Research on Reasoning with Data and Statistical Thinking: International Perspectives

Description

This book is derived from selected papers from the Fourteenth International Congress on Mathematical Education Topic Study Group 12, Teaching and Learning Statistics. It describes recent research  on curriculum, pedagogy and outreach initiatives from countries as diverse as Brazil, Chile, Columbia, Denmark, Germany, the Netherlands, Spain, Sweden, Thailand, Turkey, the United Kingdom, and the United States. The book has a focus on the use of data in the teaching and learning of statistics across grade levels and begins with an overview of the status  of statistics education and the use of data from seven different countries across the continents and the link between research and practice in those countries. Because it contains specific examples of the research, for  example, on the ways children learn,  the choice and implementation of tasks, or the role of informal inference, the book will be a great resource to those interested and involved in the teaching of statistics, curriculum developers, and statistics education researchers. Preface Background ICME-14 Topic Study Group 12: Teaching and Learning Statistics Part I: Statistics Education Across the World Part II: Data and Young Learners Part III: Data and Simulation to Support Understanding Part IV: Data and Society Part V: Statistical Learning, Reasoning, and Attitudes References Contents Introduction 1 Curriculum Development 2 Software Development 3 Scholarship Communities 4 The Changing Role of “Context” 5 An Illuminating Example 6 Conclusion References Part I: Statistics Education Across the World An International Look at the Status of Statistics Education 1 Country Survey Results 2 Electives 3 The Reality 4 Statistical Literacy 5 Data Science Bibliography References The Brazilian National Curricular Guidance and Statistics Education References Statistics and Probability Education in Germany 1 Tool Use in Germany 2 Community and New Developments 3 Outlook References New Zealand Statistics Curriculum 1 Overview 2 Resources and Assessment 3 Challenges References Statistics Education in the Philippines: Curricular Context and Challenges of Implementation 1 The Intended Statistics and Probability Curriculum at School Level 2 Challenges in Curriculum Implementation 3 Improving Statistical Pedagogy among K to 12 Mathematics Teachers in the Philippines 4 Recommendations for Future Directions References Statistics and Probability in the Curriculum in South Africa References Statistics in the School Level in Turkey 1 Data Handling in Primary School (Grades 1–4) 2 Data Handling and Probability in Middle School (Grades 5–8) 3 Data and Probability in High School (Grades 9–12) 4 Resources, Curricular Materials, and Approaches to Teach Statistics 5 The Role of Statistical Literacy and the Nature of Probability in the Curriculum 6 Reflection on the Realities and Challenges for Teaching Statistics References United States Statistics Curriculum References Part II: Data and Young Learners Elementary Students’ Responses to Quantitative Data 1 Introduction 2 Literature Review 2.1 Graphical Representations 2.2 Context 3 Methods 3.1 Methodology 3.2 Study Design 3.3 Task Sequence 3.4 Analysis 4 Findings 4.1 Focusing on the “Right” Graph and Features 4.2 Adaptation of Both Categorical and Quantitative Techniques 4.3 The Role of Context in Analysis and Inference 5 Discussion 6 Implications References Reading and Interpreting Distributions of Numerical Data in Primary School 1 Introduction 2 Theoretical Background 2.1 Primary School Students’ Understanding of Distributions of Numerical Data 2.2 Integrating the Perspectives: Framework for Primary School Students Reading and Interpreting Numerical Data 2.3 TinkerPlots: A Digital Tool to Enhance Early Statistical Thinking 3 The Study 3.1 Research Questions 3.2 Methodology 4 Developing, Realizing, and Evaluating a Teaching-Learning Unit to Support Young Students’ Statistical Thinking Concerning Numerical Data 4.1 Specifying and Structuring the Learning Content 4.2 (Re-)Developing the Design 4.3 Realizing and Evaluating Design Experiments 4.3.1 Realizing the Design Experiments 4.3.2 Evaluating the Design Experiments 5 Summary and Outlook References Young Learners Experiencing the World Through Data Modelling 1 Introduction 2 Mathematics Education and Allgemeinbildung 3 Data Modelling with Young Learners 4 Task Design and Method 5 Students’ Way Through the Data Modelling Process 5.1 How Old Are Your Parents? 5.2 How Often Do Your Parents Argue? 