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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.

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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.

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RESUMO

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.

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