Single-trial interindividual correlation shows semantic and visuospatial networks are fundamental for advanced mathematical learning.

Mathematical learning and ability are crucial for individual and national economic and technological development, but the neural mechanisms underlying advanced mathematical learning remain unclear. The current study used functional magnetic resonance imaging (fMRI) to investigate how brain networks were involved in advanced mathematical learning and transfer. We recorded fMRI data from 24 undergraduate students as they learned the advanced mathematical concept of a commutative mathematical group. After learning, participants were required to complete learning and transfer behavioural tests. Results of single-trial interindividual brain-behaviour correlation analysis found that brain activity in the semantic and visuospatial networks, and the functional connectivity within the semantic network during advanced mathematical learning were positively correlated with learning and transfer effects. Additionally, the functional connectivity between the semantic and visuospatial networks was negatively correlated with the learning and transfer effects. These findings suggest that advanced mathematical learning relies on both semantic and visuospatial networks.

Frontoparietal and salience network synchronizations during nonsymbolic magnitude processing predict brain age and mathematical performance in youth.

The development and refinement of functional brain circuits crucial to human cognition is a continuous process that spans from childhood to adulthood. Research increasingly focuses on mapping these evolving configurations, with the aim to identify markers for functional impairments and atypical development. Among human cognitive systems, nonsymbolic magnitude representations serve as a foundational building block for future success in mathematical learning and achievement for individuals. Using task-based frontoparietal (FPN) and salience network (SN) features during nonsymbolic magnitude processing alongside machine learning algorithms, we developed a framework to construct brain age prediction models for participants aged 7-30. Our study revealed differential developmental profiles in the synchronization within and between FPN and SN networks. Specifically, we observed a linear increase in FPN connectivity, concomitant with a decline in SN connectivity across the age span. A nonlinear U-shaped trajectory in the connectivity between the FPN and SN was discerned, revealing reduced FPN-SN synchronization among adolescents compared to both pediatric and adult cohorts. Leveraging the Gradient Boosting machine learning algorithm and nested fivefold stratified cross-validation with independent training datasets, we demonstrated that functional connectivity measures of the FPN and SN nodes predict chronological age, with a correlation coefficient of .727 and a mean absolute error of 2.944 between actual and predicted ages. Notably, connectivity within the FPN emerged as the most contributing feature for age prediction. Critically, a more matured brain age estimate is associated with better arithmetic performance. Our findings shed light on the intricate developmental changes occurring in the neural networks supporting magnitude representations. We emphasize brain age estimation as a potent tool for understanding cognitive development and its relationship to mathematical abilities across the critical developmental period of youth. PRACTITIONER POINTS: This study investigated the prolonged changes in the brain's architecture across childhood, adolescence, and adulthood, with a focus on task-state frontoparietal and salience networks. Distinct developmental pathways were identified: frontoparietal synchronization strengthens consistently throughout development, while salience network connectivity diminishes with age. Furthermore, adolescents show a unique dip in connectivity between these networks. Leveraging advanced machine learning methods, we accurately predicted individuals' ages based on these brain circuits, with a more mature estimated brain age correlating with better math skills.

What does gender has to do with math? Complex questions require complex answers.

Whether mathematics is a gendered domain or not is a long-lasting issue bringing along major social and educational implications. The females' underrepresentation in science, technology, engineering, and mathematics (STEM) has been considered one of the key signs of the math gender gap, although the current view largely attributes the origin of this phenomenon to sociocultural factors. Indeed, recent approaches to math gender differences reached the universal conclusion that nature and nurture exert reciprocal effects on each other, establishing the need for approaching the study of the math gender issue only once its intrinsic complexity has been accepted. Building upon a flourishing literature, this review provides an updated synthesis of the evidence for math gender equality at the start, and for math gender inequality on the go, challenging the role of biological factors. In particular, by combining recent findings from different research areas, the paper discusses the persistence of the "math male myth" and the associated "female are not good at math myth," drawing attention to the complex interplay of social and cultural forces that support such stereotypes. The suggestion is made that longevity of these myths results from the additive effects of two independent cognitive biases associated with gender stereotypes and with math stereotypes, respectively. Scholars' responsibility in amplifying these myths by pursuing some catching lines of research is also discussed.

