARC) effect in highly math-anxious individuals: An ERP study

The Spatial-Numerical Association of Response Codes (SNARC) effect was examined in highly (HMA) and low math-anxious (LMA) individuals performing a number comparison in an ERP study. The SNARC effect consists of faster latencies when the response side is congruent with number location in the mental number line (MNL). Despite the stronger SNARC effect in the HMA group, their responses in incongruent trials were slower than in congruent trials only for the largest numerical magnitudes. Moreover, HMAs showed a less positive centroparietal P3b component in incongruent trials than in congruent ones, but only for the largest magnitudes. Since the SNARC effect arises during response selection and P3b positivity decreases with the difficulty of decision, this result suggests that HMA individuals might find it more difficult than LMAs to control the conflict between the automatically activated location of numbers in the MNL and the response side, especially in more cognitively demanding trials.

Longitudinal Performance in Basic Numerical Skills Mediates the Relationship Between Socio-Economic Status and Mathematics Anxiety: Evidence From Chile

Socio-economic status (SES) and mathematical performance seem to be risk factors of mathematics anxiety (MA) in both children and adults. However, there is little evidence about how exactly these three constructs are related, especially during early stages of mathematical learning. In the present study, we assessed longitudinal performance in symbolic and non-symbolic basic numerical skills in pre-school and second grade students, as well as MA in second grade students. Participants were 451 children (average pre-school age = 5 years, 6 months) from 12 schools in Chile, which differed in school vulnerability index (SVI), an indicator of SES. We tested an explanatory model of MA that included SES and longitudinal performance in basic numerical skills as predictors. The results showed a direct effect of SES on MA and a mediating effect of performance in symbolic and non-symbolic comparison tasks in pre-school. However, in second grade, only performance in symbolic comparison significantly mediated the SES-MA relationship. These findings suggest that performance in non-symbolic comparison plays an important role in explaining MA at initial stages, but that its influence is no longer significant by the time children reach formal instruction in second grade. By contrast, as children's formal educational experience in mathematics increases, MA becomes linked primarily to symbolic numerical tasks. In sum, SES affects MA and this is due in part to the effect of SES on the development of numerical learning in pre-school, which in turn has an impact on subsequent, more complex learning, ultimately leading to differences in MA. We discuss the implications of these findings for preventing and acting upon the emergence of MA.

A meta-analysis of the relation between math anxiety and math achievement

Meta-analyses from the 1990s previously have established a significant, small-to-moderate, and negative correlation between math achievement and math anxiety. Since these publications, research has continued to investigate this relation with more diverse samples and measures. Thus, the goal of the present meta-analysis was to provide an update of the math anxiety-math achievement relation and its moderators. Analyzing 747 effect sizes accumulated from research conducted between 1992 and 2018, we found a small-to-moderate, negative, and statistically significant correlation (r = -.28) between math anxiety and math achievement. The relation was significant for all moderator subgroups, with the exception of the relation between math anxiety and assessments measuring the approximate number system. Grade level, math ability level, adolescent/adult math anxiety scales, math topic of anxiety scale, and math assessments were significant moderators of this relation. There is also a tendency for published studies to report significantly stronger correlations than unpublished studies, but overall, large, negative effect sizes are underreported. Our results are consistent with previous findings of a significant relation between math anxiety and math achievement. This association starts in childhood, remains significant through adulthood, is smaller for students in Grades 3 through 5 and postsecondary school, is larger for math anxiety than for statistics anxiety and for certain math anxiety scales, and is smaller for math exam grades and samples selected for low math ability. This work supports future research efforts to determine effective math achievement and math anxiety interventions, which may be most helpful to implement during childhood. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Professional mathematicians do not differ from others in the symbolic numerical distance and size effects

