The neural bases of the multiplication problem-size effect across countries

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

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

Arithmetic in two languages: Localizing simple multiplication processing in the adult bilingual brain

Verbally memorized multiplication tables are thought to create language-specific memories. Supporting this idea, bilinguals are typically faster and more accurate in the language in which they learned math (LA+) than in their other language (LA- ) . No study has yet revealed the underlying neurocognitive mechanisms explaining this effect, or the role of problem size in explaining the recruitment of different brain regions in LA+ and LA- . To fill this gap in the literature, 29 Spanish-English early bilingual adults, proficient in both languages, verified simple multiplication problems in each language while functional magnetic resonance imaging (fMRI) was acquired. More specifically, this study aimed to answer two questions: 1) Does LA+ recruit left superior and middle temporal gyri (STG/MTG) to a greater extent than LA- , reflecting more robust verbal representations of multiplication facts in LA+? In contrast, does LA- recruit the inferior frontal gyrus (IFG), reflecting more effortful retrieval, or the intraparietal sulcus (IPS), reflecting reliance on quantity processes? 2) Is there an interaction between language and problem size, where language differences are more pronounced for less practiced, large multiplication problems (e.g., 8 × 9) in comparison to more familiar, small problems (e.g., 2 × 3). Functional localizer tasks were used to identify hypothesis-driven regions of interest in verbal areas associated with verbal representations of arithmetic facts (left STG/MTG) and with the effortful retrieval of these facts (left IFG) and quantity areas engaged when calculation-based strategies are used (bilateral IPS). In planned analyses, no cluster reached significance for the direct comparison of languages (question 1) or for the interaction between language and problem size (question 2). An exploratory analysis found a main effect of problem size, where small problems recruited left STG/MTG and left IFG to a greater extent than large problems, suggesting greater verbal involvement for these problems in both languages. Additionally, large problems recruited right IPS to a greater extent than small problems, suggesting reliance on quantity processes. Our results suggest that proficient early bilingual adults engage similar brain regions in both languages, even for more difficult, large problems.

When multiplying is meaningful in memory: Electrophysiological signature of the problem size effect in children

Children are less fluent at verifying the answers to larger single-digit arithmetic problems compared with smaller ones. This problem size effect may reflect the structure of memory for arithmetic facts. In the current study, typically developing third to fifth graders judged the correctness of single-digit multiplication problems, presented as a sequence of three digits, that were either small (e.g., 4 3 12 vs. 4 3 16) or large (e.g., 8 7 56 vs. 8 7 64). We measured the N400, an index of access to semantic memory, along with accuracy and response time. The N400 was modulated by problem size only for correct solutions, with larger amplitude for large problems than for small problems. This suggests that only solutions that exist in memory (i.e., correct solutions) reflect a modulation of semantic access likely based on the relative frequency of encountering small versus large problems. The absence of an N400 problem size effect for incorrect solutions suggests that the behavioral problem size effects were not due to differences in initial access to memory but instead were due to a later stage of cognitive processing that was reflected in a post-N400 main effect of problem size. A second post-N400 main effect of correctness at occipital electrodes resembles the beginning of an adult-like brain response observed in prior studies. In sum, event-related brain potentials revealed different cognitive processes for correct and incorrect solutions. These results allude to a gradual transition to an adult-like brain response, from verifying multiplication problems using semantic memory to doing so using more automatic categorization.

