Cognitive and Neural Correlates of Mathematical Giftedness in Adults and Children: A Review

Cognitive characteristics of children with high mathematics achievement before they start formal schooling

This 5-year longitudinal study examined whether high mathematics achievers in primary school had cognitive advantages before entering formal education. High mathematics achievement was defined as performing above Pc 90 in Grades 1 and 3. The predominantly White sample (Mage in preschool: 64 months) included 31 high achievers (12 girls) and 114 average achievers (63 girls). We measured children's early numerical abilities, complex mathematical abilities, and general cognitive abilities in preschool (2017). High mathematics achievers had advantages on most tasks in preschool (ds > 0.62). Number order, numeral recognition, and proportional reasoning were unique predictors of belonging to the high-achieving group in primary school. This study shows that the cognitive advantages of high mathematics achievement are already observed in preschool.

Cognitive processes that underlie mathematically gifted emergent bilinguals

The purpose of this study was to determine those cognitive measures that increase the likelihood of identifying mathematically gifted students who are emerging bilinguals. Elementary school children (Grades 1, 2, and 3) were administered a battery of math, vocabulary, reading, and cognitive measures (short-term memory, inhibition, and working memory in their first language (L1: Spanish) and second language (L2: English). Multilevel polytomous logistic modeling compared mathematically gifted children with children who were average math achievers or low math achievers. The results indicated that cognitive parameters that included estimation and working memory in the L2 and problem-solving in the L1 were unique predictors that significantly influenced whether a child was categorized as gifted relative to average achievers. Relative to average achievers, L2 parameters (magnitude judgment) and English reading were significantly related to the identification of children with low math computation. The results are discussed in terms of a multidimensional model that taps domain-specific skills and general cognitive processes that increase the ability to correctly identify children who score in the gifted range in both their L1 and L2.

Internal Persistence and External Support—What Makes Chinese Teachers of the Mathematically Gifted Stick to Their Post?

Mathematically gifted students are precious human resources, educators of which make a great difference in helping them realize their potential. The retention of qualified teachers of mathematically gifted students is an issue worthy of in-depth exploration. In China, mathematics competitions are an important part of mathematics gifted education, and the teaching of the Mathematical Olympiad is a challenging profession with a high attrition rate. This qualitative study takes four seasoned and outstanding Chinese teachers as cases, collects data through individual semi-structured interviews, and uses the thematic analysis method based on Herzberg’s two-factor theory to analyze why they can persist in the field of Mathematical Olympiad teaching for more than 20 years. The results show that the motivation factors affecting retention are recognition, achievement, possibility of growth, work itself, and responsibility, and the hygiene factors are policy and interpersonal relationships. Motivation factors are the main reason for their long-term persistence, while hygiene factors are conducive to their persistence as a whole. Finally, enlightenment to educational policy and school management and suggestions for retention and development of teachers of the mathematically gifted are provided.

Parietal and hippocampal hyper-connectivity is associated with low math achievement in adolescence - A preliminary study

Mathematical cognition requires coordinated activity across multiple brain regions, leading to the emergence of resting-state functional connectivity as a method for studying the neural basis of differences in mathematical achievement. Hyper-connectivity of the intraparietal sulcus (IPS), a key locus of mathematical and numerical processing, has been associated with poor mathematical skills in childhood, whereas greater connectivity has been related to better performance in adulthood. No studies to date have considered its role in adolescence. Further, hippocampal connectivity can predict mathematical learning, yet no studies have considered its contributions to contemporaneous measures of math achievement. Here, we used seed-based resting-state fMRI analyses to examine IPS and hippocampal intrinsic functional connectivity relations to math achievement in a group of 31 adolescents (mean age = 16.42 years, range 15-17), whose math performance spanned the 1% to 99% percentile. After controlling for IQ, IPS connectivity was negatively related to math achievement, akin to findings in children. However, the specific temporo-occipital regions were more akin to the posterior loci implicated in adults. Hippocampal connectivity with frontal regions was also negatively correlated with concurrent math measures, which contrasts with results from learning studies. Finally, hyper-connectivity was not a global feature of low math performance, as math performance did not modulate connectivity of Heschl's gyrus, a control seed not involved in math cognition. Our results provide preliminary evidence that adolescence is a transitional stage in which patterns found in childhood and adulthood can be observed; most notably, hyper-connectivity continues to be related to low math ability into this period.

