Sarama / Clements / Germeroth The Development of Early Childhood Mathematics Education

1. Auflage 2017
ISBN: 978-0-12-813449-8
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band Volume 53, 322 Seiten

Reihe: Advances in Child Development and Behavior

The Development of Early Childhood Mathematics Education, Volume 53 in the Advances in Child Development and Behavior series, includes chapters that highlight some of the most recent research in the field of developmental psychology. Users will find updated chapters on a variety of topics, including sections on The DREME Network: Research and Interventions in Early Childhood Mathematics, The Use of Concrete Experiences in Early Childhood Mathematics Instruction, Interventions in Early Mathematics: Avoiding Pollution and Dilution, Coaching in Early Mathematics, and Designing Studies to Test Causal Questions About Early Math: The Development of Making Pre-K Count. Each chapter provides in-depth discussions, with this volume serving as an invaluable resource for developmental or educational psychology researchers, scholars and students. - Contains chapters that highlight some of the most recent research in the area of child development and behavior - Presents a wide array of topics that are discussed in detail

Autoren/Hrsg.

Sarama, Julie

Clements, Douglas

Germeroth, Carrie

Day-Hess, Crystal

Inhaltsverzeichnis

1;Front Cover;1
2;The Development of Early Childhood Mathematics Education;4
3;Copyright;5
4;Contents;6
5;Contributors;10
6;Preface;12
7;Chapter One: The DREME Network: Research and Interventions in Early Childhood Mathematics;16
7.1;1. The DREME Network;17
7.1.1;1.1. A Need for More Opportunity and Access;17
7.1.2;1.2. New Evidence on the Importance of Early Math;17
7.1.3;1.3. Increasing Acceptance of Academic Instruction in Preschool;18
7.1.4;1.4. DREME’s Central Goals;19
7.1.4.1;1.4.1. Increasing Capacity: Creating Resources for Early Childhood Teacher Educators;19
7.1.4.2;1.4.2. MMM Instruction: Using Math Activities to Support Math and Executive Function Skills in Early Childhood;20
7.1.4.3;1.4.3. Parents’ and Early Caregivers’ Engagement in Math Activities With Young Children;20
7.1.4.4;1.4.4. Preschool-Elementary Continuity and Coherence;22
7.2;2. MMM Instruction: An In-Depth Look at a DREME Network Project;23
7.2.1;2.1. Early Math, EF, and Curricula;23
7.2.1.1;2.1.1. Early Mathematics Curricula;23
7.2.2;2.2. EF and Mathematics;28
7.2.3;2.3. Preliminary EF Study Work;29
7.2.3.1;2.3.1. Phase 1: Description of Activities;30
7.2.3.2;2.3.2. Phase 2: Selecting Fecund Activities;33
7.2.3.3;2.3.3. Phase 3: Developing Archetype Activities;44
7.2.3.4;2.3.4. Phase 4: Microgenetic Testing of Select Archetype Activities;49
7.3;3. Conclusion;50
7.4;Acknowledgments;50
7.5;References;50
8;Chapter Two: The Use of Concrete Experiences in Early Childhood Mathematics Instruction;58
8.1;1. What Is Concrete?;59
8.2;2. What Is a Worthwhile Concrete Activity?;62
8.3;3. How Can Concrete Experiences Be Used Effectively in Early Childhood Mathematics Instruction?;66
8.3.1;3.1. Perspectives From Cognitive Psychology;66
8.3.1.1;3.1.1. Cognitive Alignment Framework;66
8.3.1.2;3.1.2. The Dual-Representation Hypothesis;70
8.3.2;3.2. Perspective Based on Dewey’s Interaction Principle and Learning Trajectories;75
8.3.2.1;3.2.1. Patterning;75
8.3.2.2;3.2.2. A Linear Representation and Its Hypothesized Developmental Prerequisites;79
8.3.2.2.1;3.2.2.1. Increasing Magnitude Principle;79
8.3.2.2.2;3.2.2.2. Successor Principle;81
8.3.2.3;3.2.3. Introducing Addition and Subtraction Using a Number-Line Model;82
8.3.2.4;3.2.4. Base-Ten and Place-Value Concepts and Skills;83
8.3.2.4.1;3.2.4.1. Understanding Multidigit Numbers in Terms of Base-Ten/Place-Value Concepts;83
8.3.2.4.2;3.2.4.2. Magnitude Comparisons and a Linear Representation to 100;86
8.3.3;3.3. Instructional Strategies for Ensuring Educative Experiences;87
8.3.3.1;3.3.1. Eight Guidelines;87
8.3.3.2;3.3.2. A Case in Point;95
8.4;4. Is There Evidence That Concrete Experiences Work?;97
8.5;5. Conclusions;99
8.6;Acknowledgments;102
8.7;References;102
9;Chapter Three: Interventions in Early Mathematics: Avoiding Pollution and Dilution;110
9.1;1. Background;111
9.2;2. The TRIAD Model;112
