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## Details

Genre/Form: | Electronic books |
---|---|

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Carmen Batanero; Manfred Borovcnik. |

ISBN: | 9463006249 9789463006248 |

OCLC Number: | 954428145 |

Description: | 1 online resource. |

Contents: | TABLE OF CONTENTS; PREFACE; CHAPTER 1: EDUCATIONAL PRINCIPLES FOR STATISTICS AND PROBABILITY; 1.1. INTRODUCTION; 1.2. FUNDAMENTAL IDEAS IN STATISTICS AND PROBABILITY; 1.2.1. Exploratory Data Analysis (Chapter 2); 1.2.2. Modelling Information by Probabilities (Chapter 3); 1.2.3. Exploring and Modelling Association (Chapter 4); 1.2.4. Sampling and Inference (Chapter 5); 1.3. COMPLEMENTARY VIEWS OF STATISTICS AND MATHEMATICS; 1.4. THE ROLE OF TECHNOLOGY; 1.5. ADAPTING THE LEVELS OF FORMALISATION TO THE DIVERSITY OF STUDENTS; 1.6. STATISTICAL AND PROBABILISTIC LITERACY 1.6.1. Statistical Literacy1.6.2. Statistical Literacy Components; 1.6.3. Actions and Resources Directed to Increase Statistical Literacy; 1.7. STATISTICAL AND PROBABILISTIC THINKING; 1.7.1. Statistical Thinking; 1.7.2. The Statistical Investigation Cycle; 1.7.3. Fundamental Types of Statistical Thinking; 1.7.4. Components of Probabilistic Thinking; 1.8. MAKING SENSE OF STATISTICS AND PROBABILITY; 1.9. STATISTICAL INVESTIGATIONS AND EXPERIMENTS; 1.10. FINAL THOUGHTS; CHAPTER 2: EXPLORATORY DATA ANALYSIS; 2.1. INTRODUCTION 2.2. A TEACHING SITUATION TO INTRODUCE ELEMENTARY STATISTICAL CONCEPTS AND PROCEDURES2.2.1. Starting Questions; 2.2.2. Exploring Qualitative Variables; 2.2.3. Exploring Numerical Variables; 2.2.4. Comparing Groups; 2.3. ADDITIONAL ACTIVITIES; 2.3.1. Exploring Continuous Variables; 2.3.2. Exploring Bivariate Relationships; 2.4. SYNTHESIS OF LEARNING GOALS; 2.4.1. Distribution and Different Types of Frequencies; 2.4.2. Simple Univariate Graphs; 2.4.3. Simple Summary Statistics; 2.4.4. Spirit of Exploratory Data Analysis (EDA); 2.4.5. Basic Strategies in Data Exploration 2.5. STUDENTS' REASONING AND POTENTIAL DIFFICULTIES2.5.1. Graphical Competencies and Communication Skills; 2.5.2. Errors in Producing Graphs; 2.5.3. Understanding Measures of Central Tendency or Centre; 2.5.4. Understanding Spread; 2.5.5. Understanding Order Statistics; 2.6. ADDITIONAL RESOURCES; 2.6.1. Journals and Books; 2.6.2. Data Sets; 2.6.3. Internet Resources; APPENDIX: DATA; CHAPTER 3: MODELLING INFORMATION BY PROBABILITIES; 3.1. INTRODUCTION; 3.2. TEACHING SITUATIONS TO CHARACTERISE PROBABILITY; 3.2.1. Frequentist Probability: Investigating Coin Tossing 3.2.2. Subjectivist Probability: The Insurance Contract3.2.3. Laplace (A Priori) Probability: Calibrating Weights of Evidence; 3.3. TEACHING SITUATIONS INTRODUCING CONDITIONAL PROBABILITY; 3.3.1. Conditional Probability and Circumstantial Evidence; 3.3.2. Conditional Probability and Compound Probability; 3.4. ADDITIONAL TEACHING ACTIVITIES; 3.4.1. Random Variables; 3.4.2. Additivity of Expected Value and Variance for Repeated Experiments; 3.4.3. Distribution Models for Standard Situations; 3.4.4. Central theorems; Central Limit Theorem; 3.5. SYNTHESIS OF LEARNING GOALS |

### Abstract:

Statistics and probability are fascinating fields, tightly interwoven with the context of the problems which have to be modelled. The authors demonstrate how investigations and experiments provide promising teaching strategies to help high-school students acquire statistical and probabilistic literacy. In the first chapter the authors put into practice the following educational principles, reflecting their views of how these subjects should be taught: a focus on the most relevant ideas and postpone extensions to later stages; illustrating the complementary/dual nature of statistical and probabilistic reasoning; utilising the potential of technology and show its limits; and reflecting on the different levels of formalisation to meet the wide variety of students' previous knowledge, abilities, and learning types. The remaining chapters deal with exploratory data analysis, modelling information by probabilities, exploring and modelling association, and with sampling and inference. Throughout the book, a modelling view of the concepts guides the presentation. In each chapter, the development of a cluster of fundamental ideas is centred around a statistical study or a real-world problem that leads to statistical questions requiring data in order to be answered. The concepts developed are designed to lead to meaningful solutions rather than remain abstract entities. For each cluster of ideas, the authors review the relevant research on misconceptions and synthesise the results of research in order to support teaching of statistics and probability in high school. What makes this book unique is its rich source of worked-through tasks and its focus on the interrelations between teaching and empirical research on understanding statistics and probability.

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