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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.

DOI: 10.1007/978-94-007-7155-0_5

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