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.

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.

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.

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.

Characterizing the neural coding of symbolic quantities.

How the brain encodes abstract numerical symbols is a fundamental question in philosophy and cognitive neuroscience alike. Here we probe the nature of symbolic number representation in the brain by characterizing the neural similarity space for symbolic quantities in regions sensitive to their semantic content. In parietal and occipital regions, the similarity space of number symbols was positively predicted by the lexical frequency of numerals in parietal and occipital areas, and was unrelated to numerical ratio. These results are more consistent with a categorical, frequency-based account of symbolic quantity encoding. In contrast, the similarity space of analog quantities was positively predicted by ratio in prefrontal, parietal and occipital regions. We thus provide an explanation for why previous work has indicated that symbolic and analog quantities are distinct: number symbols operate primarily like discrete categories sensitive to input frequency, while analog quantities operate more like approximate perceptual magnitudes. In addition, we find substantial evidence for related patterns of activity across formats in prefrontal, parietal and occipital regions. Crucially however, between-format relations were not specific to individual quantities, indicating common processing as opposed to common representation. Moreover, evidence for between-format processing was strongest for quantities that could be represented as exact, discrete values in both systems (quantities in the 'subitizing' range: 1-4). In sum, converging evidence presented here indicates that symbolic quantities are coded in the brain as discrete categories sensitive to input frequency and largely independent of approximate, analog quantities.

Qualitatively different coding of symbolic and nonsymbolic numbers in the human brain.

Are symbolic and nonsymbolic numbers coded differently in the brain? Neuronal data indicate that overlap in numerical tuning curves is a hallmark of the approximate, analogue nature of nonsymbolic number representation. Consequently, patterns of fMRI activity should be more correlated when the representational overlap between two numbers is relatively high. In bilateral intraparietal sulci (IPS), for nonsymbolic numbers, the pattern of voxelwise correlations between pairs of numbers mirrored the amount of overlap in their tuning curves under the assumption of approximate, analogue coding. In contrast, symbolic numbers showed a flat field of modest correlations more consistent with discrete, categorical representation (no systematic overlap between numbers). Directly correlating activity patterns for a given number across formats (e.g., the numeral "6" with six dots) showed no evidence of shared symbolic and nonsymbolic number-specific representations. Overall (univariate) activity in bilateral IPS was well fit by the log of the number being processed for both nonsymbolic and symbolic numbers. IPS activity is thus sensitive to numerosity regardless of format; however, the nature in which symbolic and nonsymbolic numbers are encoded is fundamentally different.

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.

Ordinality and the nature of symbolic numbers.

The view that representations of symbolic and nonsymbolic numbers are closely tied to one another is widespread. However, the link between symbolic and nonsymbolic numbers is almost always inferred from cardinal processing tasks. In the current work, we show that considering ordinality instead points to striking differences between symbolic and nonsymbolic numbers. Human behavioral and neural data show that ordinal processing of symbolic numbers (Are three Indo-Arabic numerals in numerical order?) is distinct from symbolic cardinal processing (Which of two numerals represents the greater quantity?) and nonsymbolic number processing (ordinal and cardinal judgments of dot-arrays). Behaviorally, distance-effects were reversed when assessing ordinality in symbolic numbers, but canonical distance-effects were observed for cardinal judgments of symbolic numbers and all nonsymbolic judgments. At the neural level, symbolic number-ordering was the only numerical task that did not show number-specific activity (greater than control) in the intraparietal sulcus. Only activity in left premotor cortex was specifically associated with symbolic number-ordering. For nonsymbolic numbers, activation in cognitive-control areas during ordinal processing and a high degree of overlap between ordinal and cardinal processing networks indicate that nonsymbolic ordinality is assessed via iterative cardinality judgments. This contrasts with a striking lack of neural overlap between ordinal and cardinal judgments anywhere in the brain for symbolic numbers, suggesting that symbolic number processing varies substantially with computational context. Ordinal processing sheds light on key differences between symbolic and nonsymbolic number processing both behaviorally and in the brain. Ordinality may prove important for understanding the power of representing numbers symbolically.

Who is afraid of math? Two sources of genetic variance for mathematical anxiety.

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

Numerical predictors of arithmetic success in grades 1-6.

Math relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across grades 1-6. In grades 1-2, children's ability to judge the relative magnitude of numerical symbols was most predictive of early arithmetic skills. The unique contribution of children's ability to assess ordinality in numerical symbols steadily increased across grades, overtaking all other predictors by grade 6. We found no evidence that children's ability to judge the relative magnitude of approximate, nonsymbolic numbers was uniquely predictive of arithmetic ability at any grade. Overall, symbolic number processing was more predictive of arithmetic ability than nonsymbolic number processing, though the relative importance of symbolic number ability appears to shift from cardinal to ordinal processing.

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.

Mathematics anxiety: separating the math from the anxiety.

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

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.

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.

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.

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.

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.