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Revista Iberoamericana de Tecnología en Educación y Educación en Tecnología
Article . 2019 . Peer-reviewed
License: CC BY NC
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Interpretation of linear transformations in the plane using GeoGebra

Authors: Humberto G. Gallo; Claudio Verón; Carlos Gabriel Herrera;

Interpretation of linear transformations in the plane using GeoGebra

Abstract

En el estudio de conceptos de Algebra Lineal, algunas de las dificultades cognitivas que se observan en los alumnos son derivadas de la falta de articulación de diferentes representaciones de un objeto matemático, especialmente entre el registro simbólico y su correspondiente correlación geométrica en los espacios vectoriales (R2.+.R,*) o (R3.+.R.*), prevaleciendo, en consecuencia, procedimientos de carácter algorítmicos en desmedro de lo conceptual. Fundados en la teoría de la Visualización Matemática, se propone a tales efectos el uso de software GeoGebra como herramienta didáctica en el proceso de aprendizaje de contenidos de algebra Lineal, en caso particular de transformaciones lineales. El carácter dinámico de este aplicativo permite la interpretación geométrica de la transformación, y de conceptos asociados como su núcleo e imagen, a partir de su respectiva matriz asociada, se pretende además que descubran las relaciones entre la singularidad de la matriz, con las dimensiones del núcleo e imagen de la transformación lineal.

In the study of Linear Algebra concepts, some of the cognitive difficulties observed in students, are derived from the lack of articulation of different representations of a mathematical object, especially between the symbolic register and its corresponding geometric correlation specially in vector spaces (R2.+.R,*) or (R3.+.R.*), wining, consequently, algoritmic procedures through conceptual ones. Based on the theory of Mathematics Visualization, use of Geogebra software is proposed as educational tool for the learning process of linear Algebra contents, specifically for linear transformations. The dynamic characteristic of this application allows the geometric interpretation of this transformation, and of related concepts like its nucleus and image, from its corresponding asociated matrix. Besides its pretended that students discover the relations between the singularity of the matrix and the dimensions of the nucleus and image of a linear transformation.

Facultad de Informática

Country
Argentina
Subjects by Vocabulary

Microsoft Academic Graph classification: Computer science Matrix (mathematics) Singularity Interpretation (logic) Algebra Linear map Transformation (function) Linear algebra Mathematical object Vector space

Library of Congress Subject Headings: lcsh:LC8-6691 lcsh:Special aspects of education lcsh:L lcsh:Education

Keywords

History, Ciencias Informáticas, Education, Linear transformations, Visualization, LC8-6691, L, Special aspects of education, Computer Science Applications, GeoGebra, Visualización, Transformaciones lineales

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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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