A Network Analysis of Children's Emerging Place-Value Concepts.

Examining how informal knowledge systems change after formal instruction is imperative to understanding learning processes and conceptual development and to implementing effective educational practices. We used network analyses to determine how the organization of informal knowledge about multidigit numbers in kindergartners (N = 279; mean age = 5.76 years, SD = 0.55; 135 females) supports and is transformed by a year of in-school formal instruction. The results show that in kindergarten, piecemeal knowledge about the surface properties of reading and writing multidigit numbers and the use of base-10 units to determine large quantities are strongly associated with each other and connected in a stringlike manner to other emerging skills. After a year of instruction, each skill becomes connected to the "hub" abilities of reading and writing multidigit numbers, which also become strongly connected to more advanced knowledge of base-10 principles. These findings provide new insights into how partial knowledge provides the backbone on which explicit principles are learned.

Do children with mathematical learning disabilities use the inversion principle to solve three-term arithmetic problems?: The impact of presentation mode.

Numerical inversion is the ability to understand that addition is the opposite of subtraction and vice versa. Three-term arithmetic problems can be solved without calculation using this conceptual shortcut. To verify that this principle is used, inverse problems (a + b - b) can be compared with standard problems (a + b - c). If this principle is used, performance on inverse problems will be higher than performance on standard problems because no calculation is required. To our knowledge, this principle has not been previously studied in children with mathematical learning disabilities (MLD). Our objectives were (a) to study whether 10-year-olds with MLD are able to use this conceptual principle in three-term arithmetic problems and (b) to evaluate the impact of the presentation mode. A total of 64 children with or without MLD solved three-term arithmetic problems (inverse and standard) in two presentation modes (symbolic and picture). The results showed that even though children with MLD have difficulties in performing arithmetic problems, they can do so when the inverse problem is presented with pictures. The picture presentation mode allowed children with MLD to efficiently identify and use the conceptual inversion shortcut and thus to achieve a similar performance to that of typically developing children. These results provide interesting perspectives for the care of children with MLD.

The cognitive profiles for different samples of mathematical learning difficulties and their similarity to typical development: Evidence from a longitudinal study.

Several cognitive deficits have been suggested to induce mathematical learning difficulties (MLD), but it is unclear whether the cognitive profile for all children with MLD is the same and to what extent it differs from typically developing (TD) children. This study investigated whether such a profile could be distinguished when cognitive skills and math performance are compared between TD children and children with MLD. This was accomplished by employing two-way repeated-measures analyses of covariance in 276 10-year-old participants (60 with MLD) from fourth and fifth grades. In addition, we investigated whether more restrictive selection criteria for MLD result in different mathematical and cognitive profiles by means of independent-samples t tests. Results revealed that cognitive mechanisms for math development are mostly similar for children with MLD and TD children and that variability in sample selection criteria did not produce different mathematical or cognitive profiles. To conclude, the cognitive mechanisms for math development are broadly similar for children with MLD and their TD counterparts even when different MLD samples were selected. This strengthens our idea that MLD can be defined as the worst performance on a continuous scale rather than as a discrete disorder.

Developing mental number line games to improve young children's number knowledge and basic arithmetic skills.

The learning of number knowledge in childhood may directly influence children's mathematics learning ability in subsequent periods. Previous studies also show that the difficulties in mathematics learning faced by schoolchildren are mainly rooted in the lack of number knowledge in early childhood. Focusing on the development of numerical knowledge and basic arithmetic skills in early childhood, this study designed a linear number line game based on the theory of the mental number line. Accordingly, this study examined the effectiveness of the linear number line game in children's learning of number concepts and arithmetic skills and compared the effectiveness of the linear number line game with that of two other games (a nonlinear number line game and a non-number-line game). This study adopted a quasi-experimental research design. A total of 140 young children from remote areas of eastern Taiwan participated and were divided into three experimental groups and one control group, and a pretest-posttest experiment was conducted. The experimental results showed that the linear number line game could help children to acquire numerical knowledge effectively, especially in number line estimation compared with other experimental groups. In terms of the learning effectiveness of basic arithmetic skills (e.g., addition, subtraction), the two number line games (linear and nonlinear number line games) are significantly superior to the non-number-line game (traditional number decomposition and synthesis game). This study recommends that preschool teachers use linear number line games to improve children's numerical knowledge and arithmetic skills.

