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.

Detailed analysis of the Japanese version of the Rapid Dementia Screening Test using Arabic-hiragana conversion.

AIM: The number-transcoding task on the Japanese version of the Rapid Dementia Screening Test (RDST-J) requires conversion between Arabic and Chinese numerals (209 to , 4054 to , to 681, to 2027). In this task, questions and answers are written for Chinese-Arabic conversion. We reported that the RDST-J could distinguish subjects with Alzheimer's disease with a Clinical Dementia Rating Scale score of 0.5 from controls. In this study, we investigated the impact of changing the task to a hiragana-Arabic conversion. METHODS: Participants consisted of 45 patients with a Clinical Dementia Rating Scale score of 0.5 and 52 normal controls. RESULTS: The sensitivity and specificity of total scores ≥9 on the two RDST-J versions for discriminating subjects with a Clinical Dementia Rating Scale score of 0.5 from controls were 73.1% and 75.5%, respectively, on the original version, and 71.8% and 73.0%, respectively, on the revised version. CONCLUSIONS: The sensitivity and specificity of the revised version of the RDST-J was equivalent to those of the original version.

Detailed analysis of the Japanese version of the Rapid Dementia Screening Test, revised version.

AIM: The number-transcoding task on the Japanese version of the Rapid Dementia Screening Test (RDST-J) requires mutual conversion between Arabic and Chinese numerals (209 to , 4054 to , to 681, to 2027). In this task, question and answer styles of Chinese numerals are written horizontally. We investigated the impact of changing the task so that Chinese numerals are written vertically. METHODS: Subjects were 211 patients with very mild to severe Alzheimer's disease and 42 normal controls. Mini-Mental State Examination scores ranged from 26 to 12, and Clinical Dementia Rating scores ranged from 0.5 to 3. RESULTS: Scores of all four subtasks of the transcoding task significantly improved in the revised version compared with the original version. The sensitivity and specificity of total scores ≥9 on the RDST-J original and revised versions for discriminating between controls and subjects with Clinical Dementia Rating scores of 0.5 were 63.8% and 76.6% on the original and 60.1% and 85.8% on revised version. CONCLUSIONS: The revised RDST-J total score had low sensitivity and high specificity compared with the original RDST-J for discriminating subjects with Clinical Dementia Rating scores of 0.5 from controls.

Detailed analysis of error patterns in the number-transcoding task on the Japanese version of the Rapid Dementia Screening Test.

AIM: The number-transcoding task on the Japanese version of the Rapid Dementia Screening Test requires mutual conversion between Arabic and Chinese numerals (e.g. 209 → , 4054 → , → 681, → 2027). During this task, some characteristic errors have been seen among patients with Alzheimer's disease (AD). The objective of this study was to clarify whether the frequency of appearance of error patterns differs between patients with mild and severe AD according to Clinical Dementia Rating (CDR) scores. METHODS: A total of 250 patients with AD were recruited and subsequently categorized into two groups based on CDR scores (mild AD: CDR of 0.5 or 1; severe AD: CDR of 2 or 3). We analyzed 19 qualitative error patterns, including 15 that had been reported to date and 4 previously unreported errors, in each subtest. RESULTS: The frequency of appearance of two previously reported and four previously unreported errors in the mild and severe AD groups, respectively, were statistically significant. CONCLUSIONS: Characteristic error pattern distributions in number transcoding can be observed in patients with mild and severe AD according to CDR scores and offers useful information for interpreting cognitive screening data.

Zero in the brain: A voxel-based lesion-symptom mapping study in right hemisphere damaged patients.

