Statistics and probability in high school:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Rotterdam ; Boston ; Taipei
SensePublishers
[2016]
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| Subjects: | |
| Online Access: | ASH01 UPA01 Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource (x, 223 Seiten) Diagramme |
| ISBN: | 9789463006248 |
| DOI: | 10.1007/978-94-6300-624-8 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Statistics and probability in high school
Autor: Batanero, Carmen
Jahr: 2016
TABLE OF CONTENTS Preface ix 1. Educational Principles for Statistics and Probability 1 1.1. Introduction 1 1.2. Fundamental Ideas in Statistics and Probability 2 1.2.1. Exploratory Data Analysis (Chapter 2) 3 1.2.2. Modelling Information by Probabilities (Chapter 3) 4 1.2.3. Exploring and Modelling Association (Chapter 4) 5 1.2.4. Sampling and Inference (Chapter 5) 6 1.3. Complementary Views of Statistics and Mathematics 7 1.4. The Role of Technology 10 1.5. Adapting the Levels of Formalisation to the Diversity of Students 12 1.6. Statistical and Probabilistic Literacy 12 1.6.1. Statistical Literacy 12 1.6.2. Statistical Literacy Components 13 1.6.3. Actions and Resources Directed to Increase Statistical Literacy 14 1.7. Statistical and Probabilistic Thinking 15 1.7.1. Statistical Thinking 16 1.7.2. The Statistical Investigation Cycle 16 1.7.3. Fundamental Types of Statistical Thinking 18 1.7.4. Components of Probabilistic Thinking 20 1.8. Making Sense of Statistics and Probability 21 1.9. Statistical Investigations and Experiments 22 1.10. Final Thoughts 22 2. Exploratory Data Analysis 25 2.1. Introduction 25 2.2. A Teaching Situation to Introduce Elementary Statistical Concepts and Procedures 26 2.2.1. Starting Questions 26 2.2.2. Exploring Qualitative Variables 27 2.2.3. Exploring Numerical Variables 28 2.2.4. Comparing Groups 34 2.3. Additional Activities 38 2.3.1. Exploring Continuous Variables 38 2.3.2. Exploring Bivariate Relationships 45 2.4. Synthesis of Learning Goals 46 2.4.1. Distribution and Different Types of Frequencies 47 2.4.2. Simple Univariate Graphs 48 2.4.3. Simple Summary Statistics 49 2.4.4. Spirit of Exploratory Data Analysis (EDA) 51 2.4.5. Basic Strategies in Data Exploration 52 v
TABLE OF CONTENTS 2.5. Students’ Reasoning and Potential Difficulties 54 2.5.1. Graphical Competencies and Communication Skills 54 2.5.2. Errors in Producing Graphs 56 2.5.3. Understanding Measures of Central Tendency or Centre 57 2.5.4. Understanding Spread 60 2.5.5. Understanding Order Statistics 61 2.6. Additional Resources 62 2.6.1. Journals and Books 62 2.6.2. Data Sets 63 2.6.3. Internet Resources 63 Appendix: Data 65 3. Modelling Information by Probabilities 67 3.1. Introduction 67 3.2. Teaching Situations to Characterise Probability 69 3.2.1. Frequentist Probability: Investigating Coin Tossing 69 3.2.2. Subjectivist Probability: The Insurance Contract 72 3.2.3. Laplace (A Priori) Probability: Calibrating Weights of Evidence 73 3.3. Teaching Situations Introducing Conditional Probability 74 3.3.1. Conditional Probability and Circumstantial Evidence 75 3.3.2. Conditional Probability and Compound Probability 78 3.4. Additional Teaching Activities 79 3.4.1. Random Variables 79 3.4.2. Additivity of Expected Value and Variance for Repeated Experiments 81 3.4.3. Distribution Models for Standard Situations 83 3.4.4. Central Theorems 88 3.5. Synthesis of Learning Goals 92 3.5.1. Concepts to Model and Investigate Uncertain Situations 92 3.5.2. Different Connotations of Probability 93 3.5.3. Circumstantial Evidence and Bayes’ Formula 97 3.5.4. Random Variables and Expectation 99 3.5.5. Standard Models of Distributions 100 3.5.6. Law of Large Numbers and Central Limit Theorem 101 3.6. Students’Reasoning and Potential Difficulties 104 3.6.1. Misconceptions and Heuristics (Strategies) in Probability Situations 104 3.6.2. Independence and Conditional Probability 107 3.6.3. Taking into Account Students Reasoning to Improve Teaching 108 3.7. Additional Resources and Ideas 109 3.7.1. Investigating Randomness: Generating Coin Tossing from Memory 109 3.7.2. Odds and Bayes’ Formula - Revising W eights of Evidence 109
3.7.3. Mediating Tools to Support Teaching 110
