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1 Introduction The predominant probability perspective of authors in this section of the book arises from the oft ill-defined constructs “stochastic” and “random.” The four chapters authored by Batanero, Arteaga, Serrano, and Ruiz, Saldanha and Liu, Jolfaee, Zaskis, and Sinclair, and Prodromou all rely on the meanings of these two terms from various points of view and for various purposes. Discussions of ‘stochastic’ and ‘random’ are presented in these four chapters with reference to historical, developmental, and modeling perspectives, as these authors present research results on both teachers’ and students’ conceptions and interpretations of randomness. The chapters by English and Roth have a different focus than these four. English argues that young children not only can but should have experiences with constructing their own structures and representations of data. Roth’s thesis is that a Bayesian approach to probability should be included in introductory statistics courses. While English’s work with young children provides a basis from which to build toward the development of future connections between probability and statistics, the Roth chapter has little if any connection to a stochastic perspective of probability. Prior to further reflection on the individual chapters in this section, I want to attempt some synthesis of such terms as stochastic, random, and probability from this collection of authors to provide a lens for reflecting on their contributions.

2 Stochastic The word ‘stochastic’ is regarded as an adjective in dictionaries. Among its meanings are: random; involving probability; involving guesswork. In mathematics and J.M. Shaughnessy (B) 2820 SW Huber St, Portland, OR 97219, USA e-mail: [email protected] E.J. Chernoff, B. Sriraman (eds.), Probabilistic Thinking, Advances in Mathematics Education, DOI 10.1007/978-94-007-7155-0_25, © Springer Science+Business Media Dordrecht 2014

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statistics, one refers to ‘stochastic processes’, which involve repeatable trials and possibly branching systems where each branch is assigned a probability for a path leading to a subsequent trial. It is interesting that one of the meanings of ‘stochastic’ is ‘random’, for these terms can become circular in their meaning or in our everyday language. In the teaching and learning of probability and statistics, the word ‘stochastics’ has come into popular use, especially in Europe. The word has now become a noun used by both psychologists and educators in statistics education research and in curriculum development. Generally, the word ‘stochastics’ is now often used as shorthand for ‘probability and statistics.’ However, with such a generalization of the word we can lose its original meaning. Saldanha points to the distinction made by Liu and Thompson (2007) between a stochastic and a non-stochastic conception of events. Stochastic events involve an underlying repeatable process, as opposed to a one time, non-repeatable event. Pulling samples of people from a population (say, a city) to measure so