Individual differences in working memory, nonverbal IQ, and mathematics achievement and brain mechanisms associated with symbolic and nonsymbolic number processing

Lower resting state functional connectivity partially mediates adverse effects of prenatal alcohol exposure on arithmetic performance in children

BACKGROUND

Fetal alcohol spectrum disorders (FASD) include a range of neurocognitive and behavioral impairments resulting from prenatal alcohol exposure (PAE). Among the PAE-related cognitive deficits, number processing is particularly affected. This study examines alterations in number processing networks and whether changes in functional connectivity mediate the adverse effects of PAE on arithmetic performance.

METHODS

Magnetic resonance imaging (MRI) was acquired in 57 children (mean (SD) age = 11.3 (+0.9) yr), 38 with FASD (19 fetal alcohol syndrome (FAS) or partial FAS (PFAS), 19 heavily exposed (HE)) and 19 controls. Whole-brain correlation analyses were performed from five seeds located in regions involved in number processing.

RESULTS

Children with FAS/PFAS showed dose-dependent reductions in resting state functional connectivity between the seed in the right (R) posterior superior parietal lobule and a cluster in the left (L) inferior frontal gyrus, and between a seed in the R horizontal intraparietal sulcus and clusters in the R precentral gyrus and L cerebellar lobule VI. HE children showed lower resting state functional connectivity in a subset of these regions. Lower functional connectivity in the two fronto-parietal connections partially mediated the adverse effects of PAE on arithmetic performance.

CONCLUSION

This study demonstrates PAE-related functional connectivity impairments in functional networks involved in number processing. The weaker connectivity between the R posterior superior parietal lobule and the L inferior frontal gyrus suggests that impaired verbal processing and visuospatial working memory may play a role in number processing deficits, while weaker connectivity between the R intraparietal sulcus and the R precentral gyrus points to poorer finger-based numerical representation, which has been linked to arithmetic computational skills.

An fMRI intervention study of creative mathematical reasoning: behavioral and brain effects across different levels of cognitive ability

BACKGROUND

Many learning methods of mathematical reasoning encourage imitative procedures (algorithmic reasoning, AR) instead of more constructive reasoning processes (creative mathematical reasoning, CMR). Recent research suggest that learning with CMR compared to AR leads to better performance and differential brain activity during a subsequent test. Here, we considered the role of individual differences in cognitive ability in relation to effects of CMR.

METHODS

We employed a within-subject intervention (N=72, M_Age=18.0) followed by a brain-imaging session (fMRI) one week later. A battery of cognitive tests preceded the intervention. Participants were divided into three cognitive ability groups based on their cognitive score (low, intermediate and high).

RESULTS

On mathematical tasks previously practiced with CMR compared to AR we observed better performance, and higher brain activity in key regions for mathematical cognition such as left angular gyrus and left inferior/middle frontal gyrus. The CMR-effects did not interact with cognitive ability, albeit the effects on performance were driven by the intermediate and high cognitive ability groups.

CONCLUSIONS

Encouraging pupils to engage in constructive processes when learning mathematical reasoning confers lasting learning effects on brain activation, independent of cognitive ability. However, the lack of a CMR-effect on performance for the low cognitive ability group suggest future studies should focus on individualized learning interventions, allowing more opportunities for effortful struggle with CMR.

A Systematic Review of MRI Neuroimaging for Education Research

This study aims to disclose how the magnetic resonance imaging (MRI) neuroimaging approach has been applied in education studies, and what kind of learning themes has been investigated in the reviewed MRI neuroimaging research. Based on the keywords “brain or neuroimaging or neuroscience” and “MRI or diffusion tensor imaging (DTI) or white matter or gray matter or resting-state,” a total of 25 papers were selected from the subject areas “Educational Psychology” and “Education and Educational Research” from the Web of Science and Scopus from 2000 to 2019. Content analysis showed that MRI neuroimaging and learning were studied under the following three major topics and nine subtopics: cognitive function (language, creativity, music, physical activity), science education (mathematical learning, biology learning, physics learning), and brain development (parenting, personality development). As for the type of MRI neuroimaging research, the most frequently used approaches were functional MRI, followed by structural MRI and DTI, although the choice of approach was often motivated by the specific research question. Research development trends show that the neural plasticity theme has become more prominent recently. This study concludes that in educational research, the MRI neuroimaging approach provides objective and empirical evidence to connect learning processes, outcomes, and brain mechanisms.

