Disentangling the individual and contextual effects of math anxiety: A global perspective.

Math anxiety is a common affective disorder in students that is characterized by intrusive thoughts that disrupt critical cognitive resources required for math problem-solving. Consistent associations between math anxiety and math achievement have been observed across countries and age groups, placing math anxiety among other important correlates of math achievement, such as socioeconomic status and magnitude representation ability. However, studies examining math anxiety's relation to achievement have largely focused on the effect of students' own math anxiety (individual effect), while little is known regarding the effect of math anxiety in students' educational context (contextual effect). Using three international studies of achievement (n = 1,175,515), we estimated both the individual and contextual effects of math anxiety across the globe. Results suggest that while there are consistent individual effects in virtually all countries examined, the contextual effects are varied, with only approximately half of the countries exhibiting a contextual effect. Additionally, we reveal that teacher confidence in teaching math is associated with a reduction of the individual effect, and country's level of uncertainty avoidance is related to a lessening of the contextual effect. Finally, we uncovered multiple predictors of math anxiety; notably, student perception of teacher competence was negative related with math anxiety, and parental homework involvement was positively related with math anxiety. Taken together, these results suggest that there are significant between-country differences in how math anxiety may be related with math achievement and suggest that education and cultural contexts as important considerations in understanding math anxiety's effects on achievement.

The neural correlates of retrieval and procedural strategies in mental arithmetic: A functional neuroimaging meta-analysis.

Mental arithmetic is a complex skill of great importance for later academic and life success. Many neuroimaging studies and several meta-analyses have aimed to identify the neural correlates of mental arithmetic. Previous meta-analyses of arithmetic grouped all problem types into a single meta-analytic map, despite evidence suggesting that different types of arithmetic problems are solved using different strategies. We used activation likelihood estimation (ALE) to conduct quantitative meta-analyses of mental arithmetic neuroimaging (n = 31) studies, and subsequently grouped contrasts from the 31 studies into problems that are typically solved using retrieval strategies (retrieval problems) (n = 18) and problems that are typically solved using procedural strategies (procedural problems) (n = 19). Foci were compiled to generate probabilistic maps of activation for mental arithmetic (i.e., all problem types), retrieval problems, and procedural problems. Conjunction and contrast analyses were conducted to examine overlapping and distinct activation for retrieval and procedural problems. The conjunction analysis revealed overlapping activation for retrieval and procedural problems in the bilateral inferior parietal lobules, regions typically associated with magnitude processing. Contrast analyses revealed specific activation in the left angular gyrus for retrieval problems and specific activation in the inferior frontal gyrus and cingulate gyrus for procedural problems. These findings indicate that the neural bases of arithmetic systematically differs according to problem type, providing new insights into the dynamic and task-dependent neural underpinnings of the calculating brain.

Hands-On: Investigating the role of physical manipulatives in spatial training.

Studies show that spatial interventions lead to improvements in mathematics. However, outcomes vary based on whether physical manipulatives (embodied action) are used during training. This study compares the effects of embodied and non-embodied spatial interventions on spatial and mathematics outcomes. The study has a randomized, controlled, pre-post, follow-up, training design (N = 182; mean age 8 years; 49% female; 83.5% White). We show that both embodied and non-embodied spatial training approaches improve spatial skills compared to control. However, we conclude that embodied spatial training using physical manipulatives leads to larger, more consistent gains in mathematics and greater depth of spatial processing than non-embodied training. These findings highlight the potential of spatial activities, particularly those that use physical materials, for improving children's mathematics skills.

Relations between numerical, spatial, and executive function skills and mathematics achievement: A latent-variable approach.

