Children's Arithmetic Research Articles

Activation and functional connectivity of cerebellum during reading and during arithmetic in children with combined reading and math disabilities.

Reading and math constitute important academic skills, and as such, reading disability (RD or developmental dyslexia) and math disability (MD or developmental dyscalculia) can have negative consequences for children's educational progress. Although RD and MD are different learning disabilities, they frequently co-occur. Separate theories have implicated the cerebellum and its cortical connections in RD and in MD, suggesting that children with combined reading and math disability (RD + MD) may have altered cerebellar function and disrupted functional connectivity between the cerebellum and cortex during reading and during arithmetic processing. Here we compared Control and RD + MD groups during a reading task as well as during an arithmetic task on (i) activation of the cerebellum, (ii) background functional connectivity, and (iii) task-dependent functional connectivity between the cerebellum and the cortex. The two groups (Control, RD + MD) did not differ for either task (reading, arithmetic) on any of the three measures (activation, background functional connectivity, task-dependent functional connectivity). These results do not support theories that children's deficits in reading and math originate in the cerebellum.

Are numerical abilities determined at early age? A brain morphology study in children and adolescents with and without developmental dyscalculia

The intraparietal sulcus (IPS) has been associated with numerical processing. A recent study reported that the IPS sulcal pattern was associated with arithmetic and symbolic number abilities in children and adults. In the present study, we evaluated the link between numerical abilities and the IPS sulcal pattern in children with Developmental Dyscalculia (DD) and typically developing children (TD), extending previous analyses considering other sulcal features and the postcentral sulcus (PoCS). First, we confirm the longitudinal sulcal pattern stability of the IPS and the PoCS. Second, we found a lower proportion of left sectioned IPS and a higher proportion of a double-horizontal IPS shape bilaterally in DD compared to TD. Third, our analyses revealed that arithmetic is the only aspect of numerical processing that is significantly related to the IPS sulcal pattern (sectioned vs not sectioned), and that this relationship is specific to the left hemisphere. And last, correlation analyses of age and arithmetic in children without a sectioned left IPS indicate that although they may have an inherent disadvantage in numerical abilities, these may improve with age. Thus, our results indicate that only the left IPS sulcal pattern is related to numerical abilities and that other factors co-determine numerical abilities.

Arithmetic in the Bilingual Brain: Language of Learning and Language Experience Effects on Simple Arithmetic in Children and Adults.

In 2020, 21.5% of US preschoolers spoke a language other than English at home. These children transition into English-speaking classrooms in different ways, often handling foundational concepts in two languages. Critically, some knowledge may be dependent on the language learning. For instance, both bilingual children and adults typically prefer, and exhibit higher performance on arithmetic in the language in which they learned math (LA+) compared with their other language (LA-). The typical interpretation is that arithmetic facts are accessed from memory more efficiently or solely in LA+. However, recent research suggests that bilingual arithmetic is not restricted to one language in memory, and that language experience plays an important role in performance. Moreover, evidence suggests children and adults process arithmetic fundamentally differently. Thus, bilingual arithmetic memory may manifest differently across the life span. This review outlines evidence to date at the intersection between the brain basis of bilingualism, arithmetic processing, and development.

Investigating the influence of body movements on children's mental arithmetic performance

Several lines of research have demonstrated spatial-numerical associations in both adults and children, which are thought to be based on a spatial representation of numerical information in the form of a mental number line. The acquisition of increasingly precise mental number line representations is assumed to support arithmetic learning in children. It is further suggested that sensorimotor experiences shape the development of number concepts and arithmetic learning, and that mental arithmetic can be characterized as “motion along a path” and might constitute shifts in attention along the mental number line. The present study investigated whether movements in physical space influence mental arithmetic in primary school children, and whether the expected effect depends on concurrency of body movements and mental arithmetic. After turning their body towards the left or right, 48 children aged 8 to 10 years solved simple subtraction and addition problems. Meanwhile, they either walked or stood still and looked towards the respective direction. We report a congruency effect between body orientation and operation type, i.e., higher performance for the combinations leftward orientation and subtraction and rightward orientation and addition. We found no significant difference between walking and looking conditions. The present results suggest that mental arithmetic in children is influenced by preceding sensorimotor cues and not necessarily by concurrent body movements.

