Comprensión del valor de posición: equivalencia numérica y composición aditiva como facilitadores en la escritura de numerales / Understanding Place Value: Numerical Equivalence and Additive Composition as Predictors for Writing Numerals / Compreendendo o valor posicional: equivalência numérica e composição aditiva como facilitadores na escrita de numerais

El valor de posición es una propiedad básica de los formatos de representación del Sistema de Numera- ción en Base Diez (SNBD), y su comprensión facilita el desempeño matemático de los estudiantes en diferentes grados escolares. Algunas investigaciones sugieren que nociones como la composición aditiva y la equivalencia numérica participan en la emergencia de la comprensión de este principio, sin embargo, pocos estudios han intentado analizar la relación entre estas nociones o se han interesado en indagar ­desde una perspectiva de la transcodificación numérica­, cómo estas afectan la producción de numerales arábigos durante los procesos iniciales del aprendizaje escolar. En tal sentido, esta investigación propone indagar si algunas de las invariantes del SNBD ­composición aditiva y equivalencia numérica­ facilitan la comprensión del valor de posición y la escritura numérica en estudiantes de primer grado de primaria. Participaron 96 estudiantes adscritos a escuelas públicas de Cali, Colombia, en un estudio cuasi-experimental pre-posprueba con grupo control, que involucra la aplicación de un proceso de intervención diferente para cada grupo experimental: composición aditiva y (b) equivalencia numérica. Los resultados plantean que los dos tratamientos apli- cados facilitan la comprensión del valor de posición y generan efectos diferentes en la comprensión y producción de numerales arábigos. Además, los análisis develan cambios significativos entre aplicaciones para los grupos experimentales, pero no para el grupo con- trol, lo cual sugiere que la composición aditiva y la equivalencia numérica son predictores en la escritura correcta de numerales.

The place value is a fundamental property of the base-10 system representation formats, and its under- standing facilitates the mathematical performance of children in different school grades. Some research sug- gests that notions such as additive composition and nu- merical equivalence participate in the emergence of the understanding of this principle. However, few studies have attempted to analyze the relationship between these notions or have been interested in investigating ­from a transcoding perspective numerical­ how these affect the production of Arabic numerals during the initial processes of school learning. This research explores how some invariants of the base-10 system: Additive Composition and Numerical Equivalence, facilitate the place value mastery and the numerical writing of children. First-grade students (n= 96) linked to public schools in the city of Cali, Colombia, in a quasi-experimental experimental study with a control group, which involves the application of different in- tervention processes to each experimental group: (a) numerical equivalence and (b) additive composition. The results suggest that both treatments facilitate the place value understanding and generate differ- ent effects on comprehending and producing Arabic numerals. In addition, analyses reveal significant changes between applications for the experimental groups but not for the group control, which specif- ically evidences both the additive composition and the numerical equivalence are predictors in correct number writing.

O valor posicional é uma propriedade básica dos forma- tos de representação do Sistema de Numeração Base Dez (SNBD), e sua compreensão facilita o desempenho mate- mático de alunos de diferentes séries escolares. Algumas pesquisas sugerem que noções como composição aditiva e equivalência numérica participam do surgimento da compreensão desse princípio, porém, poucos estudos têm tentado analisar a relação entre essas noções ou se interessado em investigar ­a partir de uma perspectiva de transcodificação numérica­ como essas afetam a produção de algarismos arábicos durante os processos iniciais de aprendizagem escolar. Esta investigação se propõe a investigar se alguns dos invariantes do SNBD; a composição aditiva e a equivalência numérica facilitam a compreensão do valor posicional e da escrita numérica em alunos da primeira série. Participaram do experi- mento 96 alunos da primeira série de escolas públicas de Cali, Colômbia; num estudo quase experimental pré/pós-teste com um grupo controle, que envolve a aplicação de um processo de intervenção diferen- te a cada grupo experimental; (a) composição aditiva e (b) equivalência numérica. Os resultados sugerem que os dois tratamentos aplicados facilitam a compreensão do valor posicional e geram efeitos diferentes na com- preensão e produção dos algarismos arábicos. Além disso, as análises revelam mudanças significativas entre as aplicações para os grupos experimentais, mas não para o grupo controle, o que sugere que a composi- ção aditiva e a equivalência numérica são preditores na escrita correta dos numerais.

Contributions of cognitive flexibility, inhibition and number label knowledge to numerical equivalence in 3- to 5-year-old children.

To investigate the contributions of cognitive flexibility, inhibition and number label knowledge to children's numerical equivalence, one hundred and one 3- to 5-year-olds were administered the dimensional change card sorting task, the day-night task and the give-a-number task. The numerical equivalence was assessed with the numerical matching task in three surface similarity conditions. Results showed that, in the high surface similarity condition, cognitive flexibility and label knowledge, rather than inhibition, were significant predictors of children's performance in numerical equivalence. In the low surface similarity and the cross-mapping conditions, only cognitive flexibility, rather than number label knowledge and inhibition, significantly explained the unique variance in numerical equivalence. Besides, cognitive flexibility explained more variation in numerical equivalence in the cross-mapping condition compared with the low surface similarity condition. These findings highlight different roles of cognitive flexibility, inhibition and number label knowledge in numerical equivalence in the three surface similarity conditions.

One-to-one correspondence without language.

A logical rule important in counting and representing exact number is one-to-one correspondence, the understanding that two sets are equal if each item in one set corresponds to exactly one item in the second set. The role of this rule in children's development of counting remains unclear, possibly due to individual differences in the development of language. We report that non-human primates, which do not have language, have at least a partial understanding of this principle. Baboons were given a quantity discrimination task where two caches were baited with different quantities of food. When the quantities were baited in a manner that highlighted the one-to-one relation between those quantities, baboons performed significantly better than when one-to-one correspondence cues were not provided. The implication is that one-to-one correspondence, which requires intuitions about equality and is a possible building block of counting, has a pre-linguistic origin.