Probabilistic thinking : presenting plural perspectives

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.

Series PrefaceGabriele Kaiser and Bharath Sriraman

Acknowledgements

ForewordKeith Devlin

IntroductionEgan Chernoff and Bharath Sriraman

Perspective I: Mathematics And Philosophy

Preface to Perspective I: Mathematics and PhilosophyEgan Chernoff and Gale Russell

I.I A historical and philosophical perspective on probabilityManfred 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 randomnessAndreas Eichler and Markus Vogel

I.IV A modeling perspective on probabilityMaxine Pfannkuch and Ilze Ziedins

Commentary on Perspective I: Mathematics and PhilosophyBharath Sriraman and Kyeong-Hwa Lee

Perspective II: Psychology

Preface to Perspective II: PsychologyWim van Dooren

II.I Statistical thinking: no child left behindBjrn Meder and Gerd Gigerenzer

II.II The A-B-C of probabilistic literacyLaura Martignon

II.III Intuitive conceptions of probability and the development of basic math skillsGary Brase and Sherri Martinie and Carlos Castillo-Garsow

II.IV Testing a model on probabilistic reasoningFrancesca Chiesi and Caterina Primi

II.V Revisiting the medical diagnosis problem: reconciling intuitive and analytical thinkingLisser Rye Ejersbo and Uri Leron

II.VI Rethinking probability education: perceptual judgment as epistemic resourceDor Abrahamson

II.VII Sticking to your guns: a flawed heuristic for probabilistic decision-makingDeborah Bennett

II.VIII Developing probabilistic thinking: what about peoples' conceptionsAnnie Savard

Commentary I on Perspective II: PsychologyBrian Greer

Commentary II on Perspective II: PsychologyRichard Lesh and Bharath Sriraman

PERSPECTIVE III: STOCHASTICS

Preface to Perspective III: StochasticsBharath Sriraman and Egan Chernoff

III.I Prospective primary school teachers' perception of randomnessCarmen Batanero and Pedro Arteaga and Luis Serrano and Blanca Ruiz

III.II Challenges of developing coherent probabilistic reasoning: rethinking randomness and probability from a stochastic perspectiveLuis Saldanha and Yan Liu

III.III "It is very, very random because it doesn't happen very often": examining learners' discourse on randomnessSimin Jolafee and Rina Zazkis and Nathalie Sinclair

III.IV Developing a modelling approach to probability using computer-based simulationsTheodosia Prodromou

III.V Promoting statistical literacy through data modelling in the early school years Lyn D Lyn, DLyn D

III.VI Learning Bayesian statistics in adulthoodWolff-Michael Roth

Commentary on Perspective III: StochasticsMike Shaughnessy

PERSPECTIVE IV: MATHEMATICS EDUCATION

Preface to Perspective IV: Mathematics EducationBharath Sriraman and Egan Chernoff

IV.I A practitional perspective on probabilistic thinking models and frameworks Edward S Edward, SEdward S

IV.II Experimentation in probability teaching and learningPer Nilsson

IV.III Investigating the dynamics of stochastic learning processesSusanne Prediger and Susanne Schnell

IV.IV Counting as a foundation for learning to reason about probabilityCarolyn A. Maher and Anoop Ahluwalia

IV.V Levels of probabilistic reasoning of high school students about binomial problemsErnesto Snchez and Pedro Rubn Landn

IV.VI Children's construction of sample space with respect to the law of large numbersEfi Paparistodemou

IV.VII Researching conditional probability problem solvingPedro Huerta

IV.VIII Real life experiences as hindrance in probabilistic situationsAmi Mamolo and Rina Zazkis

IV.IX Influence of culture on high school students' probabilistic thinkingSashi Sharma

IV.X Primary school students' attitudes to and beliefs about probabilitySteven Nisbet and Anne Williams

Commentary on Perspective IV: Mathematics EducationJane Watson

COMMENTARY on Probabilistic Thinking: Presenting Plural PerspectivesEgan Chernoff and Bharath Sriraman

Author Index

Subject Index

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Summary

Summary

Table of Contents