Conjeturación del teorema del valor medio para derivadas: Un acercamiento desde la detección de invariantes en dispositivos móviles con GeoGebra
Este artículo presenta los resultados de un proyecto de investigación cuyo objetivo fue describir el papel mediador de la aplicación móvil “Calculadora Gráfica” de GeoGebra sobre los procesos de conjeturación del teorema del valor medio para derivadas mediante la detección de invariantes a través de...
- Autores:
-
Ballesteros-Ballesteros, Vladimir Alfonso
Rodríguez-Cardoso, Óscar Iván
Lozano-Forero, Sébastien
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2020
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/11321
- Acceso en línea:
- https://hdl.handle.net/11323/11321
https://doi.org/10.17981/cultedusoc.12.1.2021.05
- Palabra clave:
- Aprendizaje móvil
Conjeturación
GeoGebra
Teorema del valor medio para derivadas
Mobile learning
Conjecturing process
GeoGebra
Mean value theorem for derivatives
- Rights
- openAccess
- License
- CULTURA EDUCACIÓN Y SOCIEDAD - 2020
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Conjeturación del teorema del valor medio para derivadas: Un acercamiento desde la detección de invariantes en dispositivos móviles con GeoGebra |
| dc.title.translated.eng.fl_str_mv |
Conjecturing process for the mean value theorem for derivatives: An approach from the detection of invariants in mobile devices with GeoGebra |
| title |
Conjeturación del teorema del valor medio para derivadas: Un acercamiento desde la detección de invariantes en dispositivos móviles con GeoGebra |
| spellingShingle |
Conjeturación del teorema del valor medio para derivadas: Un acercamiento desde la detección de invariantes en dispositivos móviles con GeoGebra Aprendizaje móvil Conjeturación GeoGebra Teorema del valor medio para derivadas Mobile learning Conjecturing process GeoGebra Mean value theorem for derivatives |
| title_short |
Conjeturación del teorema del valor medio para derivadas: Un acercamiento desde la detección de invariantes en dispositivos móviles con GeoGebra |
| title_full |
Conjeturación del teorema del valor medio para derivadas: Un acercamiento desde la detección de invariantes en dispositivos móviles con GeoGebra |
| title_fullStr |
Conjeturación del teorema del valor medio para derivadas: Un acercamiento desde la detección de invariantes en dispositivos móviles con GeoGebra |
| title_full_unstemmed |
Conjeturación del teorema del valor medio para derivadas: Un acercamiento desde la detección de invariantes en dispositivos móviles con GeoGebra |
| title_sort |
Conjeturación del teorema del valor medio para derivadas: Un acercamiento desde la detección de invariantes en dispositivos móviles con GeoGebra |
| dc.creator.fl_str_mv |
Ballesteros-Ballesteros, Vladimir Alfonso Rodríguez-Cardoso, Óscar Iván Lozano-Forero, Sébastien |
| dc.contributor.author.spa.fl_str_mv |
Ballesteros-Ballesteros, Vladimir Alfonso Rodríguez-Cardoso, Óscar Iván Lozano-Forero, Sébastien |
| dc.subject.spa.fl_str_mv |
Aprendizaje móvil Conjeturación GeoGebra Teorema del valor medio para derivadas |
| topic |
Aprendizaje móvil Conjeturación GeoGebra Teorema del valor medio para derivadas Mobile learning Conjecturing process GeoGebra Mean value theorem for derivatives |
| dc.subject.eng.fl_str_mv |
Mobile learning Conjecturing process GeoGebra Mean value theorem for derivatives |
| description |
Este artículo presenta los resultados de un proyecto de investigación cuyo objetivo fue describir el papel mediador de la aplicación móvil “Calculadora Gráfica” de GeoGebra sobre los procesos de conjeturación del teorema del valor medio para derivadas mediante la detección de invariantes a través de herramientas de arrastre, combinando geometría dinámica con cálculo infinitesimal. A través de un estudio de caso cualitativo, que involucró estudiantes de Ingeniería Aeronáutica, se dinamizaron los esfuerzos investigativos con el propósito de validar la hipótesis relacionada con una influencia positiva de una estrategia de aprendizaje móvil sobre el proceso de conjeturación en un curso de Cálculo Diferencial. Los resultados obtenidos permitieron evidenciar avances significativos en la conjeturación del teorema mencionado para la resolución de problemas en ingeniería y se discute cómo este tipo de recursos digitales, a través de un entorno de geometría dinámica en dispositivos móviles, puede servir como mediación para favorecer el aprendizaje del cálculo. |
