Aprendiendo funciones complejas con GeoGebra
online first
PDF (English)

Cómo citar

D’Azevedo Breda, A. M., & Dos Santos Dos Santos, J. M. (2021). Aprendiendo funciones complejas con GeoGebra. RACCEFYN. https://doi.org/10.18257/raccefyn.1504

Descargas

Los datos de descargas todavía no están disponibles.

Métricas Alternativas

Resumen

En este trabajo describimos un experimento didactico dirigido a estudiantes de An´alisis Complejo que asisten a un curso de pregrado de una universidad portuguesa. Nuestro principal objetivo es la comprensi´on del rol de GeoGebra con respeto a la visualizaci´on y como mediador tecnol´ogico, seg´un la teor´ıa de Vygotsky, en el proceso de ense˜nanza y aprendizaje de funciones complejas. El primer paso de nuestro estudio fue la concepci´on de una secuencia de tareas did´acticas y el desarrollo de herramientas GeoGebra relacionadas con los objetivos did´acticos. Aqu´ı describiremos el procedimiento relacionado con la implementaci´on de las tareas en un ambiente de aula y los resultados obtenidos en base a los datos recopilados compuestos por las asignaciones escritas producidas por los estudiantes, la grabaci´on de video del desempe˜no del estudiante durante el experimento y las construcciones de los estudiantes con GeoGebra. Todos los datos recolectados fueron analizados desde un paradigma cualitativo e interpretativo.

https://doi.org/10.18257/raccefyn.1504

Palabras clave

GeoGebra | Ense˜nanza de las Matem´aticas | Educaci´on Matem´atica | Analisis Compleja
PDF (English)

Referencias

Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational studies in mathematics, 52(3), 215–241.

Arcavi, A.,&Hadas, N. (2000). Computer mediated learning: An example of an approach. International journal of computers for mathematical learning, 5(1), 25–45. doi: 10.1023/A:1009841817245

Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practises in cabri environments. Zentralblatt f¨ur Didaktik der Mathematik, 34(3), 66–72.

Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E., Mathews, D., & Thomas, K. (1997). A framework for research and curriculum development in undergraduate mathematics education. Maa Notes,(), 37–54.

Barrera-Mora, F., & Reyes-Rodr´ıguez, A. (2013). Cognitive processes developed by students when solving mathematical problems within technological environments. The Mathematics Enthusiast, 10(1), 109–136.

Bogdan, R. C., & Biklen, S. K. (1997). Qualitative research for education an introduction to theories and models. Allyn & Bacon Boston, MA.

Breda, A., Trocado, A., & Dos Santos, J. M. D. S. (2013). O geogebra para al´em da segunda dimens˜ao. Indagatio Didactica, 5(1), 60–84. Retrieved from http://revistas.ua.pt/index.php/ID/article/view/2421/2292

Breda, A. M. D., & Dos Santos, J. M. D. S. (2015). The riemann sphere in geogebra. Sensos-e, 2(1), 2183–1432. Retrieved from http://sensos-e.ese.ipp.pt/?p=7997

Breda, A. M. D.,&Dos Santos, J. M. D. S. (2016, 05). Complex functions with GeoGebra. Teaching Mathematics and its Applications: An International Journal of the IMA, 35(2), 102–110. Retrieved from https://doi.org/10.1093/teamat/hrw010 doi: 10.1093/teamat/hrw010

Bu, L., Spector, J. M., & Haciomeroglu, E. S. (2011). Toward model-centered mathematics learning and instruction using geogebra. In L. Bu & R. Schoen (Eds.), Modelcentered learning: Pathways to mathematical understanding using geogebra (p. 13-40). Rotterdam: SensePublishers. Retrieved from https://doi.org/10.1007/978-94-6091-618-2 3 doi: 10.1007/978-94-6091-618-2 3

Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420–464). New York: Macmillan.

Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational researcher, 32(1), 9–13.

Cole, M., & Wertsch, J. V. (1996). Beyond the individual-social antinomy in discussions of Piaget and Vygotsky. Human development, 39(5), 250–256.

Danenhower, P. (2006). Introductory complex analysis at two British Columbia Universities: The first week-complex numbers. CBMS Issues in Mathematics Education, 13(), 139–170.

