Error algebraico y desempeño matemático: evidencia empírica desde una perspectiva cognitiva
DOI:
https://doi.org/10.61616/rvdc.v7i2.1625Palavras-chave:
error algebraico, desempeño matemático, pensamiento algebraico, comprensión conceptual, perspectiva cognitivaResumo
El presente estudio analiza el error algebraico como un patrón asociado al desempeño matemático desde una perspectiva cognitiva, semiótica y didáctica. El objetivo fue identificar tendencias consistentes en la producción sistemática de errores algebraicos y examinar su relación con distintas dimensiones del desempeño matemático. Se adoptó un enfoque cuantitativo con diseño no experimental, transversal y descriptivo-correlacional. La muestra estuvo conformada por 45 estudiantes de educación media superior seleccionados mediante muestreo probabilístico sistemático. El análisis se desarrolló en dos niveles complementarios: descriptivo, orientado a caracterizar la frecuencia y tipología de los errores, e inferencial, dirigido a examinar la asociación entre tipos de error algebraico y dimensiones del desempeño matemático (operatividad, comprensión conceptual y aplicación). Los resultados evidenciaron una alta prevalencia del error, particularmente en la dimensión de aplicación, así como una asociación estadísticamente significativa entre la tipología de error y el desempeño matemático (χ², p < .001), con un tamaño del efecto pequeño (V de Cramér = 0.16). Además, los errores de linealidad, generalización y cambio conceptual mostraron regularidades asociadas a dificultades de transferencia entre esquemas aritméticos y razonamiento algebraico formal. En conclusión, los hallazgos sugieren que el error algebraico puede interpretarse como una manifestación organizada de procesos de razonamiento vinculados con el desempeño matemático, particularmente en tareas que requieren comprensión conceptual, transferencia y aplicación del conocimiento algebraico.
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