Cognitive construction of the solution set of a system of linear equations with two unknowns
In this research, we propose a genetic decomposition for the solution set of a system of linear equations with two unknowns, by means of a transit from a homogeneous to a non-homogeneous linear system, in a Cartesian geometric context. To validate our genetic decomposition, we designed instruments t...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | Spanish |
| Published: |
Universitat Autònoma de Barcelona
2019-03-01
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| Series: | Enseñanza de las Ciencias |
| Subjects: | |
| Online Access: | https://ensciencias.uab.es/article/view/2194 |
| _version_ | 1797707342519730176 |
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| author | Miguel Alejandro Rodríguez Jara Arturo Mena Lorca Jaime Mena Lorca Patricia Vásquez Saldias María Elsa Del Valle Leo |
| author_facet | Miguel Alejandro Rodríguez Jara Arturo Mena Lorca Jaime Mena Lorca Patricia Vásquez Saldias María Elsa Del Valle Leo |
| author_sort | Miguel Alejandro Rodríguez Jara |
| collection | DOAJ |
| description | In this research, we propose a genetic decomposition for the solution set of a system of linear equations with two unknowns, by means of a transit from a homogeneous to a non-homogeneous linear system, in a Cartesian geometric context. To validate our genetic decomposition, we designed instruments that we applied to students from a secondary school mathematics teacher training program. Thus, and by using implicative statistics, we were able to confirm the mental constructions and mechanisms considered in our genetic decomposition. The results show lack of understanding of what a solution for a system is, difficulties in articulating the geometrical and algebraic aspects, and the convenience of using an alternative strategy in the case of systems of three or more linear equations. |
| first_indexed | 2024-03-12T06:05:57Z |
| format | Article |
| id | doaj.art-a2151f914994477da3891a25cf3b86e2 |
| institution | Directory Open Access Journal |
| issn | 0212-4521 2174-6486 |
| language | Spanish |
| last_indexed | 2024-03-12T06:05:57Z |
| publishDate | 2019-03-01 |
| publisher | Universitat Autònoma de Barcelona |
| record_format | Article |
| series | Enseñanza de las Ciencias |
| spelling | doaj.art-a2151f914994477da3891a25cf3b86e22023-09-03T03:38:59ZspaUniversitat Autònoma de BarcelonaEnseñanza de las Ciencias0212-45212174-64862019-03-01371719210.5565/rev/ensciencias.2194601Cognitive construction of the solution set of a system of linear equations with two unknownsMiguel Alejandro Rodríguez Jara0Arturo Mena Lorca1Jaime Mena Lorca2Patricia Vásquez Saldias3María Elsa Del Valle Leo4Universidad de Playa AnchaPontificia Universidad Católica de ValparaísoPontificia Universidad Católica de ValparaísoPontificia Universidad Católica de ValparaísoUniversidad de ConcepciónIn this research, we propose a genetic decomposition for the solution set of a system of linear equations with two unknowns, by means of a transit from a homogeneous to a non-homogeneous linear system, in a Cartesian geometric context. To validate our genetic decomposition, we designed instruments that we applied to students from a secondary school mathematics teacher training program. Thus, and by using implicative statistics, we were able to confirm the mental constructions and mechanisms considered in our genetic decomposition. The results show lack of understanding of what a solution for a system is, difficulties in articulating the geometrical and algebraic aspects, and the convenience of using an alternative strategy in the case of systems of three or more linear equations.https://ensciencias.uab.es/article/view/2194sistemas de ecuaciones linealesfuturos profesoreseducación secundariateoría apoe |
| spellingShingle | Miguel Alejandro Rodríguez Jara Arturo Mena Lorca Jaime Mena Lorca Patricia Vásquez Saldias María Elsa Del Valle Leo Cognitive construction of the solution set of a system of linear equations with two unknowns Enseñanza de las Ciencias sistemas de ecuaciones lineales futuros profesores educación secundaria teoría apoe |
| title | Cognitive construction of the solution set of a system of linear equations with two unknowns |
| title_full | Cognitive construction of the solution set of a system of linear equations with two unknowns |
| title_fullStr | Cognitive construction of the solution set of a system of linear equations with two unknowns |
| title_full_unstemmed | Cognitive construction of the solution set of a system of linear equations with two unknowns |
| title_short | Cognitive construction of the solution set of a system of linear equations with two unknowns |
| title_sort | cognitive construction of the solution set of a system of linear equations with two unknowns |
| topic | sistemas de ecuaciones lineales futuros profesores educación secundaria teoría apoe |
| url | https://ensciencias.uab.es/article/view/2194 |
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