Chapter
1.1. A Need for More Opportunity and Access
1.2. New Evidence on the Importance of Early Math
1.3. Increasing Acceptance of Academic Instruction in Preschool
1.4. DREME’s Central Goals
1.4.1. Increasing Capacity: Creating Resources for Early Childhood Teacher Educators
1.4.2. MMM Instruction: Using Math Activities to Support Math and Executive Function Skills in Early Childhood
1.4.3. Parents’ and Early Caregivers’ Engagement in Math Activities With Young Children
1.4.4. Preschool-Elementary Continuity and Coherence
2. MMM Instruction: An In-Depth Look at a DREME Network Project
2.1. Early Math, EF, and Curricula
2.1.1. Early Mathematics Curricula
2.3. Preliminary EF Study Work
2.3.1. Phase 1: Description of Activities
2.3.2. Phase 2: Selecting Fecund Activities
2.3.3. Phase 3: Developing Archetype Activities
2.3.4. Phase 4: Microgenetic Testing of Select Archetype Activities
Chapter Two: The Use of Concrete Experiences in Early Childhood Mathematics Instruction
2. What Is a Worthwhile Concrete Activity?
3. How Can Concrete Experiences Be Used Effectively in Early Childhood Mathematics Instruction?
3.1. Perspectives From Cognitive Psychology
3.1.1. Cognitive Alignment Framework
3.1.2. The Dual-Representation Hypothesis
3.2. Perspective Based on Dewey’s Interaction Principle and Learning Trajectories
3.2.2. A Linear Representation and Its Hypothesized Developmental Prerequisites
3.2.2.1. Increasing Magnitude Principle
3.2.2.2. Successor Principle
3.2.3. Introducing Addition and Subtraction Using a Number-Line Model
3.2.4. Base-Ten and Place-Value Concepts and Skills
3.2.4.1. Understanding Multidigit Numbers in Terms of Base-Ten/Place-Value Concepts
3.2.4.2. Magnitude Comparisons and a Linear Representation to 100
3.3. Instructional Strategies for Ensuring Educative Experiences
4. Is There Evidence That Concrete Experiences Work?
Chapter Three: Interventions in Early Mathematics: Avoiding Pollution and Dilution
2.1. Theoretical Framework
2.1.2. Administrators and Other School Leaders (Fig. 1, Factors K and I)
2.1.4. Teachers and Professional Development (Fig. 1, Factors E, N, and Q)
2.1.5. Children and Their Families (Fig. 1, Factors F, G, and P)
2.1.6. Resources, Curriculum, and Technology
2.2. The TRIAD Model’s 10 Guidelines
2.3. How the TRIAD Implementation Was Designed to Militate Against Pollution and Dilution
3. Research Evaluations: Did the TRIAD Design Mitigate Dilution and Pollution?
3.1. Initial Instantiation and Evaluations of the TRIAD Model
3.2. Full-Scale Implementation and Evaluation of TRIAD
3.3. Fighting Dilution Over Time: TRIAD and Sustainability
Chapter Four: Coaching in Early Mathematics
1. Overview of Coaching Research
1.2. Coaching in Education
1.3.1. Cognitive Coaching
1.3.2. Content-Focused Coaching
1.3.3. Instructional Coaching
1.3.4. Mathematics Coaching
1.4. Characteristics of Effective Coaches
2. Coaching/Mentoring Model for Two Large-Scale Projects in Early Math
2.1. TRIAD (Technology-Enhanced, Research-Based, Instruction, Assessment, and PD)
2.2. TRIAD Theoretical Framework
2.3. Research-Based Guidelines for Scaling Up
2.7. Implementation of Mentoring in TRIAD
2.8. Effectiveness of TRIAD as a PD Model
2.9. EMERGE (Early Math, Early Regulation: Good for Everyone)
2.10. EMERGE Theoretical Framework
2.11. EMERGE Intervention
2.14. Implementation of Coaching in EMERGE
2.15. Frequency and Duration
2.17. Qualitative Observation Notes
2.17.1. Direct Coaching Interventions
2.18. Effectiveness of EMERGE as a PD Model
Chapter Five: Notice, Explore, and Talk About Mathematics: Making a Positive Difference for Preschool Children, Families, ...
