Cover

Half Title Page

Series Page

Title Page

Copyright

Dedication

About the Authors

Acknowledgments

Contents

1. Introduction

Math Matters

What Is Math Proficiency?

Applying Response to Intervention to Math

The Instructional Hierarchy

Acquisition Stage

Fluency Stage

Maintenance Stage

Generalization Stage

Adaptation Stage

Purpose of This Book

Acquisition

Fluency

Maintenance and Generalization

Conclusion

2. Effective Core Math Curriculum and Instruction

Curricular Content

Core Instruction

Instructional Content

Instructional Practices

Supplemental Instructional Practices

Computer-Assisted Instruction

Instructional Process

Peer-Assisted Learning

Conclusion

Appendix 2.1. Peer Tutoring Intervention Brief

3. Math Screening and Determining Student Groups

Universal Screening Procedures and Tools

Curriculum-Based Measurement

Computer-Adaptive Testing

Determining Risk Status

Student Risk Is Determined—Now What?

Refining Assessment to Match Instructional Interventions

Skill-by-Treatment Interaction

Conclusion

4. Classwide Math Interventions

Enhancing Computation Fluency and Word-Problem-Solving Skills Classwide

Classwide Interventions

Cover–Copy–Compare

Detect–Practice–Repair

Taped Problems

Explicit Timing

Classroom Hot Math

Differentiating Instruction at the Classwide Level

Conclusion

5. Computer-Assisted Math Instruction in Schools

Computers in Schools

Computer-Assisted Instruction

CAI and the Instructional Hierarchy

The Effectiveness of CAI

Implementation Considerations

Evaluating Readiness

System-Level Considerations

Student Considerations

Intensity and Implementation Considerations

Program Evaluation

Evidence-Based Teaching Practices

Correspondence to Curriculum

Data-Driven Individualization

Feedback to Students

Engaging Programming

Conclusion

6. Motivation and Math

Self-Regulated Learning

Forethought Phase

Performance Phase

Self-Reflection Phase

Struggling Students

Targeting Motivation

Goals and Goal Setting

Feedback

Promoting Student Self-Monitoring of Math Strategies

Conclusion

7. Core Features of Tiers 2 and 3 Math Interventions

Students' Difficulties with Math

Content Areas to Target for Intervention

Key Intervention Features for Struggling Students

Explicit Instruction

Strategy Instruction

Sequencing Instruction

Ongoing Progress Monitoring and Feedback

Drill, Practice, and Cumulative Review

Student Verbalization

Visual Representation

Motivation and Reinforcement

Conclusion

8. Early Numeracy Interventions

What Is Number Sense?

Counting and Cardinality

Magnitude Comparison

Research-Supported Interventions

Specific Interventions Targeting Number Foundations

Broad Interventions Targeting Whole-Number Knowledge

Conclusion

Appendix 8.1. The Great Race/Race to Space Intervention Brief

9. Basic and Complex Computation Interventions

Number Combinations: Why Is Automatic Retrieval Important?

Acquisition

Fluency

Research-Supported Interventions for Number Combinations

Procedural Computation

CRA Sequence

Conclusion

Appendix 9.1. Math to Mastery Intervention Brief

Appendix 9.2. Cover–Copy–Compare Intervention Brief

Appendix 9.3. Incremental Rehearsal Intervention Brief

Appendix 9.4. Taped Problems Intervention Brief

Appendix 9.5. Explicit Timing Intervention Brief

Appendix 9.6. High-Preference/Interspersed Problems Intervention Brief

Appendix 9.7. Concrete–Representation–Abstract Intervention Brief

10. Word-Problem Solving

Building Word-Problem-Solving Interventions

Research-Supported Interventions

Schema Instruction and Representation Techniques

Cognitive Strategy Instruction

Conclusion

Appendix 10.1. "Draw-It" Word-Problem-Solving Cycle Intervention Brief

Appendix 10.2. Math Scene Investigator Intervention Brief

11. Evaluating Student Progress and Making Intervention Adjustments

Collecting and Graphing Intervention Data

Basic Considerations Prior to Adjusting/Changing Intervention Supports

Determine Whether the Student Was Present for Most (e.g., 85–95%) of the Intervention Sessions

Collect and Evaluate Treatment Integrity Data

Adjusting Interventions According to Progress Monitoring Data

Performance Exceeds the Goal Line

Performance Meets the Goal Line

Performance Is below the Goal Line

Conclusion

12. Conclusion

References

Index