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 non‐numerical 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.

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RESUMEN:Las habilidades numéricas y aritméticas son predictores críticos del éxito académico. En trabajos recientes, se ha cuestionado qué habilidades numéricas básicas se relacionan con la ejecución en aritmética, si el procesamiento de magnitudes numéricas no simbólicas o el procesamiento de magnitudes simbólicas. En el presente estudio se tomó una muestra de 104 escolares del segundo curso de Educación Infantil (EI), que completaron una tarea de comparación de magnitudes numéricas no simbólicas, una de comparación de magnitudes numéricas simbólicas y una tarea de enumeración, así como un test estandarizado de rendimiento en matemáticas (TEMA-3). Además, se controlaron habilidades cognitivas generales como inteligencia, velocidad de procesamiento, amplitud de memoria, control inhibitorio y memoria visuo-espacial. Para comprobar si las variables de procesamiento numérico predicen más allá de las variables de control, se realizó un análisis de regresión jerárquica, utilizando como variable dependiente el TEMA-3, e introduciendo las variables de control y las tareas de procesamiento numérico en sucesivos pasos. El modelo explicó el 65.5% de la varianza. Pero solo la comparación de magnitudes simbólicas y la enumeración contribuyeron a la varianza en ejecución aritmética más allá de las variables de control, mientras que la comparación de magnitudes no simbólicas no contribuyó significativamente. Estos resultados sugieren que un buen conocimiento de los números simbólicos es importante para el desarrollo matemático de los niños, y que particularmente el acceso a la magnitud desde los números simbólicos más que la representación de la magnitud per se es crucial para este desarrollo de la aritmética. Palabras clave: representación de la magnitud; comparación de magnitudes; enumeración; subitizing; competencia aritmética. Core markers of arithmetic competence in preschool children ABSTRACT:The numerical and arithmetic skills are critical predictors of academic success. In current studies, it has been questioned what numerical skills relate with arithmetic achievement, whether the non-symbolic numerical magnitudes processing or the symbolic magnitudes processing. In the current study a sample of 104 preschool children was taken. They completed a non-symbolic numerical comparison task, a symbolic numerical comparison task and a dot enumeration task, as well as a standardized arithmetic performance test (TEMA-3). Moreover, general cognitive skills such as

Recent years have witnessed an increase in research on how numeral ordering skills relate to children’s and adults’ mathematics achievement both cross-sectionally and longitudinally. Nonetheless, it remains unknown which core competency numeral ordering tasks measure, which cognitive mechanisms underlie performance on these tasks, and why numeral ordering skills relate to arithmetic and math achievement. In the current study, we focused on the processes underlying decision-making in the numeral order judgement task with triplets to investigate these questions. A drift-diffusion model for two-choice decisions was fit to data from 97 undergraduates. Findings aligned with the hypothesis that numeral ordering skills reflected the operationalization of the numerical system, where small numbers provide more evidence of an ordered response than large numbers. Furthermore, the pattern of findings suggested that arithmetic achievement was associated with the accuracy of the ordinal representations of numbers.