RtI in Math : Evidence-Based Interventions book cover
2nd Edition

RtI in Math
Evidence-Based Interventions

  • Available for pre-order. Item will ship after May 20, 2021
ISBN 9780367818999
May 20, 2021 Forthcoming by Routledge
240 Pages 114 B/W Illustrations

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Book Description

Learn how to help K-8 students who struggle in math. Now in its second edition, this book provides a variety of clear, practical strategies that can be implemented right away to boost student achievement. Discover how to design lessons that work with struggling learners, implement math intervention recommendations from the Institute of Education Sciences Practice Guides, the National Center on Intensive Intervention, and CEC, use praise and self-motivation more effectively, develop number sense and computational fluency, teach whole numbers and fractions, increase students’ problem-solving abilities, and more! This edition features an all-new overview of effective instructional practices to support academic engagement and success, ideas for intensifying instruction within tiered interventions, and a detailed set of recommendations aligned to both CCSSM and CEC/CEEDAR’s High Leverage Practices to help support students struggling to meet grade-level expectations. Extensive, current examples are provided for each strategy, as well as lesson plans, games, and resources. 

Table of Contents

Meet the Authors


Chapter 1: Overview of Response to Intervention

  • What is Response to Intervention?
    • Evidence-Based Instruction
    • Data-Driven Instruction
    • Tiered Support
    • Models of Implementation

  • Summary

Chapter 2: Using Assessment to Make Instructional Decisions

  • Step 1: Problem Identification
  • Step 2: Problem Analysis
  • Step 3: Intervention Plan Development
  • Step 4: Plan Implementation
  • Step 5: Plan Evaluation
  • Summary

Chapter 3: Overview of Evidence-Based Practices for Teaching Mathematics

  • What is the Core Curriculum?
    • Description of the core curriculum
    • Evidence-Based Practices for the Core Curriculum (Tier 1)
      • Emphasize critical concepts
      • Teach critical foundations to mastery
      • Balance conceptual understanding, fluency and problem solving
      • Use a combination of teacher-centered and student-centered approaches
      • Follow the C-P-A sequence
      • Select high quality programs and implement them with fidelity

  • Interventions to Support Students who Struggle in Mathematics (Tiers 2 & 3)
    • Use Explicit, Systematic Instruction
    • Use Visual Representations
    • Focus Intensely on Whole Numbers and Rational Numbers
    • Build Fluent Retrieval of Basic Facts
    • Teach Students to Use Underlying Structures to Solve Word Problems
    • Include Motivational Strategies
    • Intensify Instruction

  • Summary

Chapter 4: Setting the Stage: Increasing Motivation

  • Why Focus on Motivation?
  • Increasing Motivation by Creating Meaningful, Engaging Lessons
  • Using Self-Monitoring and Goal-Setting to Increase Motivation
  • Effective Use of Praise
  • Rewards
  • Summary

Chapter 5: Explicit and Systematic Instruction

  • Instructional Considerations for Struggling Learners

  • The Explicit Instruction Lesson
    • Instructional Objective
    • Lesson Introduction
      • Engage Students
      • Review Prerequisite Skills and Concepts

    • Presentation of New Content (Modeling)
    • Guided Practice
    • Independent Practice
      • Massed Practice
      • Distributed Practice

    • Lesson Closure

  • How Explicit Instruction Improves Motivation
  • Summary

Chapter 6: Concrete and Visual Representation

  • Research on the Concrete-Pictorial-Abstract (CPA) Sequence
  • Virtual Manipulatives
  • Recommendations for Implementing the CPA Sequence
  • Summary

Chapter 7: Developing Number Sense

  • Counting and Representing Whole Numbers
    • Counters
    • Touch Math
    • Ten Frames
    • Number Lines

  • Magnitude Comparison
  • Place Value
    • Base Ten Blocks
    • KP Ten-Frame Tiles
    • DigiBlocks
    • Place Value Disks
    • Household Objects

