Anatomical connectivity in children with developmental dyscalculia: A graph theory study.

Current theories postulate that numerical processing depends upon a brain circuit formed by regions and their connections; specialized in the representation and manipulation of the numerical properties of stimuli. It has been suggested that the damage of these network may cause Developmental Dyscalculia (DD): a persistent neurodevelopmental disorder that significantly interferes with academic performance and daily life activities that require mastery of mathematical notions and operations. However, most of the studies on the brain foundations of DD have focused on regions of interest associated with numerical processing, and have not addressed numerical cognition as a complex network phenomenon. The present study explored DD using a Graph Theory network approach. We studied the association between topological measures of integration and segregation of information processing in the brain proposed by Graph Theory; and individual variability in numerical performance in a group of 11 school-aged children with DD (5 of which presented with comorbidity with Developmental Dyslexia, the specific learning disorder for reading) and 17 typically developing peers. A statistically significant correlation was found between the Weber fraction (a measure of numerical representations' precision) and the Clustering Index (a measure of segregation of information processing) in the whole sample. The DD group showed significantly lower Characteristic Path Length (average shortest path length among all pairs of regions in the brain network) compared to controls. Also, differences in critical regions for the brain network performance (hubs) were found between groups. The presence of limbic hubs characterized the DD brain network while right Temporal and Frontal hubs found in controls were absent in the DD group. Our results suggest that the DD may be associated with alterations in anatomical brain connectivity that hinder the capacity to integrate and segregate numerical information.

Contribution of Attentional Networks to Basic Arithmetic Achievement in School-age Children / Contribución de las redes atencionales al rendimiento en aritmética básica en niños de edad escolar

Nowadays, there is still debate about the origin of arithmetic disabilities. Two predominant hypotheses have been developed in this regard: 1) difficulties in arithmetic appear due to a deficit in domain-specific skills (numerical skills) and 2) there is a strong relationship between the development of the domain-general processes and arithmetical skills. In this study we explore the specific contribution of orienting and executive control attentional networks to individual variability in basic mental arithmetic. Participants were elementary school children, from second to third grade, with and without difficulties in basic mental arithmetic. Results provide support for the two proposed hypotheses. Children with difficulties in arithmetic showed difficulties both in numerical skills and in attentional networks. These findings suggest that arithmetic difficulties may be associated with a heterogeneous combination of deficits, including difficulties in attentional functioning.

En la actualidad existe aún debate sobre el origen de las dificultades en aritmética. Se han desarrollado dos hipótesis predominantes al respecto: 1) las dificultades en aritmética aparecen por un déficit en las capacidades de dominio específico (capacidades numéricas) y 2) hay una estrecha relación entre el desarrollo de los procesos de dominio general y las habilidades aritméticas. En este estudio se explora la contribución específica de las redes de atención ejecutiva y orientación atencional a la explicación de la varianza en aritmética básica. Participaron niños de segundo y tercer grado de primaria, con y sin dificultades en aritmética básica. Nuestros resultados ofrecen sustento a las dos hipótesis propuestas, ya que los niños con dificultades en aritmética mostraron dificultades tanto en las capacidades numéricas como en las redes atencionales. Estos hallazgos sugieren que las dificultades en aritmética pudieran estar asociadas a una combinación heterogénea de déficits, incluyendo dificultades en el funcionamiento atencional.

Exploring basic numerical capacities in children with difficulties in simple arithmetical achievement / Exploración de las capacidades numéricas básicas en niños con dificultades en el rendimiento en aritmética básica

Abstract Introduction: Current cognitive theories suggest that mathematical learning disabilities may be caused by a dysfunction in the ability to represent non-symbolic numerosity (non-symbolic skills), by impairments in the ability to associate symbolic numerical representations with the underlying analogic non-numerical magnitude representation (symbolic and numerical mapping skills), or by a combination of both deficits. The aim of this study was to contrast the number sense hypothesis and the access deficit hypothesis, to identify the possible origin of the varying degrees of arithmetical difficulties. Method: We compared the performance of children with very low arithmetic achievement (VLA), children with low arithmetical achievement (LA), and typically achieving peers (TA), in non-symbolic, symbolic and numerical mapping tasks. Intellectual capacity and working memory were also evaluated as control variables. The sample comprised 85 Chilean children (3rd to 6th grades) from the Public General Education System. Data were included in several covariance analyses to identify potentially different behavioural profiles between groups. Results: The results showed deficits in both non-symbolic numerosity processing and number-magnitude mapping skills in children with VLA, whereas children with LA exhibited deficits in numerical mapping tasks only. Conclusions: These findings support the hypothesis of impaired non-symbolic numerical representations as the cognitive foundation of severe arithmetical difficulties. Low arithmetical achievement, in contrast, seems to be better explained by defective numerical mapping skills, which fits the access deficit hypothesis. The results presented here provide new evidence regarding the cognitive mechanisms underlying the different behavioural profiles identified in children with varying degrees of arithmetical difficulties.