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2020 |
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2020-01-01 |
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2021-01-01 00:00:00 2024-04-09T19:55:04Z |
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2021-01-01 00:00:00 2024-04-09T19:55:04Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
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Text |
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Journal article |
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http://purl.org/redcol/resource_type/ART |
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https://doi.org/10.17981/cultedusoc.12.1.2021.05 |
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Cultura Educación Sociedad |
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Abu-Al-Aish, A., Love, S., Hunaiti, Z. & Al-masaeed, S. (2014). Toward mobile learning deployment in higher education. International Journal of Mobile Learning and Organisation (IJMLO), 7(3/4), 253–276. https://doi.org/10.1504/IJMLO.2013.057165. Akour, H. (2011). Determinants of mobile learning acceptance: An empirical investigation in higher education. [Ph.D. Dissertation]. Oklahoma State University, Small city, USA. Available: https://www.proquest.com/docview/610058264 Al-Emran, M., Mezhuyev, V. & Kamaludin, A. (2018). Technology Acceptance Model in M-learning context: A systematic review. Computers & Education, 125, 389–412. https://doi.org/10.1016/j.compedu.2018.06.008 Baccaglini-Frank, A. (2019). Dragging, instrumented abduction and evidence, in processes of conjecture generation in a dynamic geometry environment. ZDM Mathematics Education, 51, 779–791. https://doi.org/10.1007/s11858-019-01046-8 Boero, P., Fenaroli, G. & Guala, E. (2018). Mathematical Argumentation in Elementary Teacher Education: The Key Role of the Cultural Analysis of the Content. In: Stylianides A., Harel G. (eds), Advances in Mathematics Education Research on Proof and Proving, (pp. 49–67). Cham: Springer. https://doi.org/10.1007/978-3-319-70996-3₄ Cabri Geometry (versión 2.1.1) [software de geometría]. Grenoble: Cabrilog. Disponible en https://cabri.com/es/ Camargo, L., Samper, C. & Perry, P. (2007). Cabri’s role in the task of proving within the activity of building part of an axiomatic system. In: D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 571–580). Larnaca: CERME. Recuperado de http://funes.uniandes.edu.co/927/1/2007Pr-CamargoCabri.pdf Cheema, S., Gulwani, S. & LaViola, J. (may, 2012). QuickDraw: improving drawing experience for geometric diagrams. In: J. Konstan, Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (pp. 1037–1064). Association for Computing Machinery, New York, United States. https://doi.org/10.1145/2207676.2208550 Creswell, J. W. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Thousand: Sage publications. Recuperado de http://www.drbrambedkarcollege.ac.in/sites/default/files/research-design-ceil.pdf Crompton, H., Burke, D., Gregory, K. H. & Grabe, C. (2016). The use of mobile learning in science: A systematic review. Journal of Science Education and Technology, 25, 149–160. https://doi.org/10.1007/s10956-015-9597-x Donaldson, R. L. (2011). Student acceptance of mobile learning. [Ph.D. Dissertation]. The Florida State University, Tallahassee, USA. Recuperado de https://fsu.digital.flvc.org/islandora/object/fsu%3A168891/datastream/PDF/view Ehmann, M., Gerhauser, M., Miller, C. & Wassermann, A. (2013). Sketchometry and jsxgraph- dynamic geometry for mobile devices. South Bohemia Mathematical Letters, 21(1), 1–7. Recuperado de http://home.pf.jcu.cz/~upvvm/2013/sbornik/clanky/09_UPVM2013_Ehmann_et_al.pdf Escuder, A. & Furner, J. M. (2011). The Impact of GeoGebra in Math Teacher’s Professional Development. In: International Conference on Technologies in Collegiate Mathematics (pp. 76–84). Denver: Pearson. Recuperado de http://archives.math.utk.edu/ICTCM/VOL23/S113/paper.pdf Geogebra Calculadora Gráfica. (versión versión 6.0.619.0) [software de geometría]. Linz: ACGG. Disponible en https://www.geogebra.org/graphing?lang=es Hamidi, H. & Chavoshi, A. (2018). Analysis of the essential factors for the adoption of mobile learning in higher education: A case study of students of the University of