Higher level domain specific skills in mathematics; The relationship between algebra, geometry, executive function skills and mathematics achievement.

Algebra and geometry are important components of mathematics that are often considered gatekeepers for future success. However, most studies that have researched the cognitive skills required for success in mathematics have only considered the domain of arithmetic. We extended models of mathematical skills to consider how executive function skills play both a direct role in secondary-school-level mathematical achievement as well as an indirect role via algebra and geometry, alongside arithmetic. We found that verbal and visuospatial working memory were indirectly associated with mathematical achievement via number fact knowledge, calculation skills, algebra and geometry. Inhibition was also indirectly associated with mathematical achievement via number fact knowledge and calculation skills. These findings highlight that there are multiple mechanisms by which executive function skills may be involved in mathematics outcomes. Therefore, using specific measures of mathematical processes as well as context-rich assessments of mathematical achievement is important to understand these mechanisms.

Endogenous control is insufficient for preventing attentional capture in children and adults.

Adults are known to have developed the ability to selectively focus their attention in a goal-driven (endogenous) manner but it is less clear at what stage in development (5-6 & 9-11 years) children can endogenously control their attention and whether they behave similarly to adults when managing distractions. In this study we administered a child-adapted cued visual search task to three age-groups: five- to six-year-olds (N = 45), nine- to eleven-year-olds (N = 42) and adults (N = 42). Participants were provided with a cue which either guided their attention towards or away from an upcoming target. On some trials, a singleton distracter was presented which participants needed to ignore. Participants completed three conditions where the cues were: 1) usually helpful (High Predictive), 2) usually unhelpful (Low Predictive) and 3) never helpful (Baseline) in guiding attention towards the target. We found that endogenous cue-utilisation develops with increasing age. Overall, nine- to eleven-year-olds and adults, but not five- to six-year-olds, utilised the endogenous cues in the High Predictive condition. However, all age-groups were unable to ignore the singleton distracter even when using endogenous control. Moreover, we found better cue-maintenance ability was related to poorer distracter-inhibition ability in early-childhood, but these skills were no longer related further on in development. We conclude that overall endogenous control is still developing in early-childhood, but an adult-like form of this skill has been acquired by mid-childhood. Furthermore, endogenous cue-utilisation was shown as insufficient for preventing attentional capture in both children and adults.

A comparison of simultaneous and sequential visuo-spatial memory in children born very preterm.

Research suggests that children born very preterm (≤32 weeks' gestation) are at greater risk of impairments in information processing (particularly when information is presented simultaneously rather than sequentially) and visuo-spatial short-term and working memory relative to children born at term. This study compared the performance of children born very preterm with their term-born peers to elucidate the nature of group differences in these areas. 113 children (65 very preterm; 48 term-born) aged 8-to-11 years completed four visuo-spatial recall tasks. Tasks varied by presentation type (simultaneous or sequential) and memory type (short-term or working memory). Both groups recalled more locations in simultaneous than sequential tasks, and in short-term than working memory tasks. In short-term memory tasks, children born at term recalled more locations than children born very preterm for the sequential task, but groups did not differ on the simultaneous task. The opposite pattern was observed in the working memory tasks, with no group differences on the sequential task, but better performance on the simultaneous task for children born at term. Our findings indicate that simultaneous processing may not be impaired in children born very preterm per se, with poorer performance observed only under high cognitive demand. This interaction suggests very preterm birth may affect the level of cognitive resources available during feature integration, the consequences of which become apparent when resources are already stretched. The impact of interactions with cognitive demand in this population should be an important consideration for educational support strategies, and for assessment in research and clinic.

Etiology of persistent mathematics difficulties from childhood to adolescence following very preterm birth.