9.2.1;2.1. Theoretical Framework;112
9.2.1.1;2.1.1. Interactions;112
9.2.1.2;2.1.2. Administrators and Other School Leaders (Fig. 1, Factors K and I);112
9.2.1.3;2.1.3. Communication;113
9.2.1.4;2.1.4. Teachers and Professional Development (Fig. 1, Factors E, N, and Q);114
9.2.1.5;2.1.5. Children and Their Families (Fig. 1, Factors F, G, and P);117
9.2.1.6;2.1.6. Resources, Curriculum, and Technology;117
9.2.2;2.2. The TRIAD Model’s 10 Guidelines;117
9.2.3;2.3. How the TRIAD Implementation Was Designed to Militate Against Pollution and Dilution;120
9.3;3. Research Evaluations: Did the TRIAD Design Mitigate Dilution and Pollution?;125
9.3.1;3.1. Initial Instantiation and Evaluations of the TRIAD Model;126
9.3.1.1;3.1.1. Implementation;126
9.3.1.2;3.1.2. Findings;129
9.3.2;3.2. Full-Scale Implementation and Evaluation of TRIAD;130
9.3.2.1;3.2.1. Implementation;130
9.3.2.2;3.2.2. Findings;131
9.3.3;3.3. Fighting Dilution Over Time: TRIAD and Sustainability;133
9.4;4. Final Words;135
9.5;Acknowledgments;136
9.6;References;136
10;Chapter Four: Coaching in Early Mathematics;142
10.1;1. Overview of Coaching Research;143
10.1.1;1.1. Coaching on Math;144
10.1.2;1.2. Coaching in Education;146
10.1.3;1.3. Coaching Models;147
10.1.3.1;1.3.1. Cognitive Coaching;147
10.1.3.2;1.3.2. Content-Focused Coaching;147
10.1.3.3;1.3.3. Instructional Coaching;148
10.1.3.4;1.3.4. Mathematics Coaching;148
10.1.4;1.4. Characteristics of Effective Coaches;149
10.2;2. Coaching/Mentoring Model for Two Large-Scale Projects in Early Math;150
10.2.1;2.1. TRIAD (Technology-Enhanced, Research-Based, Instruction, Assessment, and PD);150
10.2.2;2.2. TRIAD Theoretical Framework;152
10.2.3;2.3. Research-Based Guidelines for Scaling Up;153
10.2.4;2.4. TRIAD Intervention;155
10.2.5;2.5. Mentor Role;156
10.2.6;2.6. Mentor Training;157
10.2.7;2.7. Implementation of Mentoring in TRIAD;157
10.2.8;2.8. Effectiveness of TRIAD as a PD Model;160
10.2.9;2.9. EMERGE (Early Math, Early Regulation: Good for Everyone);161
10.2.10;2.10. EMERGE Theoretical Framework;162
10.2.11;2.11. EMERGE Intervention;163
10.2.12;2.12. EMERGE Coaches;164
10.2.13;2.13. Coach Training;166
10.2.14;2.14. Implementation of Coaching in EMERGE;166
10.2.15;2.15. Frequency and Duration;166
10.2.16;2.16. Fidelity Ratings;166
10.2.17;2.17. Qualitative Observation Notes;170
10.2.17.1;2.17.1. Direct Coaching Interventions;171
10.2.17.2;2.17.2. Identified Needs;172
10.2.18;2.18. Effectiveness of EMERGE as a PD Model;173
10.3;3. Concluding Thoughts;174
10.4;Acknowledgments;175
10.5;References;176
11;Chapter Five: Notice, Explore, and Talk About Mathematics: Making a Positive Difference for Preschool Children, Families, ...;184
11.1;1. Introduction;186
11.2;2. Importance of Young Children’s Early Mathematics Learning;186
11.2.1;2.1. Early Childhood and Learning;187
11.2.2;2.2. The Role of Families in Young Children’s Learning;189
11.2.3;2.3. Helping Families to Help Their Young Children Learn Mathematics;190
11.3;3. Noticing, Exploring, and Talking About Mathematics;192
11.3.1;3.1. Let’s Count;194
11.4;4. Evaluating the Impact of Let’s Count;197
11.4.1;4.1. Longitudinal Evaluation Method;197
11.4.2;4.2. Data Collection: Adult Participants;198
11.4.3;4.3. Data Collection: Child Participants;199
11.4.4;4.4. Methods of Analysis;200
11.4.4.1;4.4.1. Children;200
11.4.4.2;4.4.2. Adult Participants;200
11.5;5. The Impact of Let’s Count on Children’s Mathematics Knowledge;200
11.5.1;5.1. Tasks With Small Sets;200
11.5.2;5.2. Recognizing and Matching Quantities and Numerals;203
11.5.3;5.3. Pattern and Structure;203
11.5.4;5.4. Counting and Ordering Numerals;205
11.5.5;5.5. Measuring Time and Length;207
11.5.6;5.6. Properties of Shapes and Spatial Visualization;207
11.5.7;5.7. Calculating;208
11.5.8;5.8. Summary;211
11.6;6. Educators Noticing, Exploring, and Talking About Children’s Mathematics;211
11.6.1;6.1. Engaging Families With Mathematical Learning and Let’s Count;212
11.6.2;6.2. Continuity of Mathematical Learning Between Early Childhood Setting and Home;213
11.6.3;6.3. Impact of Let’s Count on Educator Confidence, Professional Identity, and Pedagogical Practice;214
11.6.4;6.4. Awareness of the Potential of Everyday Tasks for Prompting Mathematics Discussion;215
11.6.5;6.5. Sustainability of Let’s Count Over Time;217
