Lien Peters

Arithmetic in the developing brain: A review of brain imaging studies

Brain imaging studies on academic achievement offer an exciting window on experience-dependent cortical plasticity, as they allow us to understand how developing brains change when children acquire culturally transmitted skills. This contribution focuses on the learning of arithmetic, which is quintessential to mathematical development. The nascent body of brain imaging studies reveals that arithmetic recruits a large set of interconnected areas, including prefrontal, posterior parietal, occipito-temporal and hippocampal areas. This network undergoes developmental changes in its function, connectivity and structure, which are not yet fully understood. This network only partially overlaps with what has been found in adults, and clear differences are observed in the recruitment of the hippocampus, which are related to the development of arithmetic fact retrieval. Despite these emerging trends, the literature remains scattered, particularly in the context of atypical development. Acknowledging the distributed nature of the arithmetic network, future studies should focus on connectivity and analytic approaches that investigate patterns of brain activity, coupled with a careful design of the arithmetic tasks and assessments of arithmetic strategies. Such studies will produce a more comprehensive understanding of how the arithmetical brain unfolds, how it changes over time, and how it is impaired in atypical development.

Brain activity during arithmetic in symbolic and non-symbolic formats in 9–12 year old children

People process numbers in different formats, such as dot arrays (non-symbolic), Arabic digits and number words (symbolic), and use these representations when performing arithmetic calculations. It remains, however, unclear if and how these various presentation formats affect brain activity during arithmetic. We conducted an fMRI study in 23 typically developing children aged 9-12. The children were asked to subtract numbers up to 10 and had to compare the result to a reference number. Numbers were presented in non-symbolic (dot arrays), as well as symbolic formats (Arabic digits and number words). Our findings suggest that similar brain networks are recruited during arithmetic with different symbolic formats, i.e. Arabic digits and number words. On the other hand, there are clear differences between calculating with symbolic and non-symbolic formats. Specifically, calculating in symbolic formats showed increased activity in angular and supramarginal gyri, whereas arithmetic in the non-symbolic format showed increased activity in middle occipital and superior parietal lobes, as well as in superior frontal gyrus and insula. These differences in brain activity might be explained by differences in the strategies used to solve these arithmetic problems.

Strategy over operation: Neural activation in subtraction and multiplication during fact retrieval and procedural strategy use in children

Arithmetic development is characterized by strategy shifts between procedural strategy use and fact retrieval. This study is the first to explicitly investigate childrens neural activation associated with the use of these different strategies. Participants were 26 typically developing 4th graders (9‐ to 10‐year‐olds), who, in a behavioral session, were asked to verbally report on a trial‐by‐trial basis how they had solved 100 subtraction and multiplication items. These items were subsequently presented during functional magnetic resonance imaging. An event‐related design allowed us to analyze the brain responses during retrieval and procedural trials, based on the childrens verbal reports. During procedural strategy use, and more specifically for the decomposition of operands strategy, activation increases were observed in the inferior and superior parietal lobes (intraparietal sulci), inferior to superior frontal gyri, bilateral areas in the occipital lobe, and insular cortex. For retrieval, in comparison to procedural strategy use, we observed increased activity in the bilateral angular and supramarginal gyri, left middle to inferior temporal gyrus, right superior temporal gyrus, and superior medial frontal gyrus. No neural differences were found between the two operations under study. These results are the first in children to provide direct evidence for alternate neural activation when different arithmetic strategies are used and further unravel that previously found effects of operation on brain activity reflect differences in arithmetic strategy use. Hum Brain Mapp 38:4657–4670, 2017.

The neural representation of Arabic digits in visual cortex

In this study, we investigated how Arabic digits are represented in the visual cortex, and how their representation changes throughout the ventral visual processing stream, compared to the representation of letters. We probed these questions with two functional magnetic resonance imaging (fMRI) experiments. In Experiment 1, we explored whether we could find brain regions that were more activated for digits than for number words in a subtraction task. One such region was detected in lateral occipital cortex. However, the activity in this region might have been confounded by string length—number words contain more characters than digits. We therefore conducted a second experiment in which string length was systematically controlled. Experiment 2 revealed that the findings of the first experiment were task dependent (as it was only observed in a task in which numerosity was relevant) or stimulus dependent (as it was only observed when the number of characters of a stimulus was not controlled). We further explored the characteristics of the activation patterns for digit and letter strings across the ventral visual processing stream through multi-voxel pattern analyses. We found an alteration in representations throughout the ventral processing stream from clustering based on amount of visual information in primary visual cortex (V1) towards clustering based on symbolic stimulus category higher in the visual hierarchy. The present findings converge to the conclusion that in the ventral visual system, as far as can be detected with fMRI, the distinction between Arabic digits and letter strings is represented in terms of distributed patterns rather than separate regions.