The numerical distance effect (it is easier to compare numbers that are further apart) and size effect (for a constant distance, it is easier to compare smaller numbers) characterize symbolic number processing. However, evidence for a relationship between these two basic phenomena and more complex mathematical skills is mixed. Previously this relationship has only been studied in participants with normal or poor mathematical skills, not in mathematicians. Furthermore, the prevalence of these effects at the individual level is not known. Here we compared professional mathematicians, engineers, social scientists, and a reference group using the symbolic magnitude classification task with single-digit Arabic numbers. The groups did not differ with respect to symbolic numerical distance and size effects in either frequentist or Bayesian analyses. Moreover, we looked at their prevalence at the individual level using the bootstrapping method: while a reliable numerical distance effect was present in almost all participants, the prevalence of a reliable numerical size effect was much lower. Again, prevalence did not differ between groups. In summary, the phenomena were neither more pronounced nor more prevalent in mathematicians, suggesting that extremely high mathematical skills neither rely on nor have special consequences for analogue processing of symbolic numerical magnitudes.

Math Anxiety Mediates the Link Between Number Sense and Math Achievements in High Math Anxiety Young Adults

In the past few years, many studies have suggested that subjects with high sensory precision in the processing of non-symbolic numerical quantities (approximate number system; ANS) also have higher math abilities. At the same time, there has been interest in another non-cognitive factor affecting mathematical learning: mathematical anxiety (MA). MA is defined as a debilitating emotional reaction to mathematics that interferes with the manipulation of numbers and the solving of mathematical problems. Few studies have been dedicated to uncovering the interplay between ANS and MA and those have provided conflicting evidence. Here we measured ANS precision (numerosity discrimination thresholds) in a cohort of university students with either a high (>75th percentile; n = 49) or low (<25th percentile; n = 39) score on the Abbreviate Math Anxiety Scale (AMAS). We also assessed math proficiency using a standardized test (MPP: Mathematics Prerequisites for Psychometrics), visuo-spatial attention capacity by means of a Multiple Objects Tracking task (MOT) and sensory precision for non-numerical quantities (disk size). Our results confirmed previous studies showing that math abilities and ANS precision correlate in subjects with high math anxiety. Neither precision in size-discrimination nor visuo-spatial attentional capacity were found to correlate with math capacities. Interestingly, within the group with high MA, our data also revealed a relationship between ANS precision and MA, with MA playing a key role in mediating the correlation between ANS and math achievement. Taken together, our results suggest an interplay between extreme levels of MA and the sensory precision in the processing of non-symbolic numerosity.

Non-symbolic representation is modulated by math anxiety and cognitive inhibition while symbolic representation not

The present study aimed to investigate whether there are basic numerical processing deficits in high math anxiety (HMA) individuals and examine the effects of cognitive inhibition on the performance of high and low math anxiety (LMA) individuals. 35 undergraduate students were recruited to perform a numerical comparison task, a numerical Stroop task, a dot comparison task, and a dot Stroop task. Results showed the following: (1) Compared with LMA group, HMA group reacted more slowly and exhibited more fixation counts in non-symbolic representation task. (2) Inhibition condition significantly increased HMA individuals' fixation durations, whereas the fixation durations of LMA individuals were similar between inhibition and non-inhibition condition. The results demonstrated that MA might temporarily occupy individuals' working memory resources. (3) In non-symbolic representation task, the effect of numerical ratio on fixation counts was larger for HMA group than that for LMA group under inhibition condition, indicating MA might arise from a basic level deficit in numerosity processing.

Frequency-based Dissociation of Symbolic and Nonsymbolic Numerical Processing during Numerical Comparison

Recent evidence suggests that during numerical calculation, symbolic and nonsymbolic processing are functionally distinct operations. Nevertheless, both roughly recruit the same brain areas (spatially overlapping networks in the parietal cortex) and happen at the same time (roughly 250 msec poststimulus onset). We tested the hypothesis that symbolic and nonsymbolic processing are segregated by means of functionally relevant networks in different frequency ranges: high gamma (above 50 Hz) for symbolic processing and lower beta (12–17 Hz) for nonsymbolic processing. EEG signals were quantified as participants compared either symbolic numbers or nonsymbolic quantities. Larger EEG gamma-band power was observed for more difficult symbolic comparisons (ratio of 0.8 between the two numbers) than for easier comparisons (ratio of 0.2) over frontocentral regions. Similarly, beta-band power was larger for more difficult nonsymbolic comparisons than for easier ones over parietal areas. These results confirm the existence of a functional dissociation in EEG oscillatory dynamics during numerical processing that is compatible with the notion of distinct linguistic processing of symbolic numbers and approximation of nonsymbolic numerical information.

