Probabilistic Thinking: Presenting Plural Perspectives

Front Matter....Pages I-XXI
Front Matter....Pages 1-1
Preface to Perspective I: Mathematics and Philosophy....Pages 3-5
A Historical and Philosophical Perspective on Probability....Pages 7-34
From Puzzles and Paradoxes to Concepts in Probability....Pages 35-73
Three Approaches for Modelling Situations with Randomness....Pages 75-99
A Modelling Perspective on Probability....Pages 101-116
Commentary on Perspective I: The Humanistic Dimensions of Probability....Pages 117-119
Front Matter....Pages 121-121
Probabilistic Thinking: Analyses from a Psychological Perspective....Pages 123-126
Statistical Thinking: No One Left Behind....Pages 127-148
Fostering Children’s Probabilistic Reasoning and First Elements of Risk Evaluation....Pages 149-160
Intuitive Conceptions of Probability and the Development of Basic Math Skills....Pages 161-194
The Interplay Among Knowledge, Cognitive Abilities and Thinking Styles in Probabilistic Reasoning: A Test of a Model....Pages 195-214
Revisiting the Medical Diagnosis Problem: Reconciling Intuitive and Analytical Thinking....Pages 215-237
Rethinking Probability Education: Perceptual Judgment as Epistemic Resource....Pages 239-260
Sticking to Your Guns: A Flawed Heuristic for Probabilistic Decision-Making....Pages 261-281
Developing Probabilistic Thinking: What About People’s Conceptions?....Pages 283-298
Commentary on Perspective II: Psychology....Pages 299-309
A Brief Overview and Critique of Perspective II on Probabilistic and Statistical Reasoning....Pages 311-340
Front Matter....Pages 341-341
Preface to Perspective III: Stochastics....Pages 343-344
Prospective Primary School Teachers’ Perception of Randomness....Pages 345-366
Challenges of Developing Coherent Probabilistic Reasoning: Rethinking Randomness and Probability from a Stochastic Perspective....Pages 367-396
Front Matter....Pages 341-341
“It Is Very, Very Random Because It Doesn’t Happen Very Often”: Examining Learners’ Discourse on Randomness....Pages 397-416
Developing a Modelling Approach to Probability Using Computer-Based Simulations....Pages 417-439
Promoting Statistical Literacy Through Data Modelling in the Early School Years....Pages 441-457
Learning Bayesian Statistics in Adulthood....Pages 459-479
Commentary on the Chapters on Probability from a Stochastic Perspective....Pages 481-489
Front Matter....Pages 491-491
Preface to Perspective IV: Mathematics Education....Pages 493-494
A Practitional Perspective on Probabilistic Thinking Models and Frameworks....Pages 495-507
Experimentation in Probability Teaching and Learning....Pages 509-532
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....Pages 533-558
Counting as a Foundation for Learning to Reason About Probability....Pages 559-580
Levels of Probabilistic Reasoning of High School Students About Binomial Problems....Pages 581-597
Children’s Constructions of a Sample Space with Respect to the Law of Large Numbers....Pages 599-612
Researching Conditional Probability Problem Solving....Pages 613-639
Contextual Considerations in Probabilistic Situations: An Aid or a Hindrance?....Pages 641-656
Cultural Influences in Probabilistic Thinking....Pages 657-681
Primary School Students’ Attitudes To and Beliefs About Probability....Pages 683-708
Section IV Commentary: The Perspective of Mathematics Education....Pages 709-720
Commentary on Probabilistic Thinking: Presenting Plural Perspectives ....Pages 721-727
Back Matter....Pages 729-747