Commentary on the Chapters on Probability from a Stochastic Perspective

Abstract

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.