Development of navigation network revealed by resting-state and task-state functional connectivity

Humans possess the essential capacity to navigate in environment, supported by multiple brain regions constituting the navigation network. Recent studies on development of the navigation network mainly examined activation changes in the medial temporal regions. It is unclear how the large-scale organization of the whole navigation network develops and whether the network organizations under resting-state and task-state develop differently. We addressed these questions by examining functional connectivity (FC) of the navigation network in 122 children (10-13 years) and 260 adults. First, we identified a modular structure in the navigation network during resting-state that included a ventral and a dorsal module. Then, we found that the intrinsic modular structure was strengthened from children to adults, that is, adults showed stronger FC within the ventral module and weaker FC between ventral and dorsal modules than children. Further, the intrinsic modular structure was loosened when performing scene-viewing task, that is, both adults and children showed decreased within-ventral FC and increased between-module FC during task- than resting-state. Finally, the task-modulated FC changes were greater in adults than in children. In sum, our study reveals age-related changes in the navigation network organization as increasing modularity under resting-state and increasing flexibility under task-state.

Word learning dogs (Canis familiaris) provide an animal model for studying exceptional performance

Exceptional performance is present in various human activities but its origins are debated and challenging to study. We report evidence of exceptional performance and qualitative variation in learning object-names in dogs. 34 naïve family dogs and 6 knowledgeable individuals that knew multiple toy names, found in 2 years of search around the Globe, were exposed to 3 months of training to learn two novel toy-names and were tested in two-way choice tests. Only 1 naïve and all 6 knowledgeable dogs passed the tests. Additionally, only these dogs learned at least 10 new toy names over the 3 months, showing qualitative variation in this capacity. Although previous object-name knowledge could provide an explanation for the superior performance of the knowledgeable dogs, their rarity and the absence of previous training of this skill point to exceptional giftedness in these individuals, providing the basis to establish dogs as a model-species for studying talent.

The neural differences of arithmetic verification performance depend on math skill: Evidence from event-related potential

AIM

Math skill is a basic need for an individual, as a career prospect. However, little is known about early brain processes of arithmetic between individuals with different math skill. Therefore, we questioned the modulation of the amplitude of an early negative component by math skill level in an arithmetic verification paradigm using event-related potential (ERP).

METHODS

Thirty-six right-handed participants were assigned in two groups of high- and low-performing students. Their electroencephalogram was recorded while they completed an arithmetic verification task. Simple arithmetic operands were made by random digits from 1 to 9. Addition and subtraction operations were equally used in correct and incorrect responses. The accuracy scores, reaction times, and peak amplitude of the negativity in 200-400 ms time window were analyzed.

RESULTS

The high-performing group showed significantly higher response speeds, and they were more accurate than the low-performing group. The group × region interaction effect was significant. The high-performing group showed a significantly greater negativity, particularly in parietal region, while the low-performing group showed a significantly deeper negativity in frontal and prefrontal region. In the low-performing group, there were significant peak amplitude differences between the anterior and posterior areas. However, such differences were not detected in the high-performing group.

CONCLUSION

Students with different mathematical performance showed distinct patterns in early processing of arithmetic verification, as reflected by differences in negativity at 200-400 ms at anterior and posterior. This suggests that ERPs could be used to differentiate math mastery at neural level which is beneficial in educational and clinical contexts.

A Bird's eye view from below: Activity in the temporo-parietal junction predicts from-above Necker Cube percepts

The temporo-parietal junction (TPJ) consistently emerges in other-regarding behavior, including tasks probing affective phenomena such as morality and empathy. Yet the TPJ is also recruited in processes with no affective or social component, such as visuo-spatial processing and mathematical cognition. We present serendipitous findings from a perceptual decision-making task on a bistable stimulus, the Necker Cube, performed in an MRI scanner. The stimulus in question is a transparent, wire-frame cube that evokes spontaneous switches in perception. Individuals can view the cube from below or from above, though a consistent bias is shown towards seeing the cube from above. We replicate this bias, finding participants spend more time in the from-above percept. However, in testing for BOLD differences between percept orientations, we found robust responses in bilateral TPJ for the from-above > from-below perceptual state. We speculate that this neural response comes from the sensory incongruence of viewing an object from above while lying supine in the scanner. We further speculate that the TPJ resolves this incongruence by facilitating an egocentric projection. Such a function would explain the TPJ's ubiquitous response to other-regarding, visuo-spatial and mathematical cognition, as all these phenomena demand an ability to ambulate through the coordinate space. Our findings suggest the TPJ may not play a specific role in social or moral components of other-regarding behavior, such as altruism, and further indirectly suggest that "pure", allocentric altruism may not correlate with the TPJ. Results further have implications on how the TPJ may be modulated by activities such as flight or drone operation. Finally, this study highlights the possible need for congruence between stimuli and body position in neuroimaging studies.

