Probabilistic Thinking

This volume provides a necessary, current and extensive analysis of probabilistic thinking from a number of mathematicians, mathematics educators, and psychologists. The work of 58 contributing authors, investigating probabilistic thinking across the globe, is encapsulated in 6 prefaces, 29 chapters and 6 commentaries. Ultimately, the four main perspectives presented in this volume (Mathematics and Philosophy, Psychology, Stochastics and Mathematics Education) are designed to represent probabilistic thinking in a greater context.Uncertainty is part of our lives and we all have to deal with it and make decisions in spite of it. Ability to use ideas from probability theory as a way of quantifying uncertainty needs to be an integral part of our education at many levels and this book will surely play a useful role. - S.R.Srinivasa Varadhan, Recipient of the 2007 Abel Prize in Mathematics and the 2010 National Medal of Science A welcome look at probability, with philosophical and psychological perspectives that offer foundations for both students and teachers of probability at the school and university levels. Very comprehensive and promises a great deal to the reader. Teachers and students will benefit from articles that clarify the competition between the frequentist and the Bayesian views of probability. - Reuben Hersh, Author of What is Mathematics, Really? and co-author of The Mathematical Experience I often get asked why people find probability so unintuitive and difficult. After years of research, I have concluded it's because probability really is unintuitive and difficult. This ground-breaking text acknowledges the full complexity of teaching this subject: the contributions face up to the competing interpretations of probability, emphasising the close connection to both human psychology and real-world problem-solving tasks. I am personally very pleased to see the subjective interpretation taken seriously, while also admiring the suggestions for teaching the properties of modeled randomness. A very timely and valuable book. -David Spiegelhalter, Winston Professor for the Public Understanding of Risk, University of Cambridge The teaching and learning of probability is challenging in several ways - coordinating its three theoretical perspectives (classical, frequentist, and subjective); managing its relationship to statistics; and reconciling the counter-intuitive nature of much probabilistic reasoning. This volume presents a comprehensive and in-depth review of this broad range of issues, by authors with the corresponding range of expertise and perspectives. It should be an invaluable resource for teachers of probability, at all levels. -Hyman Bass, Samuel Eilenberg Distinguished University Professor of Mathematics & Mathematics Education - University of Michigan