Commentary on Probabilistic Thinking: Presenting Plural Perspectives
Those of you familiar with research investigating probabilistic thinking in the field of mathematics education, might, at this point in the book, be expecting a “wish list” for future research, which has become customary (e.g., Kapadia and Borovcnik 1991
- PDF / 153,512 Bytes
- 7 Pages / 441 x 666 pts Page_size
- 47 Downloads / 235 Views
Martin Gardner’s writing is amazingly accurate and reliable. The fact that he made a mistake is simply a testimonial to the difficulty of the [Two Child] problem. (Khovanova 2011, p. 1) But, to my surprise, Erdös said, “No, that is impossible, it should make no difference”. . . Erdös objected that he still did not understand the reason why, but [after being shown a simulation of the Monty Hall Problem] was reluctantly convinced that I was right. (Vazsonyi 1999, p. 18)
The above quotations and, more notably, the individuals involved, help cement the popular notion that probability is counterintuitive—just “Ask Marilyn”. However, as demonstrated throughout this volume, counterintuitiveness is but one of many different characteristics of probabilistic thinking. Those of you familiar with research investigating probabilistic thinking in the field of mathematics education, might, at this point in the book, be expecting a “wish list” for future research, which has become customary (e.g., Kapadia and Borovcnik 1991; Jones et al. 2007; Shaughnessy 1992); however, we will not be adding to the list of wish lists. Instead, we have decided to, in this commentary, highlight some of the overarching themes that have emerged from the significant amount of research housed in this volume. Themes emerging from each of the four main perspectives—Mathematics and Philosophy, Psychology, Stochastics and Mathematics Education—are now commented on in turn.
E.J. Chernoff (B) University of Saskatchewan, Saskatoon, Saskatchewan, Canada e-mail: [email protected] B. Sriraman The University of Montana, Missoula, MT, 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_38, © Springer Science+Business Media Dordrecht 2014
721
722
E.J. Chernoff and B. Sriraman
1 Perspective I: Mathematics and Philosophy There are three themes emerging from Perspective I: Mathematics and Philosophy that we wish to highlight. The themes are: different philosophical interpretations of probability, modeling, and subjective probability. The classical, frequentist, and subjective interpretations of probability, which we denote The Big Three, are addressed (to varying degrees) in nearly every chapter and in every perspective of this volume. Worthy of note, and not something that we would consider censoring with our editorial hand, this volume continues to see different researchers utilizing different terminology when referring to The Big Three (see, for example, Borovcnik and Kapadia, this volume). Although not censored, issues inherent in the use of different terminology are discussed in this volume (see, for example, Chernoff and Russell). While the terminology associated with The Big Three has not been solidified in this volume, many authors, within their chapters, have clearly defined their philosophical positions relative to The Big Three. Other authors in this volume, (perhaps) heeding the repeated calls for unification found in the mathematics educat
Data Loading...
