Impaired neural processing of transitive relations in children with math learning difficulty

Self-derivation through memory integration: a longitudinal examination of performance and relations with academic achievements in elementary classrooms

Self-derivation through memory integration is the cognitive process of generating new knowledge by integrating individual facts. Across two studies, we longitudinally examined developmental change, individual stability, and relations with academic performance in a diverse agricultural community. We documented children's self-derivation in their classrooms and examined the relation with self-derivation and academic performance a year later. In Study 1, we examined self-derivation (n = 94; Mage= 6.67; initially grades K and 1) using the same paradigm at both time points. We found evidence of developmental change from Time 1 to Time 2. However, self-derivation accounted for a small portion of the variance in self-derivation (reflecting individual stability) and academic performance measured one year later. In Study 2, we examined self-derivation across two different paradigms with children beginning in Grades 2 and 3 (n = 82; Mage= 8.60). Even across paradigms, we found evidence for individual stability. Year 1 self-derivation also predicted Year 2 academic performance. We posit that self-derivation through integration is a domain-general construct related to academic performance.

Neural evidence for procedural automatization during cognitive development: Intraparietal response to changes in very-small addition problem-size increases with age

Cognitive development is often thought to depend on qualitative changes in problem-solving strategies, with early developing algorithmic procedures (e.g., counting when adding numbers) considered being replaced by retrieval of associations (e.g., between operands and answers of addition problems) in adults. However, algorithmic procedures might also become automatized with practice. In a large cross-sectional fMRI study from age 8 to adulthood (n = 128), we evaluate this hypothesis by measuring neural changes associated with age-related reductions in a behavioral hallmark of mental addition, the problem-size effect (an increase in solving time as problem sum increases). We found that age-related decreases in problem-size effect were paralleled by age-related increases of activity in a region of the intraparietal sulcus that already supported the problem-size effect in 8- to 9-year-olds, at an age the effect is at least partly due to explicit counting. This developmental effect, which was also observed in the basal ganglia and prefrontal cortex, was restricted to problems with operands ≤ 4. These findings are consistent with a model positing that very-small arithmetic problems-and not larger problems-might rely on an automatization of counting procedures rather than a shift towards retrieval, and suggest a neural automatization of procedural knowledge during cognitive development.

Examination of common and unique brain regions for atypical reading and math: a meta-analysis

The purpose of this study is to identify consistencies across functional neuroimaging studies regarding common and unique brain regions/networks for individuals with reading difficulties (RD) and math difficulties (MD) compared to typically developing (TD) individuals. A systematic search of the literature, utilizing multiple databases, yielded 116 functional magnetic resonance imaging and positron emission tomography studies that met the criteria. Coordinates that directly compared TD with either RD or MD were entered into GingerALE (Brainmap.org). An activation likelihood estimate (ALE) meta-analysis was conducted to examine common and unique brain regions for RD and MD. Overall, more studies examined RD (n = 96) than MD (n = 20). Across studies, overactivation for reading and math occurred in the right insula and inferior frontal gyrus for atypically developing (AD) > TD comparisons, albeit in slightly different areas of these regions; however, inherent threshold variability across imaging studies could diminish overlying regions. For TD > AD comparisons, there were no similar or overlapping brain regions. Results indicate there were domain-specific differences for RD and MD; however, there were some similarities in the ancillary recruitment of executive functioning skills. Theoretical and practical implications for researchers and educators are discussed.

Dysfunctions associated with the intraparietal sulcus and a distributed network in individuals with math learning difficulties: An ALE meta-analysis

Math learning difficulty (MLD) is a learning disorder characterized by persistent impairments in the understanding and application of numbers independent of intelligence or schooling. The current study aims to review existing neuroimaging studies to characterize the neurobiological basis in MLD for their quantity and arithmetic dysfunctions. We identified a total of 24 studies with 728 participants through the literature. Using the activation likelihood estimate (ALE) method, we found that the most consistent neurobiological dysfunction in MLD was observed in the right intraparietal sulcus (IPS) with distinct patterns of the anterior and posterior aspects. Meanwhile, neurobiological dysfunctions were also observed in a distributed network including the fusiform gyrus, inferior temporal gyrus, insula, prefrontal cortex, anterior cingulate cortex, and claustrum. Our results suggest a core dysfunction in the right anterior IPS and left fusiform gyrus with atypically upregulated functions in brain regions for attention, working memory, visual processing, and motivation, serving as the neurobiological basis of MLD.