Predicting maths anxiety from mathematical achievement across the transition from primary to secondary education

The primary- to secondary-education transition is a substantive life event for many children. The transition can be associated with changes in the developmental trajectories of both emotional health and academic achievement. The current study looked at whether the trajectory of mathematical attainment and emotional health (anxiety) across this transition predicted later maths anxiety. A secondary analysis of data from the Twin Early Development Study (TEDS) was performed. The statistical models were fit on the 753 participants (one from each twin pair) for which there were measures of mathematical performance across the primary- to secondary-education transition and maths anxiety at age 18. Two multi-level growth models were fit predicting mathematical attainment and anxiety over the primary- to secondary-education transition. The intercepts and slopes for each child were extracted from these models and used as predictors of subsequent maths anxiety at age 18. These effects were adjusted for biological sex, socio-economic status, verbal cognitive ability and general anxiety. Maths anxiety at age 18 was significantly predicted by both pre-transition levels of anxiety and mathematical attainment and their rate of change across the primary- to secondary-education transition. However, the effects were small, suggesting that theories of maths anxiety may have overplayed the role of prior mathematical attainment and general anxiety.

Arithmetic Skill May Refine the Performance of Individuals with High Math Anxiety, Especially in the Calculation Task: An ERP Study

As a global phenomenon, the theme of math anxiety has received increasing attention. The present study aimed to investigate the relationship between math anxiety and performance and determine the role of arithmetic skill in two different tasks. Fifty-seven college freshmen were recruited to perform a comparison task and a calculation task. Only main effect of arithmetic skill was found on the behavioral level. In the comparison task, participants with high math anxiety (HMA) showed faster latencies and greater amplitudes of N1 and longer P3b latency relative to their counterparts with low math anxiety (LMA). Number, as a negative stimulus, occupied attentional resources and delayed the speed of cognitive processing for individuals with HMA. Furthermore, among those with HMA, individuals with high arithmetic skill showed larger amplitudes and shorter latencies of P2 compared with those with low airthmetic skill in the calculation task. Thus, arithmetic skill could refine the performance efficiency of individuals with HMA, especially in the calculation task. These results suggest that educational interventions emphasizing control of negative emotional responses to math stimuli will be more effective when considering different populations of mathematically competent individuals.

Profiles of Mathematics Anxiety Among 15-Year-Old Students: A Cross-Cultural Study Using Multi-Group Latent Profile Analysis

Using PISA 2012 data, the present study explored profiles of mathematics anxiety (MA) among 15-year old students from Finland, Korea, and the United States to determine the similarities and differences of MA across the three national samples by applying a multi-group latent profile analysis (LPA). The major findings were that (a) three MA profiles were found in all three national samples, i.e., Low MA, Mid MA, and High MA profile, and (b) the percentages of students classified into each of the three MA profiles differed across the Finnish, Korean, and American samples, with United States having the highest prevalence of High MA, and Finland the lowest. Multi-group LPA also provided clear and useful latent profile separation. The High MA profile demonstrated significant poorer mathematics performance and lower mathematics interest, self-efficacy, and self-concept than the Mid and Low MA profiles. Same differences appeared between the Mid and Low MA profiles. The implications of the findings seem clear: (1) it is possible that there is some relative level of universality in MA among 15-year old students which is independent of cultural context; and (2) multi-group LPA could be a useful analytic tool for research on the study of classification and cultural differences of MA.

