Use of parameters in equations and systems of linear equations: A proposal to boost variational thinking

Luis E. Hernández-Zavala; Claudia Acuña-Soto; Vicente Liern

doi:10.29333/iejme/16005

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Luis E. Hernández-Zavala ¹ ^* , Claudia Acuña-Soto ¹ , Vicente Liern ²

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¹ Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV), MEXICO² Departamento de Matemáticas para la Economía y la Empresa, Facultad de Economía, Universitat de València, SPAIN^* Corresponding Author

Abstract

Students often instrumentally use variables and unknowns without considering the variational thinking behind them. Using parameters to modify the coefficients or unknowns in equations or systems of linear equations (without altering their structure) involves consciously incorporating variational thinking into problem-solving. We will test the scope of this approach to undergraduate students by using contextual problems modelled with systems of linear equations that have one solution, infinitely many solutions, or none. In this context, knowing the solution was not enough to decide; instead, modifications to the system were necessary, and incorporating parameters proved to be very useful for this purpose. The goal is for students, in addition to seeing variational thinking as a valuable strategy for determining the validity of a solution, to develop the ability to distinguish between unknowns, variables, and parameters.

Keywords

parameters
variables
unknowns
systems of linear equations
context

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 20, Issue 2, May 2025, Article No: em0822

https://doi.org/10.29333/iejme/16005

Publication date: 01 Apr 2025

Online publication date: 19 Feb 2025

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APA

Hernández-Zavala, L. E., Acuña-Soto, C., & Liern, V. (2025). Use of parameters in equations and systems of linear equations: A proposal to boost variational thinking. International Electronic Journal of Mathematics Education, 20(2), em0822. https://doi.org/10.29333/iejme/16005

Vancouver

Hernández-Zavala LE, Acuña-Soto C, Liern V. Use of parameters in equations and systems of linear equations: A proposal to boost variational thinking. INT ELECT J MATH ED. 2025;20(2):em0822. https://doi.org/10.29333/iejme/16005

AMA

Hernández-Zavala LE, Acuña-Soto C, Liern V. Use of parameters in equations and systems of linear equations: A proposal to boost variational thinking. INT ELECT J MATH ED. 2025;20(2), em0822. https://doi.org/10.29333/iejme/16005

Chicago

Hernández-Zavala, Luis E., Claudia Acuña-Soto, and Vicente Liern. "Use of parameters in equations and systems of linear equations: A proposal to boost variational thinking". International Electronic Journal of Mathematics Education 2025 20 no. 2 (2025): em0822. https://doi.org/10.29333/iejme/16005

Harvard

Hernández-Zavala, L. E., Acuña-Soto, C., and Liern, V. (2025). Use of parameters in equations and systems of linear equations: A proposal to boost variational thinking. International Electronic Journal of Mathematics Education, 20(2), em0822. https://doi.org/10.29333/iejme/16005

MLA

Hernández-Zavala, Luis E. et al. "Use of parameters in equations and systems of linear equations: A proposal to boost variational thinking". International Electronic Journal of Mathematics Education, vol. 20, no. 2, 2025, em0822. https://doi.org/10.29333/iejme/16005