The inferior fronto-occipital fasciculus correlates with early precursors of mathematics and reading before the start of formal schooling

Diffusion-weighted imaging studies in preschoolers have almost exclusively been done in the field of reading. As a result, virtually nothing is known about white matter tracts associated with individual differences in mathematics at this age. Studying the preschoolers' brain is crucial because it allows us to identify individual differences in brain anatomy without influences of formal mathematics and reading instruction. To fill this gap, we investigated for the first time before the start of formal school entry the associations between white matter tracts and precursors of mathematics and reading simultaneously. We also investigated whether these associations were specific to mathematics and to reading, or not. We focused on four bilateral white matter tracts (arcuate fasciculus (direct, anterior), inferior fronto-occipital fasciculus, inferior longitudinal fasciculus), which have been previously correlated with mathematical performance in older children and with reading performance in children of a similar age as the current study. Participants were 56 5-year-old children (Mage = 67 months; SD = 1.8), none of which received formal instruction. Our results showed an association between the bilateral inferior fronto-occipital fasciculus and precursors of mathematics (numerical ordering, numeral knowledge) and reading (phonological awareness, letter knowledge). Follow-up regression analyses revealed that the associations found with the inferior fronto-occipital fasciculus were neither specific to mathematics nor specific to reading. These findings suggest that, already before the start of formal schooling, the inferior fronto-occipital fasciculus might be related to the neural overlap between mathematics and reading. This overlap potentially reflects one of their many shared mechanisms, such as the reliance on phonological codes or the processing of visual symbols, and these mechanisms should be exploited in future studies.

A dashboard for the evaluation of the effect of school closures on wellbeing of children and parents

BACKGROUND

We present a dashboard for the evaluation of the impact of school closures on children and parents during the first wave of the COVID pandemic in 2020 on the various components of wellbeing.

METHODS

Starting from an explorative literature search by a team of experts from diverse fields (e.g., epidemiology, virology, psychology, education, sociology), we developed a dashboard that allows for the quick evaluation of the general effect of school closures on various indicators of well-being in different groups and for the quality of the available research, at a time where a crisis is ongoing.

RESULTS

It is concluded that there is evidence that the school closures reduced the transmission of COVID in the first wave in springtime 2020. Nevertheless, a multitude of studies show that the school closures also had a negative impact on different components of wellbeing such as academic achievement, time spent on learning and mental health. Furthermore, the school closures affected not only the children and adolescents, but also the parents that were forced to provide more childcare and help with schoolwork. Longitudinal studies on large representative samples with repeated assessments of wellbeing are necessary to understand the long-term effects of the school closures.

CONCLUSIONS

The dashboard provides a first visual overview of the effects of school closures on wellbeing, and can serve as the basis for a future more systematic review and meta-analysis of the effects of school closures on wellbeing. It can be considered as a paradigm for rapid obtention of scientific evidence, during a quickly unfolding crisis, also in view of underpinning policy advice.

Aging effects and feasibility of statistical learning tasks across modalities

Knowledge on statistical learning (SL) in healthy elderly is scarce. Theoretically, it is not clear whether aging affects modality-specific and/or domain-general learning mechanisms. Practically, there is a lack of research on simplified SL tasks, which would ease the burden of testing in clinical populations. Against this background, we conducted two experiments across three modalities (auditory, visual and visuomotor) in a total of 93 younger and older adults. In Experiment 1, SL was induced in all modalities. Aging effects appeared in the tasks relying on an explicit posttest to assess SL. We hypothesize that declines in domain-general processes that predominantly modulate explicit learning mechanisms underlie these aging effects. In Experiment 2, more feasible tasks were developed for which the level of SL was maintained in all modalities, except the auditory modality. These tasks are more likely to successfully measure SL in elderly (patient) populations in which task demands can be problematic.

Longitudinal pathways of numerical abilities in preschool: Cognitive and environmental correlates and relation to primary school mathematics achievement

Children start preschool with large individual differences in their early numerical abilities. Little is known about the importance of heterogeneous patterns that exist within these individual differences. A person-centered analytic approach might be helpful to unravel these patterns and the cognitive and environmental factors that are associated with them. We applied a person-centered approach to a 5-year longitudinal study (N = 410, 213 boys) conducted in Belgium from preschool to grade 3. Preschoolers (M_age = 58.14 months, SD_age = 3.51) were selected to represent the full range of socioeconomic backgrounds. We examined via Latent Profile Analysis the heterogeneous patterns that exist in preschoolers' early numerical development using measures of counting, numeral identification, comparison, ordering, and arithmetic abilities. We investigated the association between the derived numerical ability pathways, general cognitive factors (working memory, language, spatial ability) and the home math environment. We also evaluated the relation of these early numerical ability pathways to later mathematics achievement in grade 1 and 3. Four longitudinal pathways emerged: a low (15%), below-average (28%), above-average (44%), and a high numerical ability pathway (13%). Differences between the four pathways were mostly quantitative. Most of the general cognitive factors contributed to pathway membership, whereas the home math environment and socioeconomic status (SES) did not. The pathways differed in mathematics achievement in grade 1 and 3, and most of these differences remained when the covariates were considered. The results highlight the heterogeneity that is already present in preschoolers' numerical abilities and their predictive value for subsequent mathematics achievement. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Counting many as one: Young children can understand sets as units except when counting