Technology. Telematics and Informatics, 35(4), 1053–1070. https://doi.org/10.1016/j.tele.2017.09.016 Hanna, G. (2018). Reflections on Proof as Explanation. In: Stylianides A., Harel G. (eds), Advances in Mathematics Education Research on Proof and Proving (pp. 3–18). Cham: Springer. https://doi.org/10.1007/978-3-319-70996-3₁ Hanna, G. (1995). Challenges to the importance of proof’. For the Learning of Mathematics 15(3), 42–49. Recuperado de https://flm-journal.org/Articles/7679867298F4CBEABE82D0ABEB5EC.pdf Holmes, B. & Gardner, J. (2006). E-Learning (Concepts and practice). London: SAGE Publications. http://dx.doi.org/10.4135/9781446212585 Huang, Y. (2014). Empirical Analysis on Factors Impacting Mobile Learning Acceptance in Higher Engineering Education. [Doctoral dissertation]. University of Tennessee, Knoxville, USA. Recuperado de https://trace.tennessee.edu/cgi/viewcontent.cgi?article=3166&context=utk_graddiss Joo-Nagata, J., Martinez, F., García-Bermejo, J., & García-Peñalvo, F. J. (2017). Augmented reality and pedestrian navigation through its implementation in m-learning and e-learning: Evaluation of an educational program in Chile. Computers & Education, 111, 1–17. https://doi.org/10.1016/j.compedu.2017.04.003 Karimi, S. (2016). Do learners’ characteristics matter? An exploration of mobile-learning adoption in self-directed learning. Computers in Human Behavior, 63, 769–776. https://doi.org/10.1016/j.chb.2016.06.014 Karunakaran, S. S. (2018). The Need for “Linearity” of Deductive Logic: An Examination of Expert and Novice Proving Processes. In: Stylianides A., Harel G. (eds), Advances in Mathematics Education Research on Proof and Proving (pp. 171–183). Cham: Springer. https://doi.org/10.1007/978-3-319-70996-3_12 Leung, A., Baccaglini-Frank, A. & Mariotti, M. A. (2013). Discernment in dynamic geometry environments. Educational Studies in Mathematics, 84(3), 439–460. https://doi.org/10.1007/s10649-013-9492-4 Majerek, D. (2014). Applications of GeoGebra for Teaching Mathematics. Advances in Science and Technology Research Journal, 8(24), 51–54. https://doi.org/10.12913/22998624/567 Mariotti, M. A. (2015). Transforming Images in a DGS: The semiotic potential of the dragging tool for introducing the notion of conditional statement. In: S. Rezat, M. Sebastian, A. Hattermann & Peter-Koop (Eds.), Transformation—A fundamental idea of mathematics education (pp. 155–172). New York: Springer. https://doi.org/10.1007/978-1-4614-3489-4₈ Mariotti, M. (2006). Prof and proving in mathematics education. In: A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 173–204). Rotterdam: Sense Publishers. Mariotti, M. A. & Pedemonte, B. (2019). Intuition and proof in the solution of conjecturing problems’. ZDM, 51, 759–777. https://doi.org/10.1007/s11858-019-01059-3 Ozdamli, F. (2012). Pedagogical framework of m-learning. Procedia - Social and Behavioral Sciences, 31, 927–931. https://doi.org/10.1016/j.sbspro.2011.12.171 Pedemonte, B. (2018). How Can a Teacher Support Students in Constructing a Proof? Advances in Mathematics Education Research on Proof and Proving (pp. 115–129). Cham: Springer. https://doi.org/10.1007/978-3-319-70996-3₈ Pedemonte, B. (2007). How can the relationship between argumentation and proof be analysed? Educational Studies in Mathematics, 66(1), 23–41. https://doi.org/10.1007/s10649-006-9057-x Pegrum, M. (2014). Agendas for Mobile Learning. In, M. Pegrum, Mobile learning: Languages, literacies and cultures (pp 4–16). UK. Springer. Recuperado de https://link.springer.com/chapter/10.1057/9781137309815₂ Rocha, H. (2019). Mathematical proof: from mathematics to school mathematics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377(2140), 1–12. https://doi.org/10.1098/rsta.2018.0045 Sánchez, J. C., Olmos, S. & Garcí-Peñalvo, F. (november, 2013). Mobile Learning: Tendencies and lines of research. In, F. García-Peñalvo (ed.), Proceedings of the first international conference on technological ecosystem for enhancing multiculturality (pp. 473–480). Association for Computing Machinery-ACM, New York, USA. https://doi.org/10.1145/2536536.2536609 Sánchez-Prieto, J. C., Olmos-Migueláñez, S. & García-Peñalvo, F. (2016). Informal tools in formal contexts: Development of a model to assess the acceptance of mobile technologies among teachers. Computers in Human Behavior, 55(Part A), 