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Use of Parameters in Equations and Systems of Linear Equations: A Proposal to Boost Variational Thinking

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Title: Use of Parameters in Equations and Systems of Linear Equations: A Proposal to Boost Variational Thinking
Language: English
Authors: Luis E. Hernández-Zavala (ORCID 0000-0003-0746-7503), Claudia Acuña-Soto (ORCID 0000-0003-3828-0557), Vicente Liern (ORCID 0000-0001-5883-9640)
Source: International Electronic Journal of Mathematics Education. 2025 20(2).
Availability: International Electronic Journal of Mathematics Education. Suite 124, Challenge House 616 Mitcham Road, CR0 3AA, Croydon, London, UK. Tel: +44-208-936-7681; e-mail: iejme@iejme.com; Web site: https://www.iejme.com
Peer Reviewed: Y
Page Count: 14
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: Equations (Mathematics), Mathematical Applications, Undergraduate Students, Problem Solving, Thinking Skills, Algebra, Mathematics Instruction, College Mathematics
ISSN: 1306-3030
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.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1469649
Database: ERIC
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  Availability: 0
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  Data: International Electronic Journal of Mathematics Education. Suite 124, Challenge House 616 Mitcham Road, CR0 3AA, Croydon, London, UK. Tel: +44-208-936-7681; e-mail: iejme@iejme.com; Web site: https://www.iejme.com
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  Data: 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.
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      – Text: English
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        PageCount: 14
    Subjects:
      – SubjectFull: Equations (Mathematics)
        Type: general
      – SubjectFull: Mathematical Applications
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      – SubjectFull: Undergraduate Students
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      – SubjectFull: Problem Solving
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      – SubjectFull: Thinking Skills
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      – SubjectFull: Algebra
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      – SubjectFull: Mathematics Instruction
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      – SubjectFull: College Mathematics
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      – TitleFull: Use of Parameters in Equations and Systems of Linear Equations: A Proposal to Boost Variational Thinking
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            NameFull: Luis E. Hernández-Zavala
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            NameFull: Vicente Liern
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              Y: 2025
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