Development of Early Childhood Mathematics Education (eBook)

Front Cover 1
The Development of Early Childhood Mathematics Education 4
Copyright 5
Contents 6
Contributors 10
Preface 12
Chapter One: The DREME Network: Research and Interventions in Early Childhood Mathematics 16
1. The DREME Network 17
1.1. A Need for More Opportunity and Access 17
1.2. New Evidence on the Importance of Early Math 17
1.3. Increasing Acceptance of Academic Instruction in Preschool 18
1.4. DREME’s Central Goals 19
1.4.1. Increasing Capacity: Creating Resources for Early Childhood Teacher Educators 19
1.4.2. MMM Instruction: Using Math Activities to Support Math and Executive Function Skills in Early Childhood 20
1.4.3. Parents’ and Early Caregivers’ Engagement in Math Activities With Young Children 20
1.4.4. Preschool-Elementary Continuity and Coherence 22
2. MMM Instruction: An In-Depth Look at a DREME Network Project 23
2.1. Early Math, EF, and Curricula 23
2.1.1. Early Mathematics Curricula 23
2.2. EF and Mathematics 28
2.3. Preliminary EF Study Work 29
2.3.1. Phase 1: Description of Activities 30
2.3.2. Phase 2: Selecting Fecund Activities 33
2.3.3. Phase 3: Developing Archetype Activities 44
2.3.4. Phase 4: Microgenetic Testing of Select Archetype Activities 49
3. Conclusion 50
Acknowledgments 50
References 50
Chapter Two: The Use of Concrete Experiences in Early Childhood Mathematics Instruction 58
1. What Is Concrete? 59
2. What Is a Worthwhile Concrete Activity? 62
3. How Can Concrete Experiences Be Used Effectively in Early Childhood Mathematics Instruction? 66
3.1. Perspectives From Cognitive Psychology 66
3.1.1. Cognitive Alignment Framework 66
3.1.2. The Dual-Representation Hypothesis 70
3.2. Perspective Based on Dewey’s Interaction Principle and Learning Trajectories 75
3.2.1. Patterning 75
3.2.2. A Linear Representation and Its Hypothesized Developmental Prerequisites 79
3.2.2.1. Increasing Magnitude Principle 79
3.2.2.2. Successor Principle 81
3.2.3. Introducing Addition and Subtraction Using a Number-Line Model 82
3.2.4. Base-Ten and Place-Value Concepts and Skills 83
3.2.4.1. Understanding Multidigit Numbers in Terms of Base-Ten/Place-Value Concepts 83
3.2.4.2. Magnitude Comparisons and a Linear Representation to 100 86
3.3. Instructional Strategies for Ensuring Educative Experiences 87
3.3.1. Eight Guidelines 87
3.3.2. A Case in Point 95
4. Is There Evidence That Concrete Experiences Work? 97
5. Conclusions 99
Acknowledgments 102
References 102
Chapter Three: Interventions in Early Mathematics: Avoiding Pollution and Dilution 110
1. Background 111
2. The TRIAD Model 112
2.1. Theoretical Framework 112
2.1.1. Interactions 112
2.1.2. Administrators and Other School Leaders (Fig. 1, Factors K and I) 112
2.1.3. Communication 113
2.1.4. Teachers and Professional Development (Fig. 1, Factors E, N, and Q) 114
2.1.5. Children and Their Families (Fig. 1, Factors F, G, and P) 117
2.1.6. Resources, Curriculum, and Technology 117
2.2. The TRIAD Model’s 10 Guidelines 117
2.3. How the TRIAD Implementation Was Designed to Militate Against Pollution and Dilution 120
3. Research Evaluations: Did the TRIAD Design Mitigate Dilution and Pollution? 125
3.1. Initial Instantiation and Evaluations of the TRIAD Model 126
3.1.1. Implementation 126
3.1.2. Findings 129
3.2. Full-Scale Implementation and Evaluation of TRIAD 130
3.2.1. Implementation 130
3.2.2. Findings 131
3.3. Fighting Dilution Over Time: TRIAD and Sustainability 133
4. Final Words 135
Acknowledgments 136
References 136
Chapter Four: Coaching in Early Mathematics 142
1. Overview of Coaching Research 143
1.1. Coaching on Math 144
1.2. Coaching in Education 146
1.3. Coaching Models 147
1.3.1. Cognitive Coaching 147
1.3.2. Content-Focused Coaching 147
1.3.3. Instructional Coaching 148
1.3.4. Mathematics Coaching 148
1.4. Characteristics of Effective Coaches 149
2. Coaching/Mentoring Model for Two Large-Scale Projects in Early Math 150
2.1. TRIAD (Technology-Enhanced, Research-Based, Instruction, Assessment, and PD) 150
2.2. TRIAD Theoretical Framework 152
2.3. Research-Based Guidelines for Scaling Up 153
2.4. TRIAD Intervention 155
2.5. Mentor Role 156
2.6. Mentor Training 157
2.7. Implementation of Mentoring in TRIAD 157
2.8. Effectiveness of TRIAD as a PD Model 160
2.9. EMERGE (Early Math, Early Regulation: Good for Everyone) 161
2.10. EMERGE Theoretical Framework 162
2.11. EMERGE Intervention 163
2.12. EMERGE Coaches 164
2.13. Coach Training 166
2.14. Implementation of Coaching in EMERGE 166
2.15. Frequency and Duration 166
2.16. Fidelity Ratings 166
2.17. Qualitative Observation Notes 170
2.17.1. Direct Coaching Interventions 171
2.17.2. Identified Needs 172
2.18. Effectiveness of EMERGE as a PD Model 173
3. Concluding Thoughts 174
Acknowledgments 175
References 176
Chapter Five: Notice, Explore, and Talk About Mathematics: Making a Positive Difference for Preschool Children, Families, ... 184
1. Introduction 186
2. Importance of Young Children’s Early Mathematics Learning 186
2.1. Early Childhood and Learning 187
2.2. The Role of Families in Young Children’s Learning 189
