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This study examines children's comprehension of non-essential counting features (conventional rules). The objective of the study was to determine whether the presence or absence of cardinal values in pseudoerrors and the type of conventional rule violated affects children's performance. A detection task with pseudoerrors was presented through a computer game to 146 primary school children in grades 2 through 4. The same pseudoerrors were presented both with and without cardinal values; the pseudoerrors violated conventional rules of spatial adjacency, temporal adjacency, spatial-temporal adjacency, and left-to-right direction. Half of the participants within each age group were randomly assigned to an experimental condition that included pseudoerrors with a cardinal value, and the other half were assigned to a condition that included pseudoerrors without a cardinal value. The results show that when presented with a cardinal value, children more easily recognize the optional nature of non-essential counting features. Likewise, the type of conventional rule transgressed significantly affected the children's acceptance of pseudoerrors as valid counts. Participants penalized breaches of temporal and spatial-temporal adjacency to a greater degree than breaches of spatial adjacency and left-to-right direction.

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In this study, the development of comprehension of essential and nonessential aspects of counting is examined in children ranging from 5 to 8 years of age. Essential aspects, such as logical rules, and nonessential aspects, including conventional rules, were studied. To address this, we created a computer program in which children watched counting errors (abstraction and order irrelevance errors) and pseudoerrors (with and without cardinal value errors) occurring during a detection task. The children judged whether the characters had counted the items correctly and were asked to justify their responses. In general, our data show that performance improved substantially with age in terms of both error and pseudoerror detection; furthermore, performance was better with regard to errors than to pseudoerrors as well as on pseudoerror tasks with cardinal values versus those without cardinal values. In addition, the children's justifications, for both the errors and pseudoerrors, made possible the identification of conventional rules underlying the incorrect responses. A particularly relevant trend was that children seem to progressively ignore these rules as they grow older. Nevertheless, this process does not end at 8 years of age given that the conventional rules of temporal and spatial adjacency were present in their judgments and were primarily responsible for the incorrect responses.

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La mayoría de las investigaciones sobre la conciencia étnica y el prejuicio en niños se ha basado en estudios transversales, por lo que tenemos poca información sobre los cambios intraindividuales que ocurren en esta área de desarrollo. ¿Hay una secuencia de desarrollo estable de los diferentes componentes de la conciencia étnica? ¿La preferencia por el endogrupo precede al rechazo del exogrupo, como sugieren los estudios transversales? ¿Y mantienen los niños la misma orientación afectiva hacia diferentes exogrupos? En este artículo se presenta un estudio longitudinal con 50 niños españoles de 4 a 5 años (primera medida) y de 5 a 6 años (segunda medida) en el que se evaluaron varios aspectos de su conciencia étnica y de sus actitudes hacia cuatro grupos (españoles, latinoamericanos, africanos y asiáticos), en un contexto de juego de ordenador. Los resulta-dos mostraron una significativa positividad hacia el endogrupo, pero ausencia de negatividad hacia los exogrupos, tanto en el primer tiempo de medida como en el segundo. De hecho, no hubo diferencias en las atribuciones negativas de los niños al endogrupo y a los exogrupos. Por otra parte, los análisis longitudinales mostraron que la mayoría de los niños no cambió la intensidad de su orientación afectiva hacia cada grupo étnico, un tema que ha recibido poca atención en estudios previos (AU)

Most previous research on children’s ethnic awareness and prejudice has been based on cross-sectional studies; hence we have little in-formation on the intra-individual changes that occur in this area of development. Is there a stable developmental sequence of the different components of ethnic awareness? Does in-group preference precede out-group rejection, as cross-sectional studies do suggest? And do children maintain the same affective orientation toward different out-groups? We con-ducted a longitudinal study with 50 Spanish children aged 4 to 5 years (first measure) and 5 to 6 years (second measure). We assessed several aspects of their ethnic awareness and attitudes toward four groups (Spaniards, Latin Americans, Africans and Asians), within a computer-game context. Results showed a significant in-group positivity but a lack of out-group negativity, both at time 1 and 2. In fact, children’s negative attributions to the in-group and to the out-groups did not differ. On the other hand, the longitudinal analyses revealed that most children did not change the intensity of their affective orientation to each group, an issue that has received little attention in previous studies (AU)

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En este trabajo analizamos las actitudes de 600 niños españoles de 6 a 12 años hacia 8 potenciales compañeros que diferían entre sí en dos características físicas relevantes en nuestra cultura: el color de la piel y la complexión física. Con este fin, diseñamos una prueba con diversas tareas que nos permitió conocer sus preferencias para realizar distintas actividades, así como los patrones de atribución de adjetivos (estereotipos) dirigidos hacia los distintos tipos de compañeros. Los resultados mostraron un fuerte efecto de la complexión física en todas las medidas actitudinales consideradas. Por su parte, el color de piel también determinó las respuestas de los participantes, pero en menor medida que el peso. Además, ambos tipos de prejuicios siguieron cursos evolutivos muy diferentes a lo largo de toda la Educación Primaria: los sesgos relacionados con el color de la piel se atenuaron significativamente conforme la edad de los participantes aumentaba, en concordancia con la mayoría de los estudios previos en esta área. En cambio, los sesgos relacionados con el sobrepeso se mantuvieron relativamente constantes en estas edades en una de las medidas e incluso, en la otra, se incrementaron. Los resultados nos indican en qué medida el sobrepeso puede ser fuente de discriminación y rechazo desde los primeros años de escolarización formal (AU)

