Mathematical Modelling and Technology for the Learning of Calculus: Graph of Functions and Taylor Series
Lorenza Illanes, Ruth Rodríguez Gallegos · 2013
The objective in this research is to investigate how the strategies and difficulties that the students experiment with when they work with the diverse states of the modelling process (Niss, Blum, & Galbraith, 2007; Rodriguez, 2009), and how the use of an appropriated technology improves the transitions between these states of modelling (Rodriguez, Quiroz & Illanes, 2013) for establishing a representation of a real phenomenon, using the graph of functions and their parametric analysis. Also the paper presents work with the approximation method of the Taylor Series for integration of some functions. This research is centered on some specific themes of Calculus such as the parametric analysis from the cubic and trigonometric functions, and the approximation method of Taylor Series for integration of functions (Illanes & Rodriguez, 2012). The work was done based on courses of Calculus (Differential & Integral, Salinas et al., 2012) in two semesters of 2012, at university level. The paper shows how the learning process has been enriched by mathematical modelling (Rodriguez, 2009) of real new phenomena. It also reveals the importance of how students know to model a problem with the use of specific technology (Ferreira, 2009) (graphic calculators and simulators) working in groups (Collazos & Mendoza, 2009; Woods & Chen, 2010). On the other hand, it allows them to see how the real phenomenon model can be represented by the parameters on a graph. References Collazos, C. A., & Mendoza, J. (2009). Como aprovechar el aprendizaje colaborativo en el aula . Ferreira, A. F. (2009). Las innovaciones tecnologicas y su impacto en la educacion . El Cid Editores. Illanes, L., & Rodriguez, R. (2012). Analisis de graficas de funciones en un curso de calculo a traves de la modelacion y la tecnologia. Asociacion Mexicana de Investigadores del Uso de Tecnologia en Educacion Matematica (AMIUTEM). Mexico, Monterrey Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. ICMI Study 14: Applications and modelling in mathematics education (pp. 3-32). New York: Springer. Rodriguez, R. (2009). Differential equations as a tool for mathematical modeling in physics and mathematics courses. A study of high school textbooks and the modeling processes of senior high students. In M. Blomhoi & S. Carrera (Eds.), Mathematical applications and modeling in the teaching and learning of mathematics . Proceedings of the 11th International Congress on Mathematical Education, TSG 21 (pp. 19-34). Roskilde, Denmark: Roskilde University Centre. Rodriguez, R. (2010). Aprendizaje y Ensenanza de la Modelacion: el caso de las ecuaciones diferenciales. Revista Latinoamericana de Matematica Educativa (RELIME, 2010), 13 (4-I), 191-210. Rodriguez, R., & Illanes, L. (2012). La TI-Nspire CX CAS y su uso para la modelacion del analisis grafico de funciones en un curso de Calculo. IV Simposio Latinoamericano para la Integracion de la Tecnologia en el Aula de Matematicas y Ciencias. Mexico, D.F. Rodriguez, R., Quiroz, S., & Illanes, L. (2013). Competencias de modelacion y uso de tecnologia en Ecuaciones Diferenciales. Acta Latinoamericana de Matematica Educativa (ALME 26). CLAME: Belo Horizonte, Brasil. Salinas, P., Alanis, J. A., Pulido, R., Garcia, J. L., Santos, F., & Escobedo, J. (2012). Calculo Aplicado: Competencias matematicas a traves de Contextos Vol. I & Vol. II. . Mexico: Cegage. Woods, D. M., & Chen, K. (2010). Evaluation techniques for cooperative learning. International Journal of Management and Information Systems, 14 (1), 1-5