  • Intensifying Instruction
  • Summary

Chapter 8: Operations with Whole Numbers: Addition & Subtraction

  • Developing Conceptual Understanding of Addition and Subtraction
  • Developing Computational Fluency with Basic Facts
  • Solving Multi-Digit Addition & Subtraction Problems
    • The Low Stress or Partial Sums Algorithms for Addition
    • The Standard Algorithm for Addition
    • The Standard Algorithm for Subtraction

  • Intensifying Instruction During Interventions
  • Summary

Chapter 9: Operations with Whole Numbers: Multiplication & Division

  • Developing Conceptual Understanding of Multiplication
  • Understanding Division
  • Developing Fluency with Multiplication & Division Facts
  • Multi-Digit Multiplication Algorithms
    • Multiplication with Rectangular Arrays
    • Area Models
    • The Standard Algorithm for Multiplication
    • Lattice Multiplication

  • Multi-Digit Division
    • The Standard Algorithm for Division
    • Alternative Algorithms for Division

  • Intensifying Instruction During Interventions
  • Summary

Chapter 10: Fact Fluency

  • Developing Strategies for Solving Basic Facts
    • Addition Facts
    • Subtraction Facts
    • Multiplication Facts
    • Division Facts
    • Selecting an Effective Strategy

  • Automaticity
    • Cover-Copy-Compare (CCC)
    • Classwide Peer Tutoring
    • Incremental Rehearsal
    • Taped Problems
    • Computer-Based Instruction (CBI)
    • Additional Ideas for Providing Mastery Practice

  • Summary

Chapter 11: Representing Rational Numbers

  • Fractions
    • Developing Fraction Concepts
    • Using the CPA Sequence with More Advanced Fraction Skills
    • Equivalent Fractions
    • Adding and Subtracting Fractions
    • Multiplying Fractions
    • Dividing Fractions

  • Decimals
  • Percent
  • Intensifying Instruction
  • Summary

Chapter 12: Problem Solving

  • Problem Solving in the Core Curriculum (Tier 1)
  • Teaching Problem Solving During Interventions (Tier 2 & Tier 3)
    • Adding & Subtraction Part/Whole Problems
    • Multiplying & Dividing Part/Whole Problems
    • Solving Additive Compare Problems
    • Solving Multiplicative Comparison Problems
    • Solving 2-Step Problems
    • Intensifying Instruction
    • Summary

Chapter 13: Conclusion: Using RtI to Improve Achievement in Mathematics

  • Selecting Materials for Core Instruction (Tier 1)
  • Selecting Materials for Interventions (Tiers 2 & 3)
  • Intensifying Instruction
  • Summary


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Dr. Linda Forbringer is Associate Professor and Special Education Program Director for the Department of Special Education and Communication Disorders at Southern Illinois University Edwardsville. Before joining SIUE, Dr. Forbringer served as a classroom teacher, a liaison teacher-counselor, and then administrator of a day treatment center serving kindergarten through twelfth grade students. She has presented on Response to Intervention in mathematics, differentiating instruction, and motivation at a variety of national and international conferences, including the Learning Disabilities Association, Council for Exceptional Children, International Council for Learning Disabilities, National Council of Teachers of Mathematics and National Council of Supervisors of Mathematics. Dr. Wendy Weber is Associate Professor in the Department of Special Education and Communication Disorders at Southern Illinois University Edwardsville. Dr. Weber also serves as the Principal Investigator and Project Coordinator of the Illinois Institutes of Higher Education Partnership, a federally-funded Statewide Professional Development Grant that assists teacher preparation programs integrate MTSS into course content and field experiences. In addition to her work with the IHE Partnership, Dr. Weber provides professional development and educational consulting to school districts in Southern Illinois in the areas of Response to Intervention/Multi-Tier System of Supports (MTSS), school improvement, and maximizing student engagement.