Young children frequently make a peculiar counting mistake. When asked to count units that are sets of multiple items, such as the number of families at a party, they often count discrete items (i.e., individual people) rather than the number of sets (i.e., families). One explanation concerns children's incomplete understanding of what constitutes a unit, resulting in a preference for discrete items. Here we demonstrate that children's incomplete understanding of counting also plays a role. In an experiment with 4- and 5-year-old children (N = 43), we found that even if children are able to name sets, group items into sets, and create one-to-one correspondences with sets, many children are nevertheless unable to count sets as units. We conclude that a nascent understanding of the abstraction principle of counting is also a cause of some children's counting errors.

Early white matter connectivity and plasticity in post stroke aphasia recovery

A disruption of white matter connectivity is negatively associated with language (recovery) in patients with aphasia after stroke, and behavioral gains have been shown to coincide with white matter neuroplasticity. However, most brain-behavior studies have been carried out in the chronic phase after stroke, with limited generalizability to earlier phases. Furthermore, few studies have investigated neuroplasticity patterns during spontaneous recovery (i.e., not related to a specific treatment) in the first months after stroke, hindering the investigation of potential early compensatory mechanisms. Finally, the majority of previous research has focused on damaged left hemisphere pathways, while neglecting the potential protective value of their right hemisphere counterparts for language recovery. To address these outstanding issues, we present a longitudinal study of thirty-two patients with aphasia (21 males and 11 females, M = 69.47 years, SD = 10.60 years) who were followed up for a period of 1 year with test moments in the acute (1-2 weeks), subacute (3-6 months) and chronic phase (9-12 months) after stroke. Constrained Spherical Deconvolution-based tractography was performed in the acute and subacute phase to measure Fiber Bundle Capacity (FBC), a quantitative connectivity measure that is valid in crossing fiber regions, in the bilateral dorsal arcuate fasciculus (AF) and the bilateral ventral inferior fronto-occipital fasciculus (IFOF). First, concurrent analyses revealed positive associations between the left AF and phonology, and between the bilateral IFOF and semantics in the acute - but not subacute - phase, supporting the dual-stream language model. Second, neuroplasticity analyses revealed a decrease in connection density of the bilateral AF - but not the IFOF - from the acute to the subacute phase, possibly reflecting post stroke white matter degeneration in areas adjacent to the lesion. Third, predictive analyses revealed no contribution of acute FBC measures to the prediction of later language outcomes over and above the initial language scores, suggesting no added value ofthe diffusion measures for languageprediction. Our study provides new insights on (changes in) connectivity of damaged and undamaged language pathways in patients with aphasia in the first months after stroke, as well as if/how such measures are related to language outcomes at different stages of recovery. Individual results are discussed in the light of current frameworks of language processing and aphasia recovery.

The role of the hippocampus in statistical learning and language recovery in persons with post stroke aphasia

Although several studies have aimed for accurate predictions of language recovery in post stroke aphasia, individual language outcomes remain hard to predict. Large-scale prediction models are built using data from patients mainly in the chronic phase after stroke, although it is clinically more relevant to consider data from the acute phase. Previous research has mainly focused on deficits, i.e., behavioral deficits or specific brain damage, rather than compensatory mechanisms, i.e., intact cognitive skills or undamaged brain regions. One such unexplored brain region that might support language (re)learning in aphasia is the hippocampus, a region that has commonly been associated with an individual's learning potential, including statistical learning. This refers to a set of mechanisms upon which we rely heavily in daily life to learn a range of regularities across cognitive domains. Against this background, thirty-three patients with aphasia (22 males and 11 females, M = 69.76 years, SD = 10.57 years) were followed for 1 year in the acute (1-2 weeks), subacute (3-6 months) and chronic phase (9-12 months) post stroke. We evaluated the unique predictive value of early structural hippocampal measures for short-term and long-term language outcomes (measured by the ANELT). In addition, we investigated whether statistical learning abilities were intact in patients with aphasia using three different tasks: an auditory-linguistic and visual task based on the computation of transitional probabilities and a visuomotor serial reaction time task. Finally, we examined the association of individuals' statistical learning potential with acute measures of hippocampal gray and white matter. Using Bayesian statistics, we found moderate evidence for the contribution of left hippocampal gray matter in the acute phase to the prediction of long-term language outcomes, over and above information on the lesion and the initial language deficit (measured by the ScreeLing). Non-linguistic statistical learning in patients with aphasia, measured in the subacute phase, was intact at the group level compared to 23 healthy older controls (8 males and 15 females, M = 74.09 years, SD = 6.76 years). Visuomotor statistical learning correlated with acute hippocampal gray and white matter. These findings reveal that particularly left hippocampal gray matter in the acute phase is a potential marker of language recovery after stroke, possibly through its statistical learning ability.

