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The Development of Early Childhood Mathematics Education - Development of Early Childhood Mathematics Education
von: Julie Sarama, Douglas Clements, Carrie Germeroth, Crystal Day-Hess
Elsevier Book Series, 2017
ISBN: 9780128134498
Sprache: Englisch
324 Seiten, Download: 12922 KB
Format: EPUB, PDF, auch als Online-Lesen
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The Development of Early Childhood Mathematics Education - Development of Early Childhood Mathematics Education
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 |