Current evidence suggests that numerical, spatial, and executive function (EF) skills each play critical and independent roles in the learning and performance of mathematics. However, these conclusions are largely based on isolated bodies of research and without measurement at the latent variable level. Thus, questions remain regarding the latent structure and potentially shared and unique relations between numerical, spatial, EF, and mathematics abilities. The purpose of the current study was to (i) confirm the latent structure of the hypothesized constructs of numerical, spatial, and EF skills and mathematics achievement, (ii) measure their unique and shared relations with one another, and (iii) test a set of novel hypotheses aimed to more closely reveal the underlying nature of the oft reported space-math association. Our analytical approach involved latent-variable analyses (structural equation modeling) with a sample of 4- to 11-year-old children (N = 316, Mage = 6.68 years). Results of a confirmatory factor analysis demonstrated that numerical, spatial, EF, and mathematics skills are highly related, yet separable, constructs. Follow-up structural analyses revealed that numerical, spatial, and EF latent variables explained 84% of children's mathematics achievement scores, controlling for age. However, only numerical and spatial performance were unique predictors of mathematics achievement. The observed patterns of relations and developmental trajectories remained stable across age and grade (preschool - 4th grade). Follow-up mediation analyses revealed that numerical skills, but not EF skills, partially mediated the relation between spatial skills and mathematics achievement. Overall, our results point to spatial visualization as a unique and robust predictor of children's mathematics achievement.

Cognitive Foundations of Early Mathematics: Investigating the Unique Contributions of Numerical, Executive Function, and Spatial Skills.

There is an emerging consensus that numerical, executive function (EF), and spatial skills are foundational to children's mathematical learning and development. Moreover, each skill has been theorized to relate to mathematics for different reasons. Thus, it is possible that each cognitive construct is related to mathematics through distinct pathways. The present study tests this hypothesis. One-hundred and eighty 4- to 9-year-olds (Mage = 6.21) completed a battery of numerical, EF, spatial, and mathematics measures. Factor analyses revealed strong, but separable, relations between children's numerical, EF, and spatial skills. Moreover, the three-factor model (i.e., modelling numerical, EF, and spatial skills as separate latent variables) fit the data better than a general intelligence (g-factor) model. While EF skills were the only unique predictor of number line performance, spatial skills were the only unique predictor of arithmetic (addition) performance. Additionally, spatial skills were related to the use of more advanced addition strategies (e.g., composition/decomposition and retrieval), which in turn were related to children's overall arithmetic performance. That is, children's strategy use fully mediated the relation between spatial skills and arithmetic performance. Taken together, these findings provide new insights into the cognitive foundations of early mathematics, with implications for assessment and instruction moving forward.

Number symbols are processed more automatically than nonsymbolic numerical magnitudes: Findings from a Symbolic-Nonsymbolic Stroop task.

Are number symbols (e.g., 3) and numerically equivalent quantities (e.g., •••) processed similarly or distinctly? If symbols and quantities are processed similarly then processing one format should activate the processing of the other. To experimentally probe this prediction, we assessed the processing of symbols and quantities using a Stroop-like paradigm. Participants (NStudy1 = 80, NStudy2 = 63) compared adjacent arrays of symbols (e.g., 4444 vs 333) and were instructed to indicate the side containing either the greater quantity of symbols (nonsymbolic task) or the numerically larger symbol (symbolic task). The tasks included congruent trials, where the greater symbol and quantity appeared on the same side (e.g. 333 vs. 4444), incongruent trials, where the greater symbol and quantity appeared on opposite sides (e.g. 3333 vs. 444), and neutral trials, where the irrelevant dimension was the same across both sides (e.g. 3333 vs. 333 for nonsymbolic; 333 vs. 444 for symbolic). The numerical distance between stimuli was systematically varied, and quantities in the subitizing and counting range were analyzed together and independently. Participants were more efficient comparing symbols and ignoring quantities, than comparing quantities and ignoring symbols. Similarly, while both symbols and quantities influenced each other as the irrelevant dimension, symbols influenced the processing of quantities more than quantities influenced the processing of symbols, especially for quantities in the counting rage. Additionally, symbols were less influenced by numerical distance than quantities, when acting as the relevant and irrelevant dimension. These findings suggest that symbols are processed differently and more automatically than quantities.

Effects of spatial training on mathematics performance: A meta-analysis.

