The acquisition and representation of natural numbers have been a central topic in cognitive science. However, a key question in this topic about how humans acquire the capacity to understand that numbers make 'infinite use of finite means' (or that numbers are generative) has been left unanswered. Here, we test the hypothesis that children's understanding of the syntactic rules for building complex numerals-or numerical syntax-is a crucial foundation for the acquisition of number concepts. In two independent studies, we assessed children's understanding of numerical syntax by probing their knowledge about the embedded structure of cardinal numbers using a novel task called Give-a-number Base-10 (Give-N10). In Give-N10, children were asked to give a large number of items (e.g., 32 items) from a pool that is organized in sets of ten items. Children's knowledge about the embedded structure of numbers (e.g., knowing that thirty-two items are composed of three tens and two ones) was assessed from their ability to use those sets. Study 1 tested English-speaking 5-to 10-year-olds and revealed that children's understanding of the embedded structure of numbers emerges relatively late in development (several months into kindergarten), beyond when they are capable of making a semantic induction over a local sequence of numbers. Moreover, performance in Give-N10 was predicted by children's counting fluency even when school grade was controlled for, suggesting that children's understanding of the embedded structure of numbers is founded on their earlier knowledge about the syntactic regularities in the counting sequence. In Study 2, this association was tested again in monolingual Korean kindergarteners (5-6 years), as we aimed to test the same effect in a language with a highly regular numeral system. It replicated the association between Give-N10 performance and counting fluency, and it also demonstrated that Koreanspeaking children understand the embedded structure of cardinal numbers earlier in the acquisition path than English-speaking peers, suggesting that the knowledge of numerical syntax governs children's understanding of the generative properties of numbers. Based on these observations and our theoretical analysis of the literature, we propose that the syntax for building complex numerals represents the structure of numerical thinking.

El objetivo de este artículo es analizar los errores sintácticos que niños de 1º, 2º y 3º grado de primaria cometen cuando escriben numerales dictados con un rango superior al aprendido. Sus producciones se caracterizaron en función de la manera como escriben los componentes del numeral arábigo dictado y del tipo de relaciones que utilizan para unirlos. La progresiva disminución del error sintáctico a través de los grados y la modificación de las relaciones utilizadas al escribir los componentes del numeral a través de los grados y en función del tipo de numeral permiten señalar las contribuciones

Objective. This study evaluates in three-digit numerals how the writing times between digits (Inter Digit Jump -IDJ) adjust to the predictions deduced from the transcoding models proposed by Power and Dal Martello (1990) and Barrouillet, Camos, Perruchet and Seron (2004), who explain the writing of numerals in children. Method. The study had the participation of twenty five (25) first grade children who wrote down spoken verbal numerals in three-digit numerals correctly; the duration of the Inter-Digit Jump was analyzed for four types of numerals during the course of four sessions. Results. The results of the ANOVAs showed that in the four types of numerals, the duration in the first IDJ is greater than in the second IDJ, and that the shortest durations tended to take place prior to writing the zero digit. Conclusion. These findings best fit the predictions based on the model by Barrouliet et al., (2004), which assumes that the chain of digits is produced and stored in a buffer to be subsequently produced by the graphomotor procedures, showing that in three-digit numerals the IDJ duration reflects more the production program than the syntactic structure of the verbal numerals dictated.Keywords. Number transcoding, graphomotor procedures, arabic numerals, verbal numerals. Tiempos de escritura en numerales de tres dígitos: relación entre el tiempo y la estructura sintáctica de las expresiones verbales dictadas ResumenObjetivo. El presente estudio evalúa el ajuste de los tiempos en las pausas entre dígitos, en la escritura de numerales arábigos, con las predicciones que se derivan de los modelos de transcodificación de Power y Dal Martello (1990) (2004), el cual supone que la cadena de dígitos se produce y almacena en una memoria intermedia para luego ser producida por los procedimientos de grafomotores, lo que sugiere que en los numerales de tres dígitos los tiempos en las pausas entre dígitos reflejan el programa motor de escritura más que la estructura sintáctica de los numerales verbales dictados.Palabras clave. Transcodificación numérica, procedimientos grafomotores, numerales arábigos, numerales verbales.Tempos de escritura em numerais de três dígitos: relação entre a tempo e a estrutura sintática das expressões verbais ditadas Barrouliet et al. (2004), no qual supõe que a cadeia de dígitos é produzida e armazenada numa memória intermédia para depois ser feita pelos procedimentos grafomotores, o que sugere que nos numerais de três dígitos os tempos nas pausas entre dígitos refletem o programa motor de escritura mais que a estrutura sintática dos numerais verbais ditados.

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