519–528. https://doi.org/10.1016/j.chb.2015.07.002 Selaković, M., Marinković, V. & Janičić, P. (2019). New dynamics in dynamic geometry: Dragging constructed points. Journal of Symbolic Computation, 97, 3–15. https://doi.org/10.1016/j.jsc.2018.12.002 Velichova, D. (2011). Interactive Maths with GeoGebra. International Journal of Emerging Technologies in Learning (IJET), 6(S1), 31–35. Available: https://online-journals.org/index.php/i-jet/article/view/1620 Wassie, Y. A. & Zergaw, G. A. (2019). Some of the Potential Affordances, Challenges and Limitations of Using GeoGebra in Mathematics Education. Eurasia Journal of Mathematics, Science and Technology Education, 15(8), 1–11. https://doi.org/10.29333/ejmste/108436 |
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Ballesteros-Ballesteros, Vladimir AlfonsoRodríguez-Cardoso, Óscar IvánLozano-Forero, Sébastien2021-01-01 00:00:002024-04-09T19:55:04Z2021-01-01 00:00:002024-04-09T19:55:04Z2020-01-012145-9258https://hdl.handle.net/11323/11321https://doi.org/10.17981/cultedusoc.12.1.2021.0510.17981/cultedusoc.12.1.2021.052389-7724Este artículo presenta los resultados de un proyecto de investigación cuyo objetivo fue describir el papel mediador de la aplicación móvil “Calculadora Gráfica” de GeoGebra sobre los procesos de conjeturación del teorema del valor medio para derivadas mediante la detección de invariantes a través de herramientas de arrastre, combinando geometría dinámica con cálculo infinitesimal. A través de un estudio de caso cualitativo, que involucró estudiantes de Ingeniería Aeronáutica, se dinamizaron los esfuerzos investigativos con el propósito de validar la hipótesis relacionada con una influencia positiva de una estrategia de aprendizaje móvil sobre el proceso de conjeturación en un curso de Cálculo Diferencial. Los resultados obtenidos permitieron evidenciar avances significativos en la conjeturación del teorema mencionado para la resolución de problemas en ingeniería y se discute cómo este tipo de recursos digitales, a través de un entorno de geometría dinámica en dispositivos móviles, puede servir como mediación para favorecer el aprendizaje del cálculo.This article presents the results of a research project whose main objective was to describe the mediating role of GeoGebra’s “Graphing Calculator” mobile application on the conjecturing processes of the mean value theorem for derivatives by the use of some dragging tools, which combines dynamic geometry and infinitesimal calculus. By means of a qualitative case study, involving students from aeronautical engineering, research efforts were carried out looking forward to get evidence that allow the judgement of a hypothesis involving a positive influence of a mobile learning strategy on conjecturing processes in the context of a calculus course. The results obtained allowed us to conclude significant advances in the conjecturing process of the above-mentioned theorem for the solving-problems process in engineering. The discussion of how this type of digital resources, through a dynamic geometry environment in mobile devices, could favor the learning of calculus, is also addressed.application/pdftext/htmltext/xmlspaUniversidad de la CostaCULTURA EDUCACIÓN Y SOCIEDAD - 2020https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessEsta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.http://purl.org/coar/access_right/c_abf2https://revistascientificas.cuc.edu.co/culturaeducacionysociedad/article/view/2933Aprendizaje móvilConjeturaciónGeoGebraTeorema del valor medio para derivadasMobile learningConjecturing processGeoGebraMean value theorem for derivativesConjeturación del teorema del valor medio para derivadas: Un acercamiento desde la detección de invariantes en dispositivos móviles con GeoGebraConjecturing process for the mean value theorem for derivatives: An approach from the detection of invariants in mobile devices with GeoGebraArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articleJournal articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Cultura Educación SociedadAbu-Al-Aish, A., Love, S., Hunaiti, Z. & Al-masaeed, S. (2014). Toward mobile learning deployment in higher education. International Journal of Mobile Learning and Organisation (IJMLO), 7(3/4), 253–276. https://doi.org/10.1504/IJMLO.2013.057165.Akour, H. (2011). Determinants of mobile learning acceptance: An empirical