Prior research has revealed robust and consistent relations between spatial and mathematical skills. Yet, establishing a causal relation has been met with mixed effects. To better understand whether, to what extent, and under what conditions mathematics performance can be improved through spatial training, we conducted a systematic meta-analysis of the extant literature. Our analysis included 29 studies that used controlled pre-post study designs to test the effects of spatial training on mathematics (N = 3,765; k = 89). The average effect size (Hedges's g) of training relative to control conditions was .28 (SE = .07). Critically, there was also evidence that spatial training improved individuals' spatial thinking (g = .49, SE = .09). Follow-up analyses revealed that age, use of concrete manipulatives, and type of transfer ("near" vs. "far") moderated the effects of spatial training on mathematics. As the age of participants increased from 3 to 20 years, the effects of spatial training also increased in size. Spatial training paradigms that used concrete materials (e.g., manipulatives) were more effective than those that did not (e.g., computerized training). Larger transfer effects were observed for mathematics outcomes more closely aligned to the spatial training delivered compared to outcomes more distally related. None of the other variables examined (training dosage, spatial gains, posttest timing, type of control group, experimental design, publication status) moderated the effects. Additionally, analyses of publication bias and selective outcome reporting were nonsignificant. Overall, our results support prior research and theoretical claims that spatial training is an effective means for enhancing mathematical understanding and performance. However, our meta-analysis also highlights a poor understanding of the mechanisms that support transfer. To fully realize the potential benefits of spatial training on mathematics achievement, more theoretically guided studies are needed. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Symbols Are Special: An fMRI Adaptation Study of Symbolic, Nonsymbolic, and Non-Numerical Magnitude Processing in the Human Brain.

How are different formats of magnitudes represented in the human brain? We used functional magnetic resonance imaging adaptation to isolate representations of symbols, quantities, and physical size in 45 adults. Results indicate that the neural correlates supporting the passive processing of number symbols are largely dissociable from those supporting quantities and physical size, anatomically and representationally. Anatomically, passive processing of quantities and size correlate with activation in the right intraparietal sulcus, whereas symbolic number processing, compared with quantity processing, correlates with activation in the left inferior parietal lobule. Representationally, neural patterns of activation supporting symbols are dissimilar from neural activation patterns supporting quantity and size in the bilateral parietal lobes. These findings challenge the longstanding notion that the culturally acquired ability to conceptualize symbolic numbers is represented using entirely the same brain systems that support the evolutionarily ancient system used to process quantities. Moreover, these data reveal that regions that support numerical magnitude processing are also important for the processing of non-numerical magnitudes. This discovery compels future investigations of the neural consequences of acquiring knowledge of symbolic numbers.

Integrating numerical cognition research and mathematics education to strengthen the teaching and learning of early number.

BACKGROUND: Research into numerical cognition has contributed to a large body of knowledge on how children learn and perform mathematics. This knowledge has the potential to inform mathematics education. Unfortunately, numerical cognition research and mathematics education remain disconnected from one another, lacking the proper infrastructure to allow for productive and meaningful exchange between disciplines. The present study was designed to address this gap. AIM: This study reports on the design, implementation, and effects of a 16-week (25-hour) mathematics Professional Development (PD) model for Kindergarten to Grade 3 educators and their students. A central goal of the PD was to better integrate numerical cognition research and mathematics education. SAMPLE: A total of 45 K-3 educators and 180 of their students participated. METHODS: To test the reproducibility and replicability of the model, the study was carried out across two different sites, over a two-year period, and involved a combination of two different study designs: a quasi-experimental pre-post-research design and a within-group crossover intervention design. RESULT: The results of the first implementation (Year 1), indicated that compared to a control group, both teachers and students benefited from the intervention. Teachers demonstrated gains on both a self-report measure and a test of numerical cognition knowledge, while students demonstrated gains in number line estimation, arithmetic, and numeration. In Year 2, teachers in the intervention group demonstrated greater improvements than the control group on the self-report measure, but not the test of numerical cognition knowledge. At the student level, there was some evidence of gains in numeration. CONCLUSION: The current PD model is a promising approach to better integrate research and practice. However, more research is needed to determine in which school contexts the model is most effective.

What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior.

