El aporte del procesamiento cognitivo a los puntajes en matemáticas en el Tercer Estudio Regional Comparativo y Explicativo / The contribution of cognitive processing to scores in mathematics in the Third Regional Comparative and Explanatory Study

Resumen Las pruebas internacionales de aplicación masiva permiten evaluar los aportes de los factores individuales, familiares, institucionales y nacionales al logro educativo de los estudiantes expresado en su desempeño. En este contexto, el propósito de este estudio fue proponer y evaluar un modelo de efectos centrado en el procesamiento cognitivo esencial e incidental de las actividades académicas, de acuerdo con el desempeño en las pruebas de matemáticas en estudiantes de sexto grado de 15 países (y el estado de Nuevo León de México) que participaron en el Tercer Estudio Regional Comparativo y Explicativo (TERCE). Se formuló un modelo de ecuaciones estructurales en el que se calcularon índices de procesamiento esencial (control atencional, memoria de trabajo y supervisión familiar) y procesamiento incidental (violencia percibida, uso de ocio de la computadora -videojuegos, redes sociales, reproducción de contenidos, etcétera), con base en los ítems o preguntas utilizados en el TERCE. Los índices se diseñaron y obtuvieron según el Modelo de Rasch de la Teoría de Respuesta al Ítem (TRI). El modelo planteado afecta el desempeño en la prueba en 24 puntos. La variable con mayor tamaño de efecto es el uso de ocio de computadoras en el hogar. Los resultados se discuten a la luz de las hipótesis cognitivas sobre la distribución de recursos de atención y la de entrenamiento para entender el rol de las tecnologías de la información en el proceso formativo.

Abstract International tests of massive application allow evaluating how individual, institutional, national, and family factors contribute to students' educational achievement through their performance. Consequently, education evaluation is based on the paradigm of general and specific competencies for life. One of these general competencies is the capacity to solve mathematical problems and apply logical thinking to problem-solving. In order to evaluate this general competence, standardized tests have been developed. Among these tests, the Third Regional Comparative and Explanatory Study (TERCE) in 2013 evaluated the mathematical and other areas' academic performance of children in the third and sixth grade. The TERCE Mathematics evaluation allows researchers to capture the students' academic performance in five domains: numeric, geometric, measurement, statistics, and variation, as well as their cognitive performance in objects and elements recognition and simple and complex problem-solving. In addition, to evaluate these eight dimensions, the TERCE test also asks for information regarding academic context, family environment, and teachers, among others. Despite this information, in Colombia and in general, the evaluation of the socioeconomic context over academic performance has been studied mainly considering the schools' characteristics, families' economic levels, and public expenses. Therefore, there is little evidence of the effects of psycho-pedagogical and psychological factors on academic performance. Psycho-pedagogical models emphasize the dependence of the superior processes on perceptual and attentional processes and the need for activities that demand deep processing and active involvement with information before, during, and after classes. Thus, attending simultaneously to different elements affects the development of cognitive control functions, which leads to low academic achievement and performance. Frequently, students face academic activities in different scenarios where the attentional system should divide its resources between several stimulus sources. Activities in which the attentional system focuses are "essential processing", and those not related to the main academic activity are called "incidental processing". Consequently, increasing the sources of incidental processing would decrease the attentional resources devoted to the essential processing of educational activities producing low academic performance. In this context, the study proposes and evaluates an effects model focused on essential and incidental cognitive processing of academic activities. The information was captured on the mathematics performance of sixth-grade students from 15 countries (and the state of Nuevo León de México) participating in the Third Regional Comparative and Explanatory Study (TERCE). A Structural Equations model was formulated using indices of Essential Processing (Attentional Control, Working Memory, and Family Supervision) and Incidental Processing (Perceived Violence, Leisure use of the computer, and incidental processing) based on the items or questions used in the TERCE. The indices were designed based on the Item Response Theory (IRT) model. Findings show that the proposed model affects the performance in the test by 24 points. Higher scores in essential processing produce higher scores in the mathematics component of the TERCE test. Family supervision of academic activity is the single element with the highest impact on academic performance (3.020); on the other hand, attentional control (7.48) and working memory (4.295) also impact academic performance positively. Regarding the incidental processing variables, lower levels of perceived violence (1.680), less noise and distractor in class (2.130), and higher use of computers at home for leisure activities (5.851) have the most significant impacts on academic performance. The results are discussed considering the cognitive hypotheses on the distribution of attention resources and the training hypothesis to understand information technologies' role in the academic processes. Suggestions for further research focus on the inclusion of items with a higher theoretical background that allows researchers to evaluate the impact of essential and incidental processing on academic performance using items specially designed with that goal to get more conclusive and robust results.

Effects of the math anxiety of parents and peachers on students / Efeito da ansiedade matemática de pais e professores em escolares / Efecto de la ansiedad matemática de padres y profesores en estudiantes

The aim of the study was to demonstrate a relationship between the math anxiety (MA) of parents and teachers and the MA of children and the effects on the children's performance in arithmetic. 286 children aged between 7 and 10 years and their parents and mathematics teachers participated in the study. The instruments used were: Math Anxiety Questionnaire; School Performance Test - Arithmetic subtest; Mathematical Anxiety Scale; and Raven's Colored Progressive Matrices. The results showed that advanced age of the teacher was a predictor of high levels of MA, which influenced the children's performance in arithmetic. Low parental education was associated with high MA, however, there were no correlations between parents' and children's MA. A significant difference was found between the MA mean scores for girls and boys, with the girls presenting higher levels of MA. (AU)

