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Vol. 6 Núm. 3 (2003): Noviembre

MODELOS Y TEORÍAS DE LA COMPRENSIÓN MATEMÁTICA: COMPARACIÓN DE LOS MODELOS DE PIRIE Y KIEREN SOBRE EL CRECIMIENTO DE LA COMPRENSIÓN MATEMÁTICA Y LA TEORÍA APOE

Enviado
23 diciembre 2024
Publicado
30 noviembre 2003

Resumen

La búsqueda de una descripción significativa de la comprensión ha durado ya medio siglo. Durante las últimas tres décadas, se han desarrollado nuevas e integradoras perspectivas alejadas de la distinción de Richard Skemp entre la comprensión instrumental y la relacional. Hasta 1987, Tom Schroeder documentó el crecimiento de estas perspectivas en su síntesis PME del trabajo sobre la comprensión a partir de los contrastes relacionales e instrumentales de Richard Skemp. Desde 1987, el trabajo sobre la comprensión ha progresado, y el presente documento examina los recientes marcos teóricos de la comprensión que han surgido a partir de estas raíces. Este documento se enfoca en dos marcos teóricos: el modelo de Pirie y Kieren sobre el crecimiento de la comprensión matemática y la teoría APOE de Dubinsky, haciendo referencia a otro marco teórico contemporáneo como es el trabajo de Cornu y Sierpinska sobre los obstáculos cognitivos y epistemológicos; las investigaciones sobre la definición del concepto y la imagen del concepto de Vinner y Tall; las exploraciones de Kaput sobre las representaciones múltiples y las distinciones de Sfard entre las concepciones operacionales y estructurales. Además se explican las definiciones de la comprensión propuestas por estos dos marcos, el análisis se dirige a sus elementos y construcciones, así como a sus vínculos con las caracterizaciones históricas y recientes de la comprensión. Este documento analiza porqué los modelos de Pirie y Kieren, y la teoría APOE satisfacen el criterio de Schoenfeld (2000) sobre la clasificación como una teoría y, por último, concluye con el análisis de diversas interconexiones entre estas dos teorías, así como los elementos que las distinguen de otras según sus orígenes, organizaciones, relaciones con otros marcos e implicaciones de las dos teorías tanto para evaluaciones como para prácticas pedagógicas.

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