TABLE OF CONTENTS 4. Exploring and Modelling Association 117 4.1. Introduction 117 4.2. A Teaching Situation to Explore Contingency Tables 119 4.2.1. Exploring Association in 2x2 Contingency Tables 119 4.2.2. Different Distributions in 2x2 Contingency Tables 121 4.2.3. Simple Methods to Evaluate Association in 2x2 Tables 123 4.2.4. Expected Frequencies for Independent Variables 124 4.3. Life Expectancy: A Teaching Situation to Explore Correlation and Regression 126 4.3.1. Exploring and Explaining Correlation 127 4.3.2. Fitting Models to Bivariate Data 134 4.4. Additional Activities 140 4.5. Synthesis of Learning Goals 142 4.5.1. Contingency Tables 143 4.5.2. Correlation and Regression 144 4.6. Some Potential Difficulties 148 4.6.1. Intuitive Strategies in Contingency Tables 148 4.6.2. Linear Regression and Correlation 150 4.6.3. Misconceptions Related to both Association and Correlation 153 4.7. Additional Resources and Ideas 157 4.7.1. Measures of Association in Contingency Tables 157 4.7.2. Introduction to Multivariate Visualisation 158 5. Sampling and Inference 163 5.1. Introduction 163 5.2. A Teaching Situation: The Tea-Tasting Experiment 164 5.2.1. The Lady Tasting Tea 165 5.2.2. Using Experimental Data to Test a Hypothesis 165 5.2.3. Different Approaches to Compute the ¿»-value 169 5.2.4. Sampling Distribution for the Proportion and the Effect of Sample Size 171 5.2.5. Estimating the Population Proportion by a Confidence Interval 172 5.3. Additional Activities 173 5.3.1. Exploring the Central Limit Theorem 173 5.3.2. Inference for Proportions 174 5.3.3. Inference for a Mean 176 5.3.4. Statistical Tests as Decision Rules 177 5.4. Synthesis of Learning Goals 181 5.4.1. Basic Inferential Concepts and Procedures 181 5.4.2. Additional Advanced Learning Goals 184 5.5. Some Potential Difficulties 184 5.5.1. Understanding Random Sampling and Sampling Distributions 185 5.5.2. Understanding Statistical Tests 187
5.5.3. Understanding Confidence Intervals 189 vii
TABLE OF CONTENTS 5.6. Additional Resources and Ideas 191 5.6.1. Developing Informal Ideas of Inference 191 5.6.2. Resampling Methods 191 5.6.3. Updating a Prior Distribution for a Proportion 193 References 197 Author Index 209 Subject Index 213
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| spelling | Batanero, Carmen Verfasser (DE-588)103146168X aut Statistics and probability in high school Carmen Batanero, Universidad de Granada, Spain and Manfred Borovcnik, University of Klagenfurt, Austria Rotterdam ; Boston ; Taipei SensePublishers [2016] 1 Online-Ressource (x, 223 Seiten) Diagramme txt rdacontent c rdamedia cr rdacarrier Education Education, general Erziehung Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Schulmathematik (DE-588)4153188-7 gnd rswk-swf Schulmathematik (DE-588)4153188-7 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Statistik (DE-588)4056995-0 s 1\p DE-604 Borovcnik, Manfred 1953- Verfasser (DE-588)1210952432 aut Erscheint auch als Druck-Ausgabe, Paperback 978-94-6300-622-4 Erscheint auch als Druck-Ausgabe, Hardcover 978-94-6300-623-1 https://doi.org/10.1007/978-94-6300-624-8 Verlag URL des Erstveröffentlichers Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029118426&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Batanero, Carmen Borovcnik, Manfred 1953- Statistics and probability in high school Education Education, general Erziehung Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Schulmathematik (DE-588)4153188-7 gnd |
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| title | Statistics and probability in high school |
| title_auth | Statistics and probability in high school |
| title_exact_search | Statistics and probability in high school |
| title_full | Statistics and probability in high school Carmen Batanero, Universidad de Granada, Spain and Manfred Borovcnik, University of Klagenfurt, Austria |
| title_fullStr | Statistics and probability in high school Carmen Batanero, Universidad de Granada, Spain and Manfred Borovcnik, University of Klagenfurt, Austria |
| title_full_unstemmed | Statistics and probability in high school Carmen Batanero, Universidad de Granada, Spain and Manfred Borovcnik, University of Klagenfurt, Austria |
| title_short | Statistics and probability in high school |
| title_sort | statistics and probability in high school |
| topic | Education Education, general Erziehung Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Schulmathematik (DE-588)4153188-7 gnd |
| topic_facet | Education Education, general Erziehung Statistik Wahrscheinlichkeitsrechnung Schulmathematik |
| url | https://doi.org/10.1007/978-94-6300-624-8 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029118426&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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