Abstract
In this chapter, we introduce inconceivable magnitude estimation problems as a subgroup of Fermi problems. The problems we use in our study require counting the amount of people in different situations. Based on the experience of a classroom activity carried out with 15-year-old students, we describe the process they went through to solve the problems, and discuss in which ways these problems provide knowledge to critically analyse the information that appears in the media.
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References
Albarracín, L. (2011). Sobre les estratègies de resolució de problemes d’estimació de magnituds no abastables. Unpublished PhD thesis, Universitat Autònoma de Barcelona.
Albarracín, L., & Gorgorió, N. (2012). Inconceivable magnitude estimation problems: An opportunity to introduce modelling in secondary school. Journal of Mathematical Modelling and Application, 1(7), 20–33.
Albarracín, L., & Gorgorió, N. (2014). Devising a plan to solve Fermi problems involving large numbers. Educational Studies in Mathematics, 86(1), 79–96.
Arcavi, A. (2002). The everyday and the academic in mathematics. In M. Brenner & J. Moschkovich (Eds.), Everyday and academic mathematics in the classroom (pp. 12–29). Reston: NCTM.
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.
Ärlebäck, J. B. (2011). Exploring the solving process of groups solving realistic Fermi problem from the perspective of the anthropological theory of didactics. In M. Pytlak, E. Swoboda, & T. Rowland (Eds.), Proceedings of the seventh congress of the European society for research in mathematics education (pp. 1010–1019). Rzeszów: University of Rzeszów.
Camelo, F., Mancera, G., Romero, J., García, G., & Valero, P. (2010). The importance of the relation between the socio-political context, interdisciplinarity and the learning of the mathematics. In U. Gellert, E. Jablonka, & C. Morgan (Eds.), Proceedings of the 6th international mathematics education and society conference (pp. 199–208). Berlin: Freie Universität Berlin.
Carter, H. L. (1986). Linking estimation to psychological variables in the early years. In H. L. Schoen & M. J. Zweng (Eds.), Estimation and mental computation (pp. 74–81). Reston: NCTM.
Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62(2), 211–230.
Diamond, L. J., & Plattner, M. F. (2006). Electoral systems and democracy. Baltimore: Johns Hopkins University Press.
Efthimiou, C. J., & Llewellyn, R. A. (2007). Cinema, Fermi problems and general education. Physics Education, 42(3), 253–261.
English, L. D. (2006). Mathematical modeling in the primary school. Educational Studies in Mathematics, 63(3), 303–323.
Esteley, C. B., Villarreal, M. E., & Alagia, H. R. (2010). The overgeneralization of linear models among university students’ mathematical productions: A long-term study. Mathematical Thinking and Learning, 12(1), 86–108.
Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Kluwer.
Hogan, T. P., & Brezinski, K. L. (2003). Quantitative estimation: One, two, or three abilities? Mathematical Thinking and Learning, 5(4), 259–280.
Jurdak, M. E. (2006). Contrasting perspectives and performance of high school students on problem solving in real world situated, and school contexts. Educational Studies in Mathematics, 63(3), 283–301.
Jurdak, M., & Shahin, I. (1999). An ethnographic study of the computational strategies of a group of young street vendors in Beirut. Educational Studies in Mathematics, 40(2), 155–172.
Jurdak, M., & Shahin, I. (2001). Problem solving activity in the workplace and the school: The case of constructing solids. Educational Studies in Mathematics, 47(3), 297–315.
Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2), 157–189.
Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press.
Palm, T. (2006). Word problems as simulations of real-world situations: A proposed framework. For the Learning of Mathematics, 26(1), 42–47.
Palm, T. (2008). Impact of authenticity on sense making in word problem solving. Educational Studies in Mathematics, 67(1), 37–58.
Stocker, D. (2006). Re-thinking real-world mathematics. For the Learning of Mathematics, 26(2), 29–29.
Van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessment problems in mathematics. For the Learning of Mathematics, 25(2), 2–10.
Verschaffel, L. (2002). Taking the modeling perspective seriously at the elementary level: Promises and pitfalls. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th PME international conference (pp. 64–80). Norwich: PME.
Weinstein, L., & Adam, J. A. (2008). Guesstimation: Solving the world’s problems on the back of a cocktail napkin. Princeton: Princeton University Press.
Winter, H. (1994). Modelle als Konstrukte zwischen lebensweltlichen Situationen und arithmetischen Begriffen. Grundschule, 26(3), 10–13.
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Albarracín, L., Gorgorió, N. (2015). On the Role of Inconceivable Magnitude Estimation Problems to Improve Critical Thinking. In: Gellert, U., Giménez Rodríguez, J., Hahn, C., Kafoussi, S. (eds) Educational Paths to Mathematics. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-15410-7_17
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