Relationship Between Inhibitory Control and Arithmetic in Elementary School Children With ADHD: The Mediating Role of Working Memory

Objectives: To test if inhibitory control was a significant predictor for arithmetic in children with ADHD and if the relationship between inhibitory control and arithmetic was mediated by working memory. Methods: Eighty-four children (ADHD, n = 54; Non-ADHD, n = 30) were tested on their interference control, behavioral inhibition, working memory, and arithmetic. Regression analysis was used to test the predictive role of inhibitory control in arithmetic. Moreover, mediation analysis was done to test whether working memory mediated the relationship between inhibitory control and arithmetic memory. Results: Interference control but not behavioral inhibition was a significant predictor for arithmetic. In addition, interference control had direct and indirect effects via working memory on arithmetic. Conclusions: Results demonstrated that inhibitory control contributed to arithmetic in children with ADHD. Furthermore, interference control had direct and indirect effects via working memory on arithmetic, suggesting interventions for arithmetic difficulties should involve training on both inhibition and working memory.

The influence of home environmental factors on kindergarten children's addition strategy use.

Young children vary widely in their levels of math knowledge, their abilities to solve math problems, and the strategies they use to solve math problems. As much of later math builds on children's early understanding of basic math facts and problem-solving strategies, understanding influences on children's early problem solving is important. Few studies, however, have examined the home environment in relation to children's strategy use during arithmetic problems. We examined how both structural characteristics of children's home environments, such as socioeconomic status (SES), as well as the learning environment, such as engagement in math and literacy activities at home, related to their use of problem-solving strategies for numerical addition problems. Kindergarten children from diverse backgrounds completed a measure of addition problem solving and strategy use, including simple and complex numerical problems. Strategies were coded based on a combination of accuracy and strategy sophistication, with higher scores indicating problems solved correctly with more sophisticated strategies. Parents completed a home activities questionnaire, reporting the frequency with which they and their child had engaged in math and literacy activities at home over the past month. An exploratory factor analysis identified three components of the home activities - a basic activities factor, an advanced math activities factor, and a literacy activities factor. Findings indicated that SES related to children's strategy sophistication, and frequency of engaging in advanced math and literacy activities at home predicted strategy sophistication, however, engaging in activities at home did not moderate the relations between SES and strategy sophistication. This suggests that family engagement in activities at home may promote early arithmetic skills, and that the role of home environmental characteristics should be considered in children's arithmetic strategy use and performance over development.

Emotions and arithmetic in children

How do negative emotions influence arithmetic performance and how such influence changes with age during childhood? To address these issues, I used a within-trial emotion induction procedure while children solve arithmetic problems. More specifically, 8–15 year-old participants (N = 207) solved arithmetic problems (8 + 4 = 13. True? False?) that were displayed superimposed on emotionally negative or neutral pictures. The main results showed (a) poorer performance in emotionally negative conditions in all age groups, (b) larger deleterious effects of negative emotions on harder problems, (c) decreased effects of emotions as children grow older, and (d) sequential carry-over effects of emotions in all age groups such that larger decreased performance under emotion condition relative to neutral condition occurred on current trials immediately preceded by emotional trials. These findings have important implications for furthering our understanding of how emotions influence arithmetic performance in children and how this influence changes during childhood.

The relationship between phonological processing and arithmetic in children with learning disabilities.

Phonological processing skills have not only been shown to be important for reading skills, but also for arithmetic skills. Specifically, previous research in typically developing children has suggested that phonological processing skills may be more closely related to arithmetic problems that are solved through fact retrieval (e.g., remembering the solution from memory) than procedural computation (e.g., counting). However, the relationship between phonological processing and arithmetic in children with learning disabilities (LDs) has not been investigated. Yet, understanding these relationships in children with LDs is especially important because it can help elucidate the cognitive underpinnings of math difficulties, explain why reading and math disabilities frequently co-occur, and provide information on which cognitive skills to target for interventions. In 63 children with LDs, we examined the relationship between different phonological processing skills (phonemic awareness, phonological memory, and rapid serial naming) and arithmetic. We distinguished between arithmetic problems that tend to be solved with fact retrieval versus procedural computation to determine whether phonological processing skills are differentially related to these two arithmetic processes. We found that phonemic awareness, but not phonological memory or rapid serial naming, was related to arithmetic fact retrieval. We also found no association between any phonological processing skills and procedural computation. These results converge with prior research in typically developing children and suggest that phonemic awareness is also related to arithmetic fact retrieval in children with LD. These results raise the possibility that phonemic awareness training might improve both reading and arithmetic fact retrieval skills. RESEARCH HIGHLIGHTS: Relationships between phonological processing and various arithmetic skills were investigated in children with learning disabilities (LDs) for the first time. We found phonemic awareness was related to arithmetic involving fact retrieval, but not to arithmetic involving procedural computation in LDs. The results suggest that phonemic awareness is not only important to skilled reading, but also to some aspects of arithmetic. These results raise the question of whether intervention in phonemic awareness might improve arithmetic fact retrieval skills.