There is an emerging consensus that spatial thinking plays a fundamental role in how people conceive, express, and perform mathematics. However, the underlying nature of this relationship remains elusive. Questions remain as to how, why, and under what conditions spatial skills and mathematics are linked. This review paper addresses this gap. Through a review and synthesis of research in psychology, neuroscience, and education, we examine plausible mechanistic accounts for the oft-reported close, and potentially causal, relations between spatial and mathematical thought. More specifically, this review targets candidate mechanisms that link spatial visualization skills and basic numerical competencies. The four explanatory accounts we describe and critique include the: (1) Spatial representation of numbers account, (2) shared neural processing account, (3) spatial modelling account, and (4) working memory account. We propose that these mechanisms do not operate in isolation from one another, but in concert with one another to give rise to spatial-numerical associations. Moving from the theoretical to the practical, we end our review by considering the extent to which spatial visualization abilities are malleable and transferrable to numerical reasoning. Ultimately, this paper aims to provide a more coherent and mechanistic account of spatial-numerical relations in the hope that this information may (1) afford new insights into the uniquely human ability to learn, perform, and invent abstract mathematics, and (2) on a more practical level, prove useful in the assessment and design of effective mathematics curricula and intervention moving forward.

Why Educational Neuroscience Needs Educational and School Psychology to Effectively Translate Neuroscience to Educational Practice.

The emerging discipline of educational neuroscience stands at a crossroads between those who see great promise in integrating neuroscience and education and those who see the disciplinary divide as insurmountable. However, such tension is at least partly due to the hitherto predominance of philosophy and theory over the establishment of concrete mechanisms and agents of change. If educational neuroscience is to move forward and emerge as a distinct discipline in its own right, the traditional boundaries and methods must be bridged, and an infrastructure must be in place that allows for collaborative and productive exchange. In the present paper, we argue that school psychologists have the potential to fulfill this need and represent important agents of change in establishing better connections between research and practice. More specifically, we use the National Association of School Psychologists (NASP) (2020) Domains of Practice to highlight several areas where school psychology can actively support forging connections between neuroscience and educational practice. School psychologists represent untapped potential in their knowledge, skillset, and placement to serve a vital role in building the bridge between neuroscience and education.

Neural underpinnings of numerical and spatial cognition: An fMRI meta-analysis of brain regions associated with symbolic number, arithmetic, and mental rotation.

Where and under what conditions do spatial and numerical skills converge and diverge in the brain? To address this question, we conducted a meta-analysis of brain regions associated with basic symbolic number processing, arithmetic, and mental rotation. We used Activation Likelihood Estimation (ALE) to construct quantitative meta-analytic maps synthesizing results from 83 neuroimaging papers (24-31 studies/cognitive process). All three cognitive processes were found to activate bilateral parietal regions in and around the intraparietal sulcus (IPS); a finding consistent with shared processing accounts. Numerical and arithmetic processing were associated with overlap in the left IPS, whereas mental rotation and arithmetic both showed activity in the middle frontal gyri. These patterns suggest regions of cortex potentially more specialized for symbolic number representation and domain-general mental manipulation, respectively. Additionally, arithmetic was associated with unique activity throughout the fronto-parietal network and mental rotation was associated with unique activity in the right superior parietal lobe. Overall, these results provide new insights into the intersection of numerical and spatial thought in the human brain.

What explains sex differences in math anxiety? A closer look at the role of spatial processing.

A large body of research has documented that females experience more math anxiety than males. Researchers have identified many factors that might explain the relation between sex and math anxiety. In the current study, we present a novel theoretical framework that highlights the importance of examining multiple aspects of processing across different cognitive domains. We use this framework to address the question of what best explains sex differences in math anxiety. One hundred and seventy-five undergraduate students completed a battery of cognitive tasks and affect questionnaires intended to measure actual math ability, perceived math ability, math anxiety, actual spatial ability, perceived spatial ability, and anxiety about situations requiring spatial mental manipulation (spatial anxiety). Results revealed that processes within the spatial domain but not in the mathematical domain mediated the relation between sex and math anxiety, controlling for general anxiety and cognitive ability. Moreover, within the spatial domain, spatial anxiety was the strongest mediator between sex and math anxiety, over actual and perceived spatial ability. Our findings point to spatial anxiety as a key contributor to the commonly reported sex differences in math anxiety. We conclude by raising the possibility that sex differences in math anxiety, may be rooted in sex-related differences in anxiety about or avoidance of spatial strategies in solving mathematical tasks.