Description 
1 online resource (746 pages) : illustrations 
Series 
Advances in mathematics education 

Advances in mathematics education (Springer (Firm))

Contents 
SERIES PREFACE: Gabriele Kaiser and Bharath Sriraman  ACKNOWLEDGEMENTS  FOREWORD: Keith Devlin  INTRODUCTION: Egan Chernoff and Bharath Sriraman  PERSPECTIVE I: MATHEMATICS AND PHILOSOPHY  Preface to Perspective I: Mathematics and Philosophy: Egan Chernoff and Gale Russell  I.I.A historical and philosophical perspective on probability: Manfred Borovcnik and Ramesh Kapadia  I. II. From puzzles and paradoxes to concepts in probability: Manfred Borovcnik and Ramesh Kapadia  I. III. Three approaches for modeling situation with randomness: Andreas Eichler and Markus Vogel  I. IV. A modeling perspective on probability: Maxine Pfannkuch and Ilze Ziedins  Commentary on Perspective I: Mathematics and Philosophy: Bharath Sriraman and KyeongHwa Lee  PERSPECTIVE II: PSYCHOLOGY  Preface to Perspective II: Psychology : Wim van Dooren  II. I. Statistical thinking: no child left behind: Björn Meder and Gerd Gigerenzer  II. II. The ABC of probabilistic literacy: Laura Martignon  II. III. Intuitive conceptions of probability and the development of basic math skills: Gary Brase, Sherri Martinie and Carlos CastilloGarsow  II. IV. Testing a model on probabilistic reasoning: Francesca Chiesi and Caterina Primi  II. V. Revisiting the medical diagnosis problem: reconciling intuitive and analytical thinking: Lisser Rye Ejersbo and Uri Leron  II. VI. Rethinking probability education: perceptual judgment as epistemic resource: Dor Abrahamson  II. VII. Sticking to your guns: a flawed heuristic for probabilistic decisionmaking: Deborah Bennett  II. VIII. Developing probabilistic thinking: what about peoples' conceptions: Annie Savard  Commentary I on Perspective II: Psychology : Brian Greer  Commentary II on Perspective II: Psychology: Richard Lesh and Bharath Sriraman  PERSPECTIVE III: STOCHASTICS  Preface to Perspective III: Stochastics: Bharath Sriraman and Egan Chernoff  III. I. Prospective primary school teachers' perception of randomness: Carmen Batanero, Pedro Arteaga, Luis Serrano and Blanca Ruiz  III. II. Challenges of developing coherent probabilistic reasoning: rethinking randomness and probability from a stochastic perspective: Luis Saldanha and Yan Liu  III. III. 'It is very, very random because it doesn't happen very often': examining learners' discourse on randomness: Simin Jolafee, Rina Zazkis and Nathalie Sinclair  III. IV. Developing a modelling approach to probability using computerbased simulations: Theodosia Prodromou  III. V. Promoting statistical literacy through data modelling in the early school years: Lyn D. English  III. VI. Learning Bayesian statistics in adulthood: WolffMichael Roth  Commentary on Perspective III: Stochastics: Mike Shaughnessy  PERSPECTIVE IV: MATHEMATICS EDUCATION  Preface to Perspective IV: Mathematics Education: Bharath Sriraman and Egan Chernoff  IV. I.A practitional perspective on probabilistic thinking models and frameworks: Edward S. Mooney, Cynthia Langrall and Joshua T. Hertel  IV. II. Experimentation in probability teaching and learning: Per Nilsson  IV. III. Investigating the dynamics of stochastic learning processes: Susanne Prediger and Susanne Schnell  IV. IV. Counting as a foundation for learning to reason about probability: Carolyn A. Maher and Anoop Ahluwalia  IV. V. Levels of probabilistic reasoning of high school students about binomial problems: Ernesto Sánchez and Pedro Rubén Landín  IV. VI. Children's construction of sample space with respect to the law of large numbers: Efi Paparistodemou  IV. VII. Researching conditional probability problem solving: Pedro Huerta  IV. VIII. Real life experiences as hindrance in probabilistic situations: Ami Mamolo and Rina Zazkis  IV. IX. Influence of culture on high school students' probabilistic thinking: Sashi Sharma  IV. X. Primary school students' attitudes to and beliefs about probability: Steven Nisbet and Anne Williams  Commentary on Perspective IV: Mathematics Education: Jane Watson  COMMENTARY on Probabilistic Thinking: Presenting Plural Perspectives: Egan Chernoff and Bharath Sriraman  AUTHOR INDEX  SUBJECT INDEX 
Summary 
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 coauthor 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 groundbreaking 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 realworld problemsolving 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 counterintuitive nature of much probabilistic reasoning. This volume presents a comprehensive and indepth 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 
Bibliography 
Includes bibliographical references and index 
Subject 
Education.


Education  Philosophy.


Distribution (Probability theory)


Mathematics.

Form 
Electronic book

Author 
Chernoff, Egan J.


Sriraman, Bharath.

ISBN 
9400771541 (hard cover ;) (alk. paper) 

940077155X (electronic bk.) 

9789400771543 (hard cover ;) (alk. paper) 

9789400771550 (electronic bk.) 

(hard cover ;) (alk. paper) 
