Differentiating Math Instruction: Strategies That Work for K-8 Classrooms, Second Edition Book

Preface: How to Use This Book
Acknowledgments
About the Author
1. The Mathematical Brain and High-Impact Teaching
Teaching Mathematics Through Differentiating Instruction
The Mathematical Brain
Brains as Prioritizing Filters
Number Sense
Multiple Intelligences: Avenues for Learning Math
Summary of Brain Research
Instructional Phases for Developing Math Skills
Teaching Strategy: Mathematical Games to Develop Number Sense
SHEMR: A Tool for High-Impact Learning in Mathematics Evaluating One's Own Instructional Planning
What's Next?
2. Differentiated Instruction and Response to Intervention in Mathematics
Differentiation and Response to Intervention: Refocusing Math Instruction
Teaching Phases in the Direct Instruction Lesson
Problems With Direct Instruction in a Large Class
Teaching Strategy: The Guess, Assess, and Tear Out Tactic
A Differentiated Instruction Lesson Example
Teaching Strategy: Using Guess, Assess, and Tear Out! Moving From Direct Instruction to Differentiated Instruction in Math
The Omega Group
The Mainline Instruction Group
The Beta Group
Is Further Differentiation Needed?
Anything Wrong With This Scenario? Enhancing the Differentiated Instruction Model
Guidelines for Differentiated Lesson Planning
Results of Differentiated Lessons
A Differentiated Instruction Overview: What It Is and What It Isn't
Response to Intervention in Mathematics
Case Study: A RTI for Number Sense and Early Math Skill
What's Next?
3. Differentiating for Primary and Elementary Math
Research on Math Readiness
Steps in DevelopingEarly Math Skills
Teaching Strategy: A Concrete, Semi-Concrete, Abstract Learning Tactic
Using CSA in the Classroom
CSA in the Higher Grades
Summary: CSA Tactic
Teaching Strategy: The Errorless Learning Procedures
Summary: Errorless Learning
Teaching Strategy: Classwide Peer Tutoring for Differentiating in the Math Class
What's Next?
4. Differentiating for Deep Conceptual Understanding
High-Impact Teaching for Operations in Math
The Debate on Calculators in Elementary Mathematics
Constructivist Theory and Understanding of Mathematics
Using Cognitive Guided Visualization
Scaffolded Instruction in Math
Debate on What a Scaffold Is
Graphic Representations of Word Problem Schemas
Using a Representational Strategy
Teaching Expanded Notation and Partialing
Process Mnemonics Strategies to Teach Computation
Research Support
What's Next?
5. Differentiating With Learning Strategies
The Brain Research Basis for Metacognitive Theory and Tactics
Learning Strategies for Word Problems
The Schema-Based Math Strategy
Differentiated Tear Out Activities for Story Problem Schemas
What's Next?
6. Differentiating in the Middle Grades
Working Toward Higher-Order Thinking
Teaching Strategy: Anchored Instruction
Teaching Games in Higher Grades
The PASS Strategy
Moving On Up! Math Instruction Guidelines for Secondary Learners
Appendix
References
Index