Transcoding numerals containing zero is more problematic than transcoding numbers formed by non-zero digits. However, it is currently unknown whether this is due to zeros requiring brain areas other than those traditionally associated with number representation. Here we hypothesize that transcoding zeros entails visuo-spatial and integrative processes typically associated with the right hemisphere. The investigation involved 22 right-brain-damaged patients and 20 healthy controls who completed tests of reading and writing Arabic numbers. As expected, the most significant deficit among patients involved a failure to cope with zeros. Moreover, a voxel-based lesion-symptom mapping (VLSM) analysis showed that the most common zero-errors were maximally associated to the right insula which was previously related to sensorimotor integration, attention, and response selection, yet for the first time linked to transcoding processes. Error categories involving other digits corresponded to the so-called Neglect errors, which however, constituted only about 10% of the total reading and 3% of the writing mistakes made by the patients. We argue that damage to the right hemisphere impairs the mechanism of parsing, and the ability to set-up empty-slot structures required for processing zeros in complex numbers; moreover, we suggest that the brain areas located in proximity to the right insula play a role in the integration of the information resulting from the temporary application of transcoding procedures.

What Is Specific and What Is Shared Between Numbers and Words?

Reading and spelling performance have a significant correlation with number transcoding, which is the ability to establish a relationship between the verbal and Arabic representations of numbers, when a conversion of numerical symbols from one notation to the other is necessary. The aim of the present study is to reveal shared and non-shared mechanisms involved in reading and writing of words and Arabic numerals in Brazilian school-aged children. One hundred and seventy-two children from second to fourth grades were evaluated. All of them had normal intelligence. We conducted a series of hierarchical regression models using scores on word spelling and reading single words and Arabic numerals, as dependent variables. As predictor variables we investigated intelligence, the phonological and visuospatial components of working memory (WM) and phonemic awareness. All of the writing and reading tasks (single word spelling and reading as well as number reading and number writing) were significantly correlated to each other. In the regression models, phonological WM was specifically associated to word reading. Phonemic awareness was the only cognitive variable that systematically predicted all of the school skills investigated, both numerical and word tasks. This suggests that phonemic awareness is a modular cognitive ability shared by several school tasks and might be an important factor associated to the comorbidity between dyslexia and dyscalculia.

The Japanese version of the Rapid Dementia Screening Test is effective compared to the clock-drawing test for detecting patients with mild Alzheimer's disease.

BACKGROUND: The Japanese version of the Rapid Dementia Screening Test (RDST-J) and the clock-drawing test (CDT) are both brief psychometric screening tools used to detect the severity of Alzheimer's disease. It remains unclear, however, which is more effective when screening for mild Alzheimer's disease. METHODS: We administered the RDST-J and CDT to 250 patients with very mild to severe Alzheimer's disease and to 49 healthy volunteers. Patients with a Mini-Mental State Examination score of 12-26 had Clinical Dementia Rating (CDR) scores from 0.5 to 3. Patients were divided into four groups according to CDR score. We performed one-way factorial anova between the four groups and control subjects based on the CDT and RDST-J scores. RESULTS: Data analysis revealed that RDST-J could distinguish patients with CDR 0.5 from the controls, but CDT could not. Furthermore, the sensitivity of a RDST-J score ≥8 was 57.1%, with a specificity of 81.0%, and the sensitivity of a RDST-J score ≥9 was 79.6%, with a specificity of 55.1% for discriminating CDR 0.5 from controls. CONCLUSIONS: RDST-J is a more effective tool than CDT for distinguishing CDR 0.5 from controls.

From "five" to 5 for 5 minutes: Arabic number transcoding as a short, specific, and sensitive screening tool for mathematics learning difficulties.

Number transcoding (e.g., writing 29 when hearing "twenty-nine") is one of the most basic numerical abilities required in daily life and is paramount for mathematics achievement. The aim of this study is to investigate psychometric properties of an Arabic number-writing task and its capacity to identify children with mathematics difficulties. We assessed 786 children (55% girls) from first to fourth grades, who were classified as children with mathematics difficulties (n = 103) or controls (n = 683). Although error rates were low, the task presented adequate internal consistency (0.91). Analyses revealed effective diagnostic accuracy in first and second school grades (specificity equals to 0.67 and 0.76 respectively, and sensitivity equals to 0.70 and 0.88 respectively). Moreover, items tapping the understanding of place-value syntax were the most sensitive to mathematics achievement. Overall, we propose that number transcoding is a useful tool for the assessment of mathematics abilities in early elementary school.