Children born very preterm (VP; <32 weeks' gestation) have poorer mathematics achievement than term-born peers. This study aimed to determine whether VP children's mathematics difficulties persist from primary to secondary school and to explore the nature of mathematics difficulties in adolescence. For this study, 127 VP and 95 term-born adolescents were assessed at age 11-15 years. Mathematics achievement was assessed using the Wechsler Individual Achievement Test-II. Specific mathematics skills and general cognitive skills were assessed using standardized and experimental tests. VP adolescents had poorer mathematics achievement than term-born adolescents (-10.95 points; 95% CI -16.18, -5.73) and poorer number fact knowledge, understanding of arithmetic concepts, written arithmetic, counting, reading and writing large numbers, and algebra. Between-group differences in mathematics skills were no longer significant when working memory and visuospatial skills were controlled for (p's >0.05), with the exception of writing large numbers and conceptual understanding of arithmetic. In a previous study, 83 of the VP adolescents and 49 of the term-born adolescents were assessed at age 8-10 years using measures of the same skills. Amongst these, the between-group difference in mathematics achievement remained stable over time. This study extends findings of a persistent deficit in mathematics achievement among VP children over the primary and secondary school years, and provides evidence of a deficit in factual, procedural and conceptual mathematics skills and in higher order mathematical operations among VP adolescents. We provide further evidence that VP children's mathematics difficulties are driven by deficits in domain-general rather than domain-specific cognitive skills.

No Excess of Mathematics Anxiety in Adolescents Born Very Preterm.

OBJECTIVE: To assess whether adolescents born very preterm (VP; <32 weeks' gestation) have an excess of mathematics anxiety compared with their classmates born at term. METHODS: This cohort study included 127 adolescents born VP (51% male, mean age 13.9 years, SD 0.7) and 95 term-born classmates (56% male, mean age 13.7 years, SD 0.7) who completed the Wechsler Individual Achievement Test Second UK Edition and the Mathematics Anxiety Scale-UK at the age of 11 to 15 years. Self-reported trait anxiety was assessed using a composite of 3 items from the Strengths and Difficulties Questionnaire. RESULTS: Adolescents born VP had significantly poorer mathematics attainment than adolescents born at term (difference in means: -0.64 SD; 95% confidence interval -0.95 to -0.34). However, there were no between-group differences in self-reported mathematics anxiety or trait anxiety. There were significant moderate associations between mathematics anxiety and mathematics attainment for adolescents born VP (rho: -0.45) and at term (rho: -0.54), after controlling for trait anxiety. CONCLUSION: Adolescents born VP do not have heightened mathematics anxiety compared with their term-born classmates, despite poorer attainment in mathematics. Improving domain-general cognitive skills and scaffolding learning in the classroom may be more promising avenues for intervention than attempting to reduce mathematics anxiety.

The Role of Executive Functions in Socioeconomic Attainment Gaps: Results From a Randomized Controlled Trial.

The socioeconomic attainment gap in mathematics starts early and increases over time. This study aimed to examine why this gap exists. Four-year-olds from diverse backgrounds were randomly allocated to a brief intervention designed to improve executive functions (N = 87) or to an active control group (N = 88). The study was preregistered and followed CONSORT guidelines. Executive functions and mathematical skills were measured at baseline, 1 week, 3 months, 6 months, and 1 year posttraining. Executive functions mediated the relation between socioeconomic status and mathematical skills. Children improved over training, but this did not transfer to untrained executive functions or mathematics. Executive functions may explain socioeconomic attainment gaps, but cognitive training directly targeting executive functions is not an effective way to narrow this gap.

Using drift diffusion modeling to understand inattentive behavior in preterm and term-born children.

