# Teaching Mathematics Meaningfully

## Solutions for Reaching Struggling Learners

### Second Edition

by  
#### David H. Allsopp, Ph.D. University of South Florida  
#### Tampa  
#### LouAnn H. Lovin, Ph.D. James Madison University  
#### Harrisonburg, Virginia  
and  
#### Sarah van Ingen, Ph.D. University of South Florida  
#### Tampa

Copyright © 2018 by Paul H. Brookes Publishing Co., Inc. All rights reserved.

### About the Authors

#### David H. Allsopp, Ph.D.
Professor of Special Education, College of Education, University of South Florida, 4202 East Fowler Avenue, EDU 105, Tampa, Florida 33620

#### LouAnn H. Lovin, Ph.D.
Professor of Mathematics Education, Department of Mathematics and Statistics, James Madison University, 800 South Main Street, MSC 1911, Harrisonburg, Virginia 22807

#### Sarah van Ingen, Ph.D.
Assistant Professor of Mathematics Education, Department of Childhood Education and Literacy, College of Education, University of South Florida, 4202 East Fowler Avenue, EDU 202, Tampa, Florida 33620

## Preface

Welcome to the second edition of Teaching Mathematics Meaningfully: Solutions for Reaching Struggling Learners. This edition incorporates findings from updated research since the first edition, focusing on students’ learning trajectories in mathematics and integrating that information with effective instructional practices for struggling learners.

## Purpose

The purpose of this book is to help teachers facilitate struggling learners’ access to high-quality mathematics so they can make sense of the mathematics and become mathematically proficient. It integrates two main bodies of literature: special education and mathematics education.

## Audience

This book is written for special educators, elementary and middle school educators, and both prospective and in-service teachers aiming to enhance their ability to teach mathematics effectively to struggling learners.

## Contents
- **About the Activities and Forms**
- **About the Authors**
- **Preface**
- **Acknowledgments**
- **Chapter 1: Critical Components of Meaningful and Effective Mathematics Instruction for Students with Disabilities and Other Struggling Learners**
- **Chapter 2: The Big Ideas in Mathematics and Why They Are Important**
- **Chapter 3: Children’s Mathematics: Learning Trajectories**
- **Chapter 4: Barriers to Mathematical Success for Students with Disabilities and Other Struggling Learners**
- **Chapter 5: Math Assessment and Struggling Learners**
- **Chapter 6: Making Flexible Instructional Decisions**
- **Chapter 7: Essential Instructional Approaches for Struggling Learners in Mathematics**
- **Chapter 8: Changing Expectations for Struggling Learners**
- **Chapter 9: Mathematics MTSS/RTI and Research on Mathematics Instruction for Struggling Learners**
- **Chapter 10: How to Intensify Assessment and Essential Instructional Approaches within MTSS/RTI**
- **Chapter 11: Intensifying Math Instruction Across Tiers within MTSS**
- **Chapter 12: The Teaching Mathematics Meaningfully Process**
- **References**
- **Appendices**
- **Index**

## Critical Components of Meaningful and Effective Mathematics Instruction
To achieve success with the K–12 mathematics curriculum, struggling learners need teachers who understand their difficulties and address their unique learning needs.

### Five Components of Meaningful Instruction
1. **Identify and Understand the Mathematics:** Teachers must deeply understand the big ideas in mathematics.
2. **Continuously Assess Students:** Ongoing assessment allows teachers to determine students’ understanding and adjust instruction accordingly.
3. **Determine Students' Math-Specific Learning Needs:** Understand where students are in their mathematical thinking and skills.
4. **Determine Struggling Learners’ Specific Learning Needs:** Identify performance traits and barriers that affect learning.
5. **Plan and Implement Responsive Instruction:** Instruction should be tailored to meet the needs of each student, securing a meaningful learning experience.

The book provides a multistep process supported by literature in special education and mathematics education.

## Teaching for Deep Learning
Addressing big ideas in mathematics allows struggling learners to engage with content meaningfully. The effective teaching of mathematics considers both the "what" and the "how" of mathematical instruction.

### Summary of Essential Ideas
Throughout this book, educators will evaluate their practices and amplify their effectiveness in teaching mathematics to struggling learners, ensuring all students achieve mathematical proficiency.