Math Anxiety in Combination With Low Visuospatial Memory Impairs Math Learning in Children

Math anxiety impairs academic achievements in mathematics. According to the processing efficiency theory (PET), the adverse effect is the result of reduced processing capacity in working memory (WM). However, this relationship has been examined mostly with correlational designs. Therefore, using an intervention paradigm, we examined the effects of math anxiety on math learning. Twenty-five 5th graders underwent seven training sessions of multiplication over the course of 2 weeks. Children were faster and made fewer errors in solving trained problems than untrained problems after learning. By testing the relationship between math anxiety, WM, and math learning, we found that if children have little or no math anxiety, enough WM resources are left for math learning, so learning is not impeded. If they have high math anxiety and high visuospatial WM, some WM resources are needed to deal with math anxiety but learning is still supported. However, if they have high math anxiety and low visuospatial WM capacity, math learning is significantly impaired. These children have less capacity to learn new math content as cognitive resources are diverted to deal with their math anxiety. We conclude that math anxiety not only hinders children's performance in the present but potentially has long-lasting consequences, because it impairs not only math performance but also math learning. This intervention study partially supports the PET because only the combination of high math anxiety and low WM capacity seems critical for hindering math learning. Moreover, an adverse effect of math anxiety was observed on performance effectiveness (response accuracy) but not processing efficiency (response time).

A Framework for Studying the Heterogeneity of Risk Factors in Math Anxiety

Math anxiety is a prevalent disorder which affects many people worldwide. Here, we draw together ample evidence to suggest a dynamic developmental bio-psycho-social model. The model highlights the complex pathways towards the development of math anxiety, with a focus on dynamism. That is, math anxiety is viewed here as a dynamic interplay between environmental (parenting style, as well as social style including teachers' attitude, instruction strategies and wider social effects) and intrinsic factors (i.e., neuro-cognitive and genetic predispositions, including brain malfunctions, heritability, predisposition towards general anxiety) and basic numerical cognition and affective factors. The model predicts that the dynamic interplay between these factors can either prevent or promote math anxiety's effects on the development of heterogeneous symptoms. Considering the universal nature of math anxiety, a systematic description of the vulnerability factors that contribute to the development of math anxiety is vital. Such information may be of particular value in informing the design of preventive interventions as well as of specific intervention tools.

Number line estimation in highly math-anxious individuals

In this study, we aimed to investigate the difficulties highly math-anxious individuals (HMA) may face when having to estimate a number's position in a number line task. Twenty-four HMA and 24 low math-anxiety (LMA) individuals were presented with four lines with endpoints 0-100, 0-1,000, 0-100,000, and 267-367 on a computer monitor on which they had to mark the correct position of target numbers using the mouse. Although no differences were found between groups in the frequency of their best-fit model, which was linear for all lines, the analysis of slopes and intercepts for the linear model showed that the two groups differed in performance on the less familiar lines (267-367 and 0-100,000). Lower values for the slope and higher values for the intercept were found in the HMA group, suggesting that they tended to overestimate small numbers and underestimate large numbers on these non-familiar lines. Percentage absolute error analyses confirmed that HMA individuals were less accurate than their LMA counterparts on these lines, although no group differences were found in response time. These results indicate that math anxiety is related to worse performance only in the less familiar and more difficult number line tasks. Therefore, our data challenge the idea that HMA individuals might have less precise numerical representations and support the anxiety-complexity effect posited by Ashcraft and colleagues.

Simple arithmetic: not so simple for highly math anxious individuals

Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low—compared to high—math anxious individuals perform better when they activate this network less—a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently.

Intentional and automatic processing of numerical information in mathematical anxiety: testing the influence of emotional priming

Current theoretical approaches suggest that mathematical anxiety (MA) manifests itself as a weakness in quantity manipulations. This study is the first to examine automatic versus intentional processing of numerical information using the numerical Stroop paradigm in participants with high MA. To manipulate anxiety levels, we combined the numerical Stroop task with an affective priming paradigm. We took a group of college students with high MA and compared their performance to a group of participants with low MA. Under low anxiety conditions (neutral priming), participants with high MA showed relatively intact number processing abilities. However, under high anxiety conditions (mathematical priming), participants with high MA showed (1) higher processing of the non-numerical irrelevant information, which aligns with the theoretical view regarding deficits in selective attention in anxiety and (2) an abnormal numerical distance effect. These results demonstrate that abnormal, basic numerical processing in MA is context related.