OBJECTIVE: Children born very preterm are at increased risk of inattention, but it remains unclear whether the underlying processes are the same as in their term-born peers. Drift diffusion modeling (DDM) may better characterize the cognitive processes underlying inattention than standard reaction time (RT) measures. This study used DDM to compare the processes related to inattentive behavior in preterm and term-born children. METHOD: Performance on a cued continuous performance task was compared between 33 children born very preterm (VP; ≤ 32 weeks' gestation) and 32 term-born peers (≥ 37 weeks' gestation), aged 8-11 years. Both groups included children with a wide spectrum of parent-rated inattention (above average attention to severe inattention). Performance was defined using standard measures (RT, RT variability and accuracy) and modeled using a DDM. A hierarchical regression assessed the extent to which standard or DDM measures explained variance in parent-rated inattention and whether these relationships differed between VP and term-born children. RESULTS: There were no group differences in performance on standard or DDM measures of task performance. Parent-rated inattention correlated significantly with hit rate, RT variability, and drift rate (a DDM estimate of processing efficiency) in one or both groups. Regression analysis revealed that drift rate was the best predictor of parent-rated inattention. This relationship did not differ significantly between groups. CONCLUSIONS: Findings suggest that less efficient information processing is a common mechanism underlying inattention in both VP and term-born children. This study demonstrates the benefits of using DDM to better characterize atypical cognitive processing in clinical samples. (PsycINFO Database Record (c) 2020 APA, all rights reserved).

Improving developmental and educational support for children born preterm: evaluation of an e-learning resource for education professionals.

OBJECTIVES: Children born preterm are at higher risk for special educational needs and poor academic attainment compared with term-born peers, yet education professionals receive limited training and have poor knowledge of preterm birth. We have developed an interactive e-learning resource and evaluated its efficacy in improving teachers' knowledge of preterm birth and their confidence in supporting the learning of children born preterm. SETTING: Eight primary, infant or junior schools in England. PARTICIPANTS: 61 teachers of children aged 4-11 years, of which 55 (90%) were female. INTERVENTION: Interactive e-learning resource designed to improve education professionals' knowledge of long-term outcomes following preterm birth and strategies that can be used to support children's learning (www.pretermbirth.info). In a repeated measures design, participants were given up to 30 days access to the e-learning resource, before and after which they completed the Preterm Birth Knowledge Scale (PB-KS; scores 0-33; higher scores indicate greater knowledge) to assess knowledge of outcomes of prematurity. Four Likert scale items were used to assess confidence in supporting children's learning and 10 items were used to evaluate the utility of the resource. PB-KS scores and responses on confidence item were compared pre-resource and post-resource use. RESULTS: PB-KS scores significantly increased after accessing the e-learning resource (median (95% CI): pre-resource 13 (11 to 14); post-resource 29 (28 to 30)), equating to a 2.6 SD increase in PB-KS scores. Teachers' confidence in supporting children born preterm was also significantly improved after using the resource. The utility of the resource was evaluated positively by participants with 97% reporting that they would recommend its use to others. CONCLUSIONS: The e-learning resource substantially improved teachers' knowledge of preterm birth and their confidence in supporting preterm children in the classroom. Use of this resource may represent a key advance in improving educational outcomes for children born preterm.

Cross-modal interference-control is reduced in childhood but maintained in aging: A cohort study of stimulus- and response-interference in cross-modal and unimodal Stroop tasks.

Interference-control is the ability to exclude distractions and focus on a specific task or stimulus. However, it is currently unclear whether the same interference-control mechanisms underlie the ability to ignore unimodal and cross-modal distractions. In 2 experiments we assessed whether unimodal and cross-modal interference follow similar trajectories in development and aging and occur at similar processing levels. In Experiment 1, 42 children (6-11 years), 31 younger adults (18-25 years) and 32 older adults (60-84 years) identified color rectangles with either written (unimodal) or spoken (cross-modal) distractor-words. Stimuli could be congruent, incongruent but mapped to the same response (stimulus-incongruent), or incongruent and mapped to different responses (response-incongruent); thus, separating interference occurring at early (sensory) and late (response) processing levels. Unimodal interference was worst in childhood and old age; however, older adults maintained the ability to ignore cross-modal distraction. Unimodal but not cross-modal response-interference also reduced accuracy. In Experiment 2 we compared the effect of audition on vision and vice versa in 52 children (6-11 years), 30 young adults (22-33 years) and 30 older adults (60-84 years). As in Experiment 1, older adults maintained the ability to ignore cross-modal distraction arising from either modality, and neither type of cross-modal distraction limited accuracy in adults. However, cross-modal distraction still reduced accuracy in children and children were more slowed by stimulus-interference compared with adults. We conclude that; unimodal and cross-modal interference follow different life span trajectories and differences in stimulus- and response-interference may increase cross-modal distractibility in childhood. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Cognitive predictors of parent-rated inattention in very preterm children: The role of working memory and processing speed.

