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

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 * 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 * 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 * 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
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 * 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 * 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 * 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 * 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 * 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 * Portland, OR *
Everything you need and want to know about fluency is clearly spelled out in Jennifer Bay-Williams and John SanGiovanni’s masterful new book, Figuring Out Fluency in Mathematics Teaching and Learning! This incredibly amazing resource defines what fluency is along with specific actions teachers need to take to help students understand, choose, and use effective strategies. A must-have for all math coaches and every K–8 teacher, this book provides practical tools, great activities, and fun games! After reading this book, everyone will understand that mastery, fluency, and automaticity are just not the same thing!
-- Ruth Harbin Miles * Staunton, VA *
In this practical and comprehensive resource Jennifer Bay-Williams and John SanGiovanni take a deep dive into one of the often-misinterpreted components of rigorous mathematics instruction—procedural fluency. Along with thorough explanations, engaging mathematical routines, tasks, and games, the authors offer a ‘just-right’ amount of research to ground each of the claims to powerful instruction in mathematics. This is a timely good-for-all, necessary-for-some resource for teaching/learning in mathematics. -- Yana Ioffe * North Bay, Ontario, Canada *
Figuring Out Fluency in Mathematics Teaching and Learning provides a masterful approach to unpacking the meaning of mathematical fluency while investigating widely held fallacies. The authors provide a plethora of high-cognitive demand activities that teach and develop fluency. These activities are sure to become my go-to resources for implicitly teaching fluency!
-- Melynee Naegele, President * Claremore (OK) Public Schools *