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Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8

Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8
Moving Beyond Basic Facts and Memorization

Foreword by Christina Tondevold, Because fluency practice is not a worksheet

March 2021 | 264 pages | Corwin

Because fluency practice is not a worksheet. 

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand.

Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes:

  •  “Seven Significant Strategies” to teach to students as they work toward procedural fluency.
  •  Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency.
  • Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency.
  • Suggestions for engaging families in understanding and supporting fluency.

Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.

Foreword by Christina Tondevold
What Does Fluency Really Mean and Why Does it Matter?
Fluency Fallacies and Related Truths
Good (and Necessary) Beginnings for Fluency
Seven Significant Strategies for Developing Fluency
Automaticity Beyond the Basic Facts
Fluency Practice is Not a Worksheet
Beyond Accuracy: What We Need to Assess and the Tools to Do It
Engaging Families in Fluency
Fluency Is the Focus: Planning, Agreement, and Action
Appendix A: Activity List
Appendix B: Strategies and Automaticities Reference Page

I had an epiphany reading this book. I now really understand what fluency means when my students learn math. This book will help you teach strategies that will promote metacognition in your students. They will become confident and happy learners when dealing with math.

Tamara Daugherty
Third-Grade Teacher
Orange County Public Schools, Orlando, FL

You’ve heard the saying, ‘You don’t know what you don’t know!’ After reading Figuring Out Fluency, I found realization in this statement. After more than 30 years as a mathematics educator, I thought I knew everything there was to know about fluency. Wrong! This book is a must have for those who are novices and for those who want to know what they don’t know about fluency.

Thomasenia Lott Adams
Associate Dean for Research & Faculty Development, University of Florida
Gainesville, FL

In my work as an elementary school teacher, math coach, and curriculum writer, fluency is always a hot topic of discussion in terms of how it develops and progresses across grade levels and grade spans. I truly appreciate the focus on conceptual understanding, reasonableness, and flexibility that is continually woven throughout every chapter of the book. These underpinnings alongside actionable ideas to use right away in classrooms make this book a valuable resource for any K–5 teacher or mathematics coach.

Kristin Gray
Director K–5 Curriculum and Professional Learning
Illustrative Mathematics

Fluency is so much richer than facts and algorithms, and real fluency in mathematics includes reasoning and creativity. In Figuring Out Fluency, the authors take you on a journey of understanding, implementation, and reflection. They share relatable research, usable activities for the classroom and families, and most importantly the framework for an equitable action plan.

Christine Percy
Florida Council of Teacher of Mathematics

This book is an essential resource needed in every mathematics educators’ hands! This is THE fluency playbook to ensure students engage in meaningful fluency learning.

Crystal Lancour
Supervisor of Curriculum and Instruction, Colonial School District
Middletown, DE

There is a piercing that readers will undoubtably feel at the many fallacies, unproductive beliefs, and inequities around fluency practiced in our classrooms today. Figuring Out Fluency is an incredible new book that offers mathematics educators everything they need to be equipped to create a coherent equitable approach to fluency. A MUST-READ!

Tara Fulton
District Mathematics Coordinator, Crane School District
Yuma, AZ

I strongly appreciate that Figuring Out Fluency pushes us to think about fluency as providing learners opportunities to author their own ideas while developing flexibility in thinking and understanding facts, algorithms, and procedures. When learners have the authority to engage their own ideas, this positively impacts how they see themselves as doers of mathematics. Figuring Out Fluency challenges our conceptions of what it means to be fluent, and it unpacks ways for educators to support learners, families, and other educators to deepen their understanding. I particularly love the strategies provided in this book and the framing fluency.

Robert Q. Berry, III
Samuel Braley Gray Professor of Mathematics Education, University of Virginia
Charlottesville, VA

Are you ready to help your students connect their number talks and number routines to the real world? Figuring Out Fluency will give you the routines, games, protocols, and resources you need to help your students build their fluency in number sense (considering reasonableness, strategy selection, flexibility, and more). Our students deserve the opportunity to build a positive and confident math identity. We can help support them to build this identity by providing them with access to a variety of strategies and the confidence to know when to use them.

Sarah Gat
Instructional Coach, Upper Grand District School Board
Guelph, Ontario, Canada

In far too many settings and for far too many years, fluency has been considered as being adept at implementing computational algorithms. So, thank you Jennifer Bay-Williams and John SanGiovanni for this first deep analysis of the importance of fluency. Anchored by the components of fluency—efficiency, flexibility, and accuracy—this amazing resource, which is based on both research and classroom-validated instructional practice, fully addresses the absolute necessity of conceptual understanding of operations, the important role of properties, and student access to a repertoire of methods: Real fluency. This must-have resource will truly influence teaching and teacher education.

Francis (Skip) Fennell
Professor of Education and Graduate and Professional Studies Emeritus, McDaniel College
Westminster, MD

Figuring Out Fluency goes beyond other resources currently on the market. It not only provides a robust collection of strategies and routines for developing fluency but also pays critical attention to the ways teachers can empower each and every student as mathematical thinkers who can make strategic decisions about their computation approaches. If you are looking for instruction and assessment approaches for fluency that move beyond getting the right answer, this is the resource for you.

Nicole Rigelman
Professor of Mathematics Education, Portland State University
Portland, OR

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