SWORD Weinstein, L. (2012). Guesstimation 2.0. doi:10.1515/9781400844661

[EN] Fermi problems have been widely used in Physics teaching at university level in the UnitedStates. Multiple recommendations for use in other educational areas can be found in theliterature, as the case of mathematical modeling introduction, but its presence in mathclassrooms has not been yet achieved. We present these problems and discuss about itsde nition and characteristics that make them particularly interesting for the use of mat-hematics in real contexts. We also review those aspects that have been investigated fromthe perspective of mathematics education, especially the way in which students generatemathematical models to solve them and we aim some directions that should be addressedin future research. Albarracín, L., & Gorgorió, N. (2014). Devising a plan to solve Fermi problems involving large numbers. Educational Studies in Mathematics, 86(1), 79-96. doi:10.1007/s10649-013-9528-9 Albarracín Lluís, Gorgorió Núria (2015a). 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In Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching, 3-33. Lawrence Erlbaum Associates. Lesh Richard, Hoover Mark, Hole Bonnie Kelly, Anthony and Post Thomas (2000). Principles for developing thought-revealing activities for students and teachers. In Handbook of research design in mathematics and science education, 591-645. Routledge Handbooks Online. Phillips, R., & Milo, R. (2009). A feeling for the numbers in biology. Proceedings of the National Academy of Sciences, 106(51), 21465-21471. doi:10.1073/pnas.0907732106 Poundstone William (2013). How Would You Move Mount Fuji?: Microsoft's Cult of the Puzzle. How the World's Smartest Companies Select the Most Creative Thinkers. Hachette Book Group. Reif, F., & St. John, M. (1979). Teaching physicists’ thinking skills in the laboratory. American Journal of Physics, 47(11), 950-957. doi:10.1119/1.11618 Ridgway Jim, Swan Malcolm, Burkhardt Hugh (2001). Assessing mathematical thinking via FLAG. In The teaching and learning of mathematics at university level, 423-430. Springer. Robinson, A. W. (2007). Don’t just stand there—teach Fermi problems! Physics Education, 43(1), 83-87. doi:10.1088/0031-9120/43/01/009 Schoenfeld Alan H. (1985). Mathematical problem solving. Orlando: Academic Press. Shakerin Said (2006). The art of estimation. International Journal of Engineering Education, 22 (2), 273-278. Siegel, A. W., Goldsmith, L. T., & Madson, C. R. (1982). Skill in Estimation Problems of Extent and Numerosity. Journal for Research in Mathematics Education, 13(3), 211. doi:10.2307/748557 Sriraman, B., & Knott, L. (2009). The Mathematics of Estimation: Possibilities for Interdisciplinary Pedagogy and Social Consciousness. Interchange, 40(2), 205-223. doi:10.1007/s10780-009-9090-7 Tangney Brendan, Bray Aibhín (2013). Mobile Technology, Maths Education & 21C Learning. 12th World Conference on Mobile and Contextual Learning, Bloomsbury Qatar Foundation Journals. Vul, E., & Pashler, H. (2008). Measuring the Crowd Within. Psychological Science, 19(7), 645-647. doi:10.1111/j.1467-9280.2008.02136.x Wagner, D., & Davis, B. (2010). Feeling number: grounding number sense in a sense of quantity. Educational Studies in Mathematics, 74(1), 39-51. doi:10.1007/s10649-009-9226-9 Weinstein Lawrence, Adam John A (2009). Guesstimation: Solving the world's problems on the back of a cocktail napkin. Princeton University Press. White, H. B. (2004). Math literacy. Biochemistry and Molecular Biology Education, 32(6), 410-411. doi:10.1002/bmb.2004.494032060415 Zawojewski Judith S., Lesh Richard A., English Lyn D (2003). A models and modeling perspective on the role of small group learning activities. 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Weiss Laura (2013). Les Questions de Fermi. Math-École 219, 41-47.

[ES] Los problemas de Fermi han sido ampliamente utilizados en la enseñanza de la Física a nivel universitario en Estados Unidos. En la literatura pueden encontrarse múltiples recomendaciones de uso en otros ámbitos educativos, como sería el caso de la introducción de la modelización matemática, pero todavía no se ha logrado su presencia en las aulas de matemáticas. En este artículo presentamos este tipo de problemas y discutimos sobre su definición y sus características, que los hacen especialmente interesantes para utilizar las matemáticas en contextos reales. También repasamos aquellos aspectos que ha sido investigados desde la perspectiva de la Educación Matemática, en especial la forma en la que los alumnos generan modelos matemáticos al resolverlos y apuntamos algunas direcciones que deberían ser tratadas en futuras investigaciones. Albarracín, L. (2017). Los problemas de Fermi como actividades para introducir la modelización: qué sabemos y qué más deberíamos saber. Modelling in Science Education and Learning. 10(2):117-136. doi:10.4995/msel.2017.7707 Albarracín Lluís, Lorente Cristina, Lopera, Antoni, Pérez Héctor, Gorgorió Núria (2015b). Problemas de estimación de grandes cantidades en las aulas de Educación Primaria. Epsilon: Revista de la Sociedad Andaluza de Educación Matemática Thales, 32 (89), 19-33. Albarracín, L., Chico, J., & Guinjoan, M. (2015). Aprendiendo a Enseñar Matemáticas a Partir de la Propia Experiencia. Procedia - Social and Behavioral Sciences, 196, 113-119. doi:10.1016/j.sbspro.2015.07.020 García Navarro Juan Manuel (2013). Problemas de Fermi. Suposición, estimación y aproximación. Revista de la Sociedad Andaluza de Educación Matemática Thales 84, 57-68.

Weiss Laura (2013). Questions from Fermi. Math-Ecole 219, 41-47.

Fermi problems as tasks to introducemodelling: what we know and what else weshould know

Los problemas de Fermi como actividades para introducir la modelización: qué sabemos y qué más deberíamos saber

Abstract