Arithmetic learning in children: An fMRI training study

Arithmetic learning is characterized by a change from procedural strategies to fact retrieval. fMRI training studies in adults have revealed that this change coincides with decreased activation in the prefrontal cortex (PFC) and that within the parietal lobe, a shift occurs from the intraparietal sulcus (IPS) to the angular gyrus (AG) during this change. It remains to be determined whether similar changes can be observed in children, particularly because children often recruit the hippocampus (HC) during fact retrieval, an observation that has not consistently been found in adults. In order to experimentally manipulate arithmetic strategy change, 26 typically developing 9- to-10-year-olds completed a six day at-home training of complex multiplication items (e.g. 16 × 4). Before and after training, children were presented with three multiplication conditions during fMRI: (1) complex to-be-trained/trained items, (2) complex untrained items and (3) single-digit items. Behavioral data indicated that training was successful. Similar to adults, children showed greater activity in the IPS and PFC for the untrained condition post-training, indicating that the fronto-parietal network during procedural arithmetic problem solving is already in place in children of this age. We did not observe the expected training-related changes in the HC. In contrast to what has been observed in adults, greater activity in the AG was not observed for the trained items. These results show that the brain processes that accompany the learning of arithmetic facts are different in children as compared to adults.

The value of structural brain imaging in explaining individual differences in children's arithmetic fluency

How do different measures of brain structure correlate with individual differences in arithmetic fluency? This paper builds on two previously published studies in which individual differences in children's arithmetic fluency were correlated with measures of white (Polspoel et al., 2019) and grey matter (Polspoel et al., 2020) in one sample of children. We combined the brain imaging data of these two studies with measures of cognitive abilities that have been shown to be predictive of arithmetic fluency, i.e., numerical magnitude processing, working memory and rapid automatized naming (RAN). This allowed us to investigate to which extend the observed structural brain imaging measures uniquely correlated with children's arithmetic fluency, on top of each other as well as on top of the abovementioned cognitive variables. Participants were 43 typically developing 9-10-year-olds. All measures were added to a hierarchical multiple regression model. This regression model showed that the white matter integrity of the right inferior longitudinal fasciculus and the cortical complexity of the left postcentral gyrus remained unique predictors of individual differences in arithmetic when the abovementioned cognitive variables were taken into account. This indicates that structural neuroimaging measures can explain individual differences in arithmetic performance that are not merely accounted for by relevant cognitive predictors.

Developmental brain dynamics of numerical and arithmetic abilities

The development of numerical and arithmetic abilities constitutes a crucial cornerstone in our modern and educated societies. Difficulties to acquire these central skills can lead to severe consequences for an individual's well-being and nation's economy. In the present review, we describe our current broad understanding of the functional and structural brain organization that supports the development of numbers and arithmetic. The existing evidence points towards a complex interaction among multiple domain-specific (e.g., representation of quantities and number symbols) and domain-general (e.g., working memory, visual-spatial abilities) cognitive processes, as well as a dynamic integration of several brain regions into functional networks that support these processes. These networks are mainly, but not exclusively, located in regions of the frontal and parietal cortex, and the functional and structural dynamics of these networks differ as a function of age and performance level. Distinctive brain activation patterns have also been shown for children with dyscalculia, a specific learning disability in the domain of mathematics. Although our knowledge about the developmental brain dynamics of number and arithmetic has greatly improved over the past years, many questions about the interaction and the causal involvement of the abovementioned functional brain networks remain. This review provides a broad and critical overview of the known developmental processes and what is yet to be discovered.

Next Directions in Measurement of the Home Mathematics Environment: An International and Interdisciplinary Perspective

This article synthesizes findings from an international virtual conference, funded by the National Science Foundation (NSF), focused on the home mathematics environment (HME). In light of inconsistencies and gaps in research investigating relations between the HME and children's outcomes, the purpose of the conference was to discuss actionable steps and considerations for future work. The conference was composed of international researchers with a wide range of expertise and backgrounds. Presentations and discussions during the conference centered broadly on the need to better operationalize and measure the HME as a construct - focusing on issues related to child, family, and community factors, country and cultural factors, and the cognitive and affective characteristics of caregivers and children. Results of the conference and a subsequent writing workshop include a synthesis of core questions and key considerations for the field of research on the HME. Findings highlight the need for the field at large to use multi-method measurement approaches to capture nuances in the HME, and to do so with increased international and interdisciplinary collaboration, open science practices, and communication among scholars.

Associations Between Repeating Patterning, Growing Patterning, and Numerical Ability: A Longitudinal Panel Study in 4- to 6-Year Olds

The present study aimed to analyze the direction of the associations between repeating patterning, growing patterning, and numerical ability. Participants were 410 children who were annually assessed on their repeating patterning, growing patterning, and numerical ability, at ages 4, 5, and 6 years (i.e., spring 2017, 2018, and 2019). A cross-lagged panel model identified bidirectional associations between all three abilities from ages 4 to 5 years while taking into account spatial skills. From ages 5 to 6 years, both patterning abilities predicted later numerical ability, but the reverse was no longer true. Associations between performances on both pattern types also disappeared. Results highlight the unique associations between repeating patterning, growing patterning, and numerical ability, above spatial skills.