EEG source-space synchrostate transitions and Markov modeling in the math-gifted brain during a long-chain reasoning task

To reveal transition dynamics of global neuronal networks of math-gifted adolescents in handling long-chain reasoning, this study explores momentary phase-synchronized patterns, that is, electroencephalogram (EEG) synchrostates, of intracerebral sources sustained in successive 50 ms time windows during a reasoning task and non-task idle process. Through agglomerative hierarchical clustering for functional connectivity graphs and nested iterative cosine similarity tests, this study identifies seven general and one reasoning-specific prototypical functional connectivity patterns from all synchrostates. Markov modeling is performed for the time-sequential synchrostates of each trial to characterize the interstate transitions. The analysis reveals that default mode network, central executive network (CEN), dorsal attention network, cingulo-opercular network, left/right ventral frontoparietal network, and ventral visual network aperiodically recur over non-task or reasoning process, exhibiting high predictability in interactively reachable transitions. Compared to non-gifted subjects, math-gifted adolescents show higher fractional occupancy and mean duration in CEN and reasoning-triggered transient right frontotemporal network (rFTN) in the time course of the reasoning process. Statistical modeling of Markov chains reveals that there are more self-loops in CEN and rFTN of the math-gifted brain, suggesting robust state durability in temporally maintaining the topological structures. Besides, math-gifted subjects show higher probabilities in switching from the other types of synchrostates to CEN and rFTN, which represents more adaptive reconfiguration of connectivity pattern in the large-scale cortical network for focused task-related information processing, which underlies superior executive functions in controlling goal-directed persistence and high predictability of implementing imagination and creative thinking during long-chain reasoning.

Talent Development in Achievement Domains: A Psychological Framework for Within- and Cross-Domain Research

Achievement in different domains, such as academics, music, or visual arts, plays a central role in all modern societies. Different psychological models aim to describe and explain achievement and its development in different domains. However, there remains a need for a framework that guides empirical research within and across different domains. With the talent-development-in-achievement-domains (TAD) framework, we provide a general talent-development framework applicable to a wide range of achievement domains. The overarching aim of this framework is to support empirical research by focusing on measurable psychological constructs and their meaning at different levels of talent development. Furthermore, the TAD framework can be used for constructing domain-specific talent-development models. With examples for the application of the TAD framework to the domains of mathematics, music, and visual arts, the review provided supports the suitability of the TAD framework for domain-specific model construction and indicates numerous research gaps and open questions that should be addressed in future research.

The contributions of executive functions to mathematical learning difficulties and mathematical talent during adolescence

Are mathematical learning difficulties caused by impairment of the abilities that underlie mathematical talent? Or are mathematical difficulties and talent qualitatively different? The main goal of this study was to determine whether mathematical learning difficulties are explained by the same executive functions as mathematical talent. We screened a pool of 2,682 first-year high school students and selected 48 for evaluation, dividing them into three groups: those with mathematical learning difficulties (n = 16), those with typical performance (n = 16), and those with mathematical talent (n = 16). Adolescents from the learning difficulties and talented groups had age, reading skills, and verbal and non-verbal intelligence that were similar to those of the typical performance group. Participants were administered a suite of tasks to evaluate verbal and visual short-term memory and executive functions of inhibition, shifting, and updating. Different executive functions showed different contributions at the two ends of the math ability continuum: lower levels of performance in updating visual information were related to mathematical learning difficulties, while greater shifting abilities were related to mathematical talent. Effect sizes for the differences in performance between groups were large (Hedges' g > 0.8). These results suggest that different executive functions are associated with mathematical learning difficulties and mathematical talent. We discuss how these differences in executive functions could be related to the different types of mathematical abilities that distinguish the three groups.

Non-symbolic magnitudes are represented spatially: Evidence from a non-symbolic SNARC task

A core proposition in numerical cognition is numbers are represented spatially. Evidence for this proposition comes from the "spatial numerical association of response codes" effect (SNARC) in which faster responses are made by the left/right hand judging whether one of a pair of Arabic digits is smaller/larger than the other. Less is known if a similar SNARC effect exists for non-symbolic magnitudes; and research that has been conducted used stimuli which could be translated into symbolic terms. To overcome this limitation, we employed a referent-to-target judgment paradigm in which a referent dot array (n = 30 dots) was follow by a second array of dots (e.g., n = 45 or 15 dots)-participants judged if the second array contained fewer or more dots than the referent array. Dot arrays with fewer dots were judged more quickly with the left hand compared to the right hand (i.e., a SNARC effect). Not all participants demonstrated a SNARC effect, however. Neither visuospatial working memory nor math ability was associated with the presence/absence of a non-symbolic SNARC effect. Implications of the non-symbolic SNARC effect for accounts of numerical cognition are discussed.