Writing Times in Three Digit Numerals: Relation between Times and Syntactic Structure of Verbal Expressions Dictated / Tiempos de escritura en numerales de tres dígitos: relación entre el tiempo y la estructura sintáctica de las expresiones verbales dictadas / Tempos de escritura em numerais de três dígitos: relação entre a tempo e a estrutura sintática das expressões verbais ditadas

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.

Objetivo. 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) y Barrouillet, Camos, Perruchet y Seron (2004), quienes explican el proceso de transcodificación de numerales en niños. Método. En el estudio participaron 25 niños de primer grado que escribían correctamente numerales de tres dígitos a partir de un dictado, se analizó el tiempo de las pausas entre dígitos para cuatro tipos de numeral en cuatro sesiones de trabajo. Resultados. Los análisis de varianza ANOVA mostraron que en los cuatro tipos de numerales la duración en la primera pausa es mayor que en la segunda y que los menores tiempos tienen lugar antes de escribir el dígito cero. Conclusión. Estos resultados se ajustan mejor a las predicciones basadas en el modelo de Barrouliet et al. (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.

Escopo. O presente estudo avalia o ajuste dos tempos nas pausas entre dígitos na escritura de numerais arábicos, com as predições que são derivadas dos modelos de trans-codificação de Power e Dal Martello (1990) e Barrouillet, Camos, Perruchet e Seron (2004), que explicam o processo de trans-codificação de numerais em crianças. Metodologia. No estudo participaram 25 crianças do primeiro ano que escreviam corretamente numerais de três dígitos a partir de um ditado, foi analisado o tempo das pausas entre dígitos para quatro tipos de numeral em quatro sessões de trabalho. Resultados. Os análises de variância ANOVA mostraram que nos quatro tipos de numerais a duração na primeira pausa é maior que na segunda e que os menores tempos têm lugar antes de escrever o dígito zero. Conclusão. Estos resultados ajustam-se melhor para as predições baseadas no modelo 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.

Sixty-four or four-and-sixty? The influence of language and working memory on children's number transcoding.

Number transcoding (e.g., writing 64 when hearing "sixty-four") is a basic numerical skill; rather faultlessly performed in adults, but difficult for children. In the present study, children speaking Dutch (an inversed number language) and French (a non-inversed number language) wrote Arabic digits to dictation. We also tested their IQ and their phonological, visuospatial, and executive working memory. Although the number of transcoding errors (e.g., hearing 46 but writing 56) was equal in both groups, the number of inversion errors (e.g., hearing 46 but writing 64) was significantly higher in Dutch-speaking than in French-speaking children. Regression analyses confirmed that language was the only significant predictor of inversion errors. Working-memory components, in contrast, were the only significant predictors of transcoding errors. Executive resources were important in all children. Less-skilled transcoders also differed from more-skilled transcoders in that they used semantic rather than asemantic transcoding routes. Given the observed relation between number transcoding and mathematics grades, current findings may provide useful information for educational and clinical settings.

Transcoding abilities in typical and atypical mathematics achievers: the role of working memory and procedural and lexical competencies.

Transcoding between numerical systems is one of the most basic abilities acquired by children during their early school years. One important topic that requires further exploration is how mathematics proficiency can affect number transcoding. The aim of the current study was to investigate transcoding abilities (i.e., reading Arabic numerals and writing dictation) in Brazilian children with and without mathematics difficulties, focusing on different school grades. We observed that children with learning difficulties in mathematics demonstrated lower achievement in number transcoding in both early and middle elementary school. In early elementary school, difficulties were observed in both the basic numerical lexicon and the management of numerical syntax. In middle elementary school, difficulties appeared mainly in the transcoding of more complex numbers. An error analysis revealed that the children with mathematics difficulties struggled mainly with the acquisition of transcoding rules. Although we confirmed the previous evidence on the impact of working memory capacity on number transcoding, we found that it did not fully account for the observed group differences. The results are discussed in the context of a maturational lag in number transcoding ability in children with mathematics difficulties.