Culture, Ethnicity, and Level of Education in Alzheimer's Disease

Alzheimer's disease (AD) is the most frequent cause of dementia, where the abnormal accumulation of beta-amyloid (Aβ) and tau lead to neurodegeneration as well as loss of cognitive, behavioral, and functional abilities. The present review analyzes AD from a cross-cultural neuropsychological perspective, looking at differences in culture-associated variables, neuropsychological test performance and biomarkers across ethnic and racial groups. Studies have found significant effects of culture, preferred language, country of origin, race, and ethnicity on cognitive test performance, although the definition of those grouping terms varies across studies. Together, with the substantial underrepresentation of minority groups in research, the inconsistent classification might conduce to an inaccuratte diagnosis that often results from biases in testing procedures that favor the group to which test developers belong. These biases persist even after adjusting for variables related to disadvantageous societal conditions, such as low level of education, unfavorable socioeconomic status, health care access, or psychological stressors. All too frequently, educational level is confounded with culture. Minorities often have lower educational attainment and lower quality of education, causing differences in test results that are then attributed to culture. Higher levels of education are also associated with increased cognitive reserve, a protective factor against cognitive decline in the presence of neurodegeneration. Biomarker research suggests there might be significant differences in specific biomarker profiles for each ethnicity/race in need of accurate cultural definitions to adequately predict risk and disease progression across ethnic/racial groups. Overall, this review highlights the need for diversity in all domains of AD research that lack inclusion and the collection of relevant information from these groups.

Alpha and theta oscillations in mental addition for high and low performers

While many contemporary studies aim to explore the sources of notable individual differences in arithmetic skills, this study specifically aims to highlight cognitive differences between high and low math performers. Thirty-six undergraduate female students who were identified as either high or low math performers, according to an arithmetic fluency test, were recruited. In the main experiment, EEG recordings were taken, while the participants performed a mental addition task. The mental addition problems were classified as either easy or difficult, and were presented to participants in several forms. The results indicated that problem difficulty increases the gap in accuracy attainment between high and low math performers. Additionally, high performers displayed larger alpha power during mental arithmetic in P7, corresponding to the left parietal lobe. This indicated that combining behavioral and neural data can improve our understanding of the differences between high and low math performers. Interpretations and implications are discussed.

Priming effects of arithmetic signs in 10- to 15-year-old children

In this research, 10- to 12- and 13- to 15-year-old children were presented with very simple addition and multiplication problems involving operands from 1 to 4. Critically, the arithmetic sign was presented before the operands in half of the trials, whereas it was presented at the same time as the operands in the other half. Our results indicate that presenting the 'x' sign before the operands of a multiplication problem does not speed up the solving process, irrespective of the age of children. In contrast, presenting the '+' sign before the operands of an addition problem facilitates the solving process, but only in 13 to 15-year-old children. Such priming effects of the arithmetic sign have been previously interpreted as the result of a pre-activation of an automated counting procedure, which can be applied as soon as the operands are presented. Therefore, our results echo previous conclusions of the literature that simple additions but not multiplications can be solved by fast counting procedures. More importantly, we show here that these procedures are possibly convoked automatically by children after the age of 13 years. At a more theoretical level, our results do not support the theory that simple additions are solved through retrieval of the answers from long-term memory by experts. Rather, the development of expertise for mental addition would consist in an acceleration of procedures until automatization.

Mapping Cultural Values onto the Brain: the Fragmented Landscape

Basic values are the core element of culture, explaining many important differences in social, economic and political effects. Yet the nature and the composition of cultural value systems remains highly debatable. An emerging field of cultural neuroscience promises to shed light on how societies differ in their value systems and on the low-level mechanisms through which they operate. A systematic review of 47 experimental studies using different brain research methods is conducted to identify neural systems and processes, which can be associated with specific values, irrespective of interpretations given by the authors of original studies. Key findings were extracted and systematized according to Hofstede's and some other (Trompenaars' and Gelfand's) models of national cultures. From the perspective of existing accounts of cultural value systems, existing literature provides only a very fragmented and biased view of the neural processing of values. Absolute majority of existing evidence (37 studies) of cultural differences in the brain functions can be associated with individualism-collectivism value dimension. Affectivity-Neutrality is identified in 11 studies, Tightness-Looseness - 6, Power Distance - 3; Indulgence, Long-Term Orientation and Universalism - 2, and Uncertainty Avoidance - 1. Other value dimensions from the applied models of culture are not represented at all. Key problems limiting the contribution of the contemporary culture neuroscience to the comparative studies of cultural values include: researchers' theoretical framing within the independence-interdependence paradigm, resulting in the loss of a broader perspective and alternative interpretations of findings, the lack of focus on the direct comparison of values and value dimensions, insufficiently representative and biased samples.