11.6.6;6.6. Children’s Engagement With Mathematical Learning and Mathematical Concepts;218
11.6.7;6.7. Importance of Mathematical Language;220
11.7;7. Parents Noticing, Exploring, and Talking About Children’s Mathematics;221
11.7.1;7.1. Themes Emerging From Parent Interviews;221
11.7.2;7.2. Noticing Children’s Mathematical Learning and Facilitating That Learning in the Everyday;222
11.7.3;7.3. Parent-Educator Communication About Mathematics and Let’s Count, With an Emphasis on Strengths of All Involved;224
11.7.4;7.4. Children’s Growing Confidence, Knowledge, and Enjoyment of/Engagement With Mathematics;225
11.7.5;7.5. Importance of Mathematical Language;227
11.7.6;7.6. Positive Impacts Within Families, Extending to Older, and Younger Siblings’ Inclusion in Mathematical Activities at ...;228
11.7.7;7.7. Sustainability of Let’s Count Over Time;229
11.8;8. Discussion;230
11.8.1;8.1. How Does Participation in Let’s Count Impact on Children’s Numeracy Knowledge and Dispositions as They Make the Tr ...;230
11.8.2;8.2. What Is the Impact of Let’s Count on the Educator Participants’ Knowledge, Interest, and Confidence in Mathematics ...;232
11.8.3;8.3. What Is the Impact of Let’s Count on the Participating Families’ Confidence, and Knowledge About Noticing, Investi ...;233
11.9;9. Conclusion;233
11.10;Acknowledgments;235
11.11;References;235
12;Chapter Six: Designing Studies to Test Causal Questions About Early Math: The Development of Making Pre-K Count;242
12.1;1. Making Pre-K Count and High 5s;244
12.2;2. Design Considerations for Building a Strong Test of the Effects of Math on Children’s Long-Term Outcomes;245
12.2.1;2.1. Selecting the Strongest Intervention;246
12.2.1.1;2.1.1. Review of Efficacy Evidence;246
12.2.1.2;2.1.2. Review of Content and Program Delivery;247
12.2.1.3;2.1.3. Review of Implementation Requirements and Readiness for Scale-Up;249
12.2.2;2.2. Designing tor Scale: Ensuring Strong Implementation;250
12.2.3;2.3. Considering the Counterfactual Condition and Context;253
12.2.4;2.4. Building a Rigorous Design;255
12.2.5;2.5. Measuring Children’s Outcomes Over Time;257
12.2.6;2.6. Addressing the Fade-Out of Effects;260
12.3;3. Early Findings and Conclusion;263
12.4;References;266
13;Chapter Seven: Interventions for Primary School Children With Difficulties in Mathematics;270
13.1;1. Interventions of Different Levels of Intensiveness;272
13.2;2. Examples of Small-Group Interventions;273
13.3;3. Peer Tuition and Group Collaboration;276
13.4;4. Games as an Aid to Arithmetical Intervention;278
13.5;5. Individualized Interventions: The History Behind Them;281
13.6;6. Potential Problems With Individualized Instruction and Remediation: Past and Present;283
13.7;7. Individualized Intervention Programs With Young Children: Recent Work;284
13.8;8. ``Wave 3’’ Materials in the United Kingdom;284
13.9;9. Intensive Intervention Programs for Children With Severe Difficulties;285
13.10;10. Mathematics Recovery;285
13.11;11. Numbers Count;287
13.12;12. Lighter-Touch Interventions;288
13.13;13. Catch Up Numeracy;289
13.14;14. Some Conclusions About Targeted Interventions;292
13.15;15. How Important Is Age to Intervention in Mathematics?;292
13.16;16. Training in Domain-General Cognitive Skills;293
13.17;17. Training in Piagetian Operations;293
13.18;18. Training in Metacognition;294
13.19;19. Training in Working Memory and Executive Function;294
13.20;20. Larger-Group Interventions;296
13.21;21. The Response to Intervention Approach;296
13.22;22. Conclusions;297
13.23;References;297
14;Chapter Eight: Early Executive Function and Mathematics Relations: Correlation Does Not Ensure Concordance;304
14.1;1. Binary Correlations and Concordant Performance Levels;308
14.2;2. Exploring Discordance for EF and Mathematics: A Glimpse of Two Studies;309
14.2.1;2.1. Prekindergarten Children From a Low SES Sample;309
14.2.2;2.2. Primary School Children From an Average SES Sample;311
14.2.3;2.3. Three Models of Mathematics Difficulty Based on EF and Mathematics Relations;314
14.2.3.1;2.3.1. Concordant Profiles;315
14.2.3.2;2.3.2. Discordant Profiles;316
14.2.4;2.4. Caveats Concerning Figs. 1 and 2;318
14.3;3. Conclusion;318
14.4;Acknowledgments;319
14.5;References;319
15;Back Cover;324