RESUMEN • En este artículo se expone un modelo cognitivo denominado por la teoría APOE (acró-nimo de Acción, Proceso, Objeto, Esquema) descomposición genética, que describe las estructuras y mecanismos mentales que un individuo debe desarrollar para comprender el concepto de transformación lineal. Se analiza cómo la definición funcional de la transformación lineal, su representación matricial y geométrica se relacionan a través del concepto de base ordenada. El esquema descrito a través de las diferentes relaciones entre estructuras y mecanismos mentales señala la importancia de realizar acciones sobre objetos concretos (representaciones gráficas de funciones del plano en él mismo) para lograr objetos abstractos. Este modelo permite la construcción de un esquema que puede evolucionar gracias a las diferentes experiencias de un individuo con situaciones matemáticas más sofisticadas.PALABRAS CLAVE: transformación lineal; base; representación matricial; teoría APOE; esquema.ABSTRACT • This article show a cognitive model called by the APOS theory (acronym for Action, Process, Object, Scheme) genetic decomposition, which describes the mental structures and mechanisms that a person must develop to understand the concept of linear transformation. We discussed how the functional definition of linear transformation and its matrix and geometric representation are related through the ordered basis concept. Scheme described through the different relationships between mental structures and mechanisms show the importance of actions on concrete objects (graphic representations of plane functions in itself ) to achieve abstract objects. This model allows the construction of a scheme that can evolve thanks to the different experiences of an individual with more sophisticated mathematical situations.
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