Dos Santos, J. M. D. S., & Peres, M. J. (2012). Atitudes dos alunos face ao geogebra – construc¸ ˜ao e validac¸ ˜ao de um invent´ario. Revista do Instituto GeoGebra Internacional de S˜ao Paulo., 1(1).

Dubinsky, E. (1984). A Constructivist theory of learning in undergraduate mathematics education research. ICMI.

Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (Vol. 11, pp. 95–126). Netherlands: Springer.

Dubinsky, E., Czarnocha, B., Prabhu, V., & Vidakovic, D. (1999). One theoretical perspective in undergraduate mathematics education research. In O. Zaslavsky & I. G. for the Psychology of Mathematics Education (Eds.), Proceedings of the 23rd conference of the international group for the psychology of mathematics education, [haifa, israel, july 25-30 (Vol. 4, pp. 65–73). Retrieved from http://files.eric.ed.gov/fulltext/ED436403.pdf

Dubinsky, E., & Mcdonald, M. A. (2002). Apos: A constructivist theory of learning in undergraduate mathematics education research. In D. Holton, M. Artigue, U. Kirchgr¨aber, J. Hillel, M. Niss, & A. Schoenfeld (Eds.), The teaching and learning of mathematics at university level: An icmi study (pp. 275–282). Dordrecht: Springer Netherlands. Retrieved from https://doi.org/10.1007/0-306-47231-7 25 doi: 10.1007/0-306-47231-7 25

Dubinsky, E., &Wilson, R. T. (2013). High school students’ understanding of the function concept. The Journal of Mathematical Behavior, 32(1), 83–101.

Farris, F. A. (1997). Visualizing complex-valued functions in the plane. AMC, 10(12.), .

Flashman, M. (2016). Making sense of calculus with mapping diagrams. MAA. Guba, E. G., Guba, Y. A. L., & Lincoln, Y. S. (1994). Competing paradigms in qualitative research. Handbook of qualitative research,(), . doi: http://www.uncg.edu/hdf/facultystaff/Tudge/Guba%20&%20Lincoln%201994.pdf

Guti´errez, R. A. (1996). Visualization in 3-dimensional geometry: In search of a framework. In 18 pme conference (pp. 3–19).

Harel, G. (2013). Dnr-based curricula: The case of complex numbers. Humanistic Mathematics, 3(2), 2–61.

Heid, M. K., & Blume, G. W. (2008). Algebra and function development. Research on technology and the teaching and learning of mathematics, 1(), 55–108.

Hohenwarter, M., Hohenwarter, J., Kreis, Y., & Lavicza, Z. (2008). Teaching and calculus with free dynamic mathematics software geogebra. In 11th international congress on mathematical education. ICME.

Hollebrands, K. F. (2007). The role of a dynamic software program for geometry in the strategies high school mathematics students employ. Journal for research in mathematics education,(), 164–192.

Jones, K. (2000). Providing a foundation for deductive reasoning: students’ interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics,(), 55–85.

Kreis, Y. (2004). Math´e-mat-TIC: Int´egration de l’outil informatique dans le cours de math´ematiques de la classe de 4e (Travail de candidature). Luxembourg: Minist´ere de l’ ´ Eucation Nationale et de la Formation Professionnelle. Lavicza, Z. (2010). Integrating technology into mathematics teaching at the university level. ZDM,(), 105–119. Retrieved from http://www.springerlink.com/index/1188K58KH5562T32.pdf doi: 10.1007/s11858-009-0225-1

Liste, R. L. (2014). El color din´amico de geogebra. Gaceta De La Real Sociedad Matematica Esp˜nola, 17(3), 525–547.

Mascarello, M., & Winkelmann, B. (1986). Calculus and the computer. the interplay of discrete numerical methods and calculus in the education of users of mathematics: considerations and experiences. In The influence of computers and informatics on mathematics and its teaching: Proceedings from a symposium. strasbourg, france: International commission on mathematical instruction (Vol. 1, p. 120).