Resumen Introducción: Teorías cognitivas actuales sugieren que las dificultades en el aprendizaje de las matemáticas pueden ser causadas por una disfunción en la habilidad de representar las numerosidades no-simbólicas (habilidades no-simbólicas), por dificultades en la habilidad de asociar los números con representaciones analógicas, no-simbólicas, subyacentes a la magnitud (habilidades simbólicas y de mapeo) o por una combinación de ambos déficits. El objetivo de este estudio fue contrastar la hipótesis de un déficit en el sentido del número y la hipótesis del déficit en el acceso, para identificar el posible origen de los diferentes grados de dificultades en aritmética. Método: Se comparó el desempeño de niños con muy bajo rendimiento en aritmética (VLA), niños con bajo rendimiento en aritmética (LA) y pares con rendimiento típico (TA), en tareas numéricas no-simbólicas, simbólicas y de mapeo. También se evaluaron la capacidad intelectual y la memoria de trabajo como variables de control. La muestra estuvo conformada por 85 niños chilenos (de 3ero a 6to grado) del Sistema de General de Educación Pública. Los datos fueron incluidos en varios análisis de covarianza para identificar posibles perfiles conductuales diferentes entre grupos. Resultados: Los resultados mostraron que los niños con VLA tienen déficits tanto en el procesamiento no-simbólico de la numerosidad como en las habilidades de mapeo entre los símbolos numéricos y la magnitud analógica que estos representan. Los niños con LA solo mostraron déficits en las habilidades de mapeo. Conclusiones: Estos hallazgos sustentan la hipótesis de que un daño en las representaciones numéricas no-simbólicas subyace a las dificultades severas en aritmética. Por el contrario, el bajo rendimiento en aritmética parece explicarse por deficientes habilidades de mapeo, lo cual se ajusta mejor a la hipótesis del déficit en el acceso. Los anteriores resultados, ofrecen nuevas evidencias respecto a los mecanismos cognitivos que subyacen a los perfiles conductuales identificados en los niños con diferentes grados de dificultades en aritmética.

Numerical processing profiles in children with varying degrees of arithmetical achievement.

Recent studies show basic cognitive abilities such as the rapid and precise apprehension of small numerosities in object sets ("subitizing"), verbal counting and numerical magnitude comparison significantly influence the acquisition of arithmetic and continues to modulate more advanced stages of mathematical cognition. Additionally, children with low arithmetic achievement (LAA) and Developmental Dyscalculia (DD) exhibit significant deficits in these cognitive processes. Nevertheless, the different cognitive profiles of children with varying degrees of numerical and arithmetic processing deficits have not been sufficiently characterized, despite its potential relevance to the stimulation of numerical cognition and the design of appropriate intervention strategies. Here, the cognitive profiles of groups of typically developing children, children with low arithmetical achievement and DD, exhibiting typical and atypical subitizing ability were contrasted. The results suggest that relatively independent neurocognitive mechanisms may produce distinct profiles at the behavioral level and suggest children with low arithmetic performance exhibiting atypical subitizing abilities are not only significantly slower, but rely on compensatory mechanisms and strategies compared to typical subitizers. The role of subitizing as a correlate of arithmetic fluency is revised in the light of the present findings.

Symbolic and non-symbolic number magnitude processing in children with developmental dyscalculia.

The aim of this study was to evaluate if children with Developmental Dyscalculia (DD) exhibit a general deficit in magnitude representations or a specific deficit in the connection of symbolic representations with the corresponding analogous magnitudes. DD was diagnosed using a timed arithmetic task. The experimental magnitude comparison tasks were presented in non-symbolic and symbolic formats. DD and typically developing (TD) children showed similar numerical distance and size congruity effects. However, DD children performed significantly slower in the symbolic task. These results are consistent with the access deficit hypothesis, according to which DD children's deficits are caused by difficulties accessing magnitude information from numerical symbols rather than in processing numerosities per se.