No Association Between the Home Math Environment and Numerical and Patterning Skills in a Large and Diverse Sample of 5- to 6-year-olds

Selecting a large and diverse sample of 5–6-year-old preschool children (179 boys and 174 girls; M_age = 70.03 months, SD_age = 3.43), we aimed to extend previous findings on variability in children’s home math environment (i.e., home math activities, parental expectations, and attitudes) and its association with children’s mathematical skills. We operationalized mathematics in a broader way than in previous studies, by considering not only children’s numerical skills but also their patterning skills as integral components of early mathematical development. We investigated the effects of children’s gender and socioeconomic status (SES) on their home math environment, examined the associations between children’s home math environment and their mathematical skills, and verified whether these associations were moderated by children’s gender and/or SES. Parents of 353 children completed a home math environment questionnaire and all children completed measures of their numerical (e.g., object counting) and patterning skills (e.g., extending repeating patterns). Results indicated no effect of children’s gender on their home math environment. There was no effect of SES on the performed home math activities, but small SES differences existed in parents’ math-related expectations and their attitudes. We found no evidence for associations between children’s home math environment and their mathematical skills. Furthermore, there were no moderating effects of gender or SES on these associations. One explanation for these findings might relate to the characteristics of the general preschool system in the country of the present study (Belgium). Future studies should consider the effect of the preschool learning environment because it might explain differences between studies and countries with regard to the home math environment and its association with mathematical skills.

Cognitive correlates of dyslexia, dyscalculia and comorbid dyslexia/dyscalculia: Effects of numerical magnitude processing and phonological processing

Specific learning disorders (i.e., dyscalculia and dyslexia) are common, as is their comorbidity. It has been suggested that the core cognitive deficit in dyscalculia is an impairment in numerical magnitude processing; similarly, in dyslexia, phonological processing deficits are considered to be the main cognitive deficit. Cognitive theories on comorbid dyslexia/dyscalculia have suggested a number of hypotheses about which cognitive deficits underlie the comorbidity. However, few studies have thus far directly compared the abovementioned cognitive correlates of dyscalculia and dyslexia. In this study, we assessed symbolic and non-symbolic numerical magnitude and three subcomponents of phonological processing (phonological awareness, lexical access and verbal short-term memory). In addition, we investigated children's domain-general spatial and verbal skills. The effect of these cognitive correlates on dyscalculia, dyslexia and their comorbidity was explored. We did not find differences between children with and without dyscalculia on numerical magnitude processing. On the other hand, children with dyscalculia had significantly lower spatial skills compared to children without dyscalculia. Children with dyslexia performed significantly lower on all subcomponents of phonological processing. Finally, we found an additive effect for comorbid dyslexia/dyscalculia: impairments in children with co-occurring dyslexia and dyscalculia were similar to the sum of the impairments in the isolated dyslexia and isolated dyscalculia groups. The strongest unique predictor of isolated dyscalculia and comorbid dyslexia/dyscalculia was spatial skills, the strongest unique predictor of isolated dyslexia was phonological awareness. As only a limited number of cognitive variables were assessed in this study and the sample sizes were very small, we should be cautious when interpreting these results.

A Review on Treatment-Related Brain Changes in Aphasia

Numerous studies have investigated brain changes associated with interventions targeting a range of language problems in patients with aphasia. We strive to integrate the results of these studies to examine (1) whether the focus of the intervention (i.e., phonology, semantics, orthography, syntax, or rhythmic-melodic) determines in which brain regions changes occur; and (2a) whether the most consistent changes occur within the language network or outside, and (2b) whether these are related to individual differences in language outcomes. The results of 32 studies with 204 unique patients were considered. Concerning (1), the location of treatment-related changes does not clearly depend on the type of language processing targeted. However, there is some support that rhythmic-melodic training has more impact on the right hemisphere than linguistic training. Concerning (2), we observed that language recovery is not only associated with changes in traditional language-related structures in the left hemisphere and homolog regions in the right hemisphere, but also with more medial and subcortical changes (e.g., precuneus and basal ganglia). Although it is difficult to draw strong conclusions, because there is a lack of systematic large-scale studies on this topic, this review highlights the need for an integrated approach to investigate how language interventions impact on the brain. Future studies need to focus on larger samples preserving subject-specific information (e.g., lesion effects) to cope with the inherent heterogeneity of stroke-induced aphasia. In addition, recovery-related changes in whole-brain connectivity patterns need more investigation to provide a comprehensive neural account of treatment-related brain plasticity and language recovery.