Inattention is one of the most common neurobehavioral problems following very preterm birth. Attention problems can persist into adulthood and are associated with negative socio-emotional and educational outcomes. This study aimed to determine whether the cognitive processes associated with inattention differ between term-born and very preterm children. Sixty-five children born very preterm (<33+0 weeks' gestation) aged 8-11 years were recruited alongside 48 term-born controls (?37 20 +0 weeks' gestation). Both groups included children with a wide spectrum of parent-rated inattention (above average attention to severe inattention) measured as a continuous dimension using the Strengths and Weaknesses of ADHD and Normal-Behavior (SWAN) scale. The children completed tests to assess basic cognitive processes and executive function. A hierarchical multiple regression analysis was implemented to assess which neurocognitive processes explained variance in parent-rated inattention and whether these differed between preterm and term-born children. In both groups, poorer verbal and visuospatial short-term memory and poorer visuospatial working memory independently explained variance in parent-rated inattention. Slower motor processing speed explained variance in inattention among very preterm children only. The cognitive mechanisms associated with parent-rated inattention were predominantly overlapping between groups, but relationships between motor processing speed and inattention were unique to very preterm children. These associations may reflect risk factors for inattention in term and very preterm children. Future research should assess the efficacy of these cognitive processes as potential targets for intervention.

Understanding arithmetic concepts: The role of domain-specific and domain-general skills.

A large body of research has identified cognitive skills associated with overall mathematics achievement, focusing primarily on identifying associates of procedural skills. Conceptual understanding, however, has received less attention, despite its importance for the development of mathematics proficiency. Consequently, we know little about the quantitative and domain-general skills associated with conceptual understanding. Here we investigated 8-10-year-old children's conceptual understanding of arithmetic, as well as a wide range of basic quantitative skills, numerical representations and domain-general skills. We found that conceptual understanding was most strongly associated with performance on a number line task. This relationship was not explained by the use of particular strategies on the number line task, and may instead reflect children's knowledge of the structure of the number system. Understanding the skills involved in conceptual learning is important to support efforts by educators to improve children's conceptual understanding of mathematics.

The threshold for the McGurk effect in audio-visual noise decreases with development.

Across development, vision increasingly influences audio-visual perception. This is evidenced in illusions such as the McGurk effect, in which a seen mouth movement changes the perceived sound. The current paper assessed the effects of manipulating the clarity of the heard and seen signal upon the McGurk effect in children aged 3-6 (n = 29), 7-9 (n = 32) and 10-12 (n = 29) years, and adults aged 20-35 years (n = 32). Auditory noise increased, and visual blur decreased, the likelihood of vision changing auditory perception. Based upon a proposed developmental shift from auditory to visual dominance we predicted that younger children would be less susceptible to McGurk responses, and that adults would continue to be influenced by vision in higher levels of visual noise and with less auditory noise. Susceptibility to the McGurk effect was higher in adults compared with 3-6-year-olds and 7-9-year-olds but not 10-12-year-olds. Younger children required more auditory noise, and less visual noise, than adults to induce McGurk responses (i.e. adults and older children were more easily influenced by vision). Reduced susceptibility in childhood supports the theory that sensory dominance shifts across development and reaches adult-like levels by 10 years of age.