Early cortical surface plasticity relates to basic mathematical learning.

Children lay the foundation for later academic achievement by acquiring core mathematical abilities in the first school years. Neural reorganization processes associated with individual differences in early mathematical learning, however, are still poorly understood. To fill this research gap, we followed a sample of 5-6-year-old children longitudinally to the end of second grade in school (age 7-8 years) combining magnetic resonance imaging (MRI) with comprehensive behavioral assessments. We report significant links between the rate of neuroplastic change of cortical surface anatomy, and children's early mathematical skills. In particular, most of the behavioral variance (about 73%) of children's visuospatial abilities was explained by the change in cortical thickness in the right superior parietal cortex. Moreover, half of the behavioral variance (about 55%) of children's arithmetic abilities was explained by the change in cortical folding in the right intraparietal sulcus. Additional associations for arithmetic abilities were found for cortical thickness change of the right temporal lobe, and the left middle occipital gyrus. Visuospatial abilities were related to right precentral and supramarginal thickness, as well as right medial frontal gyrus folding plasticity. These effects were independent of other individual differences in IQ, literacy and maternal education. Our findings highlight the critical role of cortical plasticity during the acquisition of fundamental mathematical abilities.

Fronto-insular-parietal network engagement underlying arithmetic word problem solving.

Mathematical word problems are ubiquitous and standard for teaching and evaluating generalization of mathematical knowledge for real-world contexts. It is therefore concerning that the neural mechanisms of word problem solving are not well understood, as these insights represent strong potential for improving education and remediating deficits in this domain. Here, we investigate neural response to word problems via functional magnetic resonance imaging (fMRI). Healthy adults performed sentence judgment tasks on word problems that either contained one-step mathematical operations, or nonarithmetic judgments on parallel narratives without any numerical information. Behavioral results suggested that the composite efficiency measurement of combining accuracy and RT did not differ between the two problem types. Arithmetic sentence judgments elicited greater activation in the fronto-insular-parietal network including intraparietal sulcus (IPS), dorsolateral prefrontal cortex (PFC), and anterior insula (AI) than narrative sentence judgment. Narrative sentence judgments, conversely, resulted in greater activation predominantly in the left ventral PFC, angular gyrus and perisylvian cortex compared with reading arithmetic sentences. Moreover, task-dependent functional connectivity analyses showed the AI circuits were more strongly coupled with IPS during arithmetic sentence judgments than nonarithmetic sentences. Finally, activations in the IPS during arithmetic were highly correlated with out-of-scanner performance on a distinct set of problems with the same characteristics. These results show arithmetic word problem performance differences may rely more heavily on fronto-insular-parietal circuits for mathematical model building than narrative text comprehension of similar difficulty. More broadly, our study suggests that quantitative measurements of brain mechanisms can provide pivotal role for uncovering crucial arithmetic skills.

What predicts mathematics achievement? Developmental change in 5- and 7-year-old children.

Many changes occur in general and specific cognitive abilities in children between 5 and 7 years of age, the period coinciding with entrance into formal schooling. The current study focused on the relative contributions of approximate number system (ANS) acuity, mapping precision between numeral symbols and their corresponding magnitude (mapping precision) and working memory (WM) capacity to mathematics achievement in 5- and 7-year-olds. Children's performance was examined in different tasks: nonsymbolic number comparison, number line estimation, working memory, mathematics achievement, and vocabulary. This latter task was used to determine whether predictors were general or specific to mathematics achievement. The results showed that ANS acuity was a significant specific predictor of mathematics achievement only in 5-year-olds, mapping precision was a significant specific predictor at the two ages, and WM was a significant general predictor only in 7-year-olds. These findings suggest that a general cognitive ability, especially WM, becomes a stronger predictor of mathematics achievement after entrance into formal schooling, whereas ANS acuity, a specific cognitive ability, loses predictive power. Moreover, mediation analyses showed that mapping precision was a partial mediator of the relation between ANS acuity and mathematics achievement in 5-year-olds but not in 7-year-olds. Conversely, in 7-year-olds but not in 5-year-olds, WM fully mediated the relation between ANS acuity and mathematics achievement. These results showed that between 5 and 7 years of age, the period of transition into formal mathematical learning, important changes occurred in the relative weights of different predictors of mathematics achievement.

