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Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8: Moving Beyond Basic Facts and Memorization [Pehme köide]

(Howard Public School System), (University of Louisville, KY)
  • Formaat: Paperback / softback, 264 pages, kõrgus x laius: 254x177 mm, kaal: 500 g
  • Sari: Corwin Mathematics Series
  • Ilmumisaeg: 15-Jun-2021
  • Kirjastus: Corwin Press Inc
  • ISBN-10: 1071818422
  • ISBN-13: 9781071818428
Teised raamatud teemal:
  • Formaat: Paperback / softback, 264 pages, kõrgus x laius: 254x177 mm, kaal: 500 g
  • Sari: Corwin Mathematics Series
  • Ilmumisaeg: 15-Jun-2021
  • Kirjastus: Corwin Press Inc
  • ISBN-10: 1071818422
  • ISBN-13: 9781071818428
Teised raamatud teemal:

Teach your students to become decision makers who rely on their own mathematical thinking.

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.

Arvustused

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 * Youve heard the saying, You dont know what you dont 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 dont 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 K5 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 fluencyefficiency, flexibility, and accuracythis 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 SanGiovannis 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 K8 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 instructionprocedural 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 *

Foreword xix
Christina Tondevold
Preface xxi
Acknowledgments xxvi
About the Authors xxviii
1 What Does Fluency Really Mean, And Why Does It Matter?
1(22)
What Is Fluency In Mathematics?
1(14)
Fluency Actions
4(5)