Fomento de la flexibilidad matemática a través de una secuencia de tareas de modelización

Referencias

Achmetli, K., Schukajlow, S., & Rakoczy, K. (2018). Multiple solutions for real-world problems, experience of competence and students’ procedural and conceptual knowledge. International Journal of Science and Mathematics Education, 17, 1605–1625. Albarracín, L., & Gorgorió, N. (2014). Devising a plan to solve Fermi problems involving large numbers. Educational Studies in Mathematics, 86(1), 79–96. Ärlebäck, J. B. (2009). On the use of realistic Fermi problems for introducing mathematical modelling in school. The Montana Mathematics Enthusiast, 6(3), 331–364. Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects. State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68. Blum, W., & Leiss, D. (2007). How do students and teachers deal with mathematical modelling problems? The example sugarloaf and the DISUM project. En C. Haines, P. L. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 222–231). Chichester, Inglaterra: Horwood. Borromeo-Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM Mathematics Education, 38(2), 86-95. Borromeo-Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Nueva York: Springer. CCSSI (2010). Common Core State Standards for Mathematics. Washington, DC: NCTM. Efthimiou, C. J., & Llewellyn, R. A. (2007). Cinema, Fermi problems and general education. Physics Education, 42(42), 253–261. Elia, I., van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education, 41(5), 605–618. Ferrando, I., Albarracín, L., Gallart, C., García-Raffi, L. M., & Gorgorió, N. (2017). Análisis de los modelos matemáticos producidos durante la resolución de problemas de Fermi. Boletim de Educação Matemática, 31(57), 220–242. Ferrando, I., Segura, C., & Pla-Castells, M. (2019a). Relation entre contexte, situation et plan de solution dans des problèmes complexes. Manuscrito no publicado. Ferrando, I., Segura, C., & Pla-Castells, M. (2019b). How many can fit here? Same question, differents resolutions: Analysis of the relationship between context and solution plan in modelling tasks. Manuscrito no publicado. Gallart, C., Ferrando, I., García-Raffi, L. M., Albarracín, L., & Gorgorió, N. (2017). Design and implementation of a tool for analysing student products when they solve Fermi problems. En G. Stillman, W. Blum, & G. Kaiser (Eds.) Mathematical modelling and applications. International perspectives on the teaching and learning of mathematical modelling (pp. 265-275). Cham, Suiza: Springer. Goldin, G. A., & McClintock, C. E. (Eds.) (1979). Task variables in mathematical problem solving. Columbus, OH: The Ohio State University. Heinze, A., Star, J.R., & Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education. ZDM Mathematics Education, 41, 535–540. Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM Mathematics Education, 38(3), 302– 310. Kilpatrick, J. (1978). Variables and methodologies in research on problem solving. En L. L. Hatfield & D. A. Bradbard (Eds.) Mathematical problem solving: Papers from a Research Workshop (pp. 14-27). Columbus, OH: The Ohio State University. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up. Helping children learn mathematics. Washington DC: National Academy Press. Leikin, R., & Levav-Waynberg, A. (2008). Solution spaces of multiple-solution connecting tasks as a mirror of the development of mathematics teachers’ knowledge. Canadian Journal of Science, Mathematics, and Technology Education, 8(3), 233–251. Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2), 157–189. Levav-Waynberg, A., & Leikin, R. (2012). The role of multiple solution tasks in developing knowledge and creativity in geometry. The Journal of Mathematical Behavior, 31, 73–90. Peter-Koop, A. (2009). Teaching and understanding mathematical modelling through Fermi-problem. En B. Clarke, B. Grevholm, & R. Millman (Eds.) Tasks in primary mathematics teacher education (pp. 131–146). New York: Springer. Puig, L., & Cerdán, F. (1988). Problemas aritméticos escolares. Madrid: Síntesis. Schukajlow, S., Krug, A., & Rakoczy, K. (2015). Effects of prompting multiple solutions for modelling problems on students’ performance. Educational Studies in Mathematics, 89, 393–417. Sriraman, B., & Lesh, R. A. (2006). Modeling conceptions revisited. ZDM Mathematics Education, 38(3), 247–254. Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404–411. Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and Instruction, 18(6), 565–579. Webb, N. L. (1980). Content and context variables in problem tasks. En G. A. Goldin & C. E. McClintock (Eds.), Task variables in mathematical problem solving. Filadelfia, PE: The Franklin Institute Press.