Meng, P.-C., Jiang, Z.-X., Shi, S.-Z., & Liang, S.-M. (2014). Study of a combination of complex function learning with mathematical modeling. In 2014 international conference on management science and management innovation (msmi 2014) (pp.357–360).

ming Zhang, Y., &Wang, D. (2013). Teaching reform on the course of complex analysis. In Proceedings of the 2013 conference on education technology and management science (icetms 2013) (p. 587-589). Atlantis Press. Retrieved from https://doi.org/10.299/icetms.2013.161 doi: https://doi.org/10.2991/icetms.2013.161

Navetta, A. (2016). Visualizing functions of complex numbers using geogebra. North American GeoGebra Journal, 5(2), .

Needham, T. (1998). Visual complex analysis. Oxford University Press. Nemirovsky, R., & Soto-Johnson, H. (2013). On the emergence of mathematical objects: The case of eaz. In Proceedings of the 16th annual conference on research in undergraduate mathematics education (p. 219-226).

Nordlander, M. C., & Nordlander, E. (2012). On the concept image of complex numbers. International Journal of Mathematical Education in Science and Technology, 43(5), 627-641. Retrieved from https://doi.org/10.1080/0020739X.2011.633629

Olive, J. (2000). Implications of using dynamic geometry technology for teaching and learning. In Conference on teaching and learning problems in geometry.

Panaoura, A., Elia, I., Gagatsis, A., & Giatilis, G. P. (2006). Geometric and algebraic approaches in the concept of complex numbers. International Journal of Mathematical Education in Science and Technology, 37(6), 681–706. doi: 10.1080/00207390600712281

Poelke, K., & Polthier, K. (2009). Lifted domain coloring. Computer Graphics Forum, 28(3), 735-742. Retrieved from https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-8659.2009.01479.x doi: 10.1111/j.1467-8659.2009.01479.x

Ponte, J. P. (2005). Gest˜ao curricular em matem´atica. O professor e o desenvolvimento curricular.

Presmeg, N. C. (1997). Generalization using imagery in mathematics. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 299–312). Lawrence Erlbaum Associates, Inc., Publishers.

Roth, W.-M. (2003). Toward an anthropology of graphing. In Toward an anthropology of graphing: Semiotic and activity-theoretic perspectives (pp. 1–21). Dordrecht: Springer Netherlands. Retrieved from https://doi.org/10.1007/978-94-010-0223-3 1 doi: 10.1007/978-94-010-0223-3 1

Salomon, G. (1990). Cognitive effects with and of computer technology. Communication Research, 17(1), 26–44. doi: 10.1177/009365090017001002

Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics,22(1), 1–36. doi: 10.1007/BF00302715

Sfard, A. (1994). Reification as the birth of metaphor. For the Learning of Mathematics,14(1), 44–55. doi: 10.1371/journal.pone.0016782

Soto-Johnson, H., & Troup, J. (2014). Reasoning on the complex plane via inscriptions and gesture. Journal of Mathematical Behavior, 36(), 109–125. doi: 10.1016/j.jmathb.2014.09.004

Tabaghi, S. G., & Sinclair, N. (2013). Using dynamic geometry software to explore eigenvectors: The emergence of dynamic-synthetic-geometric thinking. Technology, Knowledge and Learning, 18(3), 149–164. doi: 10.1007/s10758-013-9206-0

Takaˇci, D., Stankov, G., & Milanovic, I. (2015). Efficiency of learning environment using geogebra when calculus contents are learned in collaborative groups. Computers and Education, 82(), 421–431. doi: 10.1016/j.compedu.2014.12.002

Vitale, J. M., Black, J. B., & Swart, M. I. (2014). Applying grounded coordination challenges to concrete learning materials: A study of number line estimation. Journal of Educational Psychology,(), . doi: 10.1037/a0034098

Vygotsky, L. (1978). Mind in society: The development of higher psychological processes. Wegert, E. (2012). Visual complex functions: An introduction with phase portraits. Springer Basel. doi: 10.1007/978-3-0348-0180-5 1

Wegert, E., & Semmler, G. (2010). Phase plots of complex functions: a journey in illustration. Notices AMS, 58(), 768–780.

Wright, D. (2005). Graphical calculators’ in teaching secondary mathematics with ict. In S. Johnston-Wilder & D. Pimm (Eds.), Ict and the mathematics classroom-part b (p. 145-158). New York, NY, USA: McGraw-Hill.

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.

Derechos de autor 2021 Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales