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Probabilistic thinking
presenting plural perspectives
Abstract
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
Details | Table of Contents
mathematics and philosophy
pp.3-5
https://doi.org/10.1007/978-94-007-7155-0_1pp.7-34
https://doi.org/10.1007/978-94-007-7155-0_2pp.35-73
https://doi.org/10.1007/978-94-007-7155-0_3pp.75-99
https://doi.org/10.1007/978-94-007-7155-0_4the humanistic dimensions of probability
pp.117-119
https://doi.org/10.1007/978-94-007-7155-0_6analyses from a psychological perspective
pp.123-126
https://doi.org/10.1007/978-94-007-7155-0_7no one left behind
pp.127-148
https://doi.org/10.1007/978-94-007-7155-0_8pp.149-160
https://doi.org/10.1007/978-94-007-7155-0_9pp.161-194
https://doi.org/10.1007/978-94-007-7155-0_10a test of a model
pp.195-214
https://doi.org/10.1007/978-94-007-7155-0_11perceptual judgment as epistemic resource
pp.239-260
https://doi.org/10.1007/978-94-007-7155-0_13a flawed heuristic for probabilistic decision-making
pp.261-281
https://doi.org/10.1007/978-94-007-7155-0_14what about people's conceptions?
pp.283-298
https://doi.org/10.1007/978-94-007-7155-0_15psychology
pp.299-309
https://doi.org/10.1007/978-94-007-7155-0_16pp.311-340
https://doi.org/10.1007/978-94-007-7155-0_17stochastics
pp.343-344
https://doi.org/10.1007/978-94-007-7155-0_18pp.345-366
https://doi.org/10.1007/978-94-007-7155-0_19rethinking randomness and probability from a stochastic perspective
pp.367-396
https://doi.org/10.1007/978-94-007-7155-0_20examining learners' discourse on randomness
pp.397-416
https://doi.org/10.1007/978-94-007-7155-0_21pp.417-439
https://doi.org/10.1007/978-94-007-7155-0_22pp.441-457
https://doi.org/10.1007/978-94-007-7155-0_23pp.481-489
https://doi.org/10.1007/978-94-007-7155-0_25mathematics education
pp.493-494
https://doi.org/10.1007/978-94-007-7155-0_26pp.495-507
https://doi.org/10.1007/978-94-007-7155-0_27pp.509-532
https://doi.org/10.1007/978-94-007-7155-0_28a didactical research perspective, its methodological and theoretical framework, illustrated for the case of the short term–long term distinction
pp.533-558
https://doi.org/10.1007/978-94-007-7155-0_29pp.559-580
https://doi.org/10.1007/978-94-007-7155-0_30pp.581-597
https://doi.org/10.1007/978-94-007-7155-0_31pp.599-612
https://doi.org/10.1007/978-94-007-7155-0_32pp.613-639
https://doi.org/10.1007/978-94-007-7155-0_33an aid or a hindrance?
pp.641-656
https://doi.org/10.1007/978-94-007-7155-0_34pp.683-708
https://doi.org/10.1007/978-94-007-7155-0_36the perspective of mathematics education
pp.709-720
https://doi.org/10.1007/978-94-007-7155-0_37presenting plural perspectives
pp.721-727
https://doi.org/10.1007/978-94-007-7155-0_38Publication details
Publisher: Springer
Place: Dordrecht
Year: 2014
Pages: 747
Series: Advances in Mathematics Education
ISBN (hardback): 978-94-007-7154-3
ISBN (digital): 978-94-007-7155-0
Full citation:
Chernoff Egan J., Sriraman Bharath (2014) Probabilistic thinking: presenting plural perspectives. Dordrecht, Springer.