Attention to number: The convergence of numerical magnitude processing, attention, and mathematics in the inferior frontal gyrus

Research indicates that the neurocognitive system representing nonsymbolic numerical magnitudes is foundational for the development of mathematical competence. However, recent studies found that the most common task used to measure numerical acuity, the nonsymbolic number comparison task, is heavily influenced by non-numerical visual parameters of stimuli that increase executive function demands. Further, this influence may be a confound invalidating theoretical accounts of the relation between number comparison performance and mathematical competence. Instead of acuity, the relation may depend on one's ability to attend to numerical information in the face of competing, non-numerical cues. The current study investigated this issue by measuring neural activity associated with numerical magnitude processing acuity, domain-general attention, and selective attention to number via functional magnetic resonance imaging while children 8-11 years old completed a nonsymbolic number comparison task and a flanker task. Results showed that activation in the right inferior frontal gyrus during incongruent versus congruent trials of the comparison task, our construct for attention to number, predicted mathematics achievement after controlling for verbal IQ, flanker accuracy rate, and the neural congruency effect from the flanker task. In contrast, activity in frontal and parietal regions responding to differences in difficulty of numerical comparisons, our construct for numerical magnitude processing acuity, did not correlate with achievement. Together, these findings suggest a need to reframe existing models of the relation between number processing and math competence to include the interaction between attention and use of numerical information, or in other words "attention to number."

Altered Parietal Activation during Non-symbolic Number Comparison in Children with Prenatal Alcohol Exposure

Number processing is a cognitive domain particularly sensitive to prenatal alcohol exposure, which relies on intact parietal functioning. Alcohol-related alterations in brain activation have been found in the parietal lobe during symbolic number processing. However, the effects of prenatal alcohol exposure on the neural correlates of non-symbolic number comparison and the numerical distance effect have not been investigated. Using functional magnetic resonance imaging (fMRI), we examined differences in brain activation associated with prenatal alcohol exposure in five parietal regions involved in number processing during a non-symbolic number comparison task with varying degrees of difficulty. fMRI results are presented for 27 Cape Colored children (6 fetal alcohol syndome (FAS)/partial FAS, 5 heavily exposed (HE) non-sydromal, 16 controls; mean age ± SD = 11.7 ± 1.1 years). Fetal alcohol exposure was assessed by interviewing mothers using a timeline follow-back approach. Separate subject analyses were performed in each of five regions of interest, bilateral horizontal intraparietal sulci (IPS), bilateral posterior superior parietal lobules (PSPL), and left angular gyrus (left AG), using the general linear model with predictors for number comparison and difficulty level. Mean percent signal change for each predictor was extracted for each subject for each region to examine group differences and associations with continuous measures of alcohol exposure. Although groups did not differ in performance, controls activated the right PSPL more during non-symbolic number comparison than exposed children, but this was not significant after controlling for maternal smoking, and the right IPS more than children with fetal alcohol syndrome (FAS) or partial FAS. More heavily exposed children recruited the left AG to a greater extent as task difficulty increased, possibly to compensate, in part, for impairments in function in the PSPL and IPS. Notably, in non-syndromal heavily exposed children activation was impaired in the right PSPL, but spared in the right IPS. These results extend previous findings of poor right IPS recruitment during symbolic number processing in FAS/PFAS, indicating that mental representation of relative quantity is affected by prenatal alcohol exposure for both symbolic and non-symbolic representations of quantity.

The approximate number system and domain-general abilities as predictors of math ability in children with normal hearing and hearing loss