[Differential diagnosis of primary and secondary mathematical learning disability ­ indications from the dyscalculia test Basis-Math 4­8]. / Differenzialdiagnose zwischen primärer Rechenstörung und sekundärer Rechenschwäche: Hinweise aus dem Basis-Math 4-8.

Studies in children with AD(H)D without mathematical learning disability (MLD) as well as studies on the effects of methylphenidate on arithmetic have shown that most deficits in mathematics and most error types commonly described as specific to developmental dyscalculia (e. g., finger-counting, fact-retrieval deficit, complex counting, difficulties with carry/borrow procedures, self-corrections) cannot be classified as such and should thus not be used for the differential diagnosis of primary dyscalculia and secondary MLD. This article proposes using the overall score in the dyscalculia test Basis-Math 4-8 (Moser Opitz et al., 2010) as well as implausible subtraction errors as a marker for dyscalculia and the number of self-corrections made during the test as a cognitive marker for attention deficits. Hierarchical cluster analyses were calculated in a sample of 51 clinically referred children with normal IQ and suspicion of MLD, using IQ, years of schooling, overall score of the Basis-Math 4­8 and number of self-corrections in this test as variables. The results revealed a subgroup with primary dyscalculia as well as three subgroups with secondary MLD (two with attention deficit hyperactivity disorder, one with depression and one small subgroup with high IQ). In conclusion, the Basis-Math 4­8 (Moser Opitz et al., 2010) can offer substantial information for the differential diagnosis of dyscalculia and secondary deficits in mathematics due to attention problems and enable optimization of treatment decisions for the different groups.

Basic numerical processing, calculation, and working memory in children with dyscalculia and/or ADHD symptoms.

Objective: Deficits in basic numerical skills, calculation, and working memory have been found in children with developmental dyscalculia (DD) as well as children with attention-deficit/hyperactivity disorder (ADHD). This paper investigates cognitive profiles of children with DD and/or ADHD symptoms (AS) in a double dissociation design to obtain a better understanding of the comorbidity of DD and ADHD. Method: Children with DD-only (N = 33), AS-only (N = 16), comorbid DD+AS (N = 20), and typically developing controls (TD, N = 40) were assessed on measures of basic numerical processing, calculation, working memory, processing speed, and neurocognitive measures of attention. Results: Children with DD (DD, DD+AS) showed deficits in all basic numerical skills, calculation, working memory, and sustained attention. Children with AS (AS, DD+AS) displayed more selective difficulties in dot enumeration, subtraction, verbal working memory, and processing speed. Also, they generally performed more poorly in neurocognitive measures of attention, especially alertness. Children with DD+AS mostly showed an additive combination of the deficits associated with DD-only and A_Sonly, except for subtraction tasks, in which they were less impaired than expected. Conclusions: DD and AS appear to be related to largely distinct patterns of cognitive deficits, which are present in combination in children with DD+AS.

Early numerical foundations of young children's mathematical development.

This study focused on the relative contributions of the acuity of the approximate number system (ANS) and knowledge of quantitative symbols to young children's early mathematical learning. At the beginning of preschool, 191 children (Mage=46 months) were administered tasks that assessed ANS acuity and explicit knowledge of the cardinal values represented by number words, and their mathematics achievement was assessed at the end of the school year. Children's executive functions, intelligence, and preliteracy skills and their parents' educational levels were also assessed and served as covariates. Both the ANS and cardinality tasks were significant predictors of end-of-year mathematics achievement with and without control of the covariates. As simultaneous predictors and with control of the covariates, cardinality remained significantly related to mathematics achievement, but ANS acuity did not. Mediation analyses revealed that the relation between ANS acuity and mathematics achievement was fully mediated by cardinality, suggesting that the ANS may facilitate children's explicit understanding of cardinal value and in this way may indirectly influence early mathematical learning.

