Many children have significant mathematical learning disabilities (MLD, or dyscalculia) despite adequate schooling. The current study hypothesizes that MLD partly results from a deficiency in the ...Approximate Number System (ANS) that supports nonverbal numerical representations across species and throughout development. In this study of 71 ninth graders, it is shown that students with MLD have significantly poorer ANS precision than students in all other mathematics achievement groups (low, typically, and high achieving), as measured by psychophysical assessments of ANS acuity (w) and of the mappings between ANS representations and number words (cv). This relation persists even when controlling for domain-general abilities. Furthermore, this ANS precision does not differentiate low-achieving from typically achieving students, suggesting an ANS deficit that is specific to MLD.
Human mathematical competence emerges from two representational systems. Competence in some domains of mathematics, such as calculus, relies on symbolic representations that are unique to humans who ...have undergone explicit teaching. More basic numerical intuitions are supported by an evolutionarily ancient approximate number system that is shared by adults, infants and non-human animals-these groups can all represent the approximate number of items in visual or auditory arrays without verbally counting, and use this capacity to guide everyday behaviour such as foraging. Despite the widespread nature of the approximate number system both across species and across development, it is not known whether some individuals have a more precise non-verbal 'number sense' than others. Furthermore, the extent to which this system interfaces with the formal, symbolic maths abilities that humans acquire by explicit instruction remains unknown. Here we show that there are large individual differences in the non-verbal approximation abilities of 14-year-old children, and that these individual differences in the present correlate with children's past scores on standardized maths achievement tests, extending all the way back to kindergarten. Moreover, this correlation remains significant when controlling for individual differences in other cognitive and performance factors. Our results show that individual differences in achievement in school mathematics are related to individual differences in the acuity of an evolutionarily ancient, unlearned approximate number sense. Further research will determine whether early differences in number sense acuity affect later maths learning, whether maths education enhances number sense acuity, and the extent to which tertiary factors can affect both.
Do individual differences in the brain mechanisms for arithmetic underlie variability in high school mathematical competence? Using functional magnetic resonance imaging, we correlated brain ...responses to single digit calculation with standard scores on the Preliminary Scholastic Aptitude Test (PSAT) math subtest in high school seniors. PSAT math scores, while controlling for PSAT Critical Reading scores, correlated positively with calculation activation in the left supramarginal gyrus and bilateral anterior cingulate cortex, brain regions known to be engaged during arithmetic fact retrieval. At the same time, greater activation in the right intraparietal sulcus during calculation, a region established to be involved in numerical quantity processing, was related to lower PSAT math scores. These data reveal that the relative engagement of brain mechanisms associated with procedural versus memory-based calculation of single-digit arithmetic problems is related to high school level mathematical competence, highlighting the fundamental role that mental arithmetic fluency plays in the acquisition of higher-level mathematical competence.
Does knowing when mental arithmetic judgments are right--and when they are wrong--lead to more accurate judgments over time? We hypothesize that the successful detection of errors (and avoidance of ...false alarms) may contribute to the development of mental arithmetic performance. Insight into error detection abilities can be gained by examining the "calibration" of mental arithmetic judgments-that is, the alignment between confidence in judgments and the accuracy of those judgments. Calibration may be viewed as a measure of metacognitive monitoring ability. We conducted a developmental longitudinal investigation of the relationship between the calibration of children's mental arithmetic judgments and their performance on a mental arithmetic task. Annually between Grades 5 and 8, children completed a problem verification task in which they rapidly judged the accuracy of arithmetic expressions (e.g., 25 + 50 = 75) and rated their confidence in each judgment. Results showed that calibration was strongly related to concurrent mental arithmetic performance, that calibration continued to develop even as mental arithmetic accuracy approached ceiling, that poor calibration distinguished children with mathematics learning disability from both low and typically achieving children, and that better calibration in Grade 5 predicted larger gains in mental arithmetic accuracy between Grades 5 and 8. We propose that good calibration supports the implementation of cognitive control, leading to long-term improvement in mental arithmetic accuracy. Because mental arithmetic "fluency" is critical for higher-level mathematics competence, calibration of confidence in mental arithmetic judgments may represent a novel and important developmental predictor of future mathematics performance.
The linear relations between math anxiety and math cognition have been frequently studied. However, the relations between anxiety and performance on complex cognitive tasks have been repeatedly ...demonstrated to follow a curvilinear fashion. In the current studies, we aimed to address the lack of attention given to the possibility of such complex interplay between emotion and cognition in the math-learning literature by exploring the relations among math anxiety, math motivation, and math cognition. In two samples—young adolescent twins and adult college students—results showed inverted-U relations between math anxiety and math performance in participants with high intrinsic math motivation and modest negative associations between math anxiety and math performance in participants with low intrinsic math motivation. However, this pattern was not observed in tasks assessing participants' nonsymbolic and symbolic number-estimation ability. These findings may help advance the understanding of mathematics-learning processes and provide important insights for treatment programs that target improving mathematics-learning experiences and mathematical skills.
