Arithmetic learning in children: An fMRI training study

Add, subtract and multiply: Meta-analyses of brain correlates of arithmetic operations in children and adults

Mathematical operations are cognitive actions we take to calculate relations among numbers. Arithmetic operations, addition, subtraction, multiplication, and division are elemental in education. Addition is the first one taught in school and is most popular in functional magnetic resonance imaging (fMRI) studies. Division, typically taught last is least studied with fMRI. fMRI meta-analyses show that arithmetic operations activate brain areas in parietal, cingulate and insular cortices for children and adults. Critically, no meta-analysis examines concordance across brain correlates of separate arithmetic operations in children and adults. We review and examine using quantitative meta-analyses data from fMRI articles that report brain coordinates separately for addition, subtraction, multiplication, and division in children and adults. Results show that arithmetic operations elicit common areas of concordance in fronto-parietal and cingulo-opercular networks in adults and children. Between operations differences are observed primarily for adults. Interestingly, higher within-group concordance, expressed in activation likelihood estimates, is found in brain areas associated with the cingulo-opercular network rather than the fronto-parietal network in children, areas also common between adults and children. Findings are discussed in relation to constructivist cognitive theory and practical directions for future research.

Structural and transcriptional signatures of arithmetic abilities in children

Arithmetic ability is critical for daily life, academic achievement, career development, and future economic success. Individual differences in arithmetic skills among children and adolescents are related to variations in brain structures. Most existing studies have used hypothesis-driven region of interest analysis. To identify distributed brain regions related to arithmetic ability, we used data-driven cross-validated predictive models to analyze cross-sectional behavioral and structural MRI data in children and adolescents. The gray matter volume (GMV) of widespread brain regions reliably predicted arithmetic abilities measured by the Comprehensive Mathematical Abilities Test. Furthermore, we applied neuroimaging-transcriptome association analysis to explore transcriptional signatures associated with structural patterns of arithmetic ability. Structural patterns of arithmetic ability primarily correlated with transcriptional profiles enriched for genes involved in transmembrane transport and synaptic signaling. Our findings enhance our understanding of the neural and genetic mechanisms underlying children's arithmetic ability and offer a practical predictor for arithmetic skills during development.

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.

The brain lateralization and development of math functions: progress since Sperry, 1974

In 1974, Roger Sperry, based on his seminal studies on the split-brain condition, concluded that math was almost exclusively sustained by the language dominant left hemisphere. The right hemisphere could perform additions up to sums less than 20, the only exception to a complete left hemisphere dominance. Studies on lateralized focal lesions came to a similar conclusion, except for written complex calculation, where spatial abilities are needed to display digits in the right location according to the specific requirements of calculation procedures. Fifty years later, the contribution of new theoretical and instrumental tools lead to a much more complex picture, whereby, while left hemisphere dominance for math in the right-handed is confirmed for most functions, several math related tasks seem to be carried out in the right hemisphere. The developmental trajectory in the lateralization of math functions has also been clarified. This corpus of knowledge is reviewed here. The right hemisphere does not simply offer its support when calculation requires generic space processing, but its role can be very specific. For example, the right parietal lobe seems to store the operation-specific spatial layout required for complex arithmetical procedures and areas like the right insula are necessary in parsing complex numbers containing zero. Evidence is found for a complex orchestration between the two hemispheres even for simple tasks: each hemisphere has its specific role, concurring to the correct result. As for development, data point to right dominance for basic numerical processes. The picture that emerges at school age is a bilateral pattern with a significantly greater involvement of the right-hemisphere, particularly in non-symbolic tasks. The intraparietal sulcus shows a left hemisphere preponderance in response to symbolic stimuli at this age.

The role of the angular gyrus in arithmetic processing: a literature review

Since the pioneering work of the early 20th century neuropsychologists, the angular gyrus (AG), particularly in the left hemisphere, has been associated with numerical and mathematical processing. The association between the AG and numerical and mathematical processing has been substantiated by neuroimaging research. In the present review article, we will examine what is currently known about the role of the AG in numerical and mathematical processing with a particular focus on arithmetic. Specifically, we will examine the role of the AG in the retrieval of arithmetic facts in both typically developing children and adults. The review article will consider alternative accounts that posit that the involvement of the AG is not specific to arithmetic processing and will consider how numerical and mathematical processing and their association with the AG overlap with other neurocognitive processes. The review closes with a discussion of future directions to further characterize the relationship between the angular gyrus and arithmetic processing.

The neural correlates of retrieval and procedural strategies in mental arithmetic: A functional neuroimaging meta-analysis

Mental arithmetic is a complex skill of great importance for later academic and life success. Many neuroimaging studies and several meta-analyses have aimed to identify the neural correlates of mental arithmetic. Previous meta-analyses of arithmetic grouped all problem types into a single meta-analytic map, despite evidence suggesting that different types of arithmetic problems are solved using different strategies. We used activation likelihood estimation (ALE) to conduct quantitative meta-analyses of mental arithmetic neuroimaging (n = 31) studies, and subsequently grouped contrasts from the 31 studies into problems that are typically solved using retrieval strategies (retrieval problems) (n = 18) and problems that are typically solved using procedural strategies (procedural problems) (n = 19). Foci were compiled to generate probabilistic maps of activation for mental arithmetic (i.e., all problem types), retrieval problems, and procedural problems. Conjunction and contrast analyses were conducted to examine overlapping and distinct activation for retrieval and procedural problems. The conjunction analysis revealed overlapping activation for retrieval and procedural problems in the bilateral inferior parietal lobules, regions typically associated with magnitude processing. Contrast analyses revealed specific activation in the left angular gyrus for retrieval problems and specific activation in the inferior frontal gyrus and cingulate gyrus for procedural problems. These findings indicate that the neural bases of arithmetic systematically differs according to problem type, providing new insights into the dynamic and task-dependent neural underpinnings of the calculating brain.