The Contributions of Domain-General and Numerical Factors to Third-Grade Arithmetic Skills and Mathematical Learning Disability.

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed, and oral language) and numerical factors that include single-digit processing efficiency and multidigit skills such as number system knowledge and estimation. This study of 3rd graders (N = 258) finds both domain-general and numerical factors contribute independently to explaining variation in 3 significant arithmetic skills: basic calculation fluency, written multidigit computation, and arithmetic word problems. Estimation accuracy and number system knowledge show the strongest associations with every skill, and their contributions are independent of both each other and other factors. Different domain-general factors independently account for variation in each skill. Numeral comparison, a single digit processing skill, uniquely accounts for variation in basic calculation. Subsamples of children with MLD (at or below 10th percentile, n = 29) are compared with low achievement (LA, 11th to 25th percentiles, n = 42) and typical achievement (above 25th percentile, n = 187). Examination of these and subsets with persistent difficulties supports a multiple deficits view of number difficulties: Most children with number difficulties exhibit deficits in both domain-general and numerical factors. The only factor deficit common to all persistent MLD children is in multidigit skills. These findings indicate that many factors matter but multidigit skills matter most in 3rd grade mathematical achievement.

How Prior Knowledge, Gesture Instruction, and Interference After Instruction Interact to Influence Learning of Mathematical Equivalence.

Although children learn more when teachers gesture, it is not clear how gesture supports learning. Here, we sought to investigate the nature of the memory processes that underlie the observed benefits of gesture on lasting learning. We hypothesized that instruction with gesture might create memory representations that are particularly resistant to interference. We investigated this possibility in a classroom study with 402 second- and third-grade children. Participants received classroom-level instruction in mathematical equivalence using videos with or without accompanying gesture. After instruction, children solved problems that were either visually similar to the problems that were taught, and consistent with an operational interpretation of the equal sign (interference), or visually distinct from equivalence problems and without an equal sign (control) in order to assess the role of gesture in resisting interference after learning. Gesture facilitated learning, but the effects of gesture and interference varied depending on type of problem being solved and the strategies that children used to solve problems prior to instruction. Some children benefitted from gesture, while others did not. These findings have implications for understanding the mechanisms underlying the beneficial effect of gesture on mathematical learning, revealing that gesture does not work via a general mechanism like enhancing attention or engagement that would apply to children with all forms of prior knowledge.

Arithmetic fluency and number processing skills in identifying students with mathematical learning disabilities.

BACKGROUND: Students with mathematical learning disabilities (MLD) struggle with number processing skills (e.g., enumeration and number comparison) and arithmetic fluency. Traditionally, MLD is identified based on arithmetic fluency. However, number processing skills are suggested to differentiate low achievement (LA) from MLD. AIMS: This study investigated the accuracy of number processing skills in identifying students with MLD and LA, based on arithmetic fluency, and whether the classification ability of number processing skills varied as a function of grade level. METHODS AND PROCEDURES: The participants were 18,405 students (girls = 9080) from Grades 3-9 (ages 9-15). Students' basic numerical skills were assessed with an online dyscalculia screener (Functional Numeracy Assessment -Dyscalculia Battery, FUNA-DB), which included number processing and arithmetic fluency as two factors. OUTCOMES AND RESULTS: Confirmatory factor analyses supported a two-factor structure of FUNA-DB. The two-factor structure was invariant across language groups, gender, and grade levels. Receiver operating characteristics curve analyses indicated that number processing skills are a fair classifier of MLD and LA status across grade levels. The classification accuracy of number processing skills was better when predicting MLD (cut-off < 5 %) compared to LA (cut-off < 25 %). CONCLUSIONS AND IMPLICATIONS: Results highlight the need to measure both number processing and arithmetic fluency when identifying students with MLD.

