Statistics in Early Childhood and Primary Education (eBook)

Supporting Early Statistical and Probabilistic Thinking

Aisling Leavy, Maria Meletiou-Mavrotheris, Efi Paparistodemou (Herausgeber)

eBook Download: PDF

2018 | 1st ed. 2018
XXIV, 313 Seiten
Springer Singapore (Verlag)
978-981-13-1044-7 (ISBN)

Infos

This compilation focuses on the theory and conceptualisation of statistics and probability in the early years and the development of young children's (ages 3-10) understanding of data and chance. It provides a comprehensive overview of cutting-edge international research on the development of young learners' reasoning about data and chance in formal, informal, and non-formal educational contexts. The authors share insights into young children's statistical and probabilistic reasoning and provide early childhood educators and researchers with a wealth of illustrative examples, suggestions, and practical strategies on how to address the challenges arising from the introduction of statistical and probabilistic concepts in pre-school and school curricula. 

This collection will inform practices in research and teaching by providing a detailed account of current best practices, challenges, and issues, and of future trends and directions in early statistical and probabilistic learning worldwide. Further, it will contribute to future research and theory building by addressing theoretical, epistemological, and methodological considerations regarding the design of probability and statistics learning environments for young children.

Dr. Aisling Leavy is Head of STEM Education at Mary Immaculate College, University of Limerick. Her research interests include statistical thinking and reasoning, children's mathematical thinking, and mathematics teacher education. Aisling is currently an Associate Editor of Statistics Education Research Journal and General Editor of Irish Educational Studies. She publishes in international scholarly journals in the areas of statistics education, mathematics education, and prospective teachers' attitudes towards and knowledge of mathematics and statistics. 

Dr. Maria Meletiou-Mavrotheris is a Professor of Mathematics Education at the European University Cyprus, and Director of the Research Laboratory in ICT-Enhanced Education. Her research concentrates on issues related to the teaching and learning of statistics, mathematics, science, and technology education. She has produced numerous publications in scholarly international journals and edited volumes, and has been able to attract considerable funding from national and international sources. Her research record includes the coordination of multiple EU-funded projects, including the Socrates-Comenius project EarlyStatistics: Enhancing the Teaching and Learning of Early Statistical Reasoning in European Schools.

Dr. Efi Paparistodemou is a teacher educator at Cyprus Pedagogical Institute. She holds degrees in Education, Mathematics and Statistics, and a PhD in Mathematics Education. She has worked as a teacher, a special math educator, a math textbook writer and as an Assistant Professor at the European University Cyprus. Her research concentrates on issues related to statistics, probability, mathematics teacher education and technology. She has worked in European projects (e.g. EarlyStatistics) and published on mathematics and statistics education, technology education, prospective and in-service teacher development, and professional learning in mathematics.

