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

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<http://hdl.handle.net/10251/90060>
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Abstract

[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). On the role of inconceivable magnitude estimation problems to improve critical thinking. Educational Paths to Mathematics. Springer, 263-277. Albarracín, L., & Gorgorió, N. (2015). A brief guide to modelling in secondary school: estimating big numbers. Teaching Mathematics and its Applications, 34(4), 223-228. doi:10.1093/teamat/hrv006 Anderson P. and Sherman C. (2010). A Simplified Method of Fermi Estimation for the Student Innovator. Proceedings of the 14th Annual Conference of the National Collegiate Inventors and Innovators Alliance. Ärlebäck Jonas Bergman (2009). On the use of realistic Fermi problems for introducing mathematical modelling in school. The Mathematics Enthusiast 6 (3), 331-364. Ärlebäck Jonas Bergman (2011). Exploring the solving process of groups solving realistic Fermi problem from the perspective of the anthropological theory of didactics. Proceedings of the seventh congress of the European society for research in mathematics education, 1010-1019. Blum Werner, Leiss Dominik (2007). How do students and teachers deal with modelling problems. Mathematical Modelling (ICTMA 12): Education, Engineering and Economics, 222-231. Czocher, J. A. (2016). Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking. Mathematical Thinking and Learning, 18(2), 77-106. doi:10.1080/10986065.2016.1148530 Fuglestad Anne Berit, Goodchild, Simon (2008). Affordances of inquiry: the case of one teacher. Proceedings of PME32, 3, 49-56. Joram Elana, Gabriele Anthony J, Bertheau Myrna, Gelman Rochel, Subrahmanyam Kaveri (2005). Children's use of the reference point strategy for measurement estimation. Journal for Research in Mathematics Education, 4-23. Lesh Richard, Doerr Helen (2003). Foundations of a model and modeling perspective on mathematics teaching, learning, and problem solving. 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. In Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching, 337-358. Lawrence Erlbaum Associates.

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