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(ProQuest: ... denotes formulae omitted.)
Prelude
Imagine, if you will, a standard deck of 52 playing cards. Consider, now, the following two scenarios. Scenario 1: A card is drawn from the deck; the card is replaced; then a second card is drawn from the deck. What is the probability that the second card drawn is a king? The probability, in this particular scenario, Scenario 1, to no one's surprise, is 4/52 or, if you like, 1/13. Scenario 2: A card is drawn from the deck; the card is not replaced, but, rather, is placed face down beside the deck; then a second card is drawn from the deck. What is the probability that the second card drawn is a king?
Introduction
Jones, Langrall, and Mooney (2007), in their efforts "to inform the teaching and learning of probability by synthesizing research in the field" (p. 909), declared the "focus on both the classical and frequentist approaches to probability" (p. 913) as the strongest feature of the middle and high school mathematics curricula of Australia (All), the United Kingdom (UK), and the United States of America (USA). Subjective probability, a third interpretation of probability, briefly mentioned in the mathematics curricula of AU and the UK, was not considered one of the big ideas in probability for the middle and high school grades in the USA. At the end of their synthesis, the authors, speaking in more general terms, indicated that the research they reviewed calls for "a more unified development of the classical, frequentist and subjective approaches to probability" (p. 949). This particular call is not new.
Calls for a more unified approach to teaching and learning the varying probabilistic interpretations can be found in books (Burrill & Elliot, 2006; Chernoff & Sriraman, 2014; Jones, 2005; Kapadia & Borovcnik, 1991; Shulte & Smart, 1981), special journal issues (Biehler & Pratt, 2012; Borovcnik & Kapadia, 2009), and research syntheses (Borovcnik & Peard, 1996; Garfield & Ahlgren, 1988; Hawkins & Kapadia, 1984; Shaughnessy, 1992, 2003), dedicated to research on the teaching and learning of probability. Despite repeated efforts -for more than three decades -the calls continue, which is due, in part, to the hot mess that is subjective probability (Chernoff, 2014).
Subjective Probability
It appears difficult to pin...