Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties.

Catechol-O-methyltransferase (COMT) is an enzyme that is particularly important for the metabolism of dopamine. Functional polymorphisms of COMT have been implicated in working memory and numerical cognition. This is an exploratory study that aims at investigating associations between COMT polymorphisms, working memory, and numerical cognition. Elementary school children from 2th to 6th grades were divided into two groups according to their COMT val158met polymorphism [homozygous for valine allele (n = 61) vs. heterozygous plus methionine homozygous children or met+ group (n = 94)]. Both groups were matched for age and intelligence. Working memory was assessed through digit span and Corsi blocks. Symbolic numerical processing was assessed through transcoding and single-digit word problem tasks. Non-symbolic magnitude comparison and estimation tasks were used to assess number sense. Between-group differences were found in symbolic and non-symbolic numerical tasks, but not in working memory tasks. Children in the met+ group showed better performance in all numerical tasks while val homozygous children presented slower development of non-symbolic magnitude representations. These results suggest COMT-related dopaminergic modulation may be related not only to working memory, as found in previous studies, but also to the development of magnitude processing and magnitude representations.

ResumoO progresso tecnológico e econômico de um país associa-se a melhorias na qualidade de vida à custa de uma demanda crescente do desempenho cognitivo e acadêmico da população. As dificuldades de aprendizagem da matemática (DAM) representam um risco, diminuindo potencialmente o capital cognitivo de uma sociedade. Os diagnósticos e intervenções neuropsicológicos melhoram potencialmente o funcionamento cognitivo e o bem-estar dos indivíduos. Pesquisas são necessárias para um planejamento efetivo e equitativo de políticas públicas. Os critérios diagnósticos atuais das dificuldades de aprendizagem são estatísticos e arbitrários, resultando em uma heterogeneidade clínica e em um alto índice de comorbidades. Neste artigo, foram analisados, através de uma revisão de literatura, os possíveis mecanismos cognitivos envolvidos nas DAM e em outros distúrbios relacionados. Conclui-se que o processamento fonológico, a memória de trabalho, o processamento visoespacial e o senso numérico são domínios potencialmente subjacentes às DAM. Mais estudos longitudinais e integrativos que avaliem simultaneamente a contribuição destes fatores são necessários. Palavras-chave:Dificuldades de aprendizagem da matemática; senso numérico; memória de trabalho; habilidades visoespaciais; revisão. AbstractTechnological and economic progress is associated to higher living standards at the expense of growing demands on cognitive/academic performance. Mathematical learning difficulties (MLD) represent a risk factor, potentially diminishing a society's cognitive capital. Neuropsychological diagnosis and interventions potentially improve cognitive functioning and well-being. Research data are required to plan effective and equitable public policies. Current diagnostic criteria for learning difficulties are statistical and arbitrary, resulting in clinical heterogeneity and high comorbidity rates. In this paper, we discuss possible cognitive mechanisms involved in MLD and their relationship to other disorders through a literature review. It is concluded that phonological processing, working memory, visuospatial processing and number sense are domains potentially underlying MLD. More longitudinal and integrative studies, simultaneously assessing the contribution of these several factors are required.

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