Probing the Relationship Between Home Numeracy and Children's Mathematical Skills: A Systematic Review

The concept of home numeracy has been defined as parent–child interactions with numerical content. This concept started to receive increasing attention since the last decade. Most of the studies indicated that the more parents and their children engage in numerical experiences, the better children perform in mathematical tasks. However, there are also contrasting results indicating that home numeracy does not play a role or that there is a negative association between the parent–child interactions and children's mathematics performance. To shed light on these discrepancies, a systematic review searching for available articles examining the relationship between home numeracy and mathematical skills was conducted. Thirty-seven articles were retained and a p-curve analysis showed a true positive association between home numeracy and children's mathematical skills. A more qualitative investigation of the articles revealed five common findings: (1) Advanced home numeracy interactions but not basic ones are associated with children's mathematical skills. (2) Most participants in the studies were mothers, however, when both parents participated and were compared, only mothers' reports of formal home numeracy activities (i.e., explicit numeracy teaching) were linked to children's mathematical skill. (3) Formal home numeracy activities have been investigated more commonly than informal home numeracy activities (i.e., implicit numeracy teaching). (4) The number of studies that have used questionnaires to assess home numeracy is larger compared with the ones that have used observations. (5) The majority of the studies measured children's mathematical skills with comprehensive tests that index mathematical ability with one composite score rather than with specific numerical tasks. These five common findings might explain the contradictory results regarding the relationship between home numeracy and mathematical skills. Therefore, more research is necessary to draw quantitative conclusions about these five points.

The neural basis of metacognitive monitoring during arithmetic in the developing brain

In contrast to a substantial body of research on the neural basis of cognitive performance in several academic domains, less is known about how the brain generates metacognitive (MC) awareness of such performance. The existing work on the neurobiological underpinnings of metacognition has almost exclusively been done in adults and has largely focused on lower level cognitive processing domains, such as perceptual decision‐making. Extending this body of evidence, we investigated MC monitoring by asking children to solve arithmetic problems, an educationally relevant higher‐order process, while providing concurrent MC reports during fMRI acquisition. Results are reported on 50 primary school children aged 9–10 years old. The current study is the first to demonstrate that brain activity during MC monitoring, relative to the control task, increased in the left inferior frontal gyrus in children. This brain activity further correlated with children's arithmetic development over a 3‐year time period. These data are in line with the frequently suggested, yet never empirically tested, hypothesis that activity in the prefrontal cortex during arithmetic is related to the higher‐order process of MC monitoring.

Towards Greater Collaboration in Educational Neuroscience: Perspectives From the 2018 Earli-SIG22 Conference

The special issue resulting from the 2018 Earli-SIG22 conference reflects the current state of the field, the diversity of methods, the persevering limitations and promising directions towards solutions. About half of the empirical papers in this special issue that consist of three parts, uses behavioral, self-report or qualitative measures to understand the "mind" level of Mind, Brain, and Education. The other half investigates the "brain" level, using neuroimaging but also genetics or eye-tracking to gain access to the wider range of biological substrates of learning and cognition. These biological studies mostly have added value by refining psychological theories, such that these inspire new hypotheses to test in the field, to ultimately better inform teaching. Importantly, the special issue presents several approaches to more intensive, bi-directional and systematic practice-research collaborations to better connect the "mind" and "brain" levels to education, and to equip researchers to realize such collaborations successfully in the future.

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.

Interference during the retrieval of arithmetic and lexico-semantic knowledge modulates similar brain regions: Evidence from functional magnetic resonance imaging (fMRI)

Single-digit multiplications are mainly solved by memory retrieval. However, these problems are also prone to errors due to systematic interference (i.e., co-activation of interconnected but incorrect solutions). Semantic control processes are crucial to overcome this type of interference and to retrieve the correct information. Previous research suggests the importance of several brain regions such as the left inferior frontal cortex and the intraparietal sulcus (IPS) for semantic control. But, this evidence is mainly based on tasks measuring interference during the processing of lexico-semantic information (e.g., pictures or words). Here, we investigated whether semantic control during arithmetic problem solving (i.e., multiplication fact retrieval) draws upon similar or different brain mechanisms as in other semantic domains (i.e., lexico-semantic). The brain activity of 46 students was measured with fMRI while participants performed an operand-related-lure (OR) and a picture-word (PW) task. In the OR task participants had to verify the correctness of a given solution to a single-digit multiplication. Similarly, in the PW task, participants had to judge whether a presented word matches the concept displayed in a picture or not. Analyses showed that resolving interference in these two tasks modulates the activation of a widespread fronto-parietal network (e.g., left/right IFG, left insula lobe, left IPS). Importantly, conjunction analysis revealed a neural overlap in the left inferior frontal gyrus (IFG) pars triangularis and left IPS. Additional Bayesian analyses showed that regions that are thought to store lexico-semantic information (e.g., left middle temporal gyrus) did not show evidence for an arithmetic interference effect. Overall, our findings not only indicate that semantic control plays an important role in arithmetic problem solving but also that it is supported by common brain regions across semantic domains. Additionally, by conducting Bayesian analysis we confirmed the hypothesis that the semantic control network contributes differently to semantic tasks of various domains.

