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This study investigated the role of brain regions involved in arithmetic processing in explaining individual differences in financial ability in 67 50-74-year-old cognitively normal adults. Structural integrity and resting-state functional connectivity measures were collected in the MRI scanner. Outside the scanner, participants performed financial ability and other cognitive tasks, and answered questionnaires to determine dementia risk, and financial risk and protective factors. Regions of interest involved in arithmetic processing were defined, focusing on language- and quantity-processing areas in temporo-frontal and parieto-frontal cortices, respectively. Our results showed that structural integrity and functional connectivity in brain regions associated with arithmetic retrieval were positively associated with financial ability, with language skill mediating left IFG structural integrity and financial ability. Connectivity patterns suggested that reliance on quantity mechanisms (i.e. calculation) was associated with poorer financial ability. Analyses revealed that reliance on these brain mechanisms did not depend on participants' age or risk of dementia and that protective factors such as household income or financial literacy supported the maintenance of connectivity related to financial abilities., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

Math learning is explained by the interaction between cognitive, affective, and social factors. However, studies rarely investigate how these factors interact with one another to explain math performance. This study aims to fill this gap in the literature by using functional magnetic resonance imaging (fMRI) to understand the neurocognitive mechanisms underlying the interaction between parental socioeconomic status (SES) and children's math attitudes. To this aim, 57 children solved multiplication problems inside the scanner. We measured parental SES by creating two groups based on parents' occupations and measured children's math attitudes using a questionnaire. We ran a cluster-wise regression analysis examining the interaction between these two variables while controlling for the main effects of SES, math attitudes, and full IQ. The analysis revealed a cluster in the left inferior frontal gyrus (IFG), which was due to children with positive math attitudes from high socio-economic status families showing greater IFG activation when solving large multiplication problems as compared to their negative attitudes high SES peers, suggesting that they exhibited more retrieval effort to solve large multiplication problems. We discuss how this may be because they were the only ones who fully engaged in math opportunities provided by their environment., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

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., Competing Interests: DECLARATION OF COMPETING INTEREST The authors declare no conflict of interest.

Math attitudes are related to achievement, yet we do not know how the brain supports changes in math attitudes. 51 children (54.9% female, 45.1% male; 37.3% White, 33.3% Black, 11.8% Latino, 5.9% Asian, 11.8% Other) solved a multiplication task inside the scanner when they were approximately 11 (time 1; T1) and 13 (time 2; T2) years old (i.e., mean age). Results revealed clusters in the left middle to superior temporal gyri at T1 associated with math attitudes at T1 and with their longitudinal improvement. However, changes in attitudes were not associated with brain changes over time. These findings suggest that relying on the storage of arithmetic facts, involved in memory retrieval, explains the development of positive math attitudes., (© 2022 The Authors. Child Development © 2022 Society for Research in Child Development.)

Enhancing student's math achievement is a significant educational challenge. Numerous studies have shown that math attitudes can predict improvement in math performance, but no study has yet revealed the underlying neurocognitive mechanisms explaining this effect. To answer this question, 50 children underwent functional magnetic resonance imaging (fMRI) when they were 11 (time 1; T1) and 13 (time 2; T2) years old. Children solved a rhyming judgment and a single-digit multiplication task inside the scanner at T1. The rhyming task was used to independently define a verbal region of interest in the left inferior frontal gyrus (IFG). We focused on this region because of previous evidence showing math attitudes-related effects in the left IFG for children with low math skill (Demir-Lira et al., 2019). Children completed standardized testing of math attitudes at T1 and of multiplication skill both at T1 and T2. We performed a cluster-wise regression analysis to investigate the interaction between math attitudes and improvement in multiplication skill over time while controlling for the main effects of these variables, intelligence, and accuracy on the task. This analysis revealed a significant interaction in the left IFG, which was due to improvers with positive math attitudes showing enhanced activation. Our result suggests that IFG activation, possibly reflecting effort invested in retrieving multiplication facts, is one of the possible neurocognitive mechanism by which children with positive math attitudes improve in multiplication skill. Our finding suggests that teachers and parents can help children do better in math by promoting positive math attitudes., (© 2021. The Psychonomic Society, Inc.)

