It is a "small world": Relations between performance on five spatial tasks and five mathematical tasks in undergraduate students.

One of the most robust relations in cognition is that between spatial and mathematical reasoning. One important question is whether this relation is domain general or if specific relations exist between performance on different types of spatial tasks and performance on different types of mathematical tasks. In this study, we explore unique relations between performance on five spatial tasks and five mathematical tasks. An exploratory factor analysis conducted on Data Set 1 (N = 391) yielded a two-factor model, one spatial factor and one mathematical factor with significant cross-domain factor loadings. The general two-factor model structure was replicated in a confirmatory factor analysis conducted in a separate data set (N = 364) but the strength of the factor loadings differed by task. Multidimensional scaling and network-based analyses conducted on the combined data sets reveal one spatial cluster, with a central node and one more tightly interconnected mathematical cluster. Both clusters were interconnected via the math task assessing geometry and spatial sense. The unique links identified with the network-based analysis are representative of a "small-world network." These results have theoretical implications for our understanding of the spatial-mathematical relation and practical implications for our understanding of the limitations of transfer between spatial training paradigms and mathematical tasks. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Examining the Interplay between the Cognitive and Emotional Aspects of Gender Differences in Spatial Processing.

Women reliably perform worse than men on measures of spatial ability, particularly those involving mental rotation. At the same time, females also report higher levels of spatial anxiety than males. What remains unclear, however, is whether and in what ways gender differences in these cognitive and affective aspects of spatial processing may be interrelated. Here, we tested for robust gender differences across six different datasets in spatial ability and spatial anxiety (N = 1257, 830 females). Further, we tested for bidirectional mediation effects. We identified indirect relations between gender and spatial skills through spatial anxiety, as well as between gender and spatial anxiety through spatial skills. In the gender → spatial anxiety → spatial ability direction, spatial anxiety explained an average of 22.4% of gender differences in spatial ability. In the gender → spatial ability → spatial anxiety direction, spatial ability explained an average of 25.9% of gender differences in spatial anxiety. Broadly, these results support a strong relation between cognitive and affective factors when explaining gender differences in the spatial domain. However, the nature of this relation may be more complex than has been assumed in previous literature. On a practical level, the results of this study caution the development of interventions to address gender differences in spatial processing which focus primarily on either spatial anxiety or spatial ability until such further research can be conducted. Our results also speak to the need for future longitudinal work to determine the precise mechanisms linking cognitive and affective factors in spatial processing.

Investigating links between creativity anxiety, creative performance, and state-level anxiety and effort during creative thinking.

Identifying ways to enable people to reach their creative potential is a core goal of creativity research with implications for education and professional attainment. Recently, we identified a potential barrier to creative achievement: creativity anxiety (i.e., anxiety specific to creative thinking). Initial work found that creativity anxiety is associated with fewer real-world creative achievements. However, the more proximal impacts of creativity anxiety remain unexplored. In particular, understanding how to overcome creativity anxiety requires understanding how creativity anxiety may or may not impact creative cognitive performance, and how it may relate to state-level anxiety and effort while completing creative tasks. The present study sought to address this gap by measuring creativity anxiety alongside several measures of creative performance, while concurrently surveying state-level anxiety and effort. Results indicated that creativity anxiety was, indeed, predictive of poor creative performance, but only on some of the tasks included. We also found that creativity anxiety predicted both state anxiety and effort during creative performance. Interestingly, state anxiety and effort did not explain the associations between creativity anxiety and creative performance. Together, this work suggests that creativity anxiety can often be overcome in the performance of creative tasks, but likewise points to increased state anxiety and effort as factors that may make creative performance and achievement fragile in more demanding real-world contexts.

Connectome-based predictive modeling indicates dissociable neurocognitive mechanisms for numerical order and magnitude processing in children.

Symbolic numbers contain information about their relative numerical cardinal magnitude (e.g., 2 < 3) and ordinal placement in the count-list (e.g., 1, 2, 3). Previous research has primarily investigated magnitude discrimination skills and their predictive capacity for math achievement, whereas numerical ordering has been less systematically explored. At approximately 10-12 years of age, numerical order processing skills have been observed to surpass cardinal magnitude discrimination skills as the key predictor of arithmetic ability. The neurocognitive mechanisms underlying this shift remain unclear. To this end, we investigated children's (ages 10-12) neural correlates of numerical order and magnitude discrimination, as well as task-based functional connectomes and their predictive capacity for numeracy-related behavioral outcomes. Results indicated that number discrimination uniquely relied on bilateral temporoparietal correlates, whereas order processing recruited the bilateral IPS, cerebellum, and left premotor cortex. Connectome-based models were not cross-predictive for numerical order and magnitude, suggesting two dissociable mechanisms jointly supported by visuospatial working memory. Neural correlates of learning and memory were predictive of age and arithmetic ability, only for the ordinal task-connectome, indicating that the numerical order mechanism may undergo a developmental shift, dissociating it from mechanisms supporting cardinal number processing.

