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Developmental Dyscalculia (DD) signifies a failure in representing quantities, which impairs the performance of basic math operations and schooling achievement during childhood. DD is defined as “a heterogeneous disorder that produces individual differences in both development and functioning of numerical cognition, evidence-based in neuroanatomical, neuropsychological, and behavioural levels, as well as their interactions”.
Numerical cognition can be defined as the ability to represent, process and manipulate quantitiesboth symbolically and non-symbolically [1]. There is some preverbal, probably innate ability to represent and compare nonsymbolic quantities, but much numerical cognition develops with age, and depends on both domain-specific numerical abilities and domain-general cognitive abilities, such as as language, working memory, spatial abilities, executive functions, etc. The development of numerical cognition involves complex interactions between these domain-specific and domain-general abilities, their respective neural substrates, and learning experiences including, but not limited to, formal education [2]. There are many reasons for low achievement in school mathematics, but these include neurodevelopmental dysfunctions of numerical cognition. Such dysfunctions range from “transient and mild”to “persistent and severe” [3]. It is the severe and persistent dysfunctions that are often considered as a specific learning disorder, termed Developmental Dyscalculia (DD; [4]) or Mathematical Learning Disorder, whose symptoms are often already observable at preschool age [2][5][6][7][8].
The current classification of primary or secondary DD is based on aetiological elements. Primary DD comprises specific severe numeracy deficits, with no deficits in other areas; it is relatively rare and has a prevalence from 1 to 2% in school children [5][9][10]. On the other hand, secondary DD affects at least 4% of individuals [5], whose numerical dysfunctions are accompanied by other significant “non-numerical” cognitive deficits relative to chronological age or schooling [3][11]. For instance, a recent study found that attentional deficits were a core cognitive marker of secondary DD [12]. Secondary DD may involve comorbidity with other neurodevelopmental disorders, for instance, dyslexia or attention deficit hyperactivity disorder ICD-11 [13].
There are no universally accepted criteria for the diagnosis of DD. The currently general criteria acknowledged include: (i) a discrepancy with intelligence measures; (ii) cut-off scores on standardized measures of numerical cognition; (iii) inconsistency with years of schooling (delay); (iv) resistance to interventions [14]. Different diagnostic manuals adopt slightly dissimilar general criteria, and there is considerable debate in the scientific community about which psychometric criteria are the most appropriate [15]. For example, some studies use a cut-off point between the 20th and 35th percentile on standardized tests as indicative of numeracy deficits [6][7][14][16], while others use a stricter cut-off point of scores below the 10th or even 5th percentile [7][17][18]. Obviously, the more lenient the cut-off point, the higher the prevalence will be. Discrepancy between intelligence quotient and mathematical attainment level is a controversial criterion [15]. It varies across studies, both in terms of the size of the discrepancy required, and in terms of whether they include or exclude children with average or near-average mathematics scores but extremely high intelligencel quotient (IQ) [18][19][20]. DSM-V [15][21] and ICD-11 [13] concur that a specific learning disorder diverges from general learning difficulties associated with intellectual disability. Both recognise below-average IQ as a confounding factor, along with congenital encephalopathy [22] and very-preterm birth [23]. However, despite not meeting the criteria for DD, children with lower IQ scores or brain injuries will also need support to learn math. For an updated overview of the diagnostic criteria, see Castaldi, Piazza, and Iuculano [24]. Most epidemiological studies have been carried out in developed countries and have suggested a prevalence of DD between 3% and 6.5% [5][14][25]. However, especially given the lack of agreed diagnostic criteria, studies indicating a higher prevalence than the average (and even some that do not) may be grouping together remarkably diverse categories of mathematical difficulties [26]. These studies may include both children who have intrinsic and severe difficulties with numerical concepts and children who are low attainers in mathematics due to social (e.g., poverty, late start in school, poor attendance, lack of books, low parental education, etc.) or educational factors, for instance, poorer-performing schools [27]. This problem is a major concern, especially in countries with low overall educational attainment [28] combined with high levels of poverty and inequalitym where education is not standardized and there are many disadvantaged schools [29].
Therefore, studying the prevalence of a specific learning disorder requires several variables to be considered. For instance, the Basic Education Development Index indicates that the quality of schools and resources for education are not equivalent in all Brazilian regions [30]; consequently, low school achievement by international standards, such as the PISA study [31], is in common and accentuates gender gaps, especially in mathematics [29][32]. However, dyscalculia as such does not appear to be commoner in girls. For instance, there are three Brazilian epidemiological studies of DD. Ribeiro and Santos [33] used a two-phase diagnostic technique, involving screening followed by neuropsychological assessment, with a cohort of 407 students aged 8 or 9 years, enrolled in the 3rd school year of four public schools in the countryside of São Paulo State, and found 22 (5.4%) of the children to have DD. Fortes et al. [34] carried out a cross-sectional study of 1618 students from the 2nd to 6th grades in four regions in Brazil, using DSM-5 criteria for dyscalculia, a school achievement test and controlling for the variables of age, city, socioeconomic status, gender and IQ, and found a prevalence of 6.0%. Bastos et al. [35], using a mathematical screening test, found a higher prevalence (7.8%) in a cohort of 2893 (N = 128) with a greater frequency of boys.
It is still uncertain whether gender-related differences in mathematics performance depend more on school grade or age because these variables are usually overlapping [36]. Genetic factors do not seem to be a major determinant of gender differences in mathematics [37], especially given the fact that these disparities have reduced significantly in more gender-equal societies. In developed countries, such gender gaps in mathematics performance have declined progressively [38][39]. Social roles and social expectations modulate a child’s behaviour in all spheres, especially in academic ones, for instance, mothers and teachers tend to underestimate girls’ mathematics performance compared to boys [14][40], and this may elicit a long-lasting negative impact on the recruitment and retention of women in science, technology, engineering, and mathematics in adult life.
Finally, prevalence conclusions are also constrained by the variety of means of assessment for dyscalculia. School achievement and screening measures are useful for identifying low attainers in numeracy. However, these measures have sensitivity but lack specificity to identify dyscalculia since there are many environmental causes for low attainment in mathematics [17][28][29][32]. Moreover, a number of cognitive tasks involving domain-general and domain-specific measures show low diagnostic power and accuracy in school children [41][42]. Therefore, low attainers in numeracy are likely to benefit from further neuropsychological testing for diagnosis purposes. In comparison, numerical cognition batteries are designed to test for specific deficits and establish the diagnosis of dyscalculia when appropriate. The battery used, Zareki-R [43], may be seen as a potential advance in the study of DD and its diagnosis. It consists of a wide variety of subtests, measuring different components of number processing and calculation. Moreover, it has already been translated successfully into several languages and is used in many countries such as Switzerland, Germany, France, Belgium, Brazil, Algeria, etc. [44][45][46][47][48][49]. Therefore, this numerical cognition battery [5] shows promise for cross-cultural studies (e.g., [47]). For instance, Santos et al. [48] assessed 172 Brazilian children, aged 7–12 years from public schools in urban and rural areas. The study found high to moderate correlations between the subtests of this battery and the Arithmetic subtest of WISC-III, indicating good construct validity (r < 0.65). As expected, younger children obtained a lower global score than older children. Regarding rural children, the teaching method had a greater effect on performance than the home environment. Boys outperformed girls in 3 out of 12 tasks (Mental calculation, Problem-solving and Oral comparison); but the gender effect size was small for the Mental calculation and Oral comparison subtests and medium for the Problem-solving subtest.