M. Mazzocco

Individual differences in non-verbal number acuity correlate with maths achievement

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.

Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia).

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.

Preschoolers' precision of the approximate number system predicts later school mathematics performance.

The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities.

Cognitive Characteristics of Children With Mathematics Learning Disability (MLD) Vary as a Function of the Cutoff Criterion Used to Define MLD

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.

Decreased cerebellar posterior vermis size in fragile X syndrome: Correlation with neurocognitive performance

We examined whether posterior vermis size is smaller in individuals with fragile X syndrome (fra X) than in control subjects and whether this decreased size is associated with cognitive performance. Cognitive and behavioral dysfunctions have been identified in fra X; however, underlying neuropathogenic mechanisms remain unclear. MRI was used to investigate the posterior fossa in 32 males with fra X, 28 males with other causes of cognitive disability (CD), and 38 males with normal development (ND) as well as and in 37 females with fra X and 53 female control subjects. Among females with fra X, neurocognitive correlates of posterior vermis size were examined. Posterior vermis size (cross-sectional area) in males with fra X was significantly smaller compared with CD and ND groups, particularly when corrected for intracranial area. Posterior vermis size corrected for intracranial area was significantly smaller in females with fra X compared with control subjects. Compared with males with fra X and non-fra X control subjects, posterior vermis size in females with fra X was intermediate. After statistically removing the effect of mean parental IQ, posterior vermis size predicted a significant proportion of the variance (10 to 23%) of performance on full-scale, verbal, and performance IQ; block design; categories achieved on the Wisconsin Card Sorting Test; and the Rey inventory score. The size of the posterior vermis is significantly decreased in fra X, more so in males than in females. In females with fra X, posterior vermis size predicts performance on selected cognitive measures.

A Longitudinal Assessment of Executive Function Skills and Their Association with Math Performance

The present study was designed to examine both concurrent and predictive associations between scores on a measure of executive function (EF) skills, the Contingency Naming Test (CNT), during the early school-age years. A secondary aim of the study was to examine the association between EF skills and mathematics performance. We administered tests of mathematics ability, and the CNT, to 178 children at ages 6 to 7, 8 to 9, and 10 to 11 years. From the CNT we obtained measures of response fluency/efficiency, working memory, and inhibition. The results demonstrate main effects of age on all CNT measures of EF, as anticipated, and inconsistent main effects of gender or mathematics learning disability status. Rates of improvement in EF varied as a function of the working memory demands present during a given task. There were differences in concurrent and predictive correlations for different CNT performance measures. EF scores obtained during the first assessment were as strongly associated with each other as they were with EF scores obtained four years later, suggesting a moderately stable source of individual differences on cognitive performance. EF scores at age 6 to 7 years were associated with concurrent and later mathematics scores, and most of these correlations were stronger than the significant associations found between response fluency on a baseline task (with no working memory demand) and mathematics performance. These findings have implications for the stability of EF skills during the school-age years, and the role of EF in early and later elementary school mathematics performance.

The neurocognitive phenotype of female carriers of fragile X: additional evidence for specificity.

The specificity of the neurocognitive profile among women with the fragile X gene, in relation to cytogenetic expression, was examined among 22 women with ≥2% expression, 35 0% obligate carriers, and 60 controls. Measures were obtained for intellectual ability; achievement; and verbal, nonverbal, memory, and executive functions. Findings show that no group consistently demonstrated global deficits in the verbal, nonverbal or memory domains. In contrast, even when controlling for the effects of IQ, the expressing women exhibited (1) deficits on measures of executive function, (2) deficits in measures of attention and visual-spatial skills, and (3) enhanced performance on verbal, but not figural, memory. No deficits were seen among obligate carriers. This study supports the notion that executive function deficits and/or visual-spatial skills may account for the behavioral and cognitive manifestations of fragile X. J Dev Behav Pediatr 14:328–335, 1993. Index terms: fragile X, cognitive, executive function, frontal lobe, neuropsychological.

Critical Issues in Response-To-Intervention, Comprehensive Evaluation, and Specific Learning Disabilities Identification and Intervention: An Expert White Paper Consensus

Developed in concert with the Learning Disabilities Association of America (LDA), this White Paper regarding specific learning disabilities identification and intervention represents the expert consensus of 58 accomplished scholars in education, psychology, medicine, and the law. Survey responses and empirical evidence suggest that five conclusions are warranted: 1) The SLD definition should be maintained and the statutory requirements in SLD identification procedures should be strengthened; 2) neither ability-achievement discrepancy analysis nor failure to respond to intervention alone is sufficient for SLD identification; 3) a “third method” approach that identifies a pattern of psychological processing strengths and weaknesses, and achievement deficits consistent with this pattern of processing weaknesses, makes the most empirical and clinical sense; 4) an empirically-validated RTI model could be used to prevent learning problems, but comprehensive evaluations should occur for SLD identification purposes, and children with SLD need individualized interventions based on specific learning needs, not merely more intense interventions; and 5) assessment of cognitive and neuropsychological processes should be used for both SLD identification and intervention purposes.

Math Learning Disability and Math LD Subtypes Evidence from Studies of Turner Syndrome, Fragile X Syndrome, and Neurofibromatosis Type 1

The present study examined whether indicators of math learning disability are observed m 5- and 6-year-olds with neurofibromatosis type 1 (NF1) and in 5- to 6-year-old girls with Turner syndrome or fragile X syndrome. Data from 14 girls with Turner syndrome, 9 girls with fragile X syndrome, and 11 children with NF1 were compared to data from control participants matched on age, sex, IQ score, and grade level. The results indicate that girls with fragile X syndrome or Turner syndrome are significantly more likely to have specific math difficulties relative to their control group, with a larger effect size demonstrated by the group with Turner syndrome. Young children with NF1 had a heterogeneous profile not suggestive of specific math disability. The results are discussed in terms of their implications for understanding math disability subtypes and the identification of math difficulty in the early school years.

Advances in research on the fragile X syndrome.

Fragile X syndrome is a neurodevelopmental disorder that results from a single gene mutation on the X chromosome. The purpose of this review is to summarize key advances made in understanding the fragile X premutation gene seen in carriers and the full mutation gene seen in persons with the syndrome. DNA testing has replaced cytogenetic testing as the primary method for identification of fragile X, although the efficacy of protein level screening is being explored. The premutation is associated with no effects, although there is evidence of physical effects-primarily premature menopause and mild outward features of the fragile X syndrome-among premutation carriers. There is much controversy regarding premutation effects on psychological development. The few experimental studies carried out to date do not suggest noticeable or significant effects. One challenge in addressing this controversy is the sometimes ambiguous differentiation between premutation and full mutation genes. There is a well-established yet highly variable phenotype of the full mutation. Research from this decade has helped to address specific aspects of this phenotype, including the early course of its development in males, the influence of home and family environments, the nature of social difficulties and autistic features seen in boys and girls with fragile X, and the potential role of hyperarousal or hyper-reactivity. Studies in these areas, and on the role of FMR protein, will contribute towards ongoing advances in our understanding of fragile X syndrome and its mechanisms. The variability in physical, social, and cognitive features, as described in this review, is one that prohibits clear-cut screening guidelines designed to avoid high rates of both false positives and false negatives. Results from recent studies indicate the need to consider behavioral features in selecting candidates for fragile X screening. MRDD Research Reviews 2000;6:96-106.