Does anxiety explain why math-anxious people underperform in math?

Math-anxious people consistently underperform in math. The most widely accepted explanation for why this underperformance occurs is that math-anxious people experience heightened anxiety when faced with math, and this in-the-moment anxiety interferes with performance. Surprisingly, this explanation has not been tested directly. Here, using both self-report and physiological indices of anxiety, we directly test how much in-the-moment anxiety explains math-anxious underperformance. Results indicate that in-the-moment anxiety indeed explains why math-anxious people underperform-but only partially, suggesting a need to seriously consider alternative mechanisms. Results also showed that while some highly math-anxious individuals-those with high levels of heart rate variability-experienced less in-the-moment anxiety, they nevertheless performed no better at math. For these individuals, math-anxious underperformance must occur for reasons unrelated to in-the-moment anxiety. More broadly, our findings point to substantial individual heterogeneity in the mechanisms underlying math-anxious underperformance. Accounting for this mechanistic heterogeneity may prove vital for optimally boosting math performance in math-anxious individuals.

Evidence for avoidance tendencies linked to anxiety about specific types of thinking.

Anxieties that are specific to a particular kind of thinking have been demonstrated for a variety of cognitive domains. One hypothesized consequence of these anxieties is reduced interest in pursuing activities and, consequentially, careers that involve the type of thinking in question in an effort to avoid engaging in that type of thinking. There is little research addressing this avoidance hypothesis, possibly because it is difficult to categorize pursuits as objectively "creative" or "spatial". Here, we measured the perceptions that participants, themselves, hold about how much pursuits (careers and activities) involve different types of thinking. We developed a novel framework for calculating "affinity coefficients", within-person associations between perceived cognitive involvement and interest across several pursuits. Having a negative creative affinity coefficient, for instance, means being less interested in pursuits the more they are perceived as involving creative thinking. Results across three separate cognitive domains (creativity, mathematics, and spatial reasoning) reliably showed that higher anxiety in a domain uniquely predicted a lower affinity coefficient in that domain, providing consistent evidence of avoidance tendencies linked to cognition-specific anxieties. These findings suggest that feeling anxious about particular types of thinking may play a significant role in shaping our interests, both big and small.

Transfer from spatial education to verbal reasoning and prediction of transfer from learning-related neural change.

Current debate surrounds the promise of neuroscience for education, including whether learning-related neural changes can predict learning transfer better than traditional performance-based learning assessments. Longstanding debate in philosophy and psychology concerns the proposition that spatial processes underlie seemingly nonspatial/verbal reasoning (mental model theory). If so, education that fosters spatial cognition might improve verbal reasoning. Here, in a quasi-experimental design in real-world STEM classrooms, a curriculum devised to foster spatial cognition yielded transfer to improved verbal reasoning. Further indicating a spatial basis for verbal transfer, students' spatial cognition gains predicted and mediated their reasoning improvement. Longitudinal fMRI detected learning-related changes in neural activity, connectivity, and representational similarity in spatial cognition-implicated regions. Neural changes predicted and mediated learning transfer. Ensemble modeling demonstrated better prediction of transfer from neural change than from traditional measures (tests and grades). Results support in-school "spatial education" and suggest that neural change can inform future development of transferable curricula.

Testing the specificity of links between anxiety and performance within mathematics and spatial reasoning.

Anxiety within the domains of math and spatial reasoning have consistently been shown to predict performance within those domains. However, little work has focused on how specific these associations are. Across two studies, we systematically tested the degree of specificity in relations between anxiety and performance within math and spatial reasoning. Results consistently showed that anxiety within a cognitive domain predicted performance in that domain even when controlling for other forms of anxiety, providing evidence that cognition-specific anxieties are valuable for understanding cognition-specific performance. We also found that general trait anxiety did not explain a significant portion the anxiety-performance link in either math or spatial reasoning, suggesting that these anxiety-performance associations are not due to the propensity to feel anxious generally. Interestingly, while spatial anxiety did not explain any of the anxiety-performance association in math, math anxiety did explain a significant portion of the anxiety-performance link in spatial reasoning. These results suggest that, while links between anxiety and performance cannot be reduced to a single underlying general anxiety construct, there may nevertheless be overlap between domain anxieties. We end by calling for a more detailed examination of the unique and shared mechanisms linking anxiety and performance across disparate cognitive domains.