Relational language is thought to influence mathematical skills. This study examines the association between relational language and number relation skills—knowledge of cardinal, ordinal, and spatial ...principles—among 104 U.S. kindergartners (5.9 years; 44% boys; 37% White, 25% Black, 14% Asian, 24% other) in the 2017–2018 academic year. Controlling for general verbal knowledge, executive function, and counting and number identification skills, relational language predicted later number relation skills, specifically number line estimation, β = .30. Relational language did not differentially predict number line estimation performance in children with low or high number relation skills, likely due to the restricted ranges of data within subgroups. Number relation skills, specifically number line estimation and number ordering, may be a pathway between relational language and mathematical skills.
Individuals with Mathematics Learning Disabilities have persistent mathematics underperformance but vary with respect to their cognitive profiles. The present study examined mathematics ability and ...achievement, and associated mathematics-specific numerical skills and domain-general cognitive abilities, in young children with Turner syndrome compared to their matched peers. We utilized two independent peer groups so that group comparisons would account for verbal skills, a hypothesized strength of girls with Turner syndrome, and nonsymbolic magnitude comparison skills, a hypothesized difference of girls with Turner syndrome. This individual matching approach afforded characterization of mathematics profiles of girls with Turner syndrome and girls without Turner syndrome that share potential key features of the Turner syndrome phenotype. Results indicated differences in mathematics ability and nonsymbolic magnitude comparison tasks between girls with Turner syndrome and peers with similar levels of verbal skill. Mathematics ability and mathematics achievement scores of girls with Turner syndrome did not differ significantly from their peers with similar levels of accuracy on a nonsymbolic magnitude comparison task. Cognitive correlates of mathematics outcomes showed disparate patterns across groups. These quantitative and qualitative differences across profiles enhance our understanding of variation in mathematics ability in early childhood and inform how mathematics skills develop in young children with or without Turner syndrome.
Math anxiety (MA) and math performance are generally negatively correlated (Barroso et al., 2021; Namkung et al., 2019). However, the mechanisms underlying this negative association remain unclear. ...According to the attentional control theory (ACT; Eysenck et al., 2007), anxious individuals experience impaired attentional control during problem solving, which compromises their performance on cognitive tasks. In a sample of 168 elementary and middle school students, the current study used an eye-tracking approach to investigate whether math-anxious students exhibit deficits in their attentional control during a math problem solving task and whether such attentional control deficits account for the negative association between MA and performance on this math task. Consistent with the ACT, we found that students with higher MA were more likely to engage attention to both task-relevant and task-irrelevant distractors during problem solving, and their enhanced attention to these distractors was associated with their impaired performance on the math task. These findings suggest that the MA-related math performance deficit is partly mediated by impaired attentional control, which is indicated by the maladaptive attentional bias toward distracting information during math problem solving.
Educational Impact and Implications StatementStudents with higher math anxiety often show poorer math performance compared with students with lower math anxiety. One possible explanation for this phenomenon is that students with higher math anxiety are more easily distracted by extraneous information during problem solving. By examining the attention allocation patterns during an arithmetic verification task in a group of elementary and middle school students, our findings support this explanation. We argue that external distracting information may disrupt the maintenance of continuous attention that is needed for efficient math problem solving among students with high math anxiety. Thus, it is important for educators to consider practices that may dampen the distracting effect of various task-relevant and task-irrelevant distractors on the math performance among students who are highly math anxious.
Researchers of mathematics learning disability (MLD) commonly use cutoff scores to determine which participants have MLD. Some researchers apply more restrictive cutoffs than others (e.g., ...performance below the 10th vs. below the 35th percentile). Different cutoffs may lead to groups of children that differ in their profile of math and related skills, including reading, visual—spatial, and working memory skills. The present study assesses the characteristics of children with MLD based on varying MLD definitions of math performance either below the 10th percentile (n = 22) or between the 11th and 25th percentile (n = 42) on the Test of Early Math Ability, second edition (TEMA-2). Initial starting levels and growth rates for math and related skills were examined in these two MLD groups relative to a comparison group (n = 146) whose TEMA-2 performance exceeded the 25th percentile. Between kindergarten and third grade, differences emerged in the starting level and growth rate, suggesting qualitative differences among the three groups. Despite some similarities, qualitative group differences were also observed in the profiles of math-related skills across groups. These results highlight differences in student characteristics based on the definition of MLD and illustrate the value of examining skill areas associated with math performance in addition to math performance itself.
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