O objetivo do estudo foi evidenciar a relação entre a ansiedade matemática (AM) dos pais e dos professores com a AM das crianças e o desempenho destas em aritmética. Participaram do estudo 286 crianças com idade entre 7 e 10 anos e seus respectivos pais e professores de matemática. Os instrumentos utilizados foram: Questionário de Ansiedade Matemática, Teste de Desempenho Escolar - Subteste de Aritmética, Escala de Ansiedade Matemática e Matrizes Progressivas Coloridas de Raven. Os resultados mostraram que a idade avançada dos professores é um fator preditor para altos níveis de AM, o que influencia no desempenho das crianças em aritmética. A baixa escolaridade dos pais está associada a alta AM, porém não foram encontradas correlações significativas entre AM de pais e crianças. Também foi encontrada uma diferença significativa entre as médias de AM para o sexo feminino e masculino, evidenciando que meninas possuem maiores níveis de AM. (AU)

El objetivo del estudio fue resaltar la relación entre la ansiedad matemática (AM) de padres y docentes con la AM de los niños y su desempeño en aritmética y de los niños. Participaron en el estudio 286 niños entre 7 y 10 años y sus respectivos padres y profesores de matemáticas. Los instrumentos utilizados fueron: Cuestionario de AM; Prueba de Rendimiento Escolar: Subprueba aritmética; Escala de AM; Matrices Progresivas Escala Coloreada de Raven. Los resultados mostraron que la edad avanzada de los docentes es un factor predictivo para altos niveles de AM, lo que influye en el rendimiento de los niños en aritmética. La baja educación de los padres se asocia con un alto AM, pero no se encontraron correlaciones significativas entre AM de padres e hijos. Asimismo, se encontró una diferencia significativa entre las medias de AM de niñas y niños, lo que demuestra que las niñas tienen niveles más altos de AM. (AU)

Diferentes graus de ansiedade à matemática e desempenho escolar no ensino fundamental / Different degrees of mathematics anxiety, and academic performance in elementary school / Diferentes grados de ansiedad a las matemáticas y el rendimiento académico en la escuela primaria

O presente trabalho investigou aspectos cruciais relacionados à ansiedade Matemática em alunos do Ensino Fundamental. No Estudo 1, 770 estudantes responderam a uma escala de ansiedade à Matemática. Identificaram-se pequenas diferenças entre graus de ansiedade matemática e conduziram-se comparações entre gênero, período, rede de ensino e série. Não houve diferenças significativas entre gênero, rede de ensino e série, porém alunos do período vespertino apresentaram maior ansiedade. No Estudo 2, verificou-se a relação entre nenhuma/baixa e alta/extrema ansiedade e desempenho em Matemática. Selecionaram-se os dados de oito alunos que participaram do Estudo 1, divididos em baixa ansiedade, em um grupo, e alta/extrema ansiedade em outro grupo. Os alunos com maior ansiedade foram os que apresentaram notas mais altas quando comparados com os alunos que apresentaram baixa ansiedade.

The present work investigated crucial aspects related to math anxiety in elementary school students. In Study 1, 770 students responded to a math anxiety scale. It were identified different grades of math anxiety and it was made comparisons among genre, period, public or private education network, and level. There were no significant differences between gender, education network and levels, but students of evening period showed higher math anxiety. In Study 2, it was verified the relation between no/low and high/extreme anxiety and math performance. It were selected the data of eight students who participated in thE Study 1, one group with high/extreme degree of math anxiety, and the other group with low degree. Students with greater anxiety showed higher grades in math when compared to the students with low anxiety.

El presente trabajo investigó aspectos relacionados con ansiedad a las matemáticas en estudiantes de primaria. En el Estudio 1, 770 estudiantes respondieron a una escala de ansiedad matemática. Se han identificado diversos grados de ansiedad a las matemáticas y han sido realizadas comparaciones entre género, turno, red escolar pública o particular, y serie. No se encontraron diferencias significativas entre el género, la redescolar y la serie, pero los estudiantes del turno vespertino presentaran mayor ansiedad. En el estudio 2 han sido verificadas la relación entre alta/extrema ansiedad y el rendimiento en matemáticas. Los datos de ocho estudiantes que participaron del Estudio 1 han sido seleccionados, divididos en menor ansiedad, en un grupo, y ansiedad alta/extrema en otro grupo. Estudiantes con mayor ansiedad obtuvieron promedio de notas más altas que los estudiantes con baja ansiedad.

Ansiedade relacionada à matemática e diferenças de gênero: uma análise da literatura / Anxiety related to mathematics and gender differences: a literature review

A ansiedade diante da matemática é uma condição caracterizada por padrões de fuga e esquiva em situações que exigem o uso da matemática, bem como reações fisiológicas desagradáveis, atribuições negativas à matemática e autoatribuições negativas. O presente artigo objetiva sistematizar os conhecimentos atuais acerca da relação entre gênero e ansiedade matemática. É apresentada uma análise da literatura técnica que trata do tema, e são apontadas algumas lacunas a serem preenchidas por meio de pesquisas empíricas.

Mathematics anxiety is a condition characterized by patterns of escape and avoidance in situations that require the use of mathematics, as well as unpleasant physiological reactions, negative attributions to mathematics and negative self attributions. This article aims to systematize the current knowledge about the relationship between gender and mathematics anxiety. An analysis of the technical literature is presented, and some gaps to be filled through empirical research are highlighted.

La ansiedad ante las matemáticas es una condición que se caracteriza por patrones de escape y evitación en situaciones que requieran el uso de matemáticas, así como reacciones fisiológicas desagradables, atribuciones negativas a las matemáticas y auto atribuiciones negativas. Este artículo pretende sistematizar el conocimiento actual sobre la relación entre género y ansiedad matemática. Se presenta un análisis de la literatura técnica que aborda el tema y destacaron algunas lagunas de llenarse a través de la investigación empírica.