Vol. 15 No. 87 (2026)
Articles

Conceptual understanding of systems of Linear Equations in secondary education: a didactic proposal using GeoGebra

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  • Denilsón Andrés Silgado-Tuñón,
  • José Camilo Barrios Mercado,
  • Ofelia Montelongo Aguilar
Denilsón Andrés Silgado-Tuñón
Universidad Autónoma de Zacatecas, Zacatecas, México. 
Author Biography

Maestro-Investigador de la Institución Universitaria de Barranquilla. Grupo de investigación sobre el uso de la IA para enseñanza aprendizaje de las matemáticas por la Universidad Autónoma de Zacatecas, Zacatecas, México. 

José Camilo Barrios Mercado
Author Biography

Maestro-Investigador en Matemática Educativa, Universidad Autónoma de Zacatecas, Zacatecas, México. 

Ofelia Montelongo Aguilar
Universidad Autónoma de Zacatecas, Zacatecas, México.
Author Biography

Doctora-Investigador de la Unidad Académica de Matemáticas de la Universidad Autónoma de Zacatecas, Zacatecas, México.

DOI: https://doi.org/10.34069/AI/2026.87.01.8

Published 2026-06-30

Keywords

  • Mathematics,
  • geometry,
  • teaching and training,
  • problem solving,
  • secondary education.

How to Cite

Silgado-Tuñón, D. A., Barrios Mercado, J. C., & Montelongo Aguilar, O. (2026). Conceptual understanding of systems of Linear Equations in secondary education: a didactic proposal using GeoGebra. Amazonia Investiga, 15(87), 93–105. https://doi.org/10.34069/AI/2026.87.01.8

Copyright (c) 2026 Denilsón Andrés Silgado-Tuñón, José Camilo Barrios Mercado, Ofelia Montelongo Aguilar

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

This study presents a teaching proposal aimed at strengthening secondary school students’ understanding of Systems of Linear Equations (SLE) using GeoGebra software, based on Duval’s Theory of Semiotic Representation Registers and the ACE Cycle derived from APOS Theory. A didactic sequence was designed and implemented, consisting of activities focused on the conversion between algebraic and geometric representations. The proposal was applied to a group of 48 students from a secondary school in Mexico. The analysis of the results shows that the use of the digital tool GeoGebra enables students to visualize geometrically the solutions of a SLE, thereby enhancing their understanding. Students were able to recognize that a unique solution corresponds to the intersection of two lines at a single point, infinitely many solutions correspond to coincidence lines, and no solution corresponds to two lines that never intersect. By solving these systems algebraically and analyzing them geometrically, students demonstrated improvements in their reasoning, argumentation, and logical thinking skills. It is concluded that the integration of technology with mathematical topics is a fundamental resource for improving the teaching and learning of SLE at the secondary education level.

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