2. Importance of Young Children’s Early Mathematics Learning
2.1. Early Childhood and Learning
2.2. The Role of Families in Young Children’s Learning
2.3. Helping Families to Help Their Young Children Learn Mathematics
3. Noticing, Exploring, and Talking About Mathematics
4. Evaluating the Impact of Let’s Count
4.1. Longitudinal Evaluation Method
4.2. Data Collection: Adult Participants
4.3. Data Collection: Child Participants
4.4.2. Adult Participants
5. The Impact of Let’s Count on Children’s Mathematics Knowledge
5.1. Tasks With Small Sets
5.2. Recognizing and Matching Quantities and Numerals
5.3. Pattern and Structure
5.4. Counting and Ordering Numerals
5.5. Measuring Time and Length
5.6. Properties of Shapes and Spatial Visualization
6. Educators Noticing, Exploring, and Talking About Children’s Mathematics
6.1. Engaging Families With Mathematical Learning and Let’s Count
6.2. Continuity of Mathematical Learning Between Early Childhood Setting and Home
6.3. Impact of Let’s Count on Educator Confidence, Professional Identity, and Pedagogical Practice
6.4. Awareness of the Potential of Everyday Tasks for Prompting Mathematics Discussion
6.5. Sustainability of Let’s Count Over Time
6.6. Children’s Engagement With Mathematical Learning and Mathematical Concepts
6.7. Importance of Mathematical Language
7. Parents Noticing, Exploring, and Talking About Children’s Mathematics
7.1. Themes Emerging From Parent Interviews
7.2. Noticing Children’s Mathematical Learning and Facilitating That Learning in the Everyday
7.3. Parent-Educator Communication About Mathematics and Let’s Count, With an Emphasis on Strengths of All Involved
7.4. Children’s Growing Confidence, Knowledge, and Enjoyment of/Engagement With Mathematics
7.5. Importance of Mathematical Language
7.6. Positive Impacts Within Families, Extending to Older, and Younger Siblings’ Inclusion in Mathematical Activities at ...
7.7. Sustainability of Let’s Count Over Time
8.1. How Does Participation in Let’s Count Impact on Children’s Numeracy Knowledge and Dispositions as They Make the Tr ...
8.2. What Is the Impact of Let’s Count on the Educator Participants’ Knowledge, Interest, and Confidence in Mathematics ...
8.3. What Is the Impact of Let’s Count on the Participating Families’ Confidence, and Knowledge About Noticing, Investi ...
Chapter Six: Designing Studies to Test Causal Questions About Early Math: The Development of Making Pre-K Count
1. Making Pre-K Count and High 5s
2. Design Considerations for Building a Strong Test of the Effects of Math on Children’s Long-Term Outcomes
2.1. Selecting the Strongest Intervention
2.1.1. Review of Efficacy Evidence
2.1.2. Review of Content and Program Delivery
2.1.3. Review of Implementation Requirements and Readiness for Scale-Up
2.2. Designing tor Scale: Ensuring Strong Implementation
2.3. Considering the Counterfactual Condition and Context
2.4. Building a Rigorous Design
2.5. Measuring Children’s Outcomes Over Time
2.6. Addressing the Fade-Out of Effects
3. Early Findings and Conclusion
Chapter Seven: Interventions for Primary School Children With Difficulties in Mathematics
1. Interventions of Different Levels of Intensiveness
2. Examples of Small-Group Interventions
3. Peer Tuition and Group Collaboration
4. Games as an Aid to Arithmetical Intervention
5. Individualized Interventions: The History Behind Them
6. Potential Problems With Individualized Instruction and Remediation: Past and Present
7. Individualized Intervention Programs With Young Children: Recent Work
8. ``Wave 3’’ Materials in the United Kingdom
9. Intensive Intervention Programs for Children With Severe Difficulties
12. Lighter-Touch Interventions
14. Some Conclusions About Targeted Interventions
15. How Important Is Age to Intervention in Mathematics?
16. Training in Domain-General Cognitive Skills
17. Training in Piagetian Operations
18. Training in Metacognition
19. Training in Working Memory and Executive Function
20. Larger-Group Interventions
21. The Response to Intervention Approach
Chapter Eight: Early Executive Function and Mathematics Relations: Correlation Does Not Ensure Concordance
1. Binary Correlations and Concordant Performance Levels
2. Exploring Discordance for EF and Mathematics: A Glimpse of Two Studies
2.1. Prekindergarten Children From a Low SES Sample
2.2. Primary School Children From an Average SES Sample
2.3. Three Models of Mathematics Difficulty Based on EF and Mathematics Relations
2.3.1. Concordant Profiles
2.3.2. Discordant Profiles
2.4. Caveats Concerning Figs. 1 and 2
The Development of Early Childhood Mathematics Education
( Volume 53 )
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