The neural substrates of the problem size and interference effect in children's multiplication: An fMRI study

Within children's multiplication fact retrieval, performance can be influenced by various effects, such as the well-known problem size effect (i.e., smaller problems are solved faster and more accurately) and the more recent interference effect (i.e., the quality of memory representations of problems depends on previously learned problems; the more similar a problem is to a previously learned one, the more proactive interference impacts on storing in long-term-memory). This interference effect has been observed in behavioral studies, and determines a substantial part of performance beyond problem size. Unlike the problem size effect, the neural basis of the interference effect in children has not been studied. To better understand the underpinning mechanisms behind children's arithmetic fact retrieval, we aimed to investigate the neural basis of both effects in typically developing children. Twenty-four healthy 9- to 10-year-olds took part in a behavioral and fMRI scanning session, during which multiplication items had to be solved. Data were analyzed by manipulating problem size and interference level in a 2 × 2 factorial design. Concurring with previous studies, our results reveal clear behavioral effects of problem size and interference, with larger and high interfering items being solved significantly slower. On the neural level, a clear problem size effect was observed in a fronto-parietal and temporal network. The interference effect, however, was not detected; no clear neural distinctions were observed between low and high interfering items.

Distinguishing between cognitive explanations of the problem size effect in mental arithmetic via representational similarity analysis of fMRI data

Not all researchers interested in human behavior remain convinced that modern neuroimaging techniques have much to contribute to distinguishing between competing cognitive models for explaining human behavior, especially if one removes reverse inference from the table. Here, we took up this challenge in an attempt to distinguish between two competing accounts of the problem size effect (PSE), a robust finding in investigations of mathematical cognition. The PSE occurs when people solve arithmetic problems and indicates that numerically large problems are solved more slowly and erroneously than small problems. Neurocognitive explanations for the PSE can be categorized into representation-based and process-based views. Behavioral and traditional univariate neural measures have struggled to distinguish between these accounts. By contrast, a representational similarity analysis (RSA) approach with fMRI data provides competing hypotheses that can distinguish between accounts without recourse to reverse inference. To that end, our RSA (but not univariate) results provided clear evidence in favor of the representation-based over the process-based account of the PSE in multiplication; for addition, the results were less clear. Post-hoc similarity analysis distinguished still further between competing representation-based theoretical accounts. Namely, data favored the notion that individual multiplication problems are stored as individual memory traces sensitive to input frequency over a strictly magnitude-based account of memory encoding. Together, these results provide an example of how human neuroimaging evidence can directly inform cognitive-level explanations of a common behavioral phenomenon, the problem size effect. More broadly, these data may expand our understanding of calculation and memory systems in general.

More than number sense: The additional role of executive functions and metacognition in arithmetic

Arithmetic is a major building block for children's development of more complex mathematical abilities. Knowing which cognitive factors underlie individual differences in arithmetic is key to gaining further insight into children's mathematical development. The current study investigated the role of executive functions and metacognition (domain-general cognitive factors) as well as symbolic numerical magnitude processing (domain-specific cognitive factor) in arithmetic, enabling the investigation of their unique contribution in addition to each other. Participants were 127 typically developing second graders (7- and 8-year-olds). Our within-participant design took into account different components of executive functions (i.e., inhibition, shifting, and updating), different aspects of metacognitive skills (i.e., task-specific and general metacognition), and different levels of experience in arithmetic, namely addition (where second graders had extensive experience) and multiplication (where second graders were still in the learning phase). This study reveals that both updating and metacognitive monitoring are important unique predictors of arithmetic in addition to each other and to symbolic numerical magnitude processing. Our results point to a strong and unique role of task-specific metacognitive monitoring skills. These individual differences in noticing one's own errors might help one to learn from his or her mistakes.

Disentangling Neural Sources of Problem Size and Interference Effects in Multiplication

Multiplication is thought to be primarily solved via direct retrieval from memory. Two of the main factors known to influence the retrieval of multiplication facts are problem size and interference. Because these factors are often intertwined, we sought to investigate the unique influences of problem size and interference on both performance and neural responses during multiplication fact retrieval in healthy adults. Behavioral results showed that both problem size and interference explained separate unique portions of RT variance, but with significantly stronger contribution from problem size, which contrasts with previous work in children. Whole-brain fMRI results relying on a paradigm that isolated multiplication fact retrieval from response selection showed highly overlapping brain areas parametrically modulated by both problem size and interference in a large network of frontal, parietal, and subcortical brain areas. Subsequent analysis within these regions revealed problem size to be the stronger and more consistent "unique" modulating factor in overlapping regions as well as those that appeared to respond only to problem size or interference at the whole-brain level, thus underscoring the need to look beyond anatomical overlap using arbitrary thresholds. Additional unique contributions of interference (beyond problem size) were identified in right angular gyrus and subcortical regions associated with procedural processing. Together, our results suggest that problem size, relative to interference, tends to be the more dominant factor in driving behavioral and neural responses during multiplication fact retrieval in adults. Nevertheless, unique contributions of both factors demonstrate the importance of considering the overlapping and unique contributions of each in explaining the cognitive and neural bases of mental multiplication.