Although behavioral studies show large improvements in arithmetic skills in elementary school, we do not know how brain structure supports math gains in typically developing children. While some correlational studies have investigated the concurrent association between math performance and brain structure, such as gray matter volume (GMV), longitudinal studies are needed to infer if there is a causal relation. Although discrepancies in the literature on the relation between GMV and math performance have been attributed to the different demands on quantity vs. retrieval mechanisms, no study has experimentally tested this assumption. We defined regions of interests (ROIs) associated with quantity representations in the bilateral intraparietal sulcus (IPS) and associated with the storage of arithmetic facts in long-term memory in the left middle and superior temporal gyri (MTG/STG), and studied associations between GMV in these ROIs and children's performance on operations having greater demands on quantity vs. retrieval mechanisms, namely subtraction vs. multiplication. The aims of this study were threefold: First, to study concurrent associations between GMV and math performance, second, to investigate the role of GMV at the first time-point (T1) in predicting longitudinal gains in math skill to the second time-point (T2), and third, to study whether changes in GMV over time were associated with gains in math skill. Results showed no concurrent association between GMV in IPS and math performance, but a concurrent association between GMV in left MTG/STG and multiplication skill at T1. This association showed that the higher the GMV in this ROI, the higher the children's multiplication skill. Results also revealed that GMV in left IPS and left MTG/STG predicted longitudinal gains in subtraction skill only for younger children (approximately 10 years old). Whereas higher levels of GMV in left IPS at T1 predicted larger subtraction gains, higher levels of GMV in left MTG/STG predicted smaller gains. GMV in left MTG/STG did not predict longitudinal gains in multiplication skill. No significant association was found between changes in GMV over time and longitudinal gains in math. Our findings support the early importance of brain structure in the IPS for mathematical skills that rely on quantity mechanisms., Competing Interests: Declaration of Competing Interest The authors declare that they have no conflict of interest., (Copyright © 2021. Published by Elsevier Inc.)

Attitudes towards math (ATM) predict math achievement. Negative ATM are associated with avoidance of math content, while positive ATM are associated with exerting more effort on math tasks. Recent literature highlights the importance of considering interactions between ATM and math skill in examining relations to achievement. This study investigated, for the first time, the effects of the interaction between math skill and ATM on the neurocognitive basis of arithmetic processing. We examined the effect of this interaction using a single-digit multiplication task in 9- to 12-year-old children. Results showed that higher math skill was correlated with less activation in the left inferior frontal gyrus (IFG), and positive ATM were correlated with less activation in the left IFG. The relation between ATM and the neural basis of multiplication varied depending on math skill. Only among children with lower math skill, positive ATM were associated with greater activation of the left IFG. The results suggest that positive ATM in low skill children might encourage them to more fully engage the neurocognitive systems underlying controlled effort and retrieval of multiplication facts. Our results highlight the importance of examining the role of both attitudinal and cognitive factors on the neural basis of arithmetic development.

There is debate in the literature regarding how single-digit arithmetic fluency is achieved over development. While the Fact-retrieval hypothesis suggests that with practice, children shift from quantity-based procedures to verbally retrieving arithmetic problems from long-term memory, the Schema-based hypothesis claims that problems are solved through quantity-based procedures and that practice leads to these procedures becoming more automatic. To test these hypotheses, a sample of 46 typically developing children underwent functional magnetic resonance imaging (fMRI) when they were 11 years old (time 1), and 2 years later (time 2). We independently defined regions of interest (ROIs) involved in verbal and quantity processing using rhyming and numerosity judgment localizer tasks, respectively. The verbal ROIs consisted of left middle/superior temporal gyri (MTG/STG) and left inferior frontal gyrus (IFG), whereas the quantity ROIs consisted of bilateral inferior/superior parietal lobules (IPL/SPL) and bilateral middle frontal gyri (MFG)/right IFG. Participants also solved a single-digit subtraction task in the scanner. We defined the extent to which children relied on verbal vs. quantity mechanisms by selecting the 100 voxels showing maximal activation at time 1 from each ROI, separately for small and large subtractions. We studied the brain mechanisms at time 1 that predicted gains in subtraction fluency and how these mechanisms changed over time with improvement. When looking at brain activation at time 1, we found that improvers showed a larger neural problem size effect in bilateral parietal cortex, whereas no effects were found in verbal regions. Results also revealed that children who showed improvement in behavioral fluency for large subtraction problems showed decreased activation over time for large subtractions in both parietal and frontal regions implicated in quantity, whereas non-improvers maintained similar levels of activation. All children, regardless of improvement, showed decreased activation over time for large subtraction problems in verbal regions. The greater parietal problem size effect at time 1 and the reduction in activation over time for the improvers in parietal and frontal regions implicated in quantity processing is consistent with the Schema-based hypothesis arguing for more automatic procedures with increasing skill. The lack of a problem size effect at time 1 and the overall decrease in verbal regions, regardless of improvement, is inconsistent with the Fact-retrieval hypothesis., (Copyright © 2020 Suárez-Pellicioni, Berteletti and Booth.)