Symbolic and Non-Symbolic Number Magnitude Processing in Children with Developmental Dyscalculia

The aim of this study was to evaluate if children with Developmental Dyscalculia (DD) exhibit a general deficit in magnitude representations or a specific deficit in the connection of symbolic representations with the corresponding analogous magnitudes. DD was diagnosed using a timed arithmetic task. The experimental magnitude comparison tasks were presented in non-symbolic and symbolic formats. DD and typically developing (TD) children showed similar numerical distance and size congruity effects. However, DD children performed significantly slower in the symbolic task. These results are consistent with the access deficit hypothesis, according to which DD children’s deficits are caused by difficulties accessing magnitude information from numerical symbols rather than in processing numerosities per se (AU)

El objetivo de este estudio fue evaluar si los niños con Discalculia del Desarrollo (DD) presentan un déficit general en la representación de las magnitudes o un déficit específico en la conexión de las representaciones simbólicas con sus correspondientes magnitudes análogas. La DD fue diagnosticada mediante una tarea aritmética con control del tiempo de reacción. Las tareas experimentales de comparación de magnitudes se presentaron en formato no-simbólico y simbólico. Los resultados muestran que en los discalcúlicos la representación numérica parece estar intacta, lo cual se expresa en efectos de distancia numérica y congruencia de la magnitud, similares a los que exhiben los niños con un desarrollo típico. Las diferencias respecto a este grupo se encuentran solo en la velocidad de procesamiento en las tareas simbólicas. Se concluye que los datos se ajustan a la hipótesis del déficit en el acceso, por lo que las dificultades de los niños discalcúlicos parecen producto de un trastorno en la conexión entre las representaciones simbólicas y las análogas y no en la representación numérica per se (AU)

Typical development of quantity comparison in school-aged children.

Although basic numerical skills have been widely studied in the last years, very few studies have undertaken a developmental approach. The present study evaluated the development of the magnitude comparison basic numerical ability, in children from first, third and sixth grades by means of the subject's response time in numerical tasks presented in symbolic and non-symbolic formats. The results showed a significant decrease on quantities processing speed as age increases, which suggests numerical skills tend to become automatic with instruction. The differences found, concerning the general achievement pattern in each school year, might express the maturational specificities of the numerical representation system through development.

Typical development of quantity comparison in school-aged

Although basic numerical skills have been widely studied in the last years, very few studies have undertaken a developmental approach. The present study evaluated the development of the magnitude comparison basic numerical ability, in children from first, third and sixth grades by means of the subject’s response time in numerical tasks presented in symbolic and non-symbolic formats. The results showed a significant decrease on quantities processing speed as age increases, which suggests numerical skills tend to become automatic with instruction. The differences found, concerning the general achievement pattern in each school year, might express the maturational specificities of the numerical representation system through development (AU)

Aunque las capacidades numéricas básicas han sido ampliamente investigadas en los últimos años, muy pocos estudios han tenido en cuenta una perspectiva del desarrollo de las mismas. En este estudio se evaluó el desarrollo de la capacidad numérica básica de comparación de cantidades en escolares de primero, tercero y sexto grados, a través del análisis del tiempo de reacción de los sujetos en tareas numéricas presentadas en formatos simbólico y no simbólico. Los resultados mostraron una disminución significativa en la velocidad de procesamiento de las cantidades con el incremento de la edad, lo cual apunta a una automatización de las habilidades numéricas con el aumento del nivel escolar. Las diferencias encontradas en el patrón de rendimiento general en cada grado escolar podrían expresar las particularidades de la maduración del sistema de representación numérica en las diferentes etapas del desarrollo (AU)

Bases Biológicas de la Discalculia del desarrollo / Biological basis of Growth dyscalculia

El Trastorno Específico en el Aprendizaje de las Matemáticas o Discalculia del Desarrollo (DD) es un déficit severo, persistente y selectivo en el rendimiento aritmético. Aunque no han sido identificados genes responsables de este trastorno, varias investigaciones realizadas en muestras de sujetos con síndromes genéticos que presentan DD como parte de su perfil cognitivo, han reportado anomalías estructurales y funcionales en el cerebro de los mismos. En este artículo se presenta una revisión de las principales evidencias provenientes de estudios con síndromes genéticos que apoyan la determinación biológica de la Discalculia del Desarrollo…(AU)