Papiroflexia y geometría dinámica para discutir covariación en coordenadas polares

Referencias

Agnesi, M. (1748). Instituzioni analitiche ad uso della gioventú italiana. Libro Secondo del Calcolo Differenziale. Milano, Italia: Nella Regia Ducal Corte. Cantoral, R. (2013). Teoría Socioepistemológica de la Matemática Educativa. Estudios sobre construcción social del conocimiento. España: Gedisa. Carlson, M., Jacobs, S., Coe, E., Larsen, S. & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and study. Journal for Research in Mathematics Education, 33(5), 352–378. Confrey, J. & Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions. Journal for Research in Mathematics Education, 26(1), 66–86. Codero, F., Cen, C. & Suárez, L. (2010). Los funcionamientos y formas de las gráficas en los libros de texto: una práctica institucional en el bachillerato. Revista Latinoamericana de Investigación en Matemática Educativa. 13(2), 187-214. Dennis, E. & Confrey, J. (1997). Drawing Logarithmic Curves with Geometer's Sketchpad: A Method Inspired by Historical Sources. En J. King & D. Schattschneider (Eds.), Geometry Turned On: Dynamic Software in Learning, Teaching and Research. Washington D.C., USA: Mathematical Association of America. Ferrari, M, Martínez-Sierra, G. & Méndez, M. (2016). "Multiply by Adding": Development of the Logarithmic-Exponential Covariational Reasoning in High School Students. Journal of Mathematical Behavior 42, 92-108 Ferrari, M. & Farfán, R. M. (2010). Una socioepistemología de lo logarítmico. [Número especial]. Revista Latinoamericana de Investigación en Matemática Educativa 13(4), 53-68. Ferrari, M. (2008). Un acercamiento socioepistemológico a lo logarítmico: de multiplicar sumando a una primitiva. Tesis de Doctorado. Departamento de Matemática Educativa. Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional. México. Hairer, E. & Wanner, G. (1996). Analysis by Its History. New York, USA: Undergraduate Texts in Mathematics, Springer-Verlag. Hitt, F., & González-Martín, A. S. (2015). Covariation between variables in a modelling process : The ACODESA (collaborative learning, scientific debate and self-reflection) method. Educational Studies in Mathematics 88(2), 201–219. Johnson, H. L. (2012). Reasoning about variation in the intensity of change in covarying quantities involved in rate of change. Journal of Mathematical Behavior, 31(3), 313–330. doi:10.1016/j.jmathb.2012.01.001. Johnson, H. L. (2015). Together yet separate: Students’ associating amounts of change in quantities involved in rate of change. Educational Studies in Mathematics 89(1), 89-110. doi:10.1007/s10649-014-9590-y. Martínez, C. (2008). El concepto de función en la obra de Euler: un recorrido a través de la constitución del Análisis Matemático Moderno. Revista Miscelánea Matemática 46, 73-91. Montiel, M., Vidakovic, D., & Kabael, T. (2008). Relationship between studens’ understanding of functions in cartesian and polar coordinate systems, Investigations in Mathematics Learning, 1(2), 52-70 Montiel, M., Vidakovic, D., Elstak, I., & Wilhelmi, M. (2009). Using the onto-semiotic approach to identify and analyze mathematical meaning when transiting between different coordinate systems in a multivariate context. Educational Studies in Mathematics. Vol.72, pp.139-160. Moore, K. C., Paoletti, T., & Musgrave, S. (2013). Covariational reasoning and invariance among coordinate systems. Journal of Mathematical Behavior, 32(3), 461–473. doi:10.1016/j.jmathb.2013.05.002. Nagle, C., Moore-Russo, D., Viglietti, J., & Martin, K. (2013). Calculus Students’ and Instructors' Conceptualizations of Slope: a Comparison Across Academic Levels. International Journal of Science and Mathematics Education, 11, 1491–1515. doi:10.1007/s10763-013-9411-2. Oehrtman, M., Carlson, M. P. & Thompson, P. W. (2008). Foundational reasoning abilities that promote coherence in students’ understanding of functions. En M. P. Carlson & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics education (pp. 150-166). USA: Series: MAA. Ortega, I. & Ortega, T. (2004): Evolventes y espirales. Épsilon 57, 477-492. Saldanha, L. & Thompson, P. W. (1998). Re-thinking convariation from a quantitative perspectivie: Simultaneous Continuous Variation. En W. N. Berensah y S. B. Coulombe (Ed.), Proceedings of the Annual Meeting of the Psychology of Mathematics Education - North America. Raleigh, N.C: North Carolina State University. Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh, & A. E. Kelly (Eds.), Research Design in Mathematics and Science Education (pp. 267–307). Hillside, NJ: Erlbaum. Ramírez, T. & Ferrari, M. (2011). Las coordenadas polares: Algunos de sus usos en disciplinas de investigación específicas. En L. Sosa, R. Rodríguez, y E. Landa (Eds.) Memoria de la XIV Escuela de Invierno en Matemática Educativa (pp.111-117). Zacatecas. Diciembre 2011. Tomoko Fuse: Origami Instructions: Navel Shell, spiral origami art desing Disponible en: https://www.youtube.com/watch?v=-n1K_gKP_7Q Weber, E., & Thompson, P. W. (2014). Students’ images of two-variable functions and their graphs. Educational Studies in Mathematics 87(1), 67–85