Finger-Based Numerical Training Increases Sensorimotor Activation for Arithmetic in Children-An fNIRS Study.

Most children use their fingers when learning to count and calculate. These sensorimotor experiences were argued to underlie reported behavioral associations of finger gnosis and counting with mathematical skills. On the neural level, associations were assumed to originate from overlapping neural representations of fingers and numbers. This study explored whether finger-based training in children would lead to specific neural activation in the sensorimotor cortex, associated with finger movements, as well as the parietal cortex, associated with number processing, during mental arithmetic. Following finger-based training during the first year of school, trained children showed finger-related arithmetic effects accompanied by activation in the sensorimotor cortex potentially associated with implicit finger movements. This indicates embodied finger-based numerical representations after training. Results for differences in neural activation between trained children and a control group in the IPS were less conclusive. This study provides the first evidence for training-induced sensorimotor plasticity in brain development potentially driven by the explicit use of fingers for initial arithmetic, supporting an embodied perspective on the representation of numbers.

How does working memory matter in young children's arithmetic skills: The mediating role of basic number processing.

The current study investigated whether and how each component of the working memory model was associated with kindergarten children’s arithmetic performance. A total of 103 Chinese kindergarten children were administered tests of the visuospatial sketchpad, the phonological loop, the central executive, and basic number processing (i.e., number line estimation, nonverbal numerosity estimation and numerical magnitude comparison). The results showed that among the three working memory components, the central executive accounted for a significant proportion of the variance in young children’s arithmetic performance. In terms of basic number processing, number line estimation and numerical magnitude comparison had significant influences on young children’s arithmetic performance. Furthermore, numerical magnitude comparison played a mediating role between the visuospatial sketchpad and early arithmetic skills. These findings highlight the importance of working memory and basic number processing in early arithmetic skills and reveal different pathways through which the three working memory components influence young children’s arithmetic performance.

Spatial Working Memory Counts: Evidence for a Specific Association Between Visuo-spatial Working Memory and Arithmetic in Children

We examined the role of visuo-spatial working memory in different types of arithmetic ability in children. Previous research had suggested that arithmetic is not a single entity (Dowker, 2005, 2015), and also that visuo-spatial working memory is specifically involved in mathematical cognition (McKenzie et al., 2003) There has, however, been little research on the relationships between visuo-spatial working memory and different types of arithmetic. We tested 39 children in Year 2 (6 to 7 years) and Year 4 (8 to 9 years), taking measures of written arithmetic, mental oral arithmetic, and derived fact strategy use (the ability to derive unknown arithmetical facts from known facts, by using arithmetical principles). We also measured visuo-spatial working memory, verbal comprehension, and spelling ability. We investigated the relationships between visuo-spatial working memory and our three arithmetic measures, as well as spelling and verbal comprehension, to test whether these effects were specific to mathematical abilities. We found that visuo-spatial working memory was specifically associated with both verbal oral and mental written arithmetic, and but not with spelling or derived fact strategy use.

Effects of presentation modality and duration on children's strategy use: A study in computational estimation.

Two experiments were run to determine how presentation modality and duration influence children's arithmetic performance and strategy selection. Third and fourth graders were asked to find estimates for two-digit addition problems (e.g., 52 + 39). Children were tested in three conditions: (1) time-unlimited visual, (2) time-limited visual, or (3) time-limited auditory conditions. Moreover, we assessed children's working-memory updating and arithmetic fluency. Children were told which strategy to use on each problem to assess arithmetic performance while executing strategies, in Experiment 1, and were asked to choose the best strategy of three available strategies to assess strategy selection, in Experiment 2. Presentation modality influenced strategy execution (i.e., children were faster and more accurate in problems under visual than auditory conditions) but only in children with low updating abilities. In contrast, presentation modality had no effect on children's strategy selection. Presentation duration had an effect on both strategy execution and strategy selection with time-limited presentation leading to a decline in children's performance. Interestingly, specifically in children with low updating abilities, time-limited presentation led to poorer performance. Hence, efficient updating seemed to compensate for detrimental effects of auditory in comparison to visual and time-limited in comparison to time-unlimited presentation. These findings have important implications for determining conditions under which children execute strategies most efficiently and select the best strategy on each problem most often, as well as for understanding mechanisms underlying strategic behaviour.

Shared Neural Circuits for Visuospatial Working Memory and Arithmetic in Children and Adults.

Visuospatial working memory (VSWM) plays an important role in arithmetic problem solving, and the relationship between these two skills is thought to change over development. Even though neuroimaging studies have demonstrated that VSWM and arithmetic both recruit frontoparietal networks, inferences about common neural substrates have largely been made by comparisons across studies. Little work has examined how brain activation for VSWM and arithmetic converge within the same participants and whether there are age-related changes in the overlap of these neural networks. In this study, we examined how brain activity for VSWM and arithmetic overlap in 38 children and 26 adults. Although both children and adults recruited the intraparietal sulcus (IPS) for VSWM and arithmetic, children showed more focal activation within the right IPS, whereas adults recruited the bilateral IPS, superior frontal sulcus/middle frontal gyrus, and right insula. A comparison of the two groups revealed that adults recruited a more left-lateralized network of frontoparietal regions for VSWM and arithmetic compared with children. Together, these findings suggest possible neurocognitive mechanisms underlying the strong relationship between VSWM and arithmetic and provide evidence that the association between VSWM and arithmetic networks changes with age.

Cover Image

The cover image is based on the Original Article Short-term numerosity training promotes symbolic arithmetic in children with developmental dyscalculia: the mediating role of visual form perception by Xinlin Zhou, Dazhi Cheng, Qian Chen et al., https://doi.org/10.1111/desc.12910.

Exploring mechanisms of rapid automatized naming to arithmetic skills in Chinese primary schoolers

AbstractRapid automatized naming (RAN) is associated with children's arithmetic performance, which is multifactorial by nature and consists of arithmetic fluency, arithmetic procedure, and word problems. Yet, it is unclear whether RAN can predict all key aspects of arithmetic skills independently and what cognitive mechanisms may explain this relation. Using a sample of Chinese primary school students (N = 170), results showed that while RAN was associated with all key aspects of arithmetic skills, the relations of RAN–arithmetic procedure and RAN–word problems may be dependent on that of RAN–arithmetic fluency. Supporting the processing speed hypothesis, results further suggested that processing speed may underlie the relation between RAN and arithmetic performance. Findings made unique contribution to understanding the effect of RAN on arithmetic performance and cognitive mechanisms that may underpin this association in the context of Chinese culture.

The association of grey matter volume and cortical complexity with individual differences in children's arithmetic fluency

Only a small amount of studies have looked at the structural neural correlates of children's arithmetic. Furthermore, these studies mainly implemented voxel-based morphometry, which only takes the volume of regions into account, without looking at other structural properties. The current study aimed to contribute knowledge on which brain regions are important for children's arithmetic on a structural level, by not only implementing voxel-based morphometry, but also cortical complexity analyses, based on the fractal dimension index. This complexity measure describes a characteristic of surface shape. Data of 43 typically developing 9-10 year-olds were analyzed. All children were asked to take part in two test sessions: behavioral data collection and MRI data acquisition. For data analysis, mean values for volume and cortical complexity were estimated within regions of interest (ROIs) and extracted for further analysis. The selected ROIs were based on regions found to be related to children's mathematical abilities in previous research. Results point towards associations between arithmetic fluency and the volume of the right fusiform gyrus, as well as the cortical complexity of the left postcentral gyrus, right insular sulcus, and left lateral orbital sulcus. Remarkably, no significant associations were observed between the children's arithmetic fluency and the volume or cortical complexity of typically arithmetic-associated parietal regions, such as the superior parietal lobe, intraparietal sulcus, or angular gyrus. Accordingly, the current study highlights the importance of structural characteristics of brain regions other than these typically arithmetic-associated parietal regions for children's arithmetic fluency.