Many children with hearing loss (CHL) show a delay in mathematical achievement compared to children with normal hearing (CNH). This study examined whether there are differences in acuity of the approximate number system (ANS) between CHL and CNH, and whether ANS acuity is related to math achievement. Working memory (WM), short-term memory (STM), and inhibition were considered as mediators of any relationship between ANS acuity and math achievement. Seventy-five CHL were compared with 75 age- and gender-matched CNH. ANS acuity, mathematical reasoning, WM, and STM of CHL were significantly poorer compared to CNH. Group differences in math ability were no longer significant when ANS acuity, WM, or STM was controlled. For CNH, WM and STM fully mediated the relationship of ANS acuity to math ability; for CHL, WM and STM only partially mediated this relationship. ANS acuity, WM, and STM are significant contributors to hearing status differences in math achievement, and to individual differences within the group of CHL. Statement of contribution What is already known on this subject? Children with hearing loss often perform poorly on measures of math achievement, although there have been few studies focusing on basic numerical cognition in these children. In typically developing children, the approximate number system predicts math skills concurrently and longitudinally, although there have been some contradictory findings. Recent studies suggest that domain-general skills, such as inhibition, may account for the relationship found between the approximate number system and math achievement. What does this study adds? This is the first robust examination of the approximate number system in children with hearing loss, and the findings suggest poorer acuity of the approximate number system in these children compared to hearing children. The study addresses recent issues regarding the contradictory findings of the relationship of the approximate number system to math ability by examining how this relationship varies across children with normal hearing and hearing loss, and by examining whether this relationship is mediated by domain-general skills (working memory, short-term memory, and inhibition).

The effect of visual parameters on neural activation during nonsymbolic number comparison and its relation to math competency

Nonsymbolic numerical comparison task performance (whereby a participant judges which of two groups of objects is numerically larger) is thought to index the efficiency of neural systems supporting numerical magnitude perception, and performance on such tasks has been related to individual differences in math competency. However, a growing body of research suggests task performance is heavily influenced by visual parameters of the stimuli (e.g. surface area and dot size of object sets) such that the correlation with math is driven by performance on trials in which number is incongruent with visual cues. Almost nothing is currently known about whether the neural correlates of nonsymbolic magnitude comparison are also affected by visual congruency. To investigate this issue, we used functional magnetic resonance imaging (fMRI) to analyze neural activity during a nonsymbolic comparison task as a function of visual congruency in a sample of typically developing high school students (n = 36). Further, we investigated the relation to math competency as measured by the preliminary scholastic aptitude test (PSAT) in 10th grade. Our results indicate that neural activity was modulated by the ratio of the dot sets being compared in brain regions previously shown to exhibit an effect of ratio (i.e. left anterior cingulate, left precentral gyrus, left intraparietal sulcus, and right superior parietal lobe) when calculated from the average of congruent and incongruent trials, as it is in most studies, and that the effect of ratio within those regions did not differ as a function of congruency condition. However, there were significant differences in other regions in overall task-related activation, as opposed to the neural ratio effect, when congruent and incongruent conditions were contrasted at the whole-brain level. Math competency negatively correlated with ratio-dependent neural response in the left insula across congruency conditions and showed distinct correlations when split across conditions. There was a positive correlation between math competency in the right supramarginal gyrus during congruent trials and a negative correlation in the left angular gyrus during incongruent trials. Together, these findings support the idea that performance on the nonsymbolic comparison task relates to math competency and ratio-dependent neural activity does not differ by congruency condition. With regards to math competency, congruent and incongruent trials showed distinct relations between math competency and individual differences in ratio-dependent neural activity.

Predictive model for early math skills based on structural equations

Early math skills are determined by higher cognitive processes that are particularly important for acquiring and developing skills during a child's early education. Such processes could be a critical target for identifying students at risk for math learning difficulties. Few studies have considered the use of a structural equation method to rationalize these relations. Participating in this study were 207 preschool students ages 59 to 72 months, 108 boys and 99 girls. Performance with respect to early math skills, early literacy, general intelligence, working memory, and short-term memory was assessed. A structural equation model explaining 64.3% of the variance in early math skills was applied. Early literacy exhibited the highest statistical significance (β = 0.443, p < 0.05), followed by intelligence (β = 0.286, p < 0.05), working memory (β = 0.220, p < 0.05), and short-term memory (β = 0.213, p < 0.05). Correlations between the independent variables were also significant (p < 0.05). According to the results, cognitive variables should be included in remedial intervention programs.