Extending ideas of numerical order beyond the count-list from kindergarten to first grade.

Ordinal processing plays a fundamental role in both the representation and manipulation of symbolic numbers. As such, it is important to understand how children come to develop a sense of ordinality in the first place. The current study examines the role of the count-list in the development of ordinal knowledge through the investigation of two research questions: (1) Do K-1 children struggle to extend the notion of numerical order beyond the count-list, and if so (2) does this extension develop incrementally or manifest as a qualitative re-organization of how children recognize the ordinality of numerical sequences. Overall, we observed that although young children reliably identified adjacent ordered sequences (i.e., those that match the count-list; '2-3-4') as being in the correct ascending order, they performed significantly below chance on non-adjacent ordered trials (i.e., those that do not match the count-list but are in the correct order; '2-4-6') from the beginning of kindergarten to the end of first grade. Further, both qualitative and quantitative analyses supported the conclusion that the ability to extend notions of ordinality beyond the count-list emerged as a conceptual shift in ordinal understanding rather than through incremental improvements. These findings are the first to suggest that the ability to extend notions of ordinality beyond the count-list to include non-adjacent numbers is non-trivial and reflects a significant developmental hurdle that most children must overcome in order to develop a mature sense of ordinality.

From Counting to Retrieving: Neural Networks Underlying Alphabet Arithmetic Learning.

This fMRI study aimed at unraveling the neural basis of learning alphabet arithmetic facts, as a proxy of the transition from slow and effortful procedural counting-based processing to fast and effortless processing as it occurs in learning addition arithmetic facts. Neural changes were tracked while participants solved alphabet arithmetic problems in a verification task (e.g., F + 4 = J). Problems were repeated across four learning blocks. Two neural networks with opposed learning-related changes were identified. Activity in a network consisting of basal ganglia and parieto-frontal areas decreased with learning, which is in line with a reduction of the involvement of procedure-based processing. Conversely, activity in a network involving the left angular gyrus and, to a lesser extent, the hippocampus gradually increases with learning, evidencing the gradual involvement of retrieval-based processing. Connectivity analyses gave insight in the functional relationship between the two networks. Despite the opposing learning-related trajectories, it was found that both networks become more integrated. Taking alphabet arithmetic as a proxy for learning arithmetic, the present results have implications for current theories of learning arithmetic facts and can give direction to future developments.

First-year students' math anxiety predicts STEM avoidance and underperformance throughout university, independently of math ability.

Math anxiety is widely considered a potential barrier to success in STEM. Current thinking holds that math anxiety is directly linked to avoidance of and underperformance in STEM domains. However, past evidence supporting these claims is limited in important ways. Perhaps most crucially, it is possible that math anxiety predicts STEM outcomes merely as a proxy for poor math skills. Here, we tested the link between math anxiety and subsequent STEM outcomes by measuring math anxiety, math ability, and several covariates in 183 first-semester university students. We then tracked students' STEM avoidance and achievement through four years at university via official academic transcripts. Results showed that math anxiety predicted both a reduction in how many STEM courses students took and, separately (i.e., controlling for one another), lower STEM grades. Crucially, these associations held after controlling for math ability (and other covariates). That math anxiety predicts math-related academic achievement independently of Math Ability suggests that, contrary to current thinking, math anxiety's effects on academic performance likely operate via mechanisms other than negatively affecting math ability. Beyond this, we show evidence that math anxiety can account for associations between math ability and STEM outcomes, suggesting that past links between math ability and real-world outcomes may, in fact, be at least partially explainable by attitudes toward math. These findings provide clear impetus for developing and testing interventions that target math anxiety specifically and suggest that focusing on math ability without additional attention to math anxiety may fail to optimally boost STEM outcomes.

Rules of order: Evidence for a novel influence on ordinal processing of numbers.

