Solving for Why: Understanding, Assessing, and Teaching Students Who Struggle with Math, Grades K–8


Solving for Why offers educators the tools and guidance essential for successfully solving for why students struggle with mathematics. The step-by-step, RTI (Response to Intervention)—like approaches, focused on assessment and communication with students, help teachers gain insight into student understanding in a remarkably different way than recipe-type approaches that assume the same solution applies to learners with similar struggles. With Solving for Why you’ll learn how to:

  • identify a struggling math learner;
  • develop theories for why a learner may be struggling;
  • facilitate a Concrete—Representational—Abstract (CRA) Assessment;
  • implement an insightful Collaborative Study;
  • conduct powerful student interviews;
  • support learners who struggle with memory challenges, attention deficit disorder, and affective difficulties (math anxiety);
  • differentiate instruction through a main lesson—menu lesson plan; and more.

John Tapper
256 Pages

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John Tapper is an Assistant Professor of Elementary Education at the University of Hartford. He has been a teacher in a variety of schools including the Primary Program, a nongraded elementary program in Westminster, Vermont. He has worked as a math coach, curriculum director, and education researcher. Dr Tapper has worked with students and teachers on improving their understanding of mathematics throughout the United States and,. Internationally, in Eastern Europe and Japan. He has conducted education research for the Donahue Institute at the University of Massachusetts and with the Kaput Center for Research and Innovation in STEM education. John lives in Vermont with his extended family and his very mathematical dogs.

"The new Common Core standards for mathematics demand that students (and teachers!) exhibit deeper conceptual understanding. That’s music to the ears of education professor John Tapper, who says we’ve overemphasized teaching procedures—and getting right answers. In his new book, Solving for Why, he makes a powerful case for moving beyond right and wrong and exploring what students understand, where they are struggling, and most important, why they are struggling."
Read more on Common Core: Solve Math Problems by Erich Storm, from Scholastic Instructor

"Solving for Why provides an eye-opening view of mathematics interventions that are teacher-friendly with student-centered results!"

Melony M. Brady
Principal, Annie Fisher STEM Magnet School, Hartford, Connecticut

"We all remember that special student, the one who struggled so hard to learn math concepts and procedures. We all remember trying strategy after strategy, with varying degrees of success. And, we all remember the questions we used to guide our thinking about helping that child: Why did the youngster struggle? How can we "get under the hood" to better understand that child's thinking? How can we best intervene to promote success for that child and for all diverse learners in ways that are both effective and efficient? Solving for Why addresses these concerns with concrete, specific, and actionable strategies that support teachers of mathematics, coaches, learning specialists, and school leaders in closing the achievement gap in mathematics in every classroom in every school in ways that are both insightful and impactful. By focusing on interventions to support each child, Tapper's book is an excellent guide for supporting all children and the dedicated teachers who serve them."

Maryann Marrapodi
Chief Learning Officer, Teachscape

"My prediction is that Solving for Why will become a much-referenced guide in how to authentically address the complex mathematical needs of our students. As a math coach, a question I hear daily is, "How do we know what we need to know and then what do we do about it?" John Tapper provides approaches that are explicit and clear. The result is a warm and, sometimes, humorous way to begin to find our own answers to many of our most persistent questions about mathematical thinking."

Veronica May Sampson
Math coach, Windham Southeast Supervisory Union
Brattleboro, Vermont

"Solving for Why is a must-have resource for math teachers, general educators, and special educators who are seeking ways to help their struggling students become successful math learners. The powerful and practical assessment approaches help teachers get to the heart of why their students are struggling in mathematics. By gaining insights into their students' math difficulties, teachers will be able to plan effective interventions and differentiated lessons that address their students' specific learning needs. The extensive classroom examples and helpful suggestions provide a wealth of ideas for teachers to apply with their students."

Amy Brodesky
Project director, Addressing Accessibility in Mathematics
Education Development Center (EDC)

"John Tapper has developed a valuable and engaging resource for teachers of struggling math learners, filled with classroom anecdotes and written in a clear, teacher-to-teacher voice. Grounded in research on mathematics education, his approach helps teachers understand each student's thinking as an entry point to promoting deep understanding of rigorous content."

Eliot Levine
University of Massachusetts and author of One Kid at a Time: Big Lessons from a Small School

"Solving for Why is a must-read for anyone who works with struggling mathematics learners. Dr. Tapper's thirty years of experience working with elementary school students and teachers along with his solid grasp of the research base on the teaching and learning of mathematics have resulted in a book that is wise, practical, and engaging. The book's organization, conversational style, and rich classroom examples make this an enjoyable and insightful read. I highly recommend this book to novice and veteran educators alike, who are searching for strategies for how to understand, assess, and best meet the needs of their struggling learners."

Jean McGivney-Burelle
Associate Professor of Mathematics and Director of the Secondary Mathematics Education Program
University of Hartford, W. Hartford, Connecticut

"In Solving for Why, John Tapper has developed a system to support teachers as they strive to understand all students' mathematical thinking. The process of collaborative study allows and encourages teachers to create hypotheses about students' mathematical understandings and test those hypotheses with the support of colleagues. This resource should be in the professional library of all teachers, special educators, mathematics coaches, and administrators who work with struggling mathematics students."

Elizabeth Petit Cunningham
Doctoral student and former classroom teacher
University of Nebraska–Lincoln

"Solving for Why is the book our mathematics teaching profession has been long waiting for! John Tapper has provided classroom teachers, special educators, mathematics coaches and school leaders an invaluable resource for helping struggling students deeply understand mathematics. Tapper combines foundational research and principles of effective mathematics instruction for struggling math learners with meaningful classroom vignettes to create a resource that explores specific strategies at both the teacher-student and school levels. Solving for Why should be in the hands of every educator who wants all K–8 students to succeed in mathematics."

Bob Laird
Vermont Mathematics Initiative and co-author of A Focus on Fractions: Bringing Research to the Classroom

icon pdf Table of Contents    icon pdf How to Use This Resource    icon pdf Chapter Excerpt

Each chapter includes reproducible templates for ease in carrying out the assessments. A final section offers resources for supporting students who struggle with additive reasoning, multiplicative reasoning, fractions, and proportional reasoning. The reproducibles are available for download upon purchase.

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