New insights from children with early focal brain injury: Lessons to be learned from examining STEM-related skills

The study of cognitive development in children with early brain injury reveals crucial information about the developing brain and its plasticity. However, information on long-term outcomes of these children, especially in domains relevant to science, technology, engineering, and math (STEM) remains limited. In the current review, our goal is to address the existing research on cognitive development of children with pre- or perinatal focal brain lesion (PL) as it relates to children's STEM-related skills and suggest future work that could shed further light on the developmental trajectories of children with PL. We argue that examining STEM-related development in children with PL will have broader implications for our understanding of the nature of the plasticity children with PL exhibit as well as address theoretical questions in the field regarding the foundation skills for STEM, including visuospatial and mathematical skills.

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.

Fluency in symbolic arithmetic refines the approximate number system in parietal cortex

The objective of this study was to investigate, using a brain measure of approximate number system (ANS) acuity, whether the precision of the ANS is crucial for the development of symbolic numerical abilities (i.e., scaffolding hypothesis) and/or whether the experience with symbolic number processing refines the ANS (i.e., refinement hypothesis). To this aim, 38 children solved a dot comparison task inside the scanner when they were approximately 10-years old (Time 1) and once again approximately 2 years later (Time 2). To study the scaffolding hypothesis, a regression analysis was carried out by entering ANS acuity at T1 as the predictor and symbolic math performance at T2 as the dependent measure. Symbolic math performance, visuospatial WM and full IQ (all at T1) were entered as covariates of no interest. In order to study the refinement hypothesis, the regression analysis included symbolic math performance at T1 as the predictor and ANS acuity at T2 as the dependent measure, while ANS acuity, visuospatial WM and full IQ (all at T1) were entered as covariates of no interest. Our results supported the refinement hypothesis, by finding that the higher the initial level of symbolic math performance, the greater the intraparietal sulcus activation was at T2 (i.e., more precise representation of quantity). To the best of our knowledge, our finding constitutes the first evidence showing that expertise in the manipulation of symbols, which is a cultural invention, has the power to refine the neural representation of quantity in the evolutionarily ancient, approximate system of quantity representation.

Increased arithmetic complexity is associated with domain-general but not domain-specific magnitude processing in children: A simultaneous fNIRS-EEG study

The investigation of the neural underpinnings of increased arithmetic complexity in children is essential for developing educational and therapeutic approaches and might provide novel measures to assess the effects of interventions. Although a few studies in adults and children have revealed the activation of bilateral brain regions during more complex calculations, little is known about children. We investigated 24 children undergoing one-digit and two-digit multiplication tasks while simultaneously recording functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG) data. FNIRS data indicated that one-digit multiplication was associated with brain activity in the left superior parietal lobule (SPL) and intraparietal sulcus (IPS) extending to the left motor area, and two-digit multiplication was associated with activity in bilateral SPL, IPS, middle frontal gyrus (MFG), left inferior parietal lobule (IPL), and motor areas. Oscillatory EEG data indicated theta increase and alpha decrease in parieto-occipital sites for both one-digit and two-digit multiplication. The contrast of two-digit versus one-digit multiplication yielded greater activity in right MFG and greater theta increase in frontocentral sites. Activation in frontal areas and theta band data jointly indicate additional domain-general cognitive control and working memory demands for heightened arithmetic complexity in children. The similarity in parietal activation between conditions suggests that children rely on domain-specific magnitude processing not only for two-digit but-in contrast to adults-also for one-digit multiplication problem solving. We conclude that in children, increased arithmetic complexity tested in an ecologically valid setting is associated with domain-general processes but not with alteration of domain-specific magnitude processing.