Representation of numerical magnitude in math-anxious individuals

Larger distance effects in high math-anxious individuals (HMA) performing comparison tasks have previously been interpreted as indicating less precise magnitude representation in this population. A recent study by Dietrich, Huber, Moeller, and Klein limited the effects of math anxiety to symbolic comparison, in which they found larger distance effects for HMA, despite equivalent size effects. However, the question of whether distance effects in symbolic comparison reflect the properties of the magnitude representation or decisional processes is currently under debate. This study was designed to further explore the relation between math anxiety and magnitude representation through three different tasks. HMA and low math-anxious individuals (LMA) performed a non-symbolic comparison, in which no group differences were found. Furthermore, we did not replicate previous findings in an Arabic digit comparison, in which HMA individuals showed equivalent distance effects to their LMA peers. Lastly, there were no group differences in a counting Stroop task. Altogether, an explanation of math anxiety differences in terms of less precise magnitude representation is not supported.

Mothers, Intrinsic Math Motivation, Arithmetic Skills, and Math Anxiety in Elementary School

Math anxiety is influenced by environmental, cognitive, and personal factors. Yet, the concurrent relationships between these factors have not been examined. To this end, the current study investigated how the math anxiety of 30 sixth graders is affected by: (a) mother's math anxiety and maternal behaviors (environmental factors); (b) children's arithmetic skills (cognitive factors); and (c) intrinsic math motivation (personal factor). A rigorous assessment of children's math anxiety was made by using both explicit and implicit measures. The results indicated that accessible self-representations of math anxiety, as reflected by the explicit self-report questionnaire, were strongly affected by arithmetic skills. However, unconscious cognitive constructs of math anxiety, as reflected by the numerical dot-probe task, were strongly affected by environmental factors, such as maternal behaviors and mothers' attitudes toward math. Furthermore, the present study provided preliminary evidence of intergenerational transmission of math anxiety. The conclusions are that in order to better understand the etiology of math anxiety, multiple facets of parenting and children's skills should be taken into consideration. Implications for researchers, parents, and educators are discussed.

Magnitude processing and complex calculation is negatively impacted by mathematics anxiety while retrieval-based simple calculation is not

Mathematics anxiety (MA) refers to the experience of negative affect when engaging in mathematical activity. According to Ashcraft and Kirk (2001), MA selectively affects calculation with high working memory (WM) demand. On the other hand, Maloney, Ansari, and Fugelsang (2011) claim that MA affects all mathematical activities, including even the most basic ones such as magnitude comparison. The two theories make opposing predictions on the negative effect of MA on magnitude processing and simple calculation that make minimal demands on WM. We propose that MA has a selective impact on mathematical problem solving that likely involves processing of magnitude representations. Based on our hypothesis, MA will impinge upon magnitude processing even though it makes minimal demand on WM, but will spare retrieval-based, simple calculation, because it does not require magnitude processing. Our hypothesis can reconcile opposing predictions on the negative effect of MA on magnitude processing and simple calculation. In the present study, we observed a negative relationship between MA and performance on magnitude comparison and calculation with high but not low WM demand. These results demonstrate that MA has an impact on a wide range of mathematical performance, which depends on one's sense of magnitude, but spares over-practiced, retrieval-based calculation.

Individual differences in nonverbal number skills predict math anxiety

Math anxiety (MA) involves negative affect and tension when solving mathematical problems, with potentially life-long consequences. MA has been hypothesized to be a consequence of negative learning experiences and cognitive predispositions. Recent research indicates genetic and neurophysiological links, suggesting that MA stems from a basic level deficiency in symbolic numerical processing. However, the contribution of evolutionary ancient purely nonverbal processes is not fully understood. Here we show that the roots of MA may go beyond symbolic numbers. We demonstrate that MA is correlated with precision of the Approximate Number System (ANS). Individuals high in MA have poorer ANS functioning than those low in MA. This correlation remains significant when controlling for other forms of anxiety and for cognitive variables. We show that MA mediates the documented correlation between ANS precision and math performance, both with ANS and with math performance as independent variable in the mediation model. In light of our results, we discuss the possibility that MA has deep roots, stemming from a non-verbal number processing deficiency. The findings provide new evidence advancing the theoretical understanding of the developmental etiology of MA.

