Modelo explicativo de carácter longitudinal del pensamiento matemático formal: predictores de dominio general y específicos, la ansiedad matemática y variables sociodemográficas.
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Date
2025
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Universidad de Concepción
Abstract
El pensamiento matemático formal es fundamental para el éxito académico, laboral y social. Este puede ser explicado a partir de componentes cognitivos, afectivos y de variables sociodemográficas presentes desde el inicio de la educación formal. El objetivo de este estudio fue evaluar un modelo explicativo de carácter longitudinal sobre el rol de diversos predictores: de dominio general (memoria de trabajo verbal y visoespacial, control inhibitorio cognitivo, cambio atencional e inteligencia fluida), de dominio específico (como la comparación simbólica y no simbólica, el conteo y la estimación numérica) y del dominio afectivo (como la ansiedad matemática), en relación con el desarrollo del pensamiento matemático formal en estudiantes desde primero hasta segundo año de educación básica. Asimismo, se analizaron sus posibles efectos directos o mediadores y si estas relaciones se modifican al controlar por el género y la dependencia administrativa de los participantes.
El diseño de este estudio fue longitudinal, con una muestra probabilística y por conveniencia, compuesta por 154 niños y niñas de tres establecimientos educacionales de la Región Metropolitana. Para el análisis de los datos, se desarrollaron tres modelos de interacción compleja: mediación moderada, mediación serial múltiple y regresiones lineales múltiples, aplicados al inicio de primero básico y al finalizar segundo básico.
Los resultados indican que la memoria de trabajo verbal está parcialmente mediada por la comparación simbólica al finalizar segundo básico, y que esta relación se ve moderada por niveles medios y altos de ansiedad matemática. En el segundo análisis, se encontró que la dependencia administrativa, como medida proximal del nivel socioeconómico, fue mediada de manera serial por la ansiedad matemática y la memoria de trabajo en ambos momentos de medición. El género, considerado como covariable, no influyó en esta relación.
En cuanto a las regresiones lineales múltiples, durante el primer año, la memoria de trabajo verbal fue la variable con mayor poder explicativo del pensamiento matemático formal, seguida por la inteligencia fluida, el conteo, la memoria de trabajo visoespacial y el cambio atencional. Un año después, la memoria de trabajo verbal continuó siendo la variable que explicó la mayor parte de la varianza, seguida esta vez por la inteligencia fluida, el conteo y la estimación numérica. Finalmente, se discuten los hallazgos, proyecciones e implicancias prácticas en torno al desarrollo del pensamiento matemático formal.
Formal mathematical thinking is essential for academic, professional, and social success. It can be explained by cognitive and affective components, as well as sociodemographic variables present at the onset of formal education. The objective of this study was to evaluate a longitudinal explanatory model concerning the role of general-domain predictors (verbal and visuospatial working memory, cognitive inhibitory control, attentional shifting, and fluid intelligence), specific domain predictors (such as symbolic and non-symbolic comparison, counting, and numerical estimation), and affective-domain variables (such as math anxiety) in the development of formal mathematical thinking in students from first to second grade. The study also examined possible direct and mediating effects, and whether these relationships are modified when controlling for gender and administrative school dependency. This study employed a longitudinal design with a probabilistic and convenience sample of 154 boys and girls from three schools in the Metropolitan Region. To analyze the data, three models of complex interaction were developed: moderated mediation, multiple serial mediation, and multiple linear regressions, conducted at the beginning of first grade and at the end of second grade. The results indicate that verbal working memory was partially mediated by symbolic comparison at the end of second grade, and this relationship was moderated by medium and high levels of math anxiety. In the second analysis, administrative dependency, as a proximal indicator of socioeconomic status, was serially mediated by math anxiety and working memory at both time points. Gender, included as a covariate, did not influence this relationship. Regarding the multiple linear regressions, in the first year, verbal working memory was the strongest predictor of formal mathematical thinking, followed by fluid intelligence, counting, visuospatial working memory, and attentional shifting. One year later, verbal working memory remained the most significant predictor, followed by fluid intelligence, counting, and numerical estimation. Finally, the findings, projections, and practices implications for the development of formal mathematical thinking are discussed.
Formal mathematical thinking is essential for academic, professional, and social success. It can be explained by cognitive and affective components, as well as sociodemographic variables present at the onset of formal education. The objective of this study was to evaluate a longitudinal explanatory model concerning the role of general-domain predictors (verbal and visuospatial working memory, cognitive inhibitory control, attentional shifting, and fluid intelligence), specific domain predictors (such as symbolic and non-symbolic comparison, counting, and numerical estimation), and affective-domain variables (such as math anxiety) in the development of formal mathematical thinking in students from first to second grade. The study also examined possible direct and mediating effects, and whether these relationships are modified when controlling for gender and administrative school dependency. This study employed a longitudinal design with a probabilistic and convenience sample of 154 boys and girls from three schools in the Metropolitan Region. To analyze the data, three models of complex interaction were developed: moderated mediation, multiple serial mediation, and multiple linear regressions, conducted at the beginning of first grade and at the end of second grade. The results indicate that verbal working memory was partially mediated by symbolic comparison at the end of second grade, and this relationship was moderated by medium and high levels of math anxiety. In the second analysis, administrative dependency, as a proximal indicator of socioeconomic status, was serially mediated by math anxiety and working memory at both time points. Gender, included as a covariate, did not influence this relationship. Regarding the multiple linear regressions, in the first year, verbal working memory was the strongest predictor of formal mathematical thinking, followed by fluid intelligence, counting, visuospatial working memory, and attentional shifting. One year later, verbal working memory remained the most significant predictor, followed by fluid intelligence, counting, and numerical estimation. Finally, the findings, projections, and practices implications for the development of formal mathematical thinking are discussed.
Description
Tesis presentada para optar al grado de Doctora en Psicología.
Keywords
Cognición, Ansiedad matemática, Estudiantes de educación básica