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The concept of probability plays a vital role in mathematics and scientific research, as well as in our everyday lives. It has also become one of the fastest growing segments of high school and college curricula, yet learning probability within school contexts has proved more difficult than many in education realize.This chapter is in two broad parts. The first part synthesizes a discussion of randomness and probability that is situated at the nexus of bodies of literature concerned with the ontology of stochastic events and epistemology of probabilistic ideas held by people. Our synthesis foregrounds philosophical, mathematical, and psychological debates about the meaning of randomness and probability that highlight their deeply problematic nature, and therefore raises the equally problematic question of how instruction might support students' understanding of them. We propose an approach to the design of probability instruction that focuses on the development of coherent meanings of randomness and probability—that is, schemes composed of imagery and conceptual operations that stand to support students' coherent thinking and reasoning about situations that we see as entailing randomness and probability. The second part of the chapter reports on aspects of a sequence of classroom teaching experiments in high school that employed such an instructional approach. We draw on evidence from these experiments to highlight challenges in learning and teaching stochastic conceptions of probability. Our students' challenges centered on re-construing given situations as idealized random experiments involving the conceptualization of an unambiguous and essentially repeatable trial, as a basis for conceiving of the probability of an event as its anticipated long-run relative frequency.

DOI: 10.1007/978-94-007-7155-0_20

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