Behavioral studies have shown discrepant results regarding the role of phonology in predicting math gains. The objective of this study was to use fMRI to study the role of activation during a rhyming judgment task in predicting behavioral gains on math fluency, multiplication, and subtraction skill. We focused within the left middle/superior temporal gyrus and left inferior frontal gyrus, brain areas associated with the storage of phonological representations and with their access, respectively. We ran multiple regression analyses to determine whether activation predicted gains in the three math measures, separately for younger (i.e. 10 years old) and older (i.e 12 years old) children. Results showed that activation in both temporal and frontal cortex only predicted gains in fluency and multiplication skill, and only for younger children. This study suggests that both temporal and frontal cortex activation during phonological processing are important in predicting gains in math tasks that involve the retrieval of facts that are stored as phonological codes in memory. Moreover, these results were specific to younger children, suggesting that phonology is most important in the early stages of math development. When the math task involved subtractions, which relies on quantity representations, phonological processes were not important in driving gains., (Copyright © 2019 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Models of the neural basis of arithmetic argue that left inferior frontal cortex is involved in cognitive control of verbal representations of math facts in left lateral temporal cortex, whereas bilateral intra-parietal cortex is involved in numerical calculation. Lower levels of math competence for multiplications is associated with greater effortful retrieval because of less robust verbal representations and the engagement of numerical operations as a back-up strategy. Previous studies on multiplication have focused on brain activation in isolated nodes of the network, so we do not know how functional connectivity between these nodes is related to competence. Moreover, previous studies have not employed longitudinal designs, so we do not know how changes in multiplication performance over time is related to changes in its neural basis. The objective of this study was to investigate how changes in multiplication task performance is associated with changes in functional connectivity of temporal cortex with frontal and parietal cortices. Longitudinal data was collected from 45 children, with an average 2.2-year interval between the two sessions, when they were about 11 years old at time 1 (T1) and 13 years old at time 2 (T2). A Psychophysiological Interaction (PPI) analysis was carried out by defining the seed in the temporal cortex (i.e. posterior superior and middle temporal gyri) and examining changes in connectivity with frontal cortex (i.e. left inferior frontal gyrus) as well as parietal cortex (i.e. left and right inferior and superior parietal lobules). We found that children who did not improve in a multiplication task showed greater levels of functional connectivity of left temporal cortex with left inferior frontal gyrus (IFG) and left intraparietal sulcus (IPS) at T2, as compared to their peers who improved. The cluster showing greater levels of connectivity in the left IFG at T2 for the Non-improvers overlapped a cluster independently identified by a verbal localizer task and the cluster showing greater levels of connectivity in the left IPS Non-improvers overlapped a cluster independently identified by a numerosity localizer task. These results suggest that lack of improvement in multiplications are associated with greater cognitive control of verbal representations and greater engagement of numerical operations., (Copyright © 2018 Elsevier Inc. All rights reserved.)

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., (© 2018 Wiley Periodicals, Inc.)

The aim of the study was to investigate how high math-anxious (HMA) individuals react to errors in an arithmetic task. Twenty HMA and 19 low math-anxious (LMA) individuals were presented with a multi-digit addition verification task and were given response feedback. Post-error adjustment measures (response time and accuracy) were analyzed in order to study differences between groups when faced with errors in an arithmetical task. Results showed that both HMA and LMA individuals were slower to respond following an error than following a correct answer. However, post-error accuracy effects emerged only for the HMA group, showing that they were also less accurate after having committed an error than after giving the right answer. Importantly, these differences were observed only when individuals needed to repeat the same response given in the previous trial. These results suggest that, for HMA individuals, errors caused reactive inhibition of the erroneous response, facilitating performance if the next problem required the alternative response but hampering it if the response was the same. This stronger reaction to errors could be a factor contributing to the difficulties that HMA individuals experience in learning math and doing math tasks., (Copyright © 2017 Elsevier B.V. All rights reserved.)