Sex differences in number processing: Differential systems for subtraction and multiplication were confirmed in men, but not in women

Neuroimaging studies suggest segregated neuronal systems underlying number magnitude processing (e.g. subtraction) and arithmetic fact retrieval (e.g. multiplication). While number magnitude processing is thought to rely on the intraparietal sulcus (IPS) bilaterally, arithmetic fact retrieval is thought to rely on the left angular gyrus (AG). However, evidence from brain damaged patients and brain stimulation challenges this view and suggests considerable overlap between the systems underlying number magnitude processing and arithmetic fact retrieval. This study investigates, whether sex differences in number processing can account for these conflicting findings. A subtraction and a multiplication task were administered to 40 men and 34 women in their luteal phase during functional MRI. Replicating previous studies in men, we found the IPS to be more strongly activated during subtraction than multiplication, and the AG to be more strongly activated during multiplication than subtraction. However, no differences between the two tasks were observed in women.

Neural Correlates of Math Gains Vary Depending on Parental Socioeconomic Status (SES)

We used functional magnetic resonance imaging (fMRI) to examine the neural predictors of math development, and asked whether these predictors vary as a function of parental socioeconomic status (SES) in children ranging in age from 8 to 13 years. We independently localized brain regions subserving verbal versus spatial processing in order to characterize relations between activation in these regions during an arithmetic task and long-term change in math skill (up to 3 years). Neural predictors of math gains encompassed brain regions subserving both verbal and spatial processing, but the relation between relative reliance on these regions and math skill growth varied depending on parental SES. Activity in an area of the left inferior frontal gyrus (IFG) identified by the verbal localizer was related to greater growth in math skill at the higher end of the SES continuum, but lesser improvements at the lower end. Activity in an area of the right superior parietal cortex identified by the spatial localizer was related to greater growth in math skill at the lower end of the SES continuum, but lesser improvements at the higher end. Results highlight early neural mechanisms as possible neuromarkers of long-term arithmetic learning and suggest that neural predictors of math gains vary with parental SES.

Parental socioeconomic status and the neural basis of arithmetic: differential relations to verbal and visuo-spatial representations

We examined the relation of parental socioeconomic status (SES) to the neural bases of subtraction in school-age children (9- to 12-year-olds). We independently localized brain regions subserving verbal versus visuo-spatial representations to determine whether the parental SES-related differences in children's reliance on these neural representations vary as a function of math skill. At higher SES levels, higher skill was associated with greater recruitment of the left temporal cortex, identified by the verbal localizer. At lower SES levels, higher skill was associated with greater recruitment of right parietal cortex, identified by the visuo-spatial localizer. This suggests that depending on parental SES, children engage different neural systems to solve subtraction problems. Furthermore, SES was related to the activation in the left temporal and frontal cortex during the independent verbal localizer task, but it was not related to activation during the independent visuo-spatial localizer task. Differences in activation during the verbal localizer task in turn were related to differences in activation during the subtraction task in right parietal cortex. The relation was stronger at lower SES levels. This result suggests that SES-related differences in the visuo-spatial regions during subtraction might be based in SES-related verbal differences.

The arithmetic problem size effect in children: an event-related potential study

This study used for the first time event-related potentials (ERPs) to examine the well-known arithmetic problem size effect in children. The electrophysiological correlates of this problem size effect have been well documented in adults, but such information in children is lacking. In the present study, 22 typically developing 12-year-olds were asked to solve single-digit addition problems of small (sum ≤ 10) and large problem size (sum > 10) and to speak the solution into a voice key while ERPs were recorded. Children displayed similar early and late components compared to previous adult studies on the problem size effect. There was no effect of problem size on the early components P1, N1, and P2. The peak amplitude of the N2 component showed more negative potentials on left and right anterior electrodes for large additions compared to small additions, which might reflect differences in attentional and working memory resources between large and small problems. The mean amplitude of the late positivity component which follows the N2, was significantly larger for large than for small additions at right parieto-occipital electrodes, in line with previous adult data. The ERPs of the problem size effect during arithmetic might be a useful neural marker for future studies on fact retrieval impairments in children with mathematical difficulties.