2.3. Helping Families to Help Their Young Children Learn Mathematics 190
3. Noticing, Exploring, and Talking About Mathematics 192
3.1. Let’s Count 194
4. Evaluating the Impact of Let’s Count 197
4.1. Longitudinal Evaluation Method 197
4.2. Data Collection: Adult Participants 198
4.3. Data Collection: Child Participants 199
4.4. Methods of Analysis 200
4.4.1. Children 200
4.4.2. Adult Participants 200
5. The Impact of Let’s Count on Children’s Mathematics Knowledge 200
5.1. Tasks With Small Sets 200
5.2. Recognizing and Matching Quantities and Numerals 203
5.3. Pattern and Structure 203
5.4. Counting and Ordering Numerals 205
5.5. Measuring Time and Length 207
5.6. Properties of Shapes and Spatial Visualization 207
5.7. Calculating 208
5.8. Summary 211
6. Educators Noticing, Exploring, and Talking About Children’s Mathematics 211
6.1. Engaging Families With Mathematical Learning and Let’s Count 212
6.2. Continuity of Mathematical Learning Between Early Childhood Setting and Home 213
6.3. Impact of Let’s Count on Educator Confidence, Professional Identity, and Pedagogical Practice 214
6.4. Awareness of the Potential of Everyday Tasks for Prompting Mathematics Discussion 215
6.5. Sustainability of Let’s Count Over Time 217
6.6. Children’s Engagement With Mathematical Learning and Mathematical Concepts 218
6.7. Importance of Mathematical Language 220
7. Parents Noticing, Exploring, and Talking About Children’s Mathematics 221
7.1. Themes Emerging From Parent Interviews 221
7.2. Noticing Children’s Mathematical Learning and Facilitating That Learning in the Everyday 222
7.3. Parent-Educator Communication About Mathematics and Let’s Count, With an Emphasis on Strengths of All Involved 224
7.4. Children’s Growing Confidence, Knowledge, and Enjoyment of/Engagement With Mathematics 225
7.5. Importance of Mathematical Language 227
7.6. Positive Impacts Within Families, Extending to Older, and Younger Siblings’ Inclusion in Mathematical Activities at ... 228
7.7. Sustainability of Let’s Count Over Time 229
8. Discussion 230
8.1. How Does Participation in Let’s Count Impact on Children’s Numeracy Knowledge and Dispositions as They Make the Tr ... 230
8.2. What Is the Impact of Let’s Count on the Educator Participants’ Knowledge, Interest, and Confidence in Mathematics ... 232
8.3. What Is the Impact of Let’s Count on the Participating Families’ Confidence, and Knowledge About Noticing, Investi ... 233
9. Conclusion 233
Acknowledgments 235
References 235
Chapter Six: Designing Studies to Test Causal Questions About Early Math: The Development of Making Pre-K Count 242
1. Making Pre-K Count and High 5s 244
2. Design Considerations for Building a Strong Test of the Effects of Math on Children’s Long-Term Outcomes 245
2.1. Selecting the Strongest Intervention 246
2.1.1. Review of Efficacy Evidence 246
2.1.2. Review of Content and Program Delivery 247
2.1.3. Review of Implementation Requirements and Readiness for Scale-Up 249
2.2. Designing tor Scale: Ensuring Strong Implementation 250
2.3. Considering the Counterfactual Condition and Context 253
2.4. Building a Rigorous Design 255
2.5. Measuring Children’s Outcomes Over Time 257
2.6. Addressing the Fade-Out of Effects 260
3. Early Findings and Conclusion 263
References 266
Chapter Seven: Interventions for Primary School Children With Difficulties in Mathematics 270
1. Interventions of Different Levels of Intensiveness 272
2. Examples of Small-Group Interventions 273
3. Peer Tuition and Group Collaboration 276
4. Games as an Aid to Arithmetical Intervention 278
5. Individualized Interventions: The History Behind Them 281
6. Potential Problems With Individualized Instruction and Remediation: Past and Present 283
7. Individualized Intervention Programs With Young Children: Recent Work 284
8. ``Wave 3’’ Materials in the United Kingdom 284
9. Intensive Intervention Programs for Children With Severe Difficulties 285
10. Mathematics Recovery 285
11. Numbers Count 287
12. Lighter-Touch Interventions 288
13. Catch Up Numeracy 289
14. Some Conclusions About Targeted Interventions 292
15. How Important Is Age to Intervention in Mathematics? 292
16. Training in Domain-General Cognitive Skills 293
17. Training in Piagetian Operations 293
18. Training in Metacognition 294
19. Training in Working Memory and Executive Function 294
20. Larger-Group Interventions 296
21. The Response to Intervention Approach 296
22. Conclusions 297
References 297
Chapter Eight: Early Executive Function and Mathematics Relations: Correlation Does Not Ensure Concordance 304
1. Binary Correlations and Concordant Performance Levels 308
2. Exploring Discordance for EF and Mathematics: A Glimpse of Two Studies 309
2.1. Prekindergarten Children From a Low SES Sample 309
2.2. Primary School Children From an Average SES Sample 311
2.3. Three Models of Mathematics Difficulty Based on EF and Mathematics Relations 314
2.3.1. Concordant Profiles 315
2.3.2. Discordant Profiles 316
2.4. Caveats Concerning Figs. 1 and 2 318
3. Conclusion 318
Acknowledgments 319
References 319
Back Cover 324