Short-term numerosity training promotes symbolic arithmetic in children with developmental dyscalculia: The mediating role of visual form perception.

Studies have shown that numerosity-based arithmetic training can promote arithmetic learning in typically developing children as well as children with developmental dyscalculia (DD), but the cognitive mechanism underlying this training effect remains unclear. The main aim of the current study was to examine the role of visual form perception in arithmetic improvement through an 8-day numerosity training for DD children. Eighty DD children were selected from four Chinese primary schools. They were randomly divided into the intervention and control groups. The intervention group received training on an apple-collecting game, whereas the control group received an English dictation task. Children's cognitive and arithmetic performances were assessed before and after training. The results showed that the intervention group showed a significant improvement in arithmetic performance, approximate number system (ANS) acuity, and visual form perception, but not in spatial processing and sentence comprehension. The control group showed no significant improvement in any cognitive ability. Mediation analysis further showed that training-related improvement in arithmetic performance was fully mediated by the improvement in visual form perception. The results suggest that short-term numerosity training enhances the arithmetic performance of DD children by improving their visual form perception.

Altered association between executive functions and reading and math fluency tasks in children with reading difficulties compared with typical readers.

Fluent reading in children relies on executive functions (EF). Recent research suggests that EF skills also affect arithmetic abilities. Children with reading difficulties (RD) experience deficits in EF. It is still unknown to what extent these EF deficits are the basis for both reading and arithmetic skills in children with RD compared with typical readers. To define the role of EF in reading and arithmetic in children with RD and typical readers, EF measures and reading and arithmetic fluency and non-fluency measures were assessed in 8 to 12-year-old children with RD and age-matched typical readers. Comparison and correlation analyses were performed within and between the two groups. Children with RD scored lower on reading and arithmetic fluency and non-fluency tasks compared with typical readers. For both groups, fluency measures were lower than non-fluency measures. Strong correlations were found within the entire study population between fluency measures and EF, as well as between non-fluency measures and EF compared with mixed correlations observed for the groups separately. Fluency was related to subcomponents of EF expressed in both reading and arithmetic domains for the two groups. The role of each domain and comparison with non-fluency results for each group are discussed.

Kindergarten children's symbolic number comparison skills relates to 1st grade mathematics achievement: Evidence from a two-minute paper-and-pencil test

Basic numerical skills provide an important foundation for the learning of mathematics. Thus, it is critical that researchers and educators have access to valid and reliable ways of assessing young children's numerical skills. The purpose of this study was to evaluate the concurrent, predictive, and incremental validity of a two-minute paper-and-pencil measure of children's symbolic (Arabic numerals) and non-symbolic (dot arrays) comparison skills. A sample of kindergarten children (Mage = 5.86, N = 439) were assessed on the measure along with a number line estimation task, a measure of arithmetic, and several control measures. Results indicated that performance on the symbolic comparison task explained unique variance in children's arithmetic performance in kindergarten. Longitudinal analyses demonstrated that both symbolic comparison and number line estimation in kindergarten were independent predictors of 1st grade mathematics achievement. However, only symbolic comparison remained a unique predictor once language skills and processing speed were taken into account. These results suggest that a two-minute paper-and-pencil measure of children's symbolic number comparison is a reliable predictor of children's early mathematics performance.

A Mechanistic Study of the Association Between Symbolic Approximate Arithmetic Performance and Basic Number Magnitude Processing Based on Task Difficulty.

Two types of number magnitude processing – semantic and spatial – are significantly correlated with children’s arithmetic performance. However, it remains unclear whether these abilities are independent predictors of symbolic approximate arithmetic performance. The current study addressed this question by assessing 86 kindergartners (mean age of 5 years and 7 months) on semantic number processing (number comparison task), spatial number processing (number line estimation task), and symbolic approximate arithmetic performance with different levels of difficulty. The results showed that performance on both tasks of number magnitude processing was significantly correlated with symbolic approximate arithmetic performance, but the strength of these correlations was moderated by the difficulty level of the arithmetic task. The simple symbolic approximate arithmetic task was equally related to both tasks. In contrast, for more difficult symbolic approximate arithmetic tasks, the contribution of number comparison ability was smaller than that of the number line estimation ability. These results indicate that the strength of contribution of the different types of numerical processing depends on the difficulty of the symbolic approximate arithmetic task.