Relating individual differences in white matter pathways to children's arithmetic fluency: a spherical deconvolution study

Connectivity between brain regions is integral to efficient complex cognitive processing, making the study of white matter pathways in clarifying the neural mechanisms of individual differences in arithmetic abilities critical. This white matter connectivity underlying arithmetic has only been investigated through classic diffusion tensor imaging, which, due to methodological limitations, might lead to an oversimplification of the underlying anatomy. More complex non-tensor models, such as spherical deconvolution, however, allow a much more fine-grained delineation of the underlying brain anatomy. Against this background, the current study is the first to use spherical deconvolution to investigate white matter tracts and their relation to individual differences in arithmetic fluency in typically developing children. Participants were 48 typically developing 9-10-year-olds, who were all in grade 4, and who underwent structural diffusion-weighted magnetic resonance imaging scanning. Theoretically relevant white matter tracts were manually delineated with a region of interest approach, after which the hindrance modulated orientational anisotropy (HMOA) index, which provides information on the structural integrity of the tract at hand, was derived for each tract. These HMOA indices were correlated with measures of arithmetic fluency, using frequentist and Bayesian approaches. Our results point towards an association between the HMOA of the right inferior longitudinal fasciculus and individual differences in arithmetic fluency. This might reflect the efficiency with which children process Arabic numerals. Other previously found associations between white matter and individual differences in arithmetic fluency were not observed.

Patterning counts: Individual differences in children's calculation are uniquely predicted by sequence patterning

Many studies have examined the cognitive determinants of children's calculation, yet the specific contribution of children's patterning abilities to calculation remains relatively unexplored. This study investigated whether children's ability to complete sequence patterns (i.e., add the missing element into 2-4-?-8) uniquely predicted individual differences in calculation and whether these associations differed depending on the type of stimuli in these sequence patterns (i.e., number, letter, time, or rotation). Participants were 65 children in first and second grade (M_age = 7.40 years, SD = 0.44). All children completed four tasks of sequence patterning: number, letter, time, and rotation. Calculation was measured via addition and subtraction tasks. We also measured cognitive determinants of individual differences in calculation-namely symbolic number comparison, motor processing speed, visuospatial working memory, and nonverbal IQ-to verify whether patterning predicted calculation when controlling for these additional measures. We observed significant relationships between the patterning dimensions and calculation, except for the rotation dimension. Follow-up regressions, controlling for the aforementioned cognitive determinants of calculation, revealed that the number and time dimensions were strong predictors of calculation, whereas the evidence for the letter dimension was only anecdotal and the evidence for the rotation dimension was nonexistent, suggesting some degree of specificity of different types of sequence patterning in predicting calculation. Symbolic magnitude processing remained a powerful unique correlate of calculation performance. These findings add to our understanding of individual differences in calculation ability, such that sequence patterning could begin to be considered as one of the cognitive skills underlying calculation ability in young children.

Multi-method brain imaging reveals impaired representations of number as well as altered connectivity in adults with dyscalculia

Two hypotheses have been proposed about the etiology of neurodevelopmental learning disorders, such as dyslexia and dyscalculia: representation impairments and disrupted access to representations. We implemented a multi-method brain imaging approach to directly investigate these representation and access hypotheses in dyscalculia, a highly prevalent but understudied neurodevelopmental disorder in learning to calculate. We combined several magnetic resonance imaging methods and analyses, including univariate and multivariate analyses, functional and structural connectivity. Our sample comprised 24 adults with dyscalculia and 24 carefully matched controls. Results showed a clear deficit in the non-symbolic magnitude representations in parietal, temporal and frontal regions, as well as hyper-connectivity in visual brain regions in adults with dyscalculia. Dyscalculia in adults was thereby related to both impaired number representations and altered connectivity in the brain. We conclude that dyscalculia is related to impaired number representations as well as altered access to these representations.

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.

Frequency of Home Numeracy Activities Is Differentially Related to Basic Number Processing and Calculation Skills in Kindergartners

Home numeracy has been shown to play an important role in children's mathematical performance. However, findings are inconsistent as to which home numeracy activities are related to which mathematical skills. The present study disentangled between various mathematical abilities that were previously masked by the use of composite scores of mathematical achievement. Our aim was to shed light on the specific associations between home numeracy and various mathematical abilities. The relationships between kindergartners' home numeracy activities, their basic number processing and calculation skills were investigated. Participants were 128 kindergartners (Mage = 5.43 years, SD = 0.29, range: 4.88-6.02 years) and their parents. The children completed non-symbolic and symbolic comparison tasks, non-symbolic and symbolic number line estimation tasks, mapping tasks (enumeration and connecting), and two calculation tasks. Their parents completed a home numeracy questionnaire. Results indicated small but significant associations between formal home numeracy activities that involved more explicit teaching efforts (i.e., identifying numerals, counting) and children's enumeration skills. There was no correlation between formal home numeracy activities and non-symbolic number processing. Informal home numeracy activities that involved more implicit teaching attempts, such as "playing games" and "using numbers in daily life," were (weakly) correlated with calculation and symbolic number line estimation, respectively. The present findings suggest that disentangling between various basic number processing and calculation skills in children might unravel specific relations with both formal and informal home numeracy activities. This might explain earlier reported contradictory findings on the association between home numeracy and mathematical abilities.

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.