We investigated the time course of neural processing of multi-digit additions in high- (HMA) and low-math anxious (LMA) individuals. Seventeen HMA and 17 LMA individuals were presented with two-digit additions and were asked to perform a verification task. Behavioral data showed that HMA individuals were slower and more error prone than their LMA peers, and that incorrect solutions were solved more slowly and less accurately than correct ones. Moreover, HMA individuals tended to need more time and commit more errors when having to verify incorrect solutions than correct ones. ERPs time-locked to the presentation of the addends (calculation phase) and to the presentation of the proposed solution (verification phase) were also analyzed. In both phases, a P2 component of larger amplitude was found for HMA individuals than for their LMA peers. Because the P2 component is considered to be a biomarker of the mobilization of attentional resources toward emotionally negative stimuli, these results suggest that HMA individuals may have invested more attentional resources both when processing the addends (calculation phase) and when they had to report whether the proposed solution was correct or not (verification phase), as compared to their LMA peers. Moreover, in the verification phase, LMA individuals showed a larger late positive component (LPC) for incorrect solutions at parietal electrodes than their HMA counterparts. The smaller LPC shown by HMA individuals when verifying incorrect solutions suggests that these solutions may have been appeared more plausible to them than to their LMA counterparts.

Numerical comparison tasks are widely used to study the mental representation of numerical magnitude. In study, event-related brain potentials (ERPs) were recorded while 26 high math-anxious (HMA) and 27 low math-anxious (LMA) individuals were presented with pairs of single-digit Arabic numbers and were asked to decide which one had the larger numerical magnitude. The size of the numbers and the distance between them were manipulated in order to study the size and the distance effects. The results showed that both distance and size effects were larger for the HMA group. As for ERPs, results showed that the ERP distance effect had larger amplitude for both the size and distance effects in the HMA group than among their LMA counterparts. Since this component has been taken as a marker of the processing of numerical magnitude, this result suggests that HMA individuals have a less precise representation of numerical magnitude., (Copyright © 2014 Elsevier B.V. All rights reserved.)

This study uses event-related brain potentials (ERPs) to investigate the electrophysiological correlates of numeric conflict monitoring in math-anxious individuals, by analyzing whether math anxiety is related to abnormal processing in early conflict detection (as shown by the N450 component) and/or in a later, response-related stage of processing (as shown by the conflict sustained potential; Conflict-SP). Conflict adaptation effects were also studied by analyzing the effect of the previous trial's congruence in current interference. To this end, 17 low math-anxious (LMA) and 17 high math-anxious (HMA) individuals were presented with a numerical Stroop task. Groups were extreme in math anxiety but did not differ in trait or state anxiety or in simple math ability. The interference effect of the current trial (incongruent-congruent) and the interference effect preceded by congruence and by incongruity were analyzed both for behavioral measures and for ERPs. A greater interference effect was found for response times in the HMA group than in the LMA one. Regarding ERPs, the LMA group showed a greater N450 component for the interference effect preceded by congruence than when preceded by incongruity, while the HMA group showed greater Conflict-SP amplitude for the interference effect preceded by congruence than when preceded by incongruity. Our study showed that the electrophysiological correlates of numeric interference in HMA individuals comprise the absence of a conflict adaptation effect in the first stage of conflict processing (N450) and an abnormal subsequent up-regulation of cognitive control in order to overcome the conflict (Conflict-SP). More concretely, our study shows that math anxiety is related to a reactive and compensatory recruitment of control resources that is implemented only when previously exposed to a stimuli presenting conflicting information.

This paper focuses on the capacity to solve numerical incongruities in high- and lower-skilled arithmetic problem-solvers by investigating event-related brain potentials elicited by incorrect solutions to additions. Fifteen high-skill and fifteen low-skill individuals were presented with simple addition problems in a verification task. The proposed solution was manipulated by presenting correct solutions and incorrect solutions very close to the correct ones. Incorrect solutions elicited a negative component followed by a late positive component (LPC/P3b), whose amplitude was smaller for the low-skill group than for the high-skill group. Because the LPC/P3b amplitude has been taken as an indicator of the plausibility of the stimulus, this result suggests that incorrect solutions close to the correct ones appear more plausible to low-skilled individuals than to their high-skilled counterparts. This result is interpreted in terms of differences in the strength of association between problems and potential solutions depending on arithmetical skill.