Research on how people process numerical order carries implications for our theoretical understanding of what a number means and our practical understanding of the foundation upon which more sophisticated mathematics is built. Current thinking posits that ordinal processing of numbers is linked to repeated practice with the integer count list, but the mechanisms underlying this link remain unclear. For instance, in standard ordinal verification paradigms, participants more rapidly and accurately verify that count-list sequences (e.g., 3-4-5) are "in-order" than non-count-list sequences (e.g., 2-4-6), although it remains unclear whether this is due to strong count-list processing or poor non-count-list processing. If the count list primarily facilitates ordinal processing of count-list sequences, then forcing participants to classify sequences like 3-4-5 as "not-in-order" should adversely affect ordinal verification performance. We found that it does, but only moderately in single-digit sequences (d = -.26), and not at all in the case of double-digit sequences (d = -.02). Alternatively, the count list may influence ordinal processing in an exclusionary manner, creating a tendency to view anything that does not match the count-list as not-in-order. If so, then allowing participants to classify ordered (but non-count-list) sequences like 2-4-6 as not-in-order should improve ordinal verification performance. It did, with strong effects for both single-digit (d = .74) and double-digit sequences (d = 1.04). Furthermore, we demonstrated that the reverse distance effect found in standard ordinal verification paradigms is driven primarily by poor non-count-list processing. Taken together, our results advance our understanding of the mechanisms by which the count list shapes ordinal processing, even in highly numerate adults. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Connectome-Based Predictive Modeling of Creativity Anxiety.

While a recent upsurge in the application of neuroimaging methods to creative cognition has yielded encouraging progress toward understanding the neural underpinnings of creativity, the neural basis of barriers to creativity are as yet unexplored. Here, we report the first investigation into the neural correlates of one such recently identified barrier to creativity: anxiety specific to creative thinking, or creativity anxiety (Daker et al., 2019). We employed a machine-learning technique for exploring relations between functional connectivity and behavior (connectome-based predictive modeling; CPM) to investigate the functional connections underlying creativity anxiety. Using whole-brain resting-state functional connectivity data, we identified a network of connections or "edges" that predicted individual differences in creativity anxiety, largely comprising connections within and between regions of the executive and default networks and the limbic system. We then found that the edges related to creativity anxiety identified in one sample generalize to predict creativity anxiety in an independent sample. We additionally found evidence that the network of edges related to creativity anxiety were largely distinct from those found in previous work to be related to divergent creative ability (Beaty et al., 2018). In addition to being the first work on the neural correlates of creativity anxiety, this research also included the development of a new Chinese-language version of the Creativity Anxiety Scale, and demonstrated that key behavioral findings from the initial work on creativity anxiety are replicable across cultures and languages.

The relation between subitizable symbolic and non-symbolic number processing over the kindergarten school year.

A long-standing debate in the field of numerical cognition concerns the degree to which symbolic and non-symbolic processing are related over the course of development. Of particular interest is the possibility that this link depends on the range of quantities in question. Behavioral and neuroimaging research with adults suggests that symbolic and non-symbolic quantities may be processed more similarly within, relative to outside of, the subitizing range. However, it remains unclear whether this unique link exists in young children at the outset of formal education. Further, no study has yet taken numerical size into account when investigating the longitudinal influence of these skills. To address these questions, we investigated the relation between symbolic and non-symbolic processing inside versus outside the subitizing range, both cross-sectionally and longitudinally, in 540 kindergarteners. Cross-sectionally, we found a consistently stronger relation between symbolic and non-symbolic number processing within versus outside the subitizing range at both the beginning and end of kindergarten. We also show evidence for a bidirectional relation over the course of kindergarten between formats within the subitizing range, and a unidirectional relation (symbolic â†’ non-symbolic) for quantities outside of the subitizing range. These findings extend current theories on symbolic and non-symbolic magnitude development by suggesting that non-symbolic processing may in fact play a role in the development of symbolic number abilities, but that this influence may be limited to quantities within the subitizing range.

Creativity anxiety: Evidence for anxiety that is specific to creative thinking, from STEM to the arts.

Creative thinking drives progress not only in the arts but also, and perhaps especially, in the fields of science, technology, engineering, and mathematics, and it is expected to become even more valuable than technical skill as artificial intelligence outpaces human cognition. Fostering creative thinkers has become a primary focus of educators. Educationally relevant anxieties, like math anxiety, have been shown to substantially impact specific forms of achievement and engagement, both in school and in career pursuits. Identifying these anxieties has led to promising interventions to enable affected individuals to reach their potential. Somewhat surprisingly, however, the possibility of anxiety specific to creative thinking is, to our knowledge, unexplored. In this article, across multiple samples, we tested the viability of creativity anxiety as a construct. We first created a new measure, the Creativity Anxiety Scale (CAS), demonstrating validity, internal reliability, and specificity. Applying the CAS revealed that creativity-specific anxiety predicted individual differences in creative achievement and attitudes toward creativity over and above effects of general anxiety. Moreover, across diverse content domains, from science to arts, anxiety was greater for situations that required creativity than similar situations that did not. Notably, this effect was especially pronounced in women. These findings suggest that creativity anxiety may have wide-reaching impacts and distinguish creativity anxiety from anxiety about noncreative aspects of performance. Establishing creativity anxiety as a novel construct, and the CAS as a valid measurement instrument, opens a new avenue of research that promises to deepen basic understanding of creative cognition and inform development of interventions to enable greater achievement of creative potential. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Distinguishing between cognitive explanations of the problem size effect in mental arithmetic via representational similarity analysis of fMRI data.