Neural mechanisms of savant calendar calculating in autism: an MEG-study of few single cases

This study contrasted the neurological correlates of calendar calculating (CC) between those individuals with autism spectrum disorder (ASD) and typically developing individuals. CC is the ability to correctly and quickly state the day of the week of a given date. Using magnetoencephalography (MEG), we presented 126 calendar tasks with dates of the present, past, and future. Event-related magnetic fields (ERF) of 3000ms duration and brain activation patterns were compared in three savant calendar calculators with ASD (ASDCC) and three typically developing calendar calculators (TYPCC). ASDCC outperformed TYPCC in correct responses, but not in answering speed. Comparing amplitudes of their ERFs, there was a main effect of group between 1000 and 3000ms, but no further effects of hemisphere or sensor location. We conducted CLARA source analysis across the entire CC period in each individual. Both ASDCC and TYPCC exhibited activation maxima in prefrontal areas including the insulae and the left superior temporal gyrus. This is in accordance with verbal fact retrieval and working memory as well as monitoring and coordination processes. In ASDCC, additional activation sites at the right superior occipital gyrus, the right precuneus, and the right putamen point to visual-spatial strategies and are in line with the preference of autistic individuals for engaging posterior regions relatively more strongly in various reasoning and problem solving tasks.

Cultural differences in human brain activity: a quantitative meta-analysis

Psychologists have been trying to understand differences in cognition and behavior between East Asian and Western cultures within a single cognitive framework such as holistic versus analytic or interdependent versus independent processes. However, it remains unclear whether cultural differences in multiple psychological processes correspond to the same or different neural networks. We conducted a quantitative meta-analysis of 35 functional MRI studies to examine cultural differences in brain activity engaged in social and non-social processes. We showed that social cognitive processes are characterized by stronger activity in the dorsal medial prefrontal cortex, lateral frontal cortex and temporoparietal junction in East Asians but stronger activity in the anterior cingulate, ventral medial prefrontal cortex and bilateral insula in Westerners. Social affective processes are associated with stronger activity in the right dorsal lateral frontal cortex in East Asians but greater activity in the left insula and right temporal pole in Westerners. Non-social processes induce stronger activity in the left inferior parietal cortex, left middle occipital and left superior parietal cortex in East Asians but greater activations in the right lingual gyrus, right inferior parietal cortex and precuneus in Westerners. The results suggest that cultural differences in social and non-social processes are mediated by distinct neural networks. Moreover, East Asian cultures are associated with increased neural activity in the brain regions related to inference of others' mind and emotion regulation whereas Western cultures are associated with enhanced neural activity in the brain areas related to self-relevance encoding and emotional responses during social cognitive/affective processes.

Children with mathematical learning disability fail in recruiting verbal and numerical brain regions when solving simple multiplication problems

Greater skill in solving single-digit multiplication problems requires a progressive shift from a reliance on numerical to verbal mechanisms over development. Children with mathematical learning disability (MD), however, are thought to suffer from a specific impairment in numerical mechanisms. Here we tested the hypothesis that this impairment might prevent MD children from transitioning toward verbal mechanisms when solving single-digit multiplication problems. Brain activations during multiplication problems were compared in MD and typically developing (TD) children (3rd to 7th graders) in numerical and verbal regions which were individuated by independent localizer tasks. We used small (e.g., 2 × 3) and large (e.g., 7 × 9) problems as these problems likely differ in their reliance on verbal versus numerical mechanisms. Results indicate that MD children have reduced activations in both the verbal (i.e., left inferior frontal gyrus and left middle temporal to superior temporal gyri) and the numerical (i.e., right superior parietal lobule including intra-parietal sulcus) regions suggesting that both mechanisms are impaired. Moreover, the only reliable activation observed for MD children was in the numerical region when solving small problems. This suggests that MD children could effectively engage numerical mechanisms only for the easier problems. Conversely, TD children showed a modulation of activation with problem size in the verbal regions. This suggests that TD children were effectively engaging verbal mechanisms for the easier problems. Moreover, TD children with better language skills were more effective at engaging verbal mechanisms. In conclusion, results suggest that the numerical- and language-related processes involved in solving multiplication problems are impaired in MD children.