Training causes activation increase in temporo-parietal and parietal regions in children with mathematical disabilities

While arithmetic training reduces fronto-temporo-parietal activation related to domain-general processes in typically developing (TD) children, we know very little about the training-related neurocognitive changes in children with mathematical disabilities (MD), who seek evidenced-based educational interventions. In a within-participant design, a group of 20 children (age range = 10-15 years old) with MD underwent 2 weeks of arithmetic training. Brain activation was measured using functional near-infrared spectroscopy (fNIRS) before and after training to assess training-related changes. Two weeks of training led to both behavioral and brain changes. Training-specific change for trained versus untrained (control) simple multiplication solving was observed as activation increase in the bilateral temporo-parietal region including angular gyrus and middle temporal gyrus. Training-specific change for trained versus untrained (control) complex multiplication solving was observed as activation increase in the bilateral parietal region including intraparietal sulcus, superior parietal lobule, and supramarginal gyrus. Unlike the findings of a similar study in TD children, 2 weeks of multiplication training led to brain activation increase in the fronto-parietal network in children with MD. Interestingly, these brain activation differences between the current findings and a recent similar study in TD children underlie a rather similar behavioral improvement as regards response time and accuracy after 2 weeks of training. This finding provides valuable insights into underlying mechanisms of mathematics learning in special samples and suggests that the findings in TD children may not be readily generalized to children with MD.

Nurturing the Mathematical Brain: Home Numeracy Practices Are Associated With Children's Neural Responses to Arabic Numerals

Disparities in home numeracy environments contribute to variations in children's mathematical skills. However, the neural mechanisms underlying the relation between home numeracy experiences and mathematical learning are unknown. Here, parents of 66 eight-year-olds completed a questionnaire assessing the frequency of home numeracy practices. Neural adaptation to the repetition of Arabic numerals and words was measured in children using functional MRI (n = 50) to assess how sensitive the brain is to the presentation of numerical and nonnumerical information. Disparities in home numeracy practices were related to differences in digit (but not word) processing in a region of the left intraparietal sulcus (IPS) that was also related to children's arithmetic fluency. Furthermore, digit-related processing in the IPS influenced the relation between home numeracy practices and arithmetic fluency. Results were consistent with a model hypothesizing that home numeracy practices may affect children's mathematical skills by modulating the IPS response to symbolic numerical information.

The relation between home numeracy practices and a variety of math skills in elementary school children

A growing number of studies suggest that the frequency of numeracy experiences that parents provide at home may relate to children's mathematical development. However, the relation between home numeracy practices and children's numerical skills is complex and might depend upon both the type and difficulty of activities, as well as the type of math skills. Studies have also argued that this relation may be driven by factors that are not systematically controlled for in the literature, including socio-economic status (SES), parental math skills and children's IQ. Finally, as most prior studies have focused on preschoolers, it remains unclear to what extent there remains a relation between the home numeracy environment and math skills when children are in elementary school. In the present study, we tested an extensive range of math skills in 66 8-year-olds, including non-symbolic quantity processing, symbolic number understanding, transcoding, counting, and mental arithmetic. We also asked parents to complete a questionnaire about their SES, academic expectations, academic attitudes, and the numeracy practices that they provide at home. Finally, we measured their arithmetic fluency as a proxy for parental math skills. Over and above differences in socio-economic status, parental arithmetic fluency, child's IQ, and time spent with the child, we found a positive relation between the frequency of formal numeracy practices that were at or above grade level and two separate measures of mental arithmetic. We further found that the frequency of these advanced formal numeracy practices was related to parents' academic expectations. Therefore, our study shows that home numeracy experiences predict arithmetic skills in elementary school children, but only when those activities are formal and sufficiently challenging for children.