Not all researchers interested in human behavior remain convinced that modern neuroimaging techniques have much to contribute to distinguishing between competing cognitive models for explaining human behavior, especially if one removes reverse inference from the table. Here, we took up this challenge in an attempt to distinguish between two competing accounts of the problem size effect (PSE), a robust finding in investigations of mathematical cognition. The PSE occurs when people solve arithmetic problems and indicates that numerically large problems are solved more slowly and erroneously than small problems. Neurocognitive explanations for the PSE can be categorized into representation-based and process-based views. Behavioral and traditional univariate neural measures have struggled to distinguish between these accounts. By contrast, a representational similarity analysis (RSA) approach with fMRI data provides competing hypotheses that can distinguish between accounts without recourse to reverse inference. To that end, our RSA (but not univariate) results provided clear evidence in favor of the representation-based over the process-based account of the PSE in multiplication; for addition, the results were less clear. Post-hoc similarity analysis distinguished still further between competing representation-based theoretical accounts. Namely, data favored the notion that individual multiplication problems are stored as individual memory traces sensitive to input frequency over a strictly magnitude-based account of memory encoding. Together, these results provide an example of how human neuroimaging evidence can directly inform cognitive-level explanations of a common behavioral phenomenon, the problem size effect. More broadly, these data may expand our understanding of calculation and memory systems in general.

More Similar Than Different: Gender Differences in Children's Basic Numerical Skills Are the Exception Not the Rule.

This study investigates gender differences in basic numerical skills that are predictive of math achievement. Previous research in this area is inconsistent and has relied upon traditional hypothesis testing, which does not allow for assertive conclusions to be made regarding nonsignificant findings. This study is the first to compare male and female performance (N = 1,391; ages 6-13) on many basic numerical tasks using both Bayesian and frequentist analyses. The results provide strong evidence of gender similarities on the majority of basic numerical tasks measured, suggesting that a male advantage in foundational numerical skills is the exception rather than the rule.

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.

Disentangling Neural Sources of Problem Size and Interference Effects in Multiplication.

Multiplication is thought to be primarily solved via direct retrieval from memory. Two of the main factors known to influence the retrieval of multiplication facts are problem size and interference. Because these factors are often intertwined, we sought to investigate the unique influences of problem size and interference on both performance and neural responses during multiplication fact retrieval in healthy adults. Behavioral results showed that both problem size and interference explained separate unique portions of RT variance, but with significantly stronger contribution from problem size, which contrasts with previous work in children. Whole-brain fMRI results relying on a paradigm that isolated multiplication fact retrieval from response selection showed highly overlapping brain areas parametrically modulated by both problem size and interference in a large network of frontal, parietal, and subcortical brain areas. Subsequent analysis within these regions revealed problem size to be the stronger and more consistent "unique" modulating factor in overlapping regions as well as those that appeared to respond only to problem size or interference at the whole-brain level, thus underscoring the need to look beyond anatomical overlap using arbitrary thresholds. Additional unique contributions of interference (beyond problem size) were identified in right angular gyrus and subcortical regions associated with procedural processing. Together, our results suggest that problem size, relative to interference, tends to be the more dominant factor in driving behavioral and neural responses during multiplication fact retrieval in adults. Nevertheless, unique contributions of both factors demonstrate the importance of considering the overlapping and unique contributions of each in explaining the cognitive and neural bases of mental multiplication.

Numerical and Non-numerical Predictors of First Graders' Number-Line Estimation Ability.

Children's ability to map numbers into a spatial context has been shown to be a powerful predictor of math performance. Here, we investigate how three types of cognitive abilities - approximate number processing ability, symbolic number processing ability, and non-numerical cognitive abilities - predict 0-100 number-line estimation performance in first graders. While each type of measure predicts number-line performance when considered individually, when considered together, only symbolic number comparison and non-verbal reasoning predicted unique variance in number-line estimation. Moreover, the relation between symbolic number comparison and number-line ability was stronger for male students than for female students, suggesting potential gender differences in the way boys and girls accomplish mapping numbers into space. These results suggest that number-line estimation ability is largely reflective of the precision with which symbolic magnitudes are represented (at least among boys). Our findings therefore suggest that promoting children's understanding of symbolic, rather than non-symbolic, numerical magnitudes may help children learn better from number-lines in the classroom.