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.
Author(s): Gail F. Burrill, Leandro de Oliveria Souza, Enriqueta Reston
Series: Advances in Mathematics Education
Publisher: Springer
Year: 2023
Language: English
Pages: 374
City: Cham
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
