Development of geometric thought
Geometric thinking is a process in which competences are developed to understand three-dimensional space. The experience arises from the need to implement teaching methodologies that allow to optimize both the potential of teachable that has the geometry as the potential of learnability of the stude...
- Autores:
-
GALLARDO PÉREZ, HENRY DE JESÚS
Alvarado Gallardo, Oscar Andres
Vergel Ortega, Mawency
Alvarado Gallardo, Oscar Andres
Gallardo Perez, Henry De Jesus
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2019
- Institución:
- Universidad Francisco de Paula Santander
- Repositorio:
- Repositorio Digital UFPS
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.ufps.edu.co:ufps/848
- Acceso en línea:
- http://repositorio.ufps.edu.co/handle/ufps/848
- Palabra clave:
- Rights
- openAccess
- License
- Atribución 4.0 Internacional (CC BY 4.0)
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Development of geometric thought |
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Development of geometric thought |
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Development of geometric thought |
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Development of geometric thought |
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Development of geometric thought |
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Development of geometric thought |
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Development of geometric thought |
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Development of geometric thought |
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GALLARDO PÉREZ, HENRY DE JESÚS Alvarado Gallardo, Oscar Andres Vergel Ortega, Mawency Alvarado Gallardo, Oscar Andres Gallardo Perez, Henry De Jesus |
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GALLARDO PÉREZ, HENRY DE JESÚS Alvarado Gallardo, Oscar Andres Vergel Ortega, Mawency Alvarado Gallardo, Oscar Andres Gallardo Perez, Henry De Jesus |
| description |
Geometric thinking is a process in which competences are developed to understand three-dimensional space. The experience arises from the need to implement teaching methodologies that allow to optimize both the potential of teachable that has the geometry as the potential of learnability of the student with the purpose of deepening in the learnings so that, by means of the construction of models and the mathematical principle of reconstruction and invention of mathematics, emphasizing spatial thinking and leading the student to recognize geometric objects, geometric spaces and associated transformations to develop mathematical skills while strengthening their geometric thinking. |
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2019 |
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2019-09-30 |
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2021-11-10T16:35:56Z |
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10.1088/1742-6596/1329/1/012016 |
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eng |
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eng |
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Journal of Physics: Conference Series |
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Vol.1329 No.1.(2019) |
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5 |
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1 (2019) |
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1329 |
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Pérez, H. G., Ortega, M. V., & Gallardo, O. A. (2019, September). Development of geometric thought. In Journal of Physics: Conference Series (Vol. 1329, No. 1, p. 012016). IOP Publishing. |
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GALLARDO PÉREZ, HENRY DE JESÚSAlvarado Gallardo, Oscar AndresVergel Ortega, MawencyAlvarado Gallardo, Oscar Andresvirtual::616-1Gallardo Perez, Henry De Jesusvirtual::3593-12021-11-10T16:35:56Z2021-11-10T16:35:56Z2019-09-30http://repositorio.ufps.edu.co/handle/ufps/84810.1088/1742-6596/1329/1/012016Geometric thinking is a process in which competences are developed to understand three-dimensional space. The experience arises from the need to implement teaching methodologies that allow to optimize both the potential of teachable that has the geometry as the potential of learnability of the student with the purpose of deepening in the learnings so that, by means of the construction of models and the mathematical principle of reconstruction and invention of mathematics, emphasizing spatial thinking and leading the student to recognize geometric objects, geometric spaces and associated transformations to develop mathematical skills while strengthening their geometric thinking.application/pdfengJournal of Physics: Conference SeriesJournal of Physics: Conference SeriesVol.1329 No.1.(2019)51 (2019)11329Pérez, H. G., Ortega, M. V., & Gallardo, O. A. (2019, September). Development of geometric thought. In Journal of Physics: Conference Series (Vol. 1329, No. 1, p. 012016). IOP Publishing.Journal of Physics: Conference SeriesContent from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltdinfo:eu-repo/semantics/openAccessAtribución 4.0 Internacional (CC BY 4.0)http://purl.org/coar/access_right/c_abf2https://iopscience.iop.org/article/10.1088/1742-6596/1329/1/012016/metaDevelopment of geometric thoughtArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Gallardo H and Vergel M 2004 Hacia una propuesta para el aprendizaje de la geometría Acta Latinoamericana de Matemática Educativa 17 708Rodríguez M 2010 La teoría del aprendizaje significativo en la perspectiva de la psicología cognitiva (Barcelona: Ediciones Octaedro)Ausubel D, Novak J and Hanesian H 2009 Psicología educativa: Un punto de vista cognoscitivo (México: Trillas)Gardner H 1983 Multiple intelligences (Nueva York: Basic Books)Gardner H 2008 Inteligencias múltiples. La teoría en la práctica (Barcelona: Paidós)Gallardo H 2014 El modelo pedagógico dialógico crítico en la educación Respuestas 19 81Moncada J 2011 Modelo educativo basado en competencias (México: Trillas)Tobón S 2004 Formación basada en competencias: Pensamiento complejo, diseño curricular y didáctica (Bogotá: ECOE)Zabala A 2000 La práctica educativa cómo enseñar (Barcelona: Imprimeix)Ministerio de Educación Nacional 2006 Estándares básicos de competencias (Colombia: Ministerio de Educación Nacional)Acosta G, Rivera L and Acosta M 2009 Desarrollo del pensamiento lógico matemático (Bogotá: FOCO Ediciones)Van Hiele P 1959 El Pensamiento del niño y la geometría Belletin de I’Association des professeurs Mathematiques de I’Enseignement Public 198 199Saiz I 1998 La ubicación espacial en los primeros años de escolaridad Educación Matemática 10 71Gallardo H and Vergel M 2000 Exploración y aprendizaje de la geometría fractal Acta Latinoamericana de Matemática Educativa 13 186Arguedas T 2014 La geometría de la naturaleza: Benoit Mandelbrot Revista digital: Matemática, educación e internet 21 11Mandelbrot B 1993 Los objetos fractales: forma, azar, dimensión (Barcelona: Tusques)Mandelbrot B 1985 The fractal geometry of nature (New York: W. H. 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 incorporada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.
 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