Noether's theorem: from content to form. Essay on the application of a cognitive semiotic theory of learning to a didactic proposal
This paper proposes a novel methodology, based on the semiotic-cognitive theory of learning (González, 2018), to address issues of lagrangian mechanics, a subject of the higher level of physics professors and Physics undergraduates, exemplified in Noether's theorem, which links the symmetry of...
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Asociación de Profesores de Física de la Argentina
2022
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| Acceso en línea: | https://revistas.unc.edu.ar/index.php/revistaEF/article/view/37941 |
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I10-R316-article-379412023-09-12T16:59:40Z Noether's theorem: from content to form. Essay on the application of a cognitive semiotic theory of learning to a didactic proposal Teorema de Noether: del contenido a la forma. Ensayo sobre la aplicación de una teoría semiótica cognitiva de aprendizaje a una propuesta didáctica González, Rafael Michi, Tomás Orlando Semiotic-cognitive theory of learning Noether's theorem Lagrangian mechanics Teoría semiótico-cognitiva de aprendizaje Mecánica lagrangiana Teorema de Noether This paper proposes a novel methodology, based on the semiotic-cognitive theory of learning (González, 2018), to address issues of lagrangian mechanics, a subject of the higher level of physics professors and Physics undergraduates, exemplified in Noether's theorem, which links the symmetry of mechanical configurations, with the corresponding first integrals of motion. Instead of the classical way of presenting the theorem, by means of a statement, demonstration and exemplification, we start with a table of properties (including symmetries and conservation of different specific configurations) which the student is asked to relate hypothetically, and then construct a formal expression based on the Lagrange equations, by means of a recursive procedure from which the proof of the theorem is extracted as a conceptual scheme, which will finally be applied in a generic form, detached from the previous specific configurations. Although it is exemplified with a subject of lagrangian mechanics, the method is applicable in a general way, adapting it to the corresponding subject and topic. En este trabajo se plantea una metodología novedosa, basada en la teoría semiótica-cognitiva del aprendizaje (González, 2018), para abordar temas de Mecánica lagrangiana. En el contexto de esta asignatura, correspondiente al nivel superior de profesorados de Física y de licenciaturas en Física, se ejemplifica la metodología mencionada a través del abordaje del conocido teorema de Noether, el cual vincula la simetría de las configuraciones mecánicas con las correspondientes integrales primeras de movimiento. En lugar de la forma clásica de presentar el teorema (mediante el enunciado, la demostración y la ejemplificación), en este caso se parte de un cuadro de propiedades (entre ellas simetrías y conservaciones de distintas configuraciones específicas) y se solicita al estudiante que las relaciones de manera hipotética. Luego se propone construir una expresión formal con base en las ecuaciones de Lagrange, mediante un procedimiento recursivo del que se extrae la demostración del teorema como un esquema conceptual. Finalmente se aplicará este teorema en forma genérica, desprendida de las configuraciones específicas previas. Cabe aclarar que, si bien se ejemplifica con un tema de Mecánica lagrangiana, el método es aplicable de forma general, adecuándola a la materia y tema correspondientes. Asociación de Profesores de Física de la Argentina 2022-06-14 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf text/html https://revistas.unc.edu.ar/index.php/revistaEF/article/view/37941 10.55767/2451.6007.v34.n1.37941 Journal of Physics Teaching; Vol. 34 No. 1 (2022): January - June; 75-83 Revista de Enseñanza de la Física; Vol. 34 Núm. 1 (2022): Enero - Junio; 75-83 Revista de Enseñanza de la Física; v. 34 n. 1 (2022): Janeiro - Junho; 75-83 2250-6101 0326-7091 10.55767/2451.6007.v34.n1 spa https://revistas.unc.edu.ar/index.php/revistaEF/article/view/37941/37894 https://revistas.unc.edu.ar/index.php/revistaEF/article/view/37941/37953 http://creativecommons.org/licenses/by-nc-nd/4.0 |
| institution |
Universidad Nacional de Córdoba |
| institution_str |
I-10 |
| repository_str |
R-316 |
| container_title_str |
Revista de Enseñanza de la Física |
| language |
Español |
| format |
Artículo revista |
| topic |
Semiotic-cognitive theory of learning Noether's theorem Lagrangian mechanics Teoría semiótico-cognitiva de aprendizaje Mecánica lagrangiana Teorema de Noether |
| spellingShingle |
Semiotic-cognitive theory of learning Noether's theorem Lagrangian mechanics Teoría semiótico-cognitiva de aprendizaje Mecánica lagrangiana Teorema de Noether González, Rafael Michi, Tomás Orlando Noether's theorem: from content to form. Essay on the application of a cognitive semiotic theory of learning to a didactic proposal |
| topic_facet |
Semiotic-cognitive theory of learning Noether's theorem Lagrangian mechanics Teoría semiótico-cognitiva de aprendizaje Mecánica lagrangiana Teorema de Noether |
| author |
González, Rafael Michi, Tomás Orlando |
| author_facet |
González, Rafael Michi, Tomás Orlando |
| author_sort |
González, Rafael |
| title |
Noether's theorem: from content to form. Essay on the application of a cognitive semiotic theory of learning to a didactic proposal |
| title_short |
Noether's theorem: from content to form. Essay on the application of a cognitive semiotic theory of learning to a didactic proposal |
| title_full |
Noether's theorem: from content to form. Essay on the application of a cognitive semiotic theory of learning to a didactic proposal |
| title_fullStr |
Noether's theorem: from content to form. Essay on the application of a cognitive semiotic theory of learning to a didactic proposal |
| title_full_unstemmed |
Noether's theorem: from content to form. Essay on the application of a cognitive semiotic theory of learning to a didactic proposal |
| title_sort |
noether's theorem: from content to form. essay on the application of a cognitive semiotic theory of learning to a didactic proposal |
| description |
This paper proposes a novel methodology, based on the semiotic-cognitive theory of learning (González, 2018), to address issues of lagrangian mechanics, a subject of the higher level of physics professors and Physics undergraduates, exemplified in Noether's theorem, which links the symmetry of mechanical configurations, with the corresponding first integrals of motion. Instead of the classical way of presenting the theorem, by means of a statement, demonstration and exemplification, we start with a table of properties (including symmetries and conservation of different specific configurations) which the student is asked to relate hypothetically, and then construct a formal expression based on the Lagrange equations, by means of a recursive procedure from which the proof of the theorem is extracted as a conceptual scheme, which will finally be applied in a generic form, detached from the previous specific configurations. Although it is exemplified with a subject of lagrangian mechanics, the method is applicable in a general way, adapting it to the corresponding subject and topic. |
| publisher |
Asociación de Profesores de Física de la Argentina |
| publishDate |
2022 |
| url |
https://revistas.unc.edu.ar/index.php/revistaEF/article/view/37941 |
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2024-09-03T20:40:43Z |
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2024-09-03T20:40:43Z |
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