Inhalt

Foreword 7
Preface 9
Introduction 9
Edited Volume Objectives 10
Edited Volume Contents 11
Concluding Remarks 19
References 20
Contents 23
Theory and Conceptualisation of Statistics and Probability in the Early Years 25
1 Theorising Links Between Context and Structure to Introduce Powerful Statistical Ideas in the Early Years 26
1.1 Introduction 26
1.2 Literature Review and Theoretical Framework 27
1.3 Methodology 31
1.3.1 Participants and Lessons 31
1.3.2 Data Collection and Analysis 32
1.4 Results 33
1.4.1 Informally Introducing Variability, Aggregate and Population 33
1.4.2 Suggesting a Need for Data 35
1.4.3 Recording and Analysing the Data 37
1.5 Discussion 40
References 43
2 Probabilistic Thinking and Young Children: Theory and Pedagogy 44
2.1 Setting the Scene: Probability, Literacy and Children 44
2.2 Children’s Probabilistic Thinking: From Piaget and Fischbein to Contemporary Studies 46
2.3 Probability in Early Childhood Educational Practice 50
2.3.1 Curriculum Design: Constructivism and Proposed Instructional Models 50
2.3.2 Aspects of Instruction and Task Design in Probability Learning 51
2.4 Conclusion 54
References 55
Learning Statistics and Probability 58
3 Emergent Reasoning About Uncertainty in Primary School Children with a Focus on Subjective Probability 59
3.1 Theoretical Perspective 59
3.2 Review of the Literature 61
3.2.1 Children’s Use of Chance Language 61
3.2.2 Children’s Reasoning About Uncertainty 62
3.3 Methodology 63
3.3.1 Participants 63
3.3.2 The Jellybean Task 63
3.3.3 Setting and Procedure 64
3.4 Results and Discussion 66
3.4.1 Children’s Use of Chance Language 66
3.4.2 Children’s Reasoning About Uncertainty 70
3.5 Conclusions 74
References 75
4 Variation and Expectation for Six-Year-Olds 77
4.1 Introduction and Background 77
4.2 Methodology 80
4.2.1 Interview Protocols 80
4.2.2 Participants 83
4.2.3 Analysis 85
4.3 Results 85
4.3.1 Lollies Protocol 85
4.3.2 Books Protocol 87
4.3.3 Transport Protocol 89
4.3.4 Weather Protocol 90
4.3.5 Summary 91
4.4 Discussion 92
References 94
5 The Impact of Culturally Responsive Teaching on Statistical and Probabilistic Learning of Elementary Children 96
5.1 Introduction 96
5.2 Combinatorial, Probabilistic and Statistical Thinking in Childhood 97
5.3 Reasoning in a Culturally Responsive Classroom 99
5.4 Methodology 101
5.5 The Study 102
5.5.1 Goals 102
5.5.2 Context and Participants 102
5.5.3 Methods 103
5.5.4 The Episodes 103
5.6 Discussion and Conclusions 107
References 109
6 Inscriptional Capacities and Representations of Young Children Engaged in Data Collection During a Statistical Investigation 110
6.1 Introduction 111
6.2 Theoretical Perspective 111
6.2.1 Representations in Early Childhood Mathematics 111
6.2.2 Use of Representations in Statistics Education 113
6.3 Methodology 114
6.3.1 Participants 114
6.3.2 Procedure 114
6.3.3 Data Collection and Analysis 115
6.4 Findings and Discussion 116
6.4.1 Iconic Representations 120
6.4.2 Changes in Use of Iconic Representations Across Data Cycles 122
6.4.3 Efforts to Convey Meaning in Iconic Representations 123
6.4.4 Symbolic Representations 123
6.4.5 Changes in Representations 123
6.4.6 Reasoning About the Context 124
6.5 Conclusion 125
References 127
7 Scaffolding Statistical Inquiries for Young Children 129
7.1 Introduction 129
7.2 Statistical Inquiries and Investigations 130
7.3 Scaffolding 132
7.3.1 Scaffolding Framework 132
7.3.2 Research Question 133
7.4 Method 133
7.5 Illustrations from the Classroom 136
7.5.1 Problem 137
7.5.2 Planning 138
7.5.3 Data Collection 139
7.5.4 Analysis of Data 140
7.5.5 Conclusions 142
7.6 Discussion and Conclusion 144
7.7 Implications for Teaching and Research 145
References 146
8 How Kindergarten and Elementary School Students Understand the Concept of Classification 148
8.1 What Is Classification? 149
8.2 The Investigative Cycle as a Means of Developing Statistical Reasoning 150
8.3 What Is the Importance of Classification in the Statistical Investigative Cycle? 151
8.4 Errors in Classification Carried Out by Children 152
8.5 Research on the Ability to Classify 153
8.6 Method and Data Analysis 154
8.7 Results Study 1 157
8.8 Results Study 2 158
8.9 Results 161
8.10 Conclusions 163
References 164
Teaching Statistics and Probability: Curriculum Issues 166
9 Unpacking Implicit Disagreements Among Early Childhood Standards for Statistics and Probability 167
9.1 Introduction 167
9.2 Scope of the Chapter 168
9.3 Statistical Questions 169
9.4 Probability Language 172
9.5 Variability 174
9.6 Boundary Objects 176
9.7 Conclusion 177
References 178
10 Statistical Graphs in Spanish Textbooks and Diagnostic Tests for 6–8-Year-Old Children 181
10.1 Introduction 181
10.2 Theoretical Framework 182
10.2.1 Graph Semiotic Complexity 183
10.3 Curricular Guidelines Related to Statistical Graphs and External Compulsory Assessment 184
10.3.1 External Compulsory Assessment 185
10.4 Graphs in the Spanish Textbooks and External Assessment Tests 186
10.4.1 Method 187
10.4.2 Type of Graph 187
10.4.3 Context of the Task 193
10.5 Implications for Research and Teaching 196
References 197
Teaching Statistics and Probability: Tasks and Materials 199
11 Initiating Interest in Statistical Problems: The Role of Picture Story Books 200
11.1 Introduction 200
11.2 Connecting to Statistics: Real-World Problem Solving as Task and Data Context 201
11.3 Engaging Data Contexts Through Task Design 202
11.3.1 Picture Story Books: Real-World Contexts as Task and Data Context 202
11.3.2 Choosing Picture Story Books for Statistical Problems 203
11.4 The Study 204
