Disentangling the Mechanisms of Symbolic Number Processing in Adults’ Mathematics and Arithmetic Achievement

[EN]A growing body of research has shown that symbolic number processing relates to individual differences in mathematics. However, it remains unclear which mechanisms of symbolic number processing are crucial—accessing underlying magnitude representation of symbols (i.e., symbol-magnitude associations), processing relative order of symbols (i.e., symbol-symbol associations), or processing of symbols per se. To address this question, in this study adult participants performed a dots-number word matching task—thought to be a measure of symbol-magnitude associations (numerical magnitude processing) —a numeral-ordering task that focuses on symbol-symbol associations (numerical order processing), and a digit-number word matching task targeting symbolic processing per se. Results showed that both numerical magnitude and order processing were uniquely related to arithmetic achievement, beyond the effects of domain-general factors (intellectual ability, working memory, inhibitory control, and nonnumerical ordering). Importantly, results were different when a general measure of mathematics achievement was considered. Those mechanisms of symbolic number processing did not contribute to math achievement. Furthermore, a path analysis revealed that numerical magnitude and order processing might draw on a common mechanism. Each process explained a portion of the relation of the other with arithmetic (but not with a general measure of math achievement). These findings are consistent with the notion that adults’ arithmetic skills build upon symbol-magnitude associations, and they highlight the effects that different math measures have in the study of numerical cognition.This work was supported by the Ministry of Economy and Enterprise in Spain (grant number PSI2015-66802-P)

Interacción entre habilidades de dominio específico y dominio general en la competencia matemática

This article is an approach to some viewpoints about interactions between domain-specific and general cognitive tools involved in the development of mathematical competence. Many studies report positive correlations between the acuity of the numerical approximation system and formal mathematical performance, while another important group of investigations have found no evidence of a direct connection between non-symbolic and symbolic numerical representations. The challenge for future research will be to focus on correlations and possible causalities between non-symbolic and symbolic arithmetic skills and general domain cognitive skills in order to identify stable precursors of mathematical competence.  Este artículo es una aproximación a diferentes puntos de vista acerca de la interacción entre las habilidades cognitivas de dominio específico y general involucradas en el desarrollo de la competencia matemática. Muchos estudios reportan correlaciones positivas entre la agudeza del sistema de aproximación numérica y el desempeño matemático formal, mientras que otro grupo importante de investigaciones no han hallado evidencias de una conexión directa entre las representaciones numéricas no simbólicas y las simbólicas. El desafío para las futuras investigaciones será focalizar en correlaciones y posibles causalidades entre las habilidades aritméticas no simbólicas, las simbólicas y las habilidades cognitivas de dominio general con el propósito de identificar precursores estables de la competencia matemática. &nbsp

Characterizing persistent Developmental Dyscalculia: A cognitive neuroscience approach

Developmental dyscalculia (DD) is a specific learning disorder of calculation abilities. In the present thesis I report a series behavioural and functional neuroimaging studies to further elucidate the core numerical deficits underlying DD. I recruited a sample of children with DD who demonstrated persistent impairments in arithmetic. In Chapter 2, to validate the selection criteria, I compared the performance of children with and without persistent DD on a test of numerical magnitude processing. The data showed that only children with persistent DD presented with deficits in numerical magnitude processing, while those with inconsistent DD perform at the level of age-matched typically developing (TD) controls. In Chapter 3, I compared the performance of children with persistent DD on tasks assessing symbolic (e.g. Arabic digits) and non-symbolic (e.g. dot arrays) processing skills. Children with DD performed significantly worse on symbolic but not non-symbolic numerical magnitude processing tasks. These findings suggest that DD arises not from a format-independent magnitude processing deficit, but rather from difficulties in processing symbolic number representations. In Chapter 4, I investigated the influence of non-numerical variables (e.g. size) on non-symbolic numerical magnitude processing in children with and without DD. Children with DD were found to exhibit deficits in non-symbolic processing only when the visual perceptual cues were anticorrelated with numerical magnitude. When numerical magnitude and area were congruent no group differences in performance emerged. Therefore, rather than presenting with a core deficit in non-symbolic processing, children with DD have difficulties in disentangling numerical and non-numerical cues. In Chapter 5, I used functional neuroimaging to investigate whether children with DD exhibit atypical brain activation during numerical magnitude processing (symbolic, non-symbolic and mixed comparison). The data from this study revealed atypical cortical activity in the Intraparietal Sulcus (IPS) during symbolic and mixed format (comparing symbolic with non-symbolic) tasks. In contrast, children with DD did not exhibit differences in the IPS during non-symbolic numerical magnitude processing. These neuroimaging findings complement the behavioral data in Chapter 3 and 4 by suggesting that children with DD have a deficit in semantic representation of symbolic numerical magnitudes rather than a core deficit in representing both symbolic and non-symbolic numerical magnitudes. The findings from these studies provide converging evidence to support a core deficit in processing the semantic meaning of symbolic numerals in children with persistent DD

Contributions from specific and general factors to unique deficits: two cases of mathematics learning difficulties

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

The role of short-term memory and visuo-spatial skills in numerical magnitude processing: evidence from Turner syndrome

Peer reviewe

A Hand Full of Numbers: A Role for Offloading in Arithmetics Learning?

