Mathematical and pedagogical perspectives on warranting: approximating the root of 18
“The square root of 18 is closer to 4 than it is to 5 because 18 is closer to 16 than it is to 25”. Is this statement, voiced in an 8th grade class, valid? We suggest hypothetical arguments upon which this statement might be based, and analyze them from two complementary perspectives – epistemic and...
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| Formato: | Artículo revista |
| Lenguaje: | Español |
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Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación
2019
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| Acceso en línea: | https://revistas.unc.edu.ar/index.php/REM/article/view/26933 |
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I10-R366-article-26933 |
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I10-R366-article-269332023-10-25T17:48:25Z Mathematical and pedagogical perspectives on warranting: approximating the root of 18 PERSPECTIVAS MATEMÁTICAS Y PEDAGÓGICAS DE LA JUSTIFICACIÓN: APROXIMANDO LA RAÍZ DE 18 Cooper, Jason Pinto, Alon Mathematical warranting, mathematical validity, interacting perspectives. Justificación matemática, validez matemática, perspectivas interactuantes. “The square root of 18 is closer to 4 than it is to 5 because 18 is closer to 16 than it is to 25”. Is this statement, voiced in an 8th grade class, valid? We suggest hypothetical arguments upon which this statement might be based, and analyze them from two complementary perspectives – epistemic and pedagogical – drawing on Toulmin’s notion of field-dependence in argumentation and on Freeman’s classification of warrants based on the type of underlying intuition, belief or prior understanding. We propose that our investigation of this statement may serve as a model for inquiry in teacher preparation. “La raíz cuadrada de 18 está más cerca de 4 que de 5, porque 18 está más cerca de 16 que de 25”. ¿Será válida esta afirmación, escuchada en una clase de un octavo grado? Proponemos argumentos hipotéticos sobre los cuales esta afirmación estaría basada y los analizamos desde dos perspectivas complementarias – epistémica y pedagógica – apoyándonos en la noción de Toulmin sobre dependencia de campo en la argumentación y en la clasificación de Freeman de la justificación basada en el tipo de intuición, creencia o comprensión subyacentes. Proponemos que nuestro análisis de esta proposición puede ser un modelo de investigación en cursos de formación docente. Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación 2019-12-16 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Artículo evaluado por pares application/pdf https://revistas.unc.edu.ar/index.php/REM/article/view/26933 10.33044/revem.26933 Revista de Educación Matemática; Vol. 34 Núm. 3 (2019); 41-57 1852-2890 0326-8780 spa https://revistas.unc.edu.ar/index.php/REM/article/view/26933/28588 Derechos de autor 2019 Jason Cooper, Alon Pinto https://creativecommons.org/licenses/by-sa/4.0/ |
| institution |
Universidad Nacional de Córdoba |
| institution_str |
I-10 |
| repository_str |
R-366 |
| container_title_str |
Revista de Educación Matemática |
| language |
Español |
| format |
Artículo revista |
| topic |
Mathematical warranting, mathematical validity, interacting perspectives. Justificación matemática, validez matemática, perspectivas interactuantes. |
| spellingShingle |
Mathematical warranting, mathematical validity, interacting perspectives. Justificación matemática, validez matemática, perspectivas interactuantes. Cooper, Jason Pinto, Alon Mathematical and pedagogical perspectives on warranting: approximating the root of 18 |
| topic_facet |
Mathematical warranting, mathematical validity, interacting perspectives. Justificación matemática, validez matemática, perspectivas interactuantes. |
| author |
Cooper, Jason Pinto, Alon |
| author_facet |
Cooper, Jason Pinto, Alon |
| author_sort |
Cooper, Jason |
| title |
Mathematical and pedagogical perspectives on warranting: approximating the root of 18 |
| title_short |
Mathematical and pedagogical perspectives on warranting: approximating the root of 18 |
| title_full |
Mathematical and pedagogical perspectives on warranting: approximating the root of 18 |
| title_fullStr |
Mathematical and pedagogical perspectives on warranting: approximating the root of 18 |
| title_full_unstemmed |
Mathematical and pedagogical perspectives on warranting: approximating the root of 18 |
| title_sort |
mathematical and pedagogical perspectives on warranting: approximating the root of 18 |
| description |
“The square root of 18 is closer to 4 than it is to 5 because 18 is closer to 16 than it is to 25”. Is this statement, voiced in an 8th grade class, valid? We suggest hypothetical arguments upon which this statement might be based, and analyze them from two complementary perspectives – epistemic and pedagogical – drawing on Toulmin’s notion of field-dependence in argumentation and on Freeman’s classification of warrants based on the type of underlying intuition, belief or prior understanding. We propose that our investigation of this statement may serve as a model for inquiry in teacher preparation. |
| publisher |
Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación |
| publishDate |
2019 |
| url |
https://revistas.unc.edu.ar/index.php/REM/article/view/26933 |
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2024-09-03T22:36:40Z |
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2024-09-03T22:36:40Z |
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