Vision dominates audition in adults but not children: A meta-analysis of the Colavita effect.

The Colavita effect occurs when participants respond only to the visual element of an audio-visual stimulus. This visual dominance effect is proposed to arise from asymmetric facilitation and inhibition between modalities. It has also been proposed that, unlike adults, children appear predisposed to auditory information. We provide the first quantitative synthesis of studies exploring the Colavita effect, combining data from 70 experiments across 14 studies. A mixed-meta-regression model was applied to assess whether the Colavita effect is influenced by methodological factors and age group tested. Studies reporting response time data were used to test for the presence of asymmetrical facilitation between modalities. Studies with adult participants yielded a medium, approaching large, effect size. Studies exploring the Colavita effect in children yielded no Colavita effect. Across adult and child studies, no methodological factors influenced the effect. Contrary to asymmetrical facilitation, response time data suggested a general slowing under bimodal conditions. These findings suggest that whilst vision dominates in adults, this effect is absent in childhood.

When is working memory important for arithmetic? The impact of strategy and age.

Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies employed, as well as an increase in the accuracy and efficiency of strategy execution. As such it seems likely that the role of working memory in arithmetic may also change, however children and adults have never been directly compared. This study used traditional dual-task methodology, with the addition of a control load condition, to investigate the extent to which working memory requirements for different arithmetic strategies change with age between 9-11 years, 12-14 years and young adulthood. We showed that both children and adults employ working memory when solving arithmetic problems, no matter what strategy they choose. This study highlights the importance of considering working memory in understanding the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition.

Direct and indirect influences of executive functions on mathematics achievement.

Achievement in mathematics is predicted by an individual's domain-specific factual knowledge, procedural skill and conceptual understanding as well as domain-general executive function skills. In this study we investigated the extent to which executive function skills contribute to these three components of mathematical knowledge, whether this mediates the relationship between executive functions and overall mathematics achievement, and if these relationships change with age. Two hundred and ninety-three participants aged between 8 and 25years completed a large battery of mathematics and executive function tests. Domain-specific skills partially mediated the relationship between executive functions and mathematics achievement: Inhibitory control within the numerical domain was associated with factual knowledge and procedural skill, which in turn was associated with mathematical achievement. Working memory contributed to mathematics achievement indirectly through factual knowledge, procedural skill and, to a lesser extent, conceptual understanding. There remained a substantial direct pathway between working memory and mathematics achievement however, which may reflect the role of working memory in identifying and constructing problem representations. These relationships were remarkably stable from 8years through to young adulthood. Our findings help to refine existing multi-component frameworks of mathematics and understand the mechanisms by which executive functions support mathematics achievement.

Explaining the relationship between number line estimation and mathematical achievement: The role of visuomotor integration and visuospatial skills.

Performance on number line tasks, typically used as a measure of numerical representations, are reliably related to children's mathematical achievement. However, recent debate has questioned what precisely performance on the number line estimation task measures. Specifically, there has been a suggestion that this task may measure not only numerical representations but also proportional judgment skills; if this is the case, then individual differences in visuospatial skills, not just the precision of numerical representations, may explain the relationship between number line estimation and mathematical achievement. The current study investigated the relationships among visuospatial skills, visuomotor integration, number line estimation, and mathematical achievement. In total, 77 children were assessed using a number line estimation task, a standardized measure of mathematical achievement, and tests of visuospatial skills and visuomotor integration. The majority of measures were significantly correlated. In addition, the relationship between one metric from the number line estimation task (R(2)LIN) and mathematical achievement was fully explained by visuomotor integration and visuospatial skill competency. These results have important implications for understanding what the number line task measures as well as the choice of number line metric for research purposes.

Congruency effects in dot comparison tasks: convex hull is more important than dot area.

