Oscillatory electroencephalographic patterns of arithmetic problem solving in fourth graders

Numerous studies have identified neurophysiological correlates of performing arithmetic in adults. For example, oscillatory electroencephalographic (EEG) patterns associated with retrieval and procedural strategies are well established. Whereas fact retrieval has been linked to enhanced left-hemispheric theta ERS (event-related synchronization), procedural strategies are accompanied by increased bilateral alpha ERD (event-related desynchronization). It is currently not clear if these findings generalize to children. Our study is the first to investigate oscillatory EEG activity related to strategy use and arithmetic operations in children. We assessed ERD/ERS correlates of 31 children in fourth grade (aged between nine and ten years) during arithmetic problem solving. We presented multiplication and subtraction problems, which children solved with fact retrieval or a procedure. We analyzed these four problem categories (retrieved multiplications, retrieved subtractions, procedural multiplications, and procedural subtractions) in our study. In summary, we found similar strategy-related patterns to those reported in previous studies with adults. That is, retrieval problems elicited stronger left-hemispheric theta ERS and weaker alpha ERD as compared to procedural problems. Interestingly, we observed neurophysiological differences between multiplications and subtractions within retrieval problems. Although there were no response time or accuracy differences, retrieved multiplications were accompanied by larger theta ERS than retrieved subtractions. This finding could indicate that retrieval of multiplication and subtraction facts are distinct processes, and/or that multiplications are more frequently retrieved than subtractions in this age group.

Left angular gyrus disconnection impairs multiplication fact retrieval

Arithmetic fact retrieval has been suggested to recruit a left-lateralized network comprising perisylvian language areas, parietal areas such as the angular gyrus (AG), and subcortical structures such as the hippocampus. However, the underlying white matter connectivity of these areas has not been evaluated systematically so far. Using simple multiplication problems, we evaluated how disconnections in parietal brain areas affected arithmetic fact retrieval following stroke. We derived disconnectivity measures by jointly considering data from n=73 patients with acute unilateral lesions in either hemisphere and a white-matter tractography atlas (HCP-842) using the Lesion Quantification Toolbox (LQT). Whole-brain voxel-based analysis indicated a left-hemispheric cluster of white matter fibers connecting the AG and superior temporal areas to be associated with a fact retrieval deficit. Subsequent analyses of direct grey-to-grey matter disconnections revealed that disconnections of additional left-hemispheric areas (e.g., between the superior temporal gyrus and parietal areas) were significantly associated with the observed fact retrieval deficit. Results imply that disconnections of parietal areas (i.e., the AG) with language-related areas (i.e., superior and middle temporal gyri) seem specifically detrimental to arithmetic fact retrieval. This suggests that arithmetic fact retrieval recruits a widespread left-hemispheric network and emphasizes the relevance of white matter connectivity for number processing.

Monitoring the Cortical Activity of Children and Adults during Cognitive Task Completion

In this paper, we used an EEG system to monitor and analyze the cortical activity of children and adults at a sensor level during cognitive tasks in the form of a Schulte table. This complex cognitive task simultaneously involves several cognitive processes and systems: visual search, working memory, and mental arithmetic. We revealed that adults found numbers on average two times faster than children in the beginning. However, this difference diminished at the end of table completion to 1.8 times. In children, the EEG analysis revealed high parietal alpha-band power at the end of the task. This indicates the shift from procedural strategy to less demanding fact-retrieval. In adults, the frontal beta-band power increased at the end of the task. It reflects enhanced reliance on the top–down mechanisms, cognitive control, or attentional modulation rather than a change in arithmetic strategy. Finally, the alpha-band power of adults exceeded one of the children in the left hemisphere, providing potential evidence for the fact-retrieval strategy. Since the completion of the Schulte table involves a whole set of elementary cognitive functions, the obtained results were essential for developing passive brain–computer interfaces for monitoring and adjusting a human state in the process of learning and solving cognitive tasks of various types.

Oscillatory Electroencephalographic Patterns of Arithmetic Problem Solving in Fourth Graders

Numerous studies have identified neurophysiological correlates of performing arithmetic in adults. For example, oscillatory electroencephalographic (EEG) patterns associated with retrieval and procedural strategies are well established. Whereas fact retrieval has been linked to enhanced left-hemispheric theta ERS (event-related synchronization), procedural strategies are accompanied by increased bilateral alpha ERD (event-related desynchronization). It is currently not clear if these findings generalize to children.Our study is the first to investigate oscillatory EEG activity related to strategy use and arithmetic operations in children. We assessed ERD/ERS correlates of 31 children in fourth grade (aged between nine and ten years) during arithmetic problem solving. We presented multiplication and subtraction problems, which children solved with fact retrieval or via a procedure. Based on both problem size and verbal strategy reports, we analyzed these problem types separately for each operation.We found similar strategy-related patterns to those reported in previous studies with adults. That is, retrieval problems elicited stronger left-hemispheric theta ERS and weaker alpha ERD as compared to procedural problems. Interestingly, we observed differences between multiplications and subtractions within retrieval problems. Although there were no response time and accuracy differences, retrieved multiplications were accompanied by larger theta ERS than retrieved subtractions. This finding could indicate that retrieval of multiplication and subtraction facts are distinct processes, and/or that multiplications are more frequently retrieved than subtractions in this age group.

Cognitive neuroscience of dyscalculia and math learning disabilities

Dyscalculia and mathematical learning disability (MD) are neurodevelopmental disorders characterized by difficulties in reasoning about numbers. Children with MD lag behind their typically developing peers in a broad range of numerical tasks, including magnitude judgement, quantity manipulation, arithmetic fact retrieval, and problem-solving. This chapter reviews current theories and knowledge of MD and its neurobiological basis from a systems neuroscience perspective. The chapter shows that MD involves processing deficits and aberrancies in multiple neurocognitive systems associated with non-symbolic and symbolic quantity judgment, visuo-spatial working memory, associative memory, and cognitive control. Convergent evidence from task and resting-state fMRI, along with morphometric and tractography studies, is used to demarcate distributed brain circuits disrupted in MD. The chapter examines neural mechanisms underlying intervention and remediation of deficits in MD, highlighting links between brain plasticity and response to treatment. The view that emerges is of a multi-component neurodevelopmental disorder, arising from aberrancies at one or more levels of the numerical information processing hierarchy.

Natural number bias in arithmetic operations with missing numbers – A reaction time study

When reasoning about numbers, students are susceptible to a natural number bias (NNB): When reasoning about non-natural numbers they use properties of natural numbers that do not apply. The present study examined the NNB when students are asked to evaluate the validity of algebraic equations involving multiplication and division, with an unknown, a given operand, and a given result; numbers were either small or large natural numbers, or decimal numbers (e.g., 3 × _ = 12, 6 × _ = 498, 6.1 × _ = 17.2). Equations varied on number congruency (unknown operands were either natural or rational numbers), and operation congruency (operations were either consistent – e.g., a product is larger than its operand – or inconsistent with natural number arithmetic). In a response-time paradigm, 77 adults viewed equations and determined whether a number could be found that would make the equation true. The results showed that the NNB affects evaluations in two main ways: a) the tendency to think that missing numbers are natural numbers; and b) the tendency to associate each operation with specific size of result, i.e., that multiplication makes bigger and division makes smaller. The effect was larger for items with small numbers, which is likely because these number combinations appear in the multiplication table, which is automatized through primary education. This suggests that students may count on the strategy of direct fact retrieval from memory when possible. Overall the findings suggest that the NNB led to decreased student performance on problems requiring rational number reasoning.