6 Discussion 6.1 Posing Questions in a Meaningful and Interesting Context 6.2 Data Modelling with Young Learners and Allgemeinbildung 7 Conclusion References Untitled Part III: Data and Simulation to Support Understanding Investigating Mathematics Teacher Educators’ Conceptions and Criteria for an Informal Line of Best Fit 1 Introduction 2 Constructs Related with Informal Line of Best Fit and Need for Studying It 3 Previous Research and Conceptual Framework 4 Methodology 4.1 Design 4.2 Participants 5 Data Collection 5.1 Interview Protocol 6 Data Analysis 7 Results 7.1 Conceptions 7.1.1 Representer 7.1.2 Predictor 7.1.3 Signal 7.2 Criteria and Methods 7.2.1 Closest Criterion 7.2.2 Sum Deviation Criterion 7.2.3 Ellipse/Area Approach Criterion 8 Discussion and Conclusion References Introducing Density Histograms to Grades 10 and 12 Students: Design and Tryout of an Intervention Inspired by Embodied Instrumentation 1 Introduction 2 Theoretical Background 2.1 Review of the Literature on Density Histograms 2.2 Embodied Cognition and Instrumentation 3 Materials and Method 3.1 Reinventing Bin Widths 3.2 Reinventing Density in a Histogram 3.3 Confirming learning: Transfer 3.4 Method 3.4.1 Participants 3.4.2 Intervention in the Teaching and Learning Lab 3.4.3 Data Analysis—Conjectured Learning Trajectory 4 Results 4.1 Reinventing Unequal Bin Widths Task 16 4.2 Reinventing Density Histogram Task 17 5 Ideas for Redesign 6 Conclusions and Discussion References Margin of Error: Connecting Chance to Plausible 1 Introduction 2 Background 3 Building Concept Images of Margin of Error 4 The Course 5 Learning Trajectory for Margin of Error 5.1 Random Behavior and Long Run Stability 5.2 The Role of Chance 5.3 Sampling 6 Introducing Margin of Error 7 Data Analysis 8 Discussion References The Mystery of the Black Box: An Experience of Informal Inferential Reasoning 1 Introduction 2 Conceptual Framework 2.1 Statistical Inference and ISI 2.2 Lesson Study 3 Methodology 3.1 Participants 3.2 Data Collection 3.3 Tasks 3.3.1 Description of the Task of Lesson 3: Black Box Experiment 3.3.2 Description of the Task of Lesson 4: Black Box Experiment 3.4 Data Analysis 4 Results 4.1 Answers to the Task of Lesson 3: Black Box Experiment 4.2 Answers to the Task of Lesson 4: Drawing a Frequency Distribution 5 Conclusions and Discussion Appendix 1 Appendix 2 (Table B.1) References Part IV: Data and Society Critical Citizenship in Statistics Teacher Education 1 Introduction 2 Theoretical Background 2.1 Critical Citizenship 2.2 Statistical Investigations 3 Method 4 Results and Discussion 4.1 Statistical Thinking 4.2 Sense of Agency 5 Conclusions References Toward Statistical Literacy to Critically Approach Big Data in Mathematics Education 1 Introduction 2 Methodology 3 Results 4 Discussion 4.1 Big Data and Literacy: A Semantics under Construction 4.2 Big Data and Teacher Education: Limits and Possibilities 5 Final remarks References Interdisciplinary Data Workshops: Combining Statistical Consultancy Training with Practitioner Data Literacy 1 Introduction 2 Background 2.1 Contextual Background 2.2 Pedagogical Background 3 Workshops 3.1 Workshop Design 3.2 Procurement Workshops 3.3 Agriculture Workshops 4 Results 5 Conclusions References Part V: Statistical Learning, Reasoning, and Attitudes Distinctive Aspects of Reasoning in Statistics and Mathematics: Implications for Classroom Arguments 1 Background 2 Collective Argumentation 3 Reasoning 4 Classroom Arguments Illustrating Different Kinds of Reasoning 4.1 Argumentation Examples 4.2 Looking Across the Examples 5 Discussion 6 Conclusion and Implications References Sustainable Learning of Statistics 1 Introduction 1.1 Sustainable Learning of Statistics – An Example 2 The Juxtaposition of Statistical Reasoning 2.1 Deterministic and Stochastic Reasoning 2.2 Statistical Reasoning Requires Stochastic and Deterministic Reasoning 2.3 Tendency toward Deterministic Reasoning 2.4 Stochastic Reasoning and Variability 3 Variation in Learning 3.1 Phenomenography 3.2 Making Learning Possible 4 Enhancing the Sustainable Learning of Statistics 4.1 Developing Stochastic Reasoning by Applying VT 4.2 A Conjecture 5 A Pedagogical Call References How Students’ Statistics Beliefs Influence Their Attitudes: A Quantitative and a Qualitative Approach 1 Introduction 2 Background 2.1 Attitudes About Statistics 2.2 Beliefs About Statistics 2.3 Research Question 3 Methods 4 Quantitative Instrumentation 5 Results 5.1 Quantitative Influence of Beliefs on Attitudes 5.2 Insights from the Qualitative Interviews 6 Conclusion References Algebraization Levels of Activities Linked to Statistical Tables in Spanish Secondary Textbooks 1 Introduction 2 Background 2.1 Types of Statistical Tables 2.2 Elementary Algebraization Levels 2.3 Previous Research 3 Method 3.1 Description of the Sample 3.2 Analysis 4 Results 4.1 Algebraic Activity Involved in Different Statistical Tables 4.1.1 Data Tables 4.1.2 One Variable Distribution Ordinary Frequency Distribution Tables Frequency Distribution Tables with Cumulative Frequencies Distribution Table with Grouped Data 4.1.3 Two-Way Tables Two-Way Table with Categorical Data Two-Way Table with Grouped Data 4.2 Distribution of Statistical Tables in the Textbooks 5 Conclusions Appendix: Textbooks in the sample References References