Secuencias de problemas de Fermi para introducir la modelización matemática

• Autores: Lluís Albarracín, Irene Ferrando Palomares , Carlos Segura, Carlos Segura
• Localización: La investigación en modelización matemática:: un diálogo entre educadores de Latinoamérica y España / Armando Solares Rojas (ed. lit.), Armando Paulino Preciado Babb (ed. lit.), 2025, ISBN 978-607-59819-5-6, pág. 153
• Idioma: español
• Enlaces
  • Texto Completo Libro
• Resumen
  • español

    En este capítulo sintetizamos los avances en la investigación sobre el uso de problemas de Fermi para sustentar secuencias de actividades promotoras de modelos matemáticos en el aula. En primer lugar, se describen las investigaciones desarrolladas en el seno de nuestro grupo de investigación, las cuales han permitido identificar el potencial de los problemas de Fermi como actividades de modelización matemática.

    Se detallan las herramientas de análisis desarrolladas para caracterizar los modelos que generan los alumnos, así como su uso en diversas investigaciones. En segundo lugar, se detalla la fundamentación teórica y las características de las secuencias de problemas de Fermi para promover la actividad de modelización matemática en las aulas de primaria y secundaria. Finalmente, se da cuenta de los estudios que muestran la utilidad de las secuencias de problemas de Fermi en la formación del profesorado, destacando su potencial para promover la flexibilidad en la resolución de problemas en futuros maestros.

  • English

    In this chapter, we summarize progress in research into the use of Fermi problems to support sequences of activities that promote mathematical modelling in the classroom. First, we describe the research carried out in our research group that has allowed us to identify the potential of Fermi problems as mathematical modelling activities. The analysis tools developed to characterize the models generated by the students and their use in different investigations are detailed. Secondly, the theoretical basis and characteristics of Fermi problem sequences for promoting mathematical modelling activities in primary and secondary schools are detailed. Finally, we report on studies that demonstrate the usefulness of Fermi problem sequences in teacher training, highlighting their potential to promote flexibility in problem solving in future teachers.