The dot comparison task, in which participants select the more numerous of two dot arrays, has become the predominant method of assessing Approximate Number System (ANS) acuity. Creation of the dot arrays requires the manipulation of visual characteristics, such as dot size and convex hull. For the task to provide a valid measure of ANS acuity, participants must ignore these characteristics and respond on the basis of number. Here, we report two experiments that explore the influence of dot area and convex hull on participants' accuracy on dot comparison tasks. We found that individuals' ability to ignore dot area information increases with age and display time. However, the influence of convex hull information remains stable across development and with additional time. This suggests that convex hull information is more difficult to inhibit when making judgements about numerosity and therefore it is crucial to control this when creating dot comparison tasks.

The development of stimulus and response interference control in midchildhood.

Interference control, the ability to overcome distraction from irrelevant information, undergoes considerable improvement during childhood, yet the mechanisms driving these changes remain unclear. The present study investigated the relative influence of interference at the level of the stimulus or the response. Seven-, 10-, and 20-year-olds completed a flanker paradigm in which stimulus and response interference was experimentally manipulated. The influence of stimulus interference decreased from 7 to 10 years, whereas there was no difference in response interference across age groups. The findings demonstrate that a range of processes contribute to the development of interference control and may influence performance to a greater or lesser extent depending on the task requirements and the age of the child.

Differential modulation of the N2 and P3 event-related potentials by response conflict and inhibition.

BACKGROUND: Developing reliable and specific neural markers of cognitive processes is essential to improve understanding of healthy and atypical brain function. Despite extensive research there remains uncertainty as to whether two electrophysiological markers of cognitive control, the N2 and P3, are better conceptualised as markers of response inhibition or response conflict. The present study aimed to directly compare the effects of response inhibition and response conflict on the N2 and P3 event-related potentials, within-subjects. METHOD: A novel hybrid go/no-go flanker task was performed by 19 healthy adults aged 18-25 years while EEG data were collected. The response congruence of a central target stimulus and 4 flanking stimuli was manipulated between trials to vary the degree of response conflict. Response inhibition was required on a proportion of trials. N2 amplitude was measured at two frontal electrode sites; P3 amplitude was measured at 4 midline electrode sites. RESULTS: N2 amplitude was greater on incongruent than congruent trials but was not enhanced by response inhibition when the stimulus array was congruent. P3 amplitude was greater on trials requiring response inhibition; this effect was more pronounced at frontal electrodes. P3 amplitude was also enhanced on incongruent compared with congruent trials. DISCUSSION: The findings support a role for N2 amplitude as a marker of response conflict and for the frontal shift of the P3 as a marker of response inhibition. This paradigm could be applied to clinical groups to help clarify the precise nature of impaired action control in disorders such as attention deficit/hyperactivity disorders (ADHD).

Nature and origins of mathematics difficulties in very preterm children: a different etiology than developmental dyscalculia.

BACKGROUND: Children born very preterm (<32 wk) are at high risk for mathematics learning difficulties that are out of proportion to other academic and cognitive deficits. However, the etiology of mathematics difficulties in very preterm children is unknown. We sought to identify the nature and origins of preterm children's mathematics difficulties. METHODS: One hundred and fifteen very preterm children aged 8-10 y were assessed in school with a control group of 77 term-born classmates. Achievement in mathematics, working memory, visuospatial processing, inhibition, and processing speed were assessed using standardized tests. Numerical representations and specific mathematics skills were assessed using experimental tests. RESULTS: Very preterm children had significantly poorer mathematics achievement, working memory, and visuospatial skills than term-born controls. Although preterm children had poorer performance in specific mathematics skills, there was no evidence of imprecise numerical representations. Difficulties in mathematics were associated with deficits in visuospatial processing and working memory. CONCLUSION: Mathematics difficulties in very preterm children are associated with deficits in working memory and visuospatial processing not numerical representations. Thus, very preterm children's mathematics difficulties are different in nature from those of children with developmental dyscalculia. Interventions targeting general cognitive problems, rather than numerical representations, may improve very preterm children's mathematics achievement.