Linear and nonlinear profiles of weak behavioral and neural differentiation between numerical operations in children with math learning difficulties

Mathematical knowledge is constructed hierarchically during development from a basic understanding of addition and subtraction, two foundational and inter-related, but semantically distinct, numerical operations. Early in development, children show remarkable variability in their numerical problem-solving skills and difficulties in solving even simple addition and subtraction problems are a hallmark of math learning difficulties. Here, we use novel quantitative analyses to investigate whether less distinct representations are associated with poor problem-solving abilities in children during the early stages of math-skill acquisition. Crucially, we leverage dimensional and categorical analyses to identify linear and nonlinear neurobehavioral profiles of individual differences in math skills. Behaviorally, performance on the two different numerical operations was less differentiated in children with low math abilities, and lower problem-solving efficiency stemmed from weak evidence-accumulation during problem-solving. Children with low numerical abilities also showed less differentiated neural representations between addition and subtraction operations in multiple cortical areas, including the fusiform gyrus, intraparietal sulcus, anterior temporal cortex and insula. Furthermore, analysis of multi-regional neural representation patterns revealed significantly higher network similarity and aberrant integration of representations within a fusiform gyrus-intraparietal sulcus pathway important for manipulation of numerical quantity. These findings identify the lack of distinct neural representations as a novel neurobiological feature of individual differences in children's numerical problem-solving abilities, and an early developmental biomarker of low math skills. More generally, our approach combining dimensional and categorical analyses overcomes pitfalls associated with the use of arbitrary cutoffs for probing neurobehavioral profiles of individual differences in math abilities.

Spatial Ability in Children with Mathematics Learning Disorder (MLD) and Its Impact on Executive Functions

Mathematics Learning Disorder (MLD) has been found to be related to impairments in cognitive functions. Spatial ability (SA), which is made up of eight single but unified elements can be assumed to have a leading part in different areas of math skills. The first objective of this study was to explore differences in SA factors in 128 school children of third to sixth grade with and without MLD. The Flexibility of Closure, Closure Speed, Perceptual Speed, Visualization, Spatial Relation, Spatial Orientation, Spatial Temporal, and Wayfinding were measured through eight tasks. The second objective of the study was to explore the SA factors' ability to predict the performance of MLD participants in three executive functions. The results revealed that participants with MLD had poorer performance in all the SA tasks and it took longer to finish the visualization, spatial relation, and spatial orientation tasks compared to children with typical development (TD). Regression analysis indicated that some of the SA factors could predict working memory and cognitive flexibility, but they were unable to predict response inhibition. Regarding these results, applying SA factors in cognitive rehabilitation programs of children with MLD seems necessary.

Neural representations of transitive relations predict current and future math calculation skills in children

A large body of evidence suggests that math learning in children is built upon innate mechanisms for representing numerical quantities in the intraparietal sulcus (IPS). Learning math, however, is about more than processing quantitative information. It is also about understanding relations between quantities and making inferences based on these relations. Consistent with this idea, recent behavioral studies suggest that the ability to process transitive relations (A > B, B > C, therefore A > C) may contribute to math skills in children. Here we used fMRI coupled with a longitudinal design to determine whether the neural processing of transitive relations in children could predict their current and future math skills. At baseline (T₁), children (n = 31) processed transitive relations in an MRI scanner. Math skills were measured at T₁ and again 1.5 years later (T₂). Using a machine learning approach with cross-validation, we found that activity associated with the representation of transitive relations in the IPS predicted math calculation skills at both T₁ and T₂. Our study highlights the potential of neurobiological measures of transitive reasoning for forecasting math skills in children, providing additional evidence for a link between this type of reasoning and math learning.

A brain connectivity characterization of children with different levels of mathematical achievement based on graph metrics

Recent studies aiming to facilitate mathematical skill development in primary school children have explored the electrophysiological characteristics associated with different levels of arithmetic achievement. The present work introduces an alternative EEG signal characterization using graph metrics and, based on such features, a classification analysis using a decision tree model. This proposal aims to identify group differences in brain connectivity networks with respect to mathematical skills in elementary school children. The methods of analysis utilized were signal-processing (EEG artifact removal, Laplacian filtering, and magnitude square coherence measurement) and the characterization (Graph metrics) and classification (Decision Tree) of EEG signals recorded during performance of a numerical comparison task. Our results suggest that the analysis of quantitative EEG frequency-band parameters can be used successfully to discriminate several levels of arithmetic achievement. Specifically, the most significant results showed an accuracy of 80.00% (α band), 78.33% (δ band), and 76.67% (θ band) in differentiating high-skilled participants from low-skilled ones, averaged-skilled subjects from all others, and averaged-skilled participants from low-skilled ones, respectively. The use of a decision tree tool during the classification stage allows the identification of several brain areas that seem to be more specialized in numerical processing.