Abstract
In this chapter, we argue for three interconnected ways of thinking about probability—“true” probability, model probability, and empirical probability—and for attention to notions of “good”, “poor” and “no” model. We illustrate these ways of thinking from the simple situation of throwing a die to the more complex situation of modelling bed numbers in an intensive care unit, which applied probabilists might consider. We then propose a reference framework for the purpose of thinking about the teaching and learning of probability from a modelling perspective and demonstrate with examples the thinking underpinning the framework. Against this framework we analyse a theory-driven and a data-driven learning approach to probability modelling used by two research groups in the probability education field. The implications of our analysis of these research groups’ approach to learning probability and of our framework and ways of thinking about probability for teaching are discussed.
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References
Abrahamson, D. (2006). Learning chance: lessons form a learning-axes and bridging tools perspective. In A. Rossman & B. Chance (Eds.), Proceedings of the seventh international conference on teaching statistics, Working cooperatively in statistics education, Salvador, Brazil, July 2006, Voorburg: International Statistical Institute. Online: http://www.stat.auckland.ac.nz/~iase/publications.php.
Batanero, C., & Sanchez, E. (2005). What is the nature of high school students’ conceptions and misconceptions about probability? In G. Jones (Ed.), Exploring probability in school: challenges for teaching and learning (pp. 241–266). New York: Springer.
Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. In G. Jones (Ed.), Exploring probability in school: challenges for teaching and learning (pp. 15–37). New York: Springer.
Borovcnik, M. (2006). Probabilistic and statistical thinking. In M. Bosch (Ed.), Proceedings of the fourth congress of the European Society for Research in Mathematics Education, Sant Feliu de Guixols, Spain, 17–21 February 2005 (pp. 484–506). http://ermeweb.free.fr/CERME4/.
Borovcnik, M. (2011). Strengthening the role of probability within statistics curricula. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics—challenges for teaching and teacher education: a joint ICMI/IASE study: the 18th ICMI study (pp. 71–83). New York: Springer.
Borovcnik, M., & Kapadia, R. (2011). Modelling in probability and statistics. In J. Maasz & J. O’Donoghue (Eds.), Real-world problems for secondary school mathematics students: case studies (pp. 1–43). Rotterdam: Sense Publishers.
Chaput, B., Girard, J., & Henry, M. (2011). Frequentist approach: modelling and simulation in statistics and probability teaching. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics—challenges for teaching and teacher education: a joint ICMI/IASE study: the 18th ICMI study (pp. 85–95). New York: Springer.
Chen, W., Frew, K., Ihaka, R., McKee, A., & Ziedins, I. (2011). Simulation and capacity planning for a cardio-vascular intensive care unit (in preparation).
Greer, B., & Mukhopadhyay, S. (2005). Teaching and learning the mathematization of uncertainty: historical, cultural, social, and political contexts. In G. Jones (Ed.), Exploring probability in school: challenges for teaching and learning (pp. 297–324). New York: Springer.
Ireland, S., & Watson, J. (2009). Building a connection between experimental and theoretical aspects of probability. International Electronic Journal of Mathematics Education, 4(3), 339–370.
Jones, G. (2005). Introduction. In G. Jones (Ed.), Exploring probability in school: challenges for teaching and learning (pp. 1–12). New York: Springer.
Kahneman, D., Slovic, P., & Tversky, A. (Eds.) (1982). Judgment under uncertainty: heuristics and biases. New York: Press Syndicate of the University of Cambridge.
Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6(1), 59–98.
Konold, C., & Kazak, S. (2008). Reconnecting data and chance. Technology Innovations in Statistics Education, 2(1). http://escholarship.org/uc/item/38p7c94v.
Konold, C., & Miller, C. D. (2005). TinkerPlots: dynamic data exploration. Emeryville: Key Curriculum.
Konold, C., Harradine, A., & Kazak, S. (2007). Understanding distributions by modeling them. International Journal of Computers for Mathematical Learning, 12, 195–216.
Konold, C., Madden, S., Pollatsek, A., Pfannkuch, M., Wild, C., Ziedins, I., Finzer, W., Horton, N. J., & Kazak, S. (2011). Conceptual challenges in coordinating theoretical and data-centered estimates of probability. Mathematical Thinking and Learning, 13 (1&2), 68–86.
Lecoutre, M. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23, 557–568.
Lee, H., & Lee, J. (2009). Reasoning about probabilistic phenomenon: lessons learned and applied in software design. Technology Innovations in Statistics Education, 3(2). http://escholarship.org/uc/item/1b54h9s9.
Lehrer, R., Kim, M., & Schauble, L. (2007). Supporting the development of conceptions of statistics by engaging students in measuring and modeling variability. International Journal of Computers for Mathematical Learning, 12, 195–216.
Liu, Y., & Thompson, P. (2007). Teachers’ understandings of probability. Cognition and Instruction, 25(2), 113–160.
Nickerson, R. (2004). Cognition and chance: the psychology of probabilistic reasoning. Mahwah: Erlbaum.
Pratt, D. (2005). How do teachers foster students’ understanding of probability? In G. Jones (Ed.), Exploring probability in school: challenges for teaching and learning (pp. 171–190). New York: Springer.
Shaughnessy, M. (2003). Research on students’ understandings of probability. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 216–226). Reston: National Council of Teachers of Mathematics.
Stohl, H., & Tarr, J. E. (2002). Developing notions of inference using probability simulation tools. Journal of Mathematical Behavior, 21(3), 319–337.
Watson, J. (2005). The probabilistic reasoning of middle school students. In G. Jones (Ed.), Exploring probability in school: challenges for teaching and learning (pp. 145–170). New York: Springer.
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Pfannkuch, M., Ziedins, I. (2014). A Modelling Perspective on Probability. In: Chernoff, E., Sriraman, B. (eds) Probabilistic Thinking. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7155-0_5
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DOI: https://doi.org/10.1007/978-94-007-7155-0_5
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