Investigating the relationship between two home numeracy measures: A questionnaire and observations during Lego building and book reading

Home numeracy has been defined as the parent-child interactions that include experiences with numerical content in daily-life settings. Previous studies have commonly operationalized home numeracy either via questionnaires or via observational methods. These studies have shown that both types of measures are positively related to variability in children's mathematical skills. This study investigated whether these distinctive data collection methods index the same aspect of home numeracy. The frequencies of home numeracy activities and parents' opinions about their children's mathematics education were assessed via a questionnaire. The amount of home numeracy talk was observed via two semi-structured videotaped parent-child activity sessions (Lego building and book reading). Children's mathematical skills were examined with two calculation subtests. We observed that parents' reports and number of observed numeracy interactions were not related to each other. Interestingly, parents' reports of numeracy activities were positively related to children's calculation abilities, whereas the observed home numeracy talk was negatively related to children's calculation abilities. These results indicate that these two methods tap on different aspects of home numeracy. Statement of contribution What is already known on this subject? Home numeracy, that is, parent-child interactions that include experiences with numerical content, is supposed to have a positive impact on calculation or mathematical ability in general. Despite many positive results, some studies have failed to find such an association. Home numeracy has been assessed with questionnaires on the frequency of numerical experiences and observations of parent-child interactions; however, those two measures of home numeracy have never been compared directly. What does this study add? This study assessed home numeracy through questionnaires and observations in the 44 parent-child dyads and showed that home numeracy measures derived from questionnaires and observations are not related. Moreover, the relation between the reported frequency of home numeracy activities and calculation on the one hand, and parent-child number talk (derived from observations) and calculation on the other hand is in opposite directions; the frequency of activities is positively related to calculation performance; and the amount of number talk is negatively related to calculation. This study shows that both measures tap into different aspects of home numeracy and can be an important factor explaining inconsistencies in literature.

Verbal and action-based measures of kindergartners' SFON and their associations with number-related utterances during picture book reading

BACKGROUND

Young children's spontaneous focusing on numerosity (SFON) as measured by experimental tasks is related to their mathematics achievement. This association is hypothetically explained by children's self-initiated practice in number recognition during everyday activities. As such, experimentally measured SFON should be associated with SFON exhibited during everyday activities and play. However, prior studies investigating this assumed association provided inconsistent findings.

AIMS

We aimed to address this issue by investigating the association between kindergartners' SFON as measured by two different experimental tasks and the frequency of their number-related utterances during a typical picture book reading activity.

SAMPLE

Participants were 65 4- to 6-year-olds in kindergarten (before the start of formal education).

METHODS

Kindergartners individually participated in two sessions. First, they completed an action-based SFON Imitation task and a verbal SFON Picture task, with a short visuo-motor task in between. Next, children were invited to spontaneously comment on the pictures of a picture book during a typical picture book reading activity.

RESULTS

Results revealed a positive association between children's SFON as measured by the Picture task and the frequency of their number-related utterances during typical picture book reading, but no such association for the Imitation task.

CONCLUSIONS

Our findings indicate that children with higher SFON as measured by a verbal experimental task also tend to focus more frequently on number during verbal everyday activities, such as picture book reading. In view of the divergent associations between our SFON measures under study with everyday number activities, the current data suggest that SFON may not be a unitary construct and/or might be task-dependent.

The principles and practices of educational neuroscience: Comment on Bowers (2016)

In his recent critique of Educational Neuroscience, Bowers argues that neuroscience has no role to play in informing education, which he equates with classroom teaching. Neuroscience, he suggests, adds nothing to what we can learn from psychology. In this commentary, we argue that Bowers' assertions misrepresent the nature and aims of the work in this new field. We suggest that, by contrast, psychological and neural levels of explanation complement rather than compete with each other. Bowers' analysis also fails to include a role for educational expertise-a guiding principle of our new field. On this basis, we conclude that his critique is potentially misleading. We set out the well-documented goals of research in Educational Neuroscience, and show how, in collaboration with educators, significant progress has already been achieved, with the prospect of even greater progress in the future. (PsycINFO Database Record

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 children's 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 children's 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. © 2017 Wiley Periodicals, Inc.

The role of physical digit representation and numerical magnitude representation in children's multiplication fact retrieval

Arithmetic facts, in particular multiplication tables, are thought to be stored in long-term memory and to be interference prone. At least two representations underpinning these arithmetic facts have been suggested: a physical representation of the digits and a numerical magnitude representation. We hypothesized that both representations are possible sources of interference that could explain individual differences in multiplication fact performance and/or in strategy use. We investigated the specificity of these interferences on arithmetic fact retrieval and explored the relation between interference and performance on the different arithmetic operations and on general mathematics achievement. Participants were 79 fourth-grade children (M_age=9.6 years) who completed a products comparison and a multiplication production task with verbal strategy reports. Performances on a speeded calculation test including the four operations and on a general mathematics achievement test were also collected. Only the interference coming from physical representations was a significant predictor of the performance across multiplications. However, both the magnitude and physical representations were unique predictors of individual differences in multiplication. The frequency of the retrieval strategy across multiplication problems and across individuals was determined only by the physical representation, which therefore is suggested as being responsible for memory storage issues. Interestingly, this impact of physical representation was not observed when predicting performance on subtraction or on general mathematical achievement. In contrast, the impact of the numerical magnitude representation was more general in that it was observed across all arithmetic operations and in general mathematics achievement.