Construction and mental mechanisms for learning matrix theorem associated with a linear transformation

María Trigueros Gaisman, Isabel Maturana Peña,
Marcela Parraguez González y Miguel Rodríguez Jara

Abstract:Based on apos theory (Actions, Processes, Objects and Schemes) as a theoretical and methodological framework, we investigate the mental constructions and mechanisms required to construct the associated matrix of a Linear Transformation (matl). We design a genetic decomposition
(dg) of the theorem matl to discuss how college students learn it. We report three cases of study. The results show how students construct the concept of coordinates of a vector as an object, but have difficulty using it in the construction of the coordinate matrix associated to the image of vectors. Results also show students’ difficulties to construct matl as an object and the crucial role of considering tl as a function in order to attain a deep comprehension of tmatl.

Key words: Matrix associate, Linear Transformation, apos Theory, Linear Algebra.


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