11.4.1 Study Participants, Data Collection and Analysis 205
11.4.2 Picture Books and the Data Modelling Activities 206
11.5 Children’s Spontaneous Responses, Questions and Comments 206
11.5.1 Baxter Brown’s Messy Room (English, 2009a) 206
11.5.2 Michael Recycle (Bethel, 2008) 208
11.5.3 Litterbug Doug (Bethel, 2009) 209
11.6 Characteristics of Picture Story Books that Stimulate Interest in the Data Context 210
11.6.1 Limiting and Misdirecting Interest 210
11.6.2 Capturing Interest: Uncertainty and the Unresolved Problem 211
11.6.3 Capturing Interest: Personal Connection 211
11.6.4 Capturing Interest: The Resolved Problem and the Role of the Character 212
11.7 Stimulating Interest in Statistical Problems 213
References 214
12 Teachers’ Reflection on Challenges for Teaching Probability in the Early Years 217
12.1 Introduction 217
12.2 Theoretical Perspective 218
12.2.1 Learning and Teaching Probability in the Early Years 218
12.2.2 Mathematics Teaching and Reflection 220
12.3 Methodology 221
12.3.1 Research Design: Participants and Context of Study 221
12.3.2 Instruments, Data Collection and Analysis Procedure 221
12.4 Results: The Existence of Randomness 222
12.4.1 Stage 1: Lesson Planning 222
12.4.2 Stage 2: Lesson Implementation 224
12.4.3 Stage 3: Reflection 225
12.5 Discussion 226
12.6 Limitations of the Study 228
12.7 Implications for Teacher Education and Future Research 228
References 229
13 Design, Implementation, and Evaluation of an Instructional Sequence to Lead Primary School Students to Comparing Groups in Statistical Projects 232
13.1 Introduction 232
13.2 Conducting Statistical Projects in Primary School 233
13.2.1 Understanding Statistical Displays 234
13.2.2 Exploring Large Datasets 235
13.2.3 Comparing Groups 236
13.3 Design and Implementation of Activities to Enhance Early Statistical Reasoning and to Lead Grade 4 Students to Comparing Groups 237
13.4 Study of Primary School Students’ Statistical Reasoning When Comparing Groups After Attending to Our Activities 244
13.5 Results 248
13.6 Conclusion and Discussion 250
References 252
14 Data Representations in Early Statistics: Data Sense, Meta-Representational Competence and Transnumeration 254
14.1 Introduction 254
14.2 Background 255
14.2.1 Statistical Literacy 255
14.2.2 Representations in Statistics Education 256
14.2.3 Reading and Building Our Own Representations 256
14.3 Conceptual Framework 257
14.3.1 Meta-Representational Competence 257
14.3.2 Some Components of Representations 258
14.3.3 Transnumeration 258
14.3.4 Statistical Thinking 259
14.3.5 Data Sense 259
14.4 Methodology 260
14.4.1 Participants and Context 260
14.4.2 Statistics Lesson Design by Teachers in Lesson Study 260
14.5 Statistics Lessons in Preschool and School 261
14.5.1 Preschool Lesson (Three Preschool Pupils) 261
14.5.2 Second Grade Lesson (Two Pupils) 263
14.5.3 The Role of the Teacher in Statistics Lessons 267
14.6 Conclusions 267
14.7 Projections and Opportunities 268
References 269
15 Supporting Young Children to Develop Combinatorial Reasoning 272
15.1 Statement of Problem 272
15.2 Theoretical Framework 274
15.2.1 Multiplicative Reasoning 276
15.2.2 Combinatorics and Combinatorial Counting Problems 276
15.3 Methodology 277
15.4 Results 278
15.5 Discussion 282
15.6 Conclusions and Implications 285
References 286
Teaching Statistics and Probability: Modelling 288
16 Integrating Games into the Early Statistics Classroom: Teachers’ Professional Development on Game-Enhanced Learning 289
16.1 Introduction 290
16.2 Theoretical Perspective 291
16.3 Methodology 293
16.3.1 Conceptual Framework 293
16.3.2 Research Design: Scope and Context of Study 293
16.3.3 Instruments, Data Collection, and Analysis Procedure 295
16.4 Results 295
16.4.1 Changes in Attitudes and Perceptions Regarding Game-Enhanced Learning 296
16.4.2 Changes in Participants’ TPACK Competency for Using Digital Games 297
16.4.3 Transfer and Adoption of TPACK Competencies to Teaching Practice 300
16.5 Conclusions and Implications for Teaching and Research 304
References 305
17 Young Children’s Statistical Literacy in Modelling with Data and Chance 308
17.1 Defining Statistical Literacy 308
17.2 Developing Statistical Literacy Through Modelling 309
17.3 Variation 310
17.4 Informal Inference 311
17.5 Investigations in Modelling with Data and Chance 312
17.5.1 Background 312
17.5.2 Design and Analysis 312
17.5.3 Investigation Implementation 313
17.6 Sample of Findings 315
17.6.1 Identifying Variation 315
17.6.2 Drawing Inferences 316
17.6.3 Creating Representations and Interpreting Resultant Models 317
17.7 Discussion and Concluding Points 320
References 324

Produkt-Details

• Erscheint lt. Verlag: 23.7.2018
• Reihe/Serie: Early Mathematics Learning and Development
• Reihe/Serie: Early Mathematics Learning and Development
• Zusatzinfo: XXIV, 313 p. 73 illus.
• Verlagsort: Singapore
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Sozialwissenschaften ► Pädagogik ► Vorschulpädagogik
• Schlagworte: constructivist gaming environments • Early childhood education • early childhood teachers • early statistical reasoning • game-enhanced learning • inference and informal inference • inscription capacities • Learning and Instruction • lesson planning • mathematics education • picture books • probability language • Problem Solving • statistical inquiry • statistical investigation • statistical literacy, thinking and reasoning • stochastical reasoning • Teacher Education • Teaching and learning • variability and variation
• ISBN-10: 981-13-1044-0 / 9811310440
• ISBN-13: 978-981-13-1044-7 / 9789811310447