A Systematic Investigation of Accuracy and Response Time Based Measures Used to Index ANS Acuity

The approximate number system (ANS) was proposed to be a building block for later mathematical abilities. Several measures have been used interchangeably to assess ANS acuity. Some of these measures were based on accuracy data, whereas others relied on response time (RT) data or combined accuracy and RT data. Previous studies challenged the view that all these measures can be used interchangeably, because low correlations between some of the measures had been observed. These low correlations might be due to poor reliability of some of the measures, since the majority of these measures are mathematically related. Here we systematically investigated the relationship between common ANS measures while avoiding the potential confound of poor reliability. Our first experiment revealed high correlations between all accuracy based measures supporting the assumption that all of them can be used interchangeably. In contrast, not all RT based measures were highly correlated. Additionally, our results revealed a speed-accuracy trade-off. Thus, accuracy and RT based measures provided conflicting conclusions regarding ANS acuity. Therefore, we investigated in two further experiments which type of measure (accuracy or RT) is more informative about the underlying ANS acuity, depending on participants’ preferences for accuracy or speed. To this end, we manipulated participants’ preferences for accuracy or speed both explicitly using different task instructions and implicitly varying presentation duration. Accuracy based measures were more informative about the underlying ANS acuity than RT based measures. Moreover, the influence of the underlying representations on accuracy data was more pronounced when participants preferred accuracy over speed after the accuracy instruction as well as for long or unlimited presentation durations. Implications regarding the diffusion model as a theoretical framework of dot comparison as well as regarding the relationship between ANS acuity and math performance are discussed.

Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students' level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of 4 years as a variable. The sampled students were initially assessed by means of an Early Numeracy Test, and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence. The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students' performance in EMCs was a strong predictor for achievement in mathematics for students between 8 and 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain.

Working Memory and Number Sense as Predictors of Mathematical (Dis-)Ability

Recent research has pointed to two possible causes of mathematical (dis-)ability: working memory and number sense, although only few studies have compared the relations between working memory and mathematics and between number sense and mathematics. In this study, both constructs were studied in relation to mathematics in general, and to mathematical learning disabilities (MLD) in particular. The sample consisted of 154 children aged between 6 and 10 years, including 26 children with MLD. Children performing low on either number sense or visual-spatial working memory scored lower on math tests than children without such a weakness. Children with a double weakness scored the lowest. These results confirm the important role of both visual-spatial working memory and number sense in mathematical development.

Numerical magnitude processing deficits in children with mathematical difficulties are independent of intelligence

Developmental dyscalculia (DD) is thought to arise from difficulties in the ability to process numerical magnitudes. Most research relied on IQ-discrepancy based definitions of DD and only included individuals with normal IQ, yet little is known about the role of intelligence in the association between numerical magnitude processing and mathematical difficulties (MD). The present study examined numerical magnitude processing in matched groups of 7- to 8-year-olds (n=42) who had either discrepant MD (poor math scores, average IQ), nondiscrepant MD (poor math scores, below-average IQ) or no MD. Both groups of children with MD showed similar impairments in numerical magnitudes processing compared to controls, suggesting that the association between numerical magnitude processing deficits and MD is independent of intelligence.

The development of numerical magnitude processing and its association with working memory in children with mild intellectual disabilities

The present research examined numerical magnitude processing and its association with working memory in children with mild intellectual disabilities (MID). We investigated the performance of 8-year-old children with MID on a symbolic (Arabic digits) and non-symbolic (dot patterns) magnitude comparison task by means of a chronological-age/ability-level-match design. We also examined whether the predicted problems with numerical magnitude comparison could be explained by working memory by using three working memory tasks. Findings revealed that children with MID performed more poorly than their chronological age-matched peers on both the symbolic and non-symbolic magnitude comparison tasks, suggesting impairments in these children's ability to represent numerical magnitudes. They also performed more poorly on working memory compared to their typically developing age- and ability-matched peers, but when these differences in working memory performance were additionally controlled for, the group differences on the numerical magnitude comparison tasks remained. Both symbolic numerical magnitude processing and central executive functioning predicted addition performance in children with MID.

Working memory in nonsymbolic approximate arithmetic processing: a dual-task study with preschoolers

Preschool children have been proven to possess nonsymbolic approximate arithmetic skills before learning how to manipulate symbolic math and thus before any formal math instruction. It has been assumed that nonsymbolic approximate math tasks necessitate the allocation of Working Memory (WM) resources. WM has been consistently shown to be an important predictor of children's math development and achievement. The aim of our study was to uncover the specific role of WM in nonsymbolic approximate math. For this purpose, we conducted a dual-task study with preschoolers with active phonological, visual, spatial, and central executive interference during the completion of a nonsymbolic approximate addition dot task. With regard to the role of WM, we found a clear performance breakdown in the central executive interference condition. Our findings provide insight into the underlying cognitive processes involved in storing and manipulating nonsymbolic approximate numerosities during early arithmetic.