How Math Anxiety Relates to Number-Space Associations

Given the considerable prevalence of math anxiety, it is important to identify the factors contributing to it in order to improve mathematical learning. Research on math anxiety typically focusses on the effects of more complex arithmetic skills. Recent evidence, however, suggests that deficits in basic numerical processing and spatial skills also constitute potential risk factors of math anxiety. Given these observations, we determined whether math anxiety also depends on the quality of spatial-numerical associations. Behavioral evidence for a tight link between numerical and spatial representations is given by the SNARC (spatial-numerical association of response codes) effect, characterized by faster left-/right-sided responses for small/large digits respectively in binary classification tasks. We compared the strength of the SNARC effect between high and low math anxious individuals using the classical parity judgment task in addition to evaluating their spatial skills, arithmetic performance, working memory and inhibitory control. Greater math anxiety was significantly associated with stronger spatio-numerical interactions. This finding adds to the recent evidence supporting a link between math anxiety and basic numerical abilities and strengthens the idea that certain characteristics of low-level number processing such as stronger number–space associations constitute a potential risk factor of math anxiety.

Multidimensionality in the Measurement of Math-Specific Anxiety and its Relationship with Mathematical Performance

Traditionally, mathematical anxiety has been utilized as a unidimensional construct. However, math-specific anxiety may have distinguishable factors, and taking these factors into account may better illuminate the relationship between anxiety and mathematics performance. Drawing from the Western Reserve Reading and Math Project (N = 244 children, mean age = 12.28 years), the present study examined math-specific anxiety and mathematics problem evaluation, utilizing a structural equation modeling approach with an item-level measurement model structure. Results suggested math-specific anxiety tapped into three factors: anxiety about performing mathematical calculations, anxiety about math in classroom situations, and anxiety about math tests. Among the three math anxiety factors, only calculation anxiety was significantly and negatively related to math performance while holding other anxiety factors constant. Implications for the measurement of math-specific anxiety are discussed.

Mathematics Anxiety: What Have We Learned in 60 Years?

The construct of mathematics anxiety has been an important topic of study at least since the concept of “number anxiety” was introduced by Dreger and Aiken (1957), and has received increasing attention in recent years. This paper focuses on what research has revealed about mathematics anxiety in the last 60 years, and what still remains to be learned. We discuss what mathematics anxiety is; how distinct it is from other forms of anxiety; and how it relates to attitudes to mathematics. We discuss the relationships between mathematics anxiety and mathematics performance. We describe ways in which mathematics anxiety is measured, both by questionnaires, and by physiological measures. We discuss some possible factors in mathematics anxiety, including genetics, gender, age, and culture. Finally, we describe some research on treatment. We conclude with a brief discussion of what still needs to be learned.

Is Math Anxiety Always Bad for Math Learning? The Role of Math Motivation

The linear relations between math anxiety and math cognition have been frequently studied. However, the relations between anxiety and performance on complex cognitive tasks have been repeatedly demonstrated to follow a curvilinear fashion. In the current studies, we aimed to address the lack of attention given to the possibility of such complex interplay between emotion and cognition in the math-learning literature by exploring the relations among math anxiety, math motivation, and math cognition. In two samples-young adolescent twins and adult college students-results showed inverted-U relations between math anxiety and math performance in participants with high intrinsic math motivation and modest negative associations between math anxiety and math performance in participants with low intrinsic math motivation. However, this pattern was not observed in tasks assessing participants' nonsymbolic and symbolic number-estimation ability. These findings may help advance the understanding of mathematics-learning processes and provide important insights for treatment programs that target improving mathematics-learning experiences and mathematical skills.

The influence of math anxiety on symbolic and non-symbolic magnitude processing

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.