investigation in higher education. [Ph.D. Dissertation]. Oklahoma State University, Small city, USA. Available: https://www.proquest.com/docview/610058264Al-Emran, M., Mezhuyev, V. & Kamaludin, A. (2018). Technology Acceptance Model in M-learning context: A systematic review. Computers & Education, 125, 389–412. https://doi.org/10.1016/j.compedu.2018.06.008Baccaglini-Frank, A. (2019). Dragging, instrumented abduction and evidence, in processes of conjecture generation in a dynamic geometry environment. ZDM Mathematics Education, 51, 779–791. https://doi.org/10.1007/s11858-019-01046-8Boero, P., Fenaroli, G. & Guala, E. (2018). Mathematical Argumentation in Elementary Teacher Education: The Key Role of the Cultural Analysis of the Content. In: Stylianides A., Harel G. (eds), Advances in Mathematics Education Research on Proof and Proving, (pp. 49–67). Cham: Springer. https://doi.org/10.1007/978-3-319-70996-3₄Cabri Geometry (versión 2.1.1) [software de geometría]. Grenoble: Cabrilog. Disponible en https://cabri.com/es/Camargo, L., Samper, C. & Perry, P. (2007). Cabri’s role in the task of proving within the activity of building part of an axiomatic system. In: D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 571–580). Larnaca: CERME. Recuperado de http://funes.uniandes.edu.co/927/1/2007Pr-CamargoCabri.pdfCheema, S., Gulwani, S. & LaViola, J. (may, 2012). QuickDraw: improving drawing experience for geometric diagrams. In: J. Konstan, Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (pp. 1037–1064). Association for Computing Machinery, New York, United States. https://doi.org/10.1145/2207676.2208550Creswell, J. W. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Thousand: Sage publications. Recuperado de http://www.drbrambedkarcollege.ac.in/sites/default/files/research-design-ceil.pdfCrompton, H., Burke, D., Gregory, K. H. & Grabe, C. (2016). The use of mobile learning in science: A systematic review. Journal of Science Education and Technology, 25, 149–160. https://doi.org/10.1007/s10956-015-9597-xDonaldson, R. L. (2011). Student acceptance of mobile learning. [Ph.D. Dissertation]. The Florida State University, Tallahassee, USA. Recuperado de https://fsu.digital.flvc.org/islandora/object/fsu%3A168891/datastream/PDF/viewEhmann, M., Gerhauser, M., Miller, C. & Wassermann, A. (2013). Sketchometry and jsxgraph- dynamic geometry for mobile devices. South Bohemia Mathematical Letters, 21(1), 1–7. Recuperado de http://home.pf.jcu.cz/~upvvm/2013/sbornik/clanky/09_UPVM2013_Ehmann_et_al.pdfEscuder, A. & Furner, J. M. (2011). The Impact of GeoGebra in Math Teacher’s Professional Development. In: International Conference on Technologies in Collegiate Mathematics (pp. 76–84). Denver: Pearson. Recuperado de http://archives.math.utk.edu/ICTCM/VOL23/S113/paper.pdfGeogebra Calculadora Gráfica. (versión versión 6.0.619.0) [software de geometría]. Linz: ACGG. Disponible en https://www.geogebra.org/graphing?lang=esHamidi, H. & Chavoshi, A. (2018). Analysis of the essential factors for the adoption of mobile learning in higher education: A case study of students of the University of Technology. Telematics and Informatics, 35(4), 1053–1070. https://doi.org/10.1016/j.tele.2017.09.016Hanna, G. (2018). Reflections on Proof as Explanation. In: Stylianides A., Harel G. (eds), Advances in Mathematics Education Research on Proof and Proving (pp. 3–18). 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Some of the Potential Affordances, Challenges and Limitations of Using GeoGebra in Mathematics Education. Eurasia Journal of Mathematics, Science and Technology Education, 15(8), 1–11. https://doi.org/10.29333/ejmste/1084368463112https://revistascientificas.cuc.edu.co/culturaeducacionysociedad/article/download/2933/3112https://revistascientificas.cuc.edu.co/culturaeducacionysociedad/article/download/2933/3113https://revistascientificas.cuc.edu.co/culturaeducacionysociedad/article/download/2933/3114Núm. 1 , Año 2021 : Cultura Educación y SociedadPublicationOREORE.xmltext/xml2851https://repositorio.cuc.edu.co/bitstreams/671addc4-83aa-4163-bac0-9b264b140ab7/download70677ef54fa4903c52bafa021248fa57MD5111323/11321oai:repositorio.cuc.edu.co:11323/113212024-09-17 11:09:41.327https://creativecommons.org/licenses/by-nc-nd/4.0/CULTURA EDUCACIÓN Y SOCIEDAD - 2020metadata.onlyhttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.co |