Enumeration of small and large numerosities in adolescents with mathematical learning disorders

Impaired large numerosity estimation and intact subitizing in developmental dyscalculia

It is believed that the approximate estimation of large sets and the exact quantification of small sets (subitizing) are supported by two different systems, the Approximate Number System (ANS) and Object Tracking System (OTS), respectively. It is a current matter of debate whether they are both impaired in developmental dyscalculia (DD), a specific learning disability in symbolic number processing and calculation. Here we tackled this question by asking 32 DD children and 32 controls to perform a series of tasks on visually presented sets, including exact enumeration of small sets as well as comparison of large, uncountable sets. In children with DD, we found poor sensitivity in processing large numerosities, but we failed to find impairments in the exact enumeration of sets within the subitizing range. We also observed deficits in visual short-term memory skills in children with dyscalculia that, however, did not account for their low ANS acuity. Taken together, these results point to a dissociation between quantification skills in dyscalculia, they highlight a link between DD and low ANS acuity and provide support for the notion that DD is a multifaceted disability that covers multiple cognitive skills.

The Diagnosis and Treatment of Dyscalculia

BACKGROUND

3-7% of all children, adolescents, and adults suffer from dyscalculia. Severe, persistent difficulty performing arithmetical calculations leads to marked impairment in school, at work, and in everyday life and elevates the risk of comorbid mental disorders. The state of the evidence underlying various methods of diagnosing and treating this condition is unclear.

METHODS

Systematic literature searches were carried out from April 2015 to June 2016 in the PsycInfo, PSYNDEX, MEDLINE, ProQuest, ERIC, Cochrane Library, ICTRP, and MathEduc databases. The main search terms on dyscalculia were the German terms "Rechenstörung," "Rechenschwäche," and "Dyskalkulie" and the English terms "dyscalculia," "math disorder, and "math disability." The data from the retrieved studies were evaluated in a meta-analysis, and corresponding recommendations on the diagnosis and treatment of dyscalculia were jointly issued by the 20 societies and associations that participated in the creation of this guideline.

RESULTS

The diagnosis of dyscalculia should only be made if the person in question displays below-average mathematical performance when seen in the context of relevant information from the individual history, test findings, clinical examination, and further psychosocial assessment. The treatment should be directed toward the individual mathematical problem areas. The mean effect size found across all intervention trials was 0.52 (95% confidence interval [0.42; 0.62]). Treatment should be initiated early on in the primary-school years and carried out by trained specialists in an individual setting; comorbid symptoms and disorders should also receive attention. Persons with dyscalculia are at elevated risk of having dyslexia as well (odds ratio [OR]: 12.25); the same holds for attention deficit/hyperactivity disorder and for other mental disorders, both internalizing (such as anxiety and depression) and externalizing (e.g., disorders characterized by aggression and rule-breaking).

CONCLUSION

Symptom-specific interventions involving the training of specific mathematical content yield the best results. There is still a need for high-quality intervention trials and for suitable tests and learning programs for older adolescents and adults.

Dyscalculia and the Calculating Brain

Dyscalculia, like dyslexia, affects some 5% of school-age children but has received much less investigative attention. In two thirds of affected children, dyscalculia is associated with another developmental disorder like dyslexia, attention-deficit disorder, anxiety disorder, visual and spatial disorder, or cultural deprivation. Infants, primates, some birds, and other animals are born with the innate ability, called subitizing, to tell at a glance whether small sets of scattered dots or other items differ by one or more item. This nonverbal approximate number system extends mostly to single digit sets as visual discrimination drops logarithmically to "many" with increasing numerosity (size effect) and crowding (distance effect). Preschoolers need several years and specific teaching to learn verbal names and visual symbols for numbers and school agers to understand their cardinality and ordinality and the invariance of their sequence (arithmetic number line) that enables calculation. This arithmetic linear line differs drastically from the nonlinear approximate number system mental number line that parallels the individual number-tuned neurons in the intraparietal sulcus in monkeys and overlying scalp distribution of discrete functional magnetic resonance imaging activations by number tasks in man. Calculation is a complex skill that activates both visual and spatial and visual and verbal networks. It is less strongly left lateralized than language, with approximate number system activation somewhat more right sided and exact number and arithmetic activation more left sided. Maturation and increasing number skill decrease associated widespread non-numerical brain activations that persist in some individuals with dyscalculia, which has no single, universal neurological cause or underlying mechanism in all affected individuals.

Preschool predictors of mathematics in first grade children with autism spectrum disorder

Up till now, research evidence on the mathematical abilities of children with autism spectrum disorder (ASD) has been scarce and provided mixed results. The current study examined the predictive value of five early numerical competencies for four domains of mathematics in first grade. Thirty-three high-functioning children with ASD were followed up from preschool to first grade and compared with 54 typically developing children, as well as with normed samples in first grade. Five early numerical competencies were tested in preschool (5-6 years): verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Four domains of mathematics were used as outcome variables in first grade (6-7 years): procedural calculation, number fact retrieval, word/language problems, and time-related competences. Children with ASD showed similar early numerical competencies at preschool age as typically developing children. Moreover, they scored average on number fact retrieval and time-related competences and higher on procedural calculation and word/language problems compared to the normed population in first grade. When predicting first grade mathematics performance in children with ASD, both verbal subitizing and counting seemed to be important to evaluate at preschool age. Verbal subitizing had a higher predictive value in children with ASD than in typically developing children. Whereas verbal subitizing was predictive for procedural calculation, number fact retrieval, and word/language problems, counting was predictive for procedural calculation and, to a lesser extent, number fact retrieval. Implications and directions for future research are discussed.