Early childhood teachers' feedback in natural mathematical learning situations: Development and validation of a detailed category system.

In many countries, early mathematical learning takes place in informal and play-based situations. To support children's mathematical learning, the interactions that occur in the daily contact between the early childhood (EC) teacher and the child in kindergarten play an important role. In these interactions, the feedback provided by the EC teacher is considered to have effects on learning. However, how EC teachers actually give specific or non-specific feedback in everyday activities and play situations with a potential for mathematical learning (natural mathematical learning situations) has been little studied so far. To comprehensively characterize the EC teacher's feedback in natural mathematical learning situations, the current study developed a detailed category system based on categories from previous feedback studies, conducted under various conditions and with different objectives. To verify our category system, we coded mathematical teacher-child interactions (N = 162). The coding provided us with evidence that the category system allows to capture the given feedback in natural mathematical learning situations reliably and in detail. The category system can be useful for further research examining the effects of naturally given feedback on children's mathematical learning and, in the long run, for training teachers in the use of potentially supportive feedback in natural learning situations.

The Effects of Visual Cueing on Students with and without Math Learning Difficulties in Online Problem Solving: Evidence from Eye Movement.

This study investigated the impact of visual cueing on attention guidance, deep-thinking promotion, and performance optimization in arithmetic word problem solving for students with mathematical learning difficulties (MLD). The participants included eight students with MLD and twenty students without MLD who attempted to solve mathematical word problems with and without visual cueing. Eye movements were recorded during the tasks. A repeated-measure design and nonparametric tests were applied to enhance the statistical power of the study. The data analysis results indicated that visual cueing effectively guided and sustained the attention of students with MLD, reducing their off-task duration. However, it showed limited influence in facilitating deep thinking and performance improvement for these students. There were no significant attention-guidance or performance-improvement effects observed in the problem-solving processes of students without MLD, who initially demonstrated better concentration levels and performance. The potential explanations for these findings are further discussed in this paper.

Brain-anatomy image data set for problem solving associated with reversal error: Volumetric data.

Reversal Error (RE) is a common error in algebra problem solving. This error occurs when students recognize the information in the statement but make mistakes when translating some sentences from natural language to algebraic language, reversing the relationship between two variables in comparison word problems. Structural Magnetic Resonance Image (sMRI) data were collected with the purpose of identifying brain anatomical regions related to the RE phenomenon. The aim of the research was to investigate the brain anatomy differences between participants who failed more than 50% of the answers on the task (N=15) and those who responded correctly 100% of the time (N=18). sMRI analysis revealed differences between the two groups, and details about these data can be found in Ventura-Campos et al. (2022) [1]. This data set contains the sMRI (raw data, pre-processed images), and an excel file with personal information such as age and gender, the scanner with which their sMRI were collected, and the group to which each of the 33 subjects belonged.

Enhancing Time Reading and Recording Skills in First-Grade Children with Learning Difficulties Using the "Clock Motor Game".

This study aimed to explore the effect of the motor game, "Clock Motor Games", on the improvement of "Reading and Recording of Time" (RRT) in children with Grade 1 mathematical learning difficulties (MLDs). A within-school cluster-randomized intervention study was conducted with 232 children (aged 6-7 years) with limited physical education experience (0.7 ± 0.3 years). The participants were divided into two groups: a control group, which received conventional teaching on time without any additional motor activities, and an experimental group, which incorporated the concept of time with the "Clock Motor Game", for 3 weeks. The Clock-Reading Test was administered before the intervention (T0), immediately after each session (T1), and five weeks after the intervention (T2) in both groups. The results demonstrated that the experimental group exhibited significantly greater improvements in RRT performance compared to the control group (U = 4416.5; p < 0.001; r = 0.3; medium effect). Additionally, the experimental group was more likely to show progress and less likely to experience regression or stagnation compared to the control group (25% vs. 38.4%). The findings suggest that practicing "Clock Motor Games" can positively contribute to the RRT ability in children with Grade 1 MLD.