Finger counting has been associated to arithmetic learning in children. We examined children with (n = 14) and without (n = 84) mathematics learning difficulties with ages between 8 and 11 years. Deficits in finger gnosia were found in association to mathematical difficulties. Finger gnosia was particularly relevant for the performance in word problems requiring active manipulation of small magnitudes in the range between 1 and 10. Moreover, the deficits in finger gnosia could not be attributed to a shortage in working memory capacity but rather to a specific inability to use fingers to transiently represent magnitudes, tagging to be counted objects, and reducing the cognitive load necessary to solve arithmetic problems. Since finger gnosia was more related to symbolic than to non-symbolic magnitude processing, finger-related representation of magnitude seems to be an important link for learning the mapping of analog onto discrete symbolic magnitudes

Early cortical surface plasticity relates to basic mathematical learning

Children lay the foundation for later academic achievement by acquiring core mathematical abilities in the first school years. Neural reorganization processes associated with individual differences in early mathematical learning, however, are still poorly understood. To fill this research gap, we followed a sample of 5-6-year-old children longitudinally to the end of second grade in school (age 7–8 years) combining magnetic resonance imaging (MRI) with comprehensive behavioral assessments. We report significant links between the rate of neuroplastic change of cortical surface anatomy, and children's early mathematical skills. In particular, most of the behavioral variance (about 73%) of children's visuospatial abilities was explained by the change in cortical thickness in the right superior parietal cortex. Moreover, half of the behavioral variance (about 55%) of children's arithmetic abilities was explained by the change in cortical folding in the right intraparietal sulcus. Additional associations for arithmetic abilities were found for cortical thickness change of the right temporal lobe, and the left middle occipital gyrus. Visuospatial abilities were related to right precentral and supramarginal thickness, as well as right medial frontal gyrus folding plasticity. These effects were independent of other individual differences in IQ, literacy and maternal education. Our findings highlight the critical role of cortical plasticity during the acquisition of fundamental mathematical abilities

Number Processing in Infants and Children Born Very Preterm

Individuals born very preterm (<32 weeks; VP) have notably poorer attainment in mathematics than their term-born peers. Only a handful of studies have investigated basic numerical skills in VP children and the underlying mechanisms associated with problems with mathematics in this population are still not fully comprehended. Basic processes underlying numerical cognition can go awry very early in development and there is a lack of knowledge of early trajectories of acquisition of numerical skills in infants born prematurely. This thesis reports on a series of studies investigating number processing in very preterm infants and children. These make use of a combination of tools, such as neurodevelopmental assessments, eye-tracking, event-related-potentials, neuropsychological evaluations and experimental tasks. Specifically, cross-sectional studies investigated numerical sensitivity in VP infants aged six and twelve months. Behavioural and electrophysiological measures assessing a range of domain-general and domain-specific skills associated with mathematics performance were also investigated in VP school-aged children. The results showed that, during the first year of post-natal life, VP infants do not exhibit differential developmental trajectories in the basic ability to discriminate numerosities compared to infants born at full term, although they required a longer time to discriminate the new number of elements. Later in development, school-aged VP children demonstrated difficulties in processing basic numerical information. Electrophysiological data demonstrated that this might be associated with deficits in sensory and attention resources and not necessarily in how VP children encode number-related information. Difficulties in processing numerical information, however, have only a marginal impact on their performance in mathematics. We tentatively conclude that difficulties in mathematics in individuals born very prematurely are largely associated with domain-general skills

Dyscalculia from a developmental and differential perspective

Developmental dyscalculia (DD) and its treatment are receiving increasing research attention. A PsychInfo search for peer-reviewed articles with dyscalculia as a title word reveals 31 papers published from 1991–2001, versus 74 papers published from 2002–2012. Still, these small counts reflect the paucity of research on DD compared to dyslexia, despite the prevalence of mathematical difficulties. In the UK, 22% of adults have mathematical difficulties sufficient to impose severe practical and occupational restrictions (Bynner and Parsons, 1997; National Center for Education Statistics, 2011). It is unlikely that all of these individuals with mathematical difficulties have DD, but criteria for defining and diagnosing dyscalculia remain ambiguous (Mazzocco and Myers, 2003). What is treated as DD in one study may be conceptualized as another form of mathematical impairment in another study. Furthermore, DD is frequently—but, we believe, mistakenly- considered a largely homogeneous disorder. Here we advocate a differential and developmental perspective on DD focused on identifying behavioral, cognitive, and neural sources of individual differences that contribute to our understanding of what DD is and what it is not