• Referencias bibliográficas
  • Abassian, A., Safi, F., Bush, S., & Bostic, J. (2020). Five different perspectives on mathematical modeling in mathematics education....
  • Albarracín, L. (2021). Large Number Estimation as a Vehicle to Promote Mathematical Modeling. Early Childhood Education Journal, 49(4), 681–691....
  • Albarracín, L., & Ärlebäck, J. B. (2019). Characterizing mathematical activities promoted by Fermi problems. For the Learning of Mathematics,...
  • Albarracín, L., Ferrando, I., & Gorgorió, N. (2021). The Role of Context for Characterising Students’ Strategies when Estimating Large...
  • Albarracín, L., & Gorgorió, N. (2013). Problemas de estimación de grandes cantidades: modelización e influencia del contexto. Revista...
  • Albarracín, L., & Gorgorió, N. (2014). Devising a plan to solve Fermi problems involving large numbers. Educational Studies in Mathematics,...
  • Albarracín, L., & Gorgorió, N. (2015). A brief guide to modelling in secondary school: estimating big numbers. Teaching Mathematics and...
  • Albarracín, L., & Gorgorió, N. (2018). Students estimating large quantities: From simple strategies to the population density model....
  • Albarracín, L., & Gorgorió, N. (2019). Using Large Number Estimation Problems in Primary Education Classrooms to Introduce Mathematical...
  • Albarracín, L., Segura, C., Ferrando, I., & Gorgorió, N. (2022). Supporting mathematical modelling by upscaling real context in a sequence...
  • Ärlebäck, J. B. (2009). On the use of realistic Fermi problems for introducing mathematical modelling in school. The Mathematics Enthusiast,...
  • Barahmeh, H. M., Hamad, A. M. B., & Barahmeh, N. M. (2017). The Effect of Fermi Questions in the Development of Science Processes Skills...
  • Baturo, A., & Nason, R. (1996). Students teachers’ subject matter knowledge within the domain of area measurement. Educational Studies...
  • Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of mathematical modelling and application,...
  • Blum, W., & Leisß, D. (2007). How do Students and Teachers Deal with Modelling Problems. En C. Haines, P. Galbraith, W. Blum, & S....
  • Borromeo Ferri, R. (2010). On the influence of mathematical thinking styles on learners’ modeling behavior. Journal für Mathematik-Didaktik,...
  • Borromeo Ferri, R. (2021). Mandatory Mathematical Modelling in School: What Do We Want the Teachers to Know?. En F. K. S. Leung, G. Stillman,...
  • Chapman, O. (2013). Mathematical-task knowledge for teaching. Journal of Mathematics Teacher Education, 16(1), 1-6. https://doi.org/g39zkk
  • Crouch, R., & Haines, C. (2007). Exemplar Models: Expert-Novice student behaviours. Mathematical Modelling: Education, Engineering and...
  • Czocher, J. A. (2016). Introducing modeling transition diagrams as a tool to connect mathematical modeling to mathematical thinking. Mathematical...
  • Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in...
  • Efthimiou, C. J., & Llewellyn, R. A. (2007). Cinema, Fermi problems and general education. Physics Education, 42(3), 253–261. https://doi.org/bxh3w4
  • Elia, I., van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem...
  • Ferrando, I. & Albarracín, L. (2021) Students from grade 2 to grade 10 solving a Fermi problem: analysis of emerging models. Mathematics...
  • Ferrando, I., Albarracín, L., Gallart, C., García-Raffi, L. M., & Gorgorió, N. (2017). Análisis de los modelos matemáticos producidos...
  • Ferrando, I., & Segura, C. (2020). Fomento de la flexibilidad matemática a través de una secuencia de tareas de modelización. Avances...
  • Ferrando, I., Segura, C., & Pla-Castells, M. (2020). Relations entre contexte, situation et schéma de résolution dans les problèmes d’estimation....
  • Ferrando, I., Segura, C., & Pla-Castells, M. (2021). Analysis of the relationship between context and solution plan in modelling tasks...
  • Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM,...
  • Gallart, C., Ferrando, I., García-Raffi, L. M., Albarracín, L., & Gorgorió, N. (2017). Design and implementation of a tool for analysing...
  • Greefrath, G., & Frenken, L. (2021). Fermi problems in standardized assessment in grade 8. Quadrante, 30(1), 52–73. https://doi.org/10.48489/quadrante.23587
  • Greer, B., Verschaffel, L., & Mukhopadhyay, S. (2007). Modelling for life: Mathematics and children’s experience. En W. Blum, W. Henne,...
  • Haberzettl, N., Klett, S., & Schukajlow, S. (2018). Mathematik rund um die Schule— Modellieren mit Fermi-Aufgaben. En K. Eilerts, &...
  • Henze, J., & Fritzlar, T. (2010). Primary school children’s model building processes by the example of Fermi questions. En A. Ambrus...
  • Heinze, A., Star, J.R., & Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education....
  • Hickendorff, M. (2022). Flexibility and Adaptivity in Arithmetic Strategy Use: What Children Know and What They Show. Journal of Numerical...
  • Huincahue-Arcos, J., Borromeo-Ferri, R., & Mena-Lorca, J. (2018). El conocimiento de la modelación matemática desde la reflexión en la...
  • Joram, E., Gabriele, A. J., Bertheau, M., Gelman, R., & Subrahmanyam, K. (2005). Children's use of the reference point strategy for...
  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302–310....
  • Klock, H., & Siller, H.-S. (2020). A Time-Based Measurement of the Intensity of Difficulties in the Modelling Process. En H. Wessels,...
  • Krawitz, J., Schukajlow, S., & Van Dooren, W. (2018). Unrealistic responses to realistic problems with missing information: What are...
  • Ko, P. Y., & Marton, F. (2004). Variation and the secret of the virtuoso. En F. Marton, & A. B. M. Tsui (Eds.), Classroom discourse...
  • Leikin, R., & Levav-Waynberg, A. (2008). Solution spaces of multiple-solution connecting tasks as a mirror of the development of mathematics...
  • Leiss, D., Plath, J., & Schwippert, K. (2019). Language and mathematics-key factors influencing the comprehension process in reality-based...
  • Lesh, R. A., & Doerr, H. M. (Eds.) (2003a). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning,...
  • Lesh, R. A., & Doerr, H. M. (2003b). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem...
  • Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2),...
  • Lesh, R. A., Hoover, M., Hole, B., Kelly, A. E., & Post, T. (2000). Principles for developing thought-revealing activities for students...
  • Montejo-Gámez, J., Fernández-Ahumada, E., & Adamuz-Povedano, N. (2021). A tool for the analysis and characterization of school mathematical...
  • Okamoto, H., Hartmann, M., & Kawasaki, T. (2023). Analysis of the Relationship between Creativity in Fermi Problems Measured by Applying...
  • Pla-Castells, M., & Ferrando, I. (2019). Downscaling and upscaling Fermi problems. En Jankvist, U. T., Van den Heuvel-Panhuizen, M.,...
  • Pollak, H. O. (1969). How can we teach application of mathematics? Educational Studies in Mathematics, 2,(2), 393–404. https://doi.org/10.1007/BF00303471...
  • Pólya, G. (1945). How to solve it. Princeton University Press. Raviv, D., Harris, A., & Dezotti, T. (2016). Estimation as an essential...
  • Schukajlow, S., Krug, A., & Rakoczy, K. (2015). Effects of prompting multiple solutions for modelling problems on students’ performance....
  • Schukajlow, S., Krawitz, J., Kanefke, J., Blum, W., & Radkocy, K. (2023). Open modelling problems: cognitive barriers and instructional...
  • Segura, C. (2022). Flexibilidad y rendimiento en la resolución de problemas de estimación en contexto real. Un estudio con futuros maestro....
  • Segura, C., & Ferrando, I. (2021). Classification and Analysis of Pre-Service Teachers’ Errors in Solving Fermi Problems. Education Sciences,...
  • Segura, C., & Ferrando, I. (2023). Pre-service teachers’ flexibility and performance in solving Fermi problems. Educational Studies in...
  • Segura, C., Ferrando, I., & Albarracín, L. (2021). Análisis de los factores de complejidad en planes de resolución individuales y resoluciones...
  • Segura, C., Ferrando, I., & Albarracín, L. (2023). Does collaborative and experiential work influence the solution of real-context estimation...
  • Sriraman, B., & Knott, L. (2009). The Mathematics of Estimation: Possibilities for Interdisciplinary Pedagogy and Social Consciousness....
  • Sriraman, B., & Lesh, R. (2006). Modeling conceptions revisited. ZDM, 38(3), 247–254. https://doi.org/10.1007/BF02652808
  • Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and instruction, 18(6),...
  • Stasson, M.F., Kameda, T., Parks, C.D., Zimmerman, S.K., & Davis, J.H. (1991). Effects of assigned group consensus requirement on group...
  • Taggart, G. L., Adams, P. E., Eltze, E., Heinrichs, J., Hohman, J., & Hickman, K. (2007). Fermi Questions. Mathematics Teaching in the...
  • Thompson, A. G. (1985). Teachers’ conceptions of mathematics and the teaching of problem solving. En E. A. Silver (Ed.), Teaching and learning...
  • Zawojewski, J. S., Lesh, R. A., & English, L. D. (2003). A models and modeling perspective on the role of small group learning activities....