Springer | 2014 | 746 páginas | RAR- pdf | 9,1 Mb
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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.
Contents
Perspective I: Mathematics and Philosophy
Preface to Perspective I: Mathematics and Philosophy . . 3
Egan J. Chernoff and Gale L. Russell
A Historical and Philosophical Perspective on Probability . . 7
Manfred Borovcnik and Ramesh Kapadia
From Puzzles and Paradoxes to Concepts in Probability . . 35
Manfred Borovcnik and Ramesh Kapadia
Three Approaches for Modelling Situations with Randomness . . 75
Andreas Eichler and Markus Vogel
A Modelling Perspective on Probability . . 101
Maxine Pfannkuch and Ilze Ziedins
Commentary on Perspective I: The Humanistic Dimensions of Probability . . 117
Bharath Sriraman and Kyeonghwa Lee
Perspective II: Psychology
Probabilistic Thinking: Analyses from a Psychological Perspective . . . 123
Wim Van Dooren
Statistical Thinking: No One Left Behind . . 127
Björn Meder and Gerd Gigerenzer
Fostering Children’s Probabilistic Reasoning and First Elements of Risk Evaluation . . 149
Laura Martignon
Intuitive Conceptions of Probability and the Development of Basic Math Skills . . . 161
Gary L. Brase, Sherri Martinie, and Carlos Castillo-Garsow
The Interplay Among Knowledge, Cognitive Abilities and Thinking Styles in Probabilistic Reasoning: A Test of a Model . . 195
Francesca Chiesi and Caterina Primi
Revisiting the Medical Diagnosis Problem: Reconciling Intuitive and Analytical Thinking .215
Lisser Rye Ejersbo and Uri Leron
Rethinking Probability Education: Perceptual Judgment as Epistemic Resource . . 239
Dor Abrahamson
Sticking to Your Guns: A Flawed Heuristic for Probabilistic Decision-Making . . 261
Deborah Bennett
Developing Probabilistic Thinking: What About People’s Conceptions? 283
Annie Savard
Commentary on Perspective II: Psychology . . 299
Brian Greer
A Brief Overview and Critique of Perspective II on Probabilistic and Statistical Reasoning . . . 311
Richard Lesh and Bharath Sriraman
Perspective III: Stochastics
Preface to Perspective III: Stochastics . . . 343
Egan J. Chernoff and Gale L. Russell
Prospective Primary School Teachers’ Perception of Randomness . . . 345
Carmen Batanero, Pedro Arteaga, Luis Serrano, and Blanca Ruiz
Challenges of Developing Coherent Probabilistic Reasoning: Rethinking Randomness and Probability from a Stochastic Perspective . . 367
Luis Saldanha and Yan Liu
“It Is Very, Very Random Because It Doesn’t Happen Very Often”: Examining Learners’ Discourse on Randomness . . 397
Simin Jolfaee, Rina Zazkis, and Nathalie Sinclair
Developing a Modelling Approach to Probability Using Computer-Based Simulations . . 417
Theodosia Prodromou
Promoting Statistical Literacy Through Data Modelling in the Early School Years . . 441
Lyn D. English
Learning Bayesian Statistics in Adulthood . . . 459
Wolff-Michael Roth
Commentary on the Chapters on Probability from a Stochastic Perspective . . 481
J. Michael Shaughnessy
Perspective IV: Mathematics Education
Preface to Perspective IV: Mathematics Education. . 493
Egan J. Chernoff and Gale L. Russell
A Practitional Perspective on Probabilistic Thinking Models and Frameworks . . 495
Edward S. Mooney, Cynthia W. Langrall, and Joshua T. Hertel
Experimentation in Probability Teaching and Learning . . 509
Per Nilsson
Investigating the Dynamics of Stochastic Learning Processes: A Didactical Research Perspective, Its Methodological and Theoretical Framework, Illustrated for the Case of the Short Term–Long Term Distinction . . . 533
Susanne Prediger and Susanne Schnell
Counting as a Foundation for Learning to Reason About Probability . . 559
Carolyn A. Maher and Anoop Ahluwalia
Levels of Probabilistic Reasoning of High School Students About Binomial Problems . . 581
Ernesto Sánchez and Pedro Rubén Landín
Children’s Constructions of a Sample Space with Respect to the Law of Large Numbers 599
Efi Paparistodemou
Researching Conditional Probability Problem Solving. . . 613
M. Pedro Huerta
Contextual Considerations in Probabilistic Situations: An Aid or a Hindrance? . . 641
Ami Mamolo and Rina Zazkis
Cultural Influences in Probabilistic Thinking . . 657
Sashi Sharma
Primary School Students’ Attitudes To and Beliefs About Probability . 683
Anne Williams and Steven Nisbet
Section IV Commentary: The Perspective of Mathematics Education 709
Jane M. Watson
Commentary on Probabilistic Thinking: Presenting Plural Perspectives 721
Egan J. Chernoff and Bharath Sriraman
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