This paper analyzes the attitudes of 600 Spanish children from 6 to 12 years to 8 potential mates that differed in two important physical characteristics in our culture: the color of the skin and physique. To this end, we designed a test with various tasks that allowed us know your preferences for different activities, and attribution patterns of adjectives (stereotypes) directed toward different types of peers. The results showed a strong effect of physique in all attitudinal measures considered. For its part, the skin color also determined the responses of the participants, but less so than weight. Furthermore, both types of prejudice followed very different developmental courses throughout Primary Education: biases associated with skin color has faded significantly as the age of participants increased, in line with most previous studies on this area. Instead, biases related to being overweight remained relatively constant at these ages in one of the measures and even, on the other, increased. The results indicate the extent to which being overweight can be a source of discrimination and rejection from the first years of formal schooling (AU)

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Los problemas de división con resto son especialmente complejos, como han mostrado numerosos estudios. El objetivo de esta investigación era establecer si las dificultades de los estudiantes procedían de una representación inicial inapropiada o de una interpretación inadecuada de las respuestas numéricas. También queríamos determinar si los tipos de resto se podían agrupar en dos bloques, dependiendo de que la respuesta correspondiese directamente a los términos de la división o no. Evaluamos 49 estudiantes de secundaria con una edad media de 12 años;10 meses. Los participantes resolvieron problemas de Grupos Iguales Partitivos y de Medida con cuatro Tipos de Resto: Resto-no-Divisible, Resto-Divisible, Resto-Resultado y Reajustar-Cociente-Incrementándolo-Parcialmente. Nuestros datos mostraron que: (a) la elección de la división como procedimien-to de resolución fue muy elevada en ambos Modelos de División, aunque los problemas Partitivos fueron más fáciles que los de Medida; (b) el porcentaje de interpretaciones correctas fue superior a los encontrados en otras investigaciones; y (c) cuando la respuesta consistía en el cociente o el resto el éxito fue superior que cuando había que Reajustar-Cociente-Incrementándolo-Parcialmente. Para finalizar, la principal dificultad de los estudiantes al resolver estos problemas parece girar en torno a la representación inicial deficitaria del problema

Division-With-Remainder problems are particularly complex as suggested in many works. The aim of the present research was to establish whether students’ difficulties in these problems came from an inadequate initial representation or from an inadequate final interpretation of the numerical answers. We also wanted to determine whether types of remainders could be grouped into two blocks depending on whether the answer was directly matched to one of the terms of the division or not. To this end, we tested forty-nine secondary students with a mean age of 12 years and 10 months. The participants solved Partitive and Quotitive Equal-Groups problems involving four Types of Remainder: Remainder-Not-Divisible, Remainder-Divisible, Remainder-as-the-Result, and Readjusted-Quotient-by-Partial-Increments. Our data showed that: (a) although the selection of division as the resolution procedure was very high in both Models of Division, Partitive problems were easier than Quotitive ones; (b) the percentage of correct interpretations was higher than the percentages reported in other researches; and (c) success in problems whose answers were the quotient or the remainder was higher than in Readjusted-Quotient-by-Partial-Increments problems. To conclude, the main difficulty of students when solving Division-With-Remainder problems seems to be in the inadequate initial representation of the problem

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Los niños pequeños tienen un conjunto de habilidades matemáticas que les permite enfrentarse con éxito a problemas con estructura aditiva y multiplicativa. Con objeto de determinar el alcance de esta afirmación, hemos evaluado a los mismos niños en dos ocasiones (i.e., cuando tenían 4-5 años y posteriormente a los 5-6 años) en problemas de Cambio y Grupos Iguales, usando objetos para facilitar el proceso de representación de las cantidades. Los resultados mostraron que: (1) el nivel de rendimiento de los niños, independientemente del momento de medición, era muy elevado en todos los problemas; (2) tan sólo se observó un cierto retroceso en el rendimiento en los problemas de sustracción; (3) en todos los problemas los procedimientos de resolución se basaban en general en la representación directa de las cantidades; (4) las estrategias de conteo aparecían exclusivamente en los problemas de adición y sustracción y las de conocimientos derivados, principalmente, en los de multiplicación y división; (5) la variabilidad de las estrategias dependía del tipo de operación y momento de medición y finalmente, (6) el cambio de estrategias era gradual y no abrupto

Young children posses a wide range of arithmetical abilities that enable them to successfully face word problem, with additive and multiplicative structures. To test this, we have assessed the participants twice (i.e., when they were 4 to 5 years old and when they were 5 to 6 years old) with Change and Equal Groups problems, where objects were available to ease the representation of the quantities of the problems. The result showed that: (1) the level of children’s success was very high, regardless the moment of assessment and the kind of problem; (2) only the subtraction problems registered a decrease during the second assessment; (3) the procedures of resolution were mainly based on the direct representation of the quantities for all kind of problems; (4) the counting strategies were used only in the additive and subtractive problems, while the derived fact strategies were mainly applied in the multiplication and division problems; (5) the variability in the use of the strategies was affected by the kind of operation involved in the problem and the moment of the assessment; and finally (6) strategy change seemed to be gradual rather than abrupt

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