Allsopp2e excerpt.pdf
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
Contents
About the Activities and Forms ... v
About the Authors ... vii
Preface ... ix
Acknowledgments ... xv
1 Critical Components of Meaningful and Effective Mathematics Instruction for Students with Disabilities and Other Struggling Learners ... 1
I Identify and Understand the Mathematics
2 The Big Ideas in Mathematics and Why They Are Important ... 15
3 Children’s Mathematics: Learning Trajectories ... 41
II Learning the Needs of Your Students and the Importance of Continuous Assessment
4 Barriers to Mathematical Success for Students with Disabilities and Other Struggling Learners ... 69
5 Math Assessment and Struggling Learners ... 97
III Plan and Implement Responsive Instruction
6 Making Flexible Instructional Decisions: A Continuum of Instructional Choices for Struggling Learners ... 137
7 Essential Instructional Approaches for Struggling Learners in Mathematics ... 155
8 Changing Expectations for Struggling Learners: Integrating the Essential Instructional Approaches with the NCTM Mathematics Teaching Practices ... 217
9 Mathematics MTSS/RTI and Research on Mathematics Instruction for Struggling Learners ... 239
10 How to Intensify Assessment and Essential Instructional Approaches within MTSS/RTI ... 247
11 Intensifying Math Instruction Across Tiers within MTSS: Evaluating System-Wide Use of MTSS ... 269
IV Bringing It All Together
12 The Teaching Mathematics Meaningfully Process ... 281
References ... 299
Appendices
A Take Action Activities ... 313
B ARC Assessment Planning Form ... 337
C Peer-Tutoring Practice Activity ... 341
D Using a Think-Aloud ... 343
E Case Study ... 345
Index ... 375
About the Authors
David H. Allsopp, Ph.D.
Professor of Special Education, College of Education, University of South Florida.
LouAnn H. Lovin, Ph.D.
Professor of Mathematics Education, Department of Mathematics and Statistics, James Madison University.
Sarah van Ingen, Ph.D.
Assistant Professor of Mathematics Education, Department of Childhood Education and Literacy, College of Education, University of South Florida.
Preface
Welcome to the second edition of Teaching Mathematics Meaningfully: Solutions for Reaching Struggling Learners. Since the first edition, additional research has been published detailing how students in general, students with disabilities, and other struggling learners progress in their reasoning and understanding in various mathematical domains.
Purpose
Meaning is the seminal theme of this book. Its purpose is to help teachers facilitate struggling learners’ access to high-quality mathematics so those learners can make sense of the mathematics and become mathematically proficient.
Audience
This book is written for special educators, elementary and middle school educators, and prospective and in-service teachers who strive to enhance their ability to teach mathematics effectively to struggling learners.
How the Book is Organized
The book begins with an introductory chapter followed by 11 additional chapters organized in four parts. It provides a conceptual framework for meaningful and effective mathematics instruction for struggling learners, ensuring collaboration between special education and mathematics education.
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, instructional approaches that address their unique learning needs, and a commitment from teachers to help them reach understanding.
Five Components of Meaningful and Effective Mathematics Instruction
- Identify and Understand the Mathematics: Teachers should explicitly identify, deeply understand, and teach the big ideas in mathematics.
- Continuously Assess Students: Continuous assessment should inform instructional decisions, showing how well students understand target ideas.
- Determine Students’ Math-Specific Learning Needs: Understanding where students are in their mathematical thinking and skills is crucial.
- Determine Struggling Learners’ Specific Learning Needs: Teacher awareness of the performance traits of struggling learners informs instructional decisions.
- Plan and Implement Responsive Instruction: Responsive instruction based on continuous assessment makes mathematics accessible to learners.