Developmental trajectories of children’s symbolic numerical magnitude processing skills and associated cognitive competencies

Although symbolic numerical magnitude processing skills are key for learning arithmetic, their developmental trajectories remain unknown. Therefore, we delineated during the first 3years of primary education (5-8years of age) groups with distinguishable developmental trajectories of symbolic numerical magnitude processing skills using a model-based clustering approach. Three clusters were identified and were labeled as inaccurate, accurate but slow, and accurate and fast. The clusters did not differ in age, sex, socioeconomic status, or IQ. We also tested whether these clusters differed in domain-specific (nonsymbolic magnitude processing and digit identification) and domain-general (visuospatial short-term memory, verbal working memory, and processing speed) cognitive competencies that might contribute to childrens ability to (efficiently) process the numerical meaning of Arabic numerical symbols. We observed minor differences between clusters in these cognitive competencies except for verbal working memory for which no differences were observed. Follow-up analyses further revealed that the above-mentioned cognitive competencies did not merely account for the cluster differences in childrens development of symbolic numerical magnitude processing skills, suggesting that other factors account for these individual differences. On the other hand, the three trajectories of symbolic numerical magnitude processing revealed remarkable and stable differences in childrens arithmetic fact retrieval, which stresses the importance of symbolic numerical magnitude processing for learning arithmetic.

Dyscalculia and dyslexia: Different behavioral, yet similar brain activity profiles during arithmetic

Brain disorders are often investigated in isolation, but very different conclusions might be reached when studies directly contrast multiple disorders. Here, we illustrate this in the context of specific learning disorders, such as dyscalculia and dyslexia. While children with dyscalculia show deficits in arithmetic, children with dyslexia present with reading difficulties. Furthermore, the comorbidity between dyslexia and dyscalculia is surprisingly high. Different hypotheses have been proposed on the origin of these disorders (number processing deficits in dyscalculia, phonological deficits in dyslexia) but these have never been directly contrasted in one brain imaging study. Therefore, we compared the brain activity of children with dyslexia, children with dyscalculia, children with comorbid dyslexia/dyscalculia and healthy controls during arithmetic in a design that allowed us to disentangle various processes that might be associated with the specific or common neural origins of these learning disorders. Participants were 62 children aged 9 to 12, 39 of whom had been clinically diagnosed with a specific learning disorder (dyscalculia and/or dyslexia). All children underwent fMRI scanning while performing an arithmetic task in different formats (dot arrays, digits and number words). At the behavioral level, children with dyscalculia showed lower accuracy when subtracting dot arrays, and all children with learning disorders were slower in responding compared to typically developing children (especially in symbolic formats). However, at the neural level, analyses pointed towards substantial neural similarity between children with learning disorders: Control children demonstrated higher activation levels in frontal and parietal areas than the three groups of children with learning disorders, regardless of the disorder. A direct comparison between the groups of children with learning disorders revealed similar levels of neural activation throughout the brain across these groups. Multivariate subject generalization analyses were used to statistically test the degree of similarity, and confirmed that the neural activation patterns of children with dyslexia, dyscalculia and dyslexia/dyscalculia were highly similar in how they deviated from neural activation patterns in control children. Collectively, these results suggest that, despite differences at the behavioral level, the brain activity profiles of children with different learning disorders during arithmetic may be more similar than initially thought.

Episodic elaboration: Investigating the structure of retrieved past events and imagined future events

Five experiments investigated the cognitive processes involved in the elaboration of past and future events. A production listing procedure was used, in which participants listed details of each event in forwards chronological order, backwards chronological order, or free order. For both past and future events, forwards and free ordering conditions were reliably faster than backwards order. Production rates between past and future temporal directions did not differ in Experiments 1a, 1b, and 3. However, in Experiment 2, the elaboration of future events was faster than the elaboration of past events. This pattern can be explained by the findings of Experiment 4, in which production rates were faster for likely events than for unlikely events but only in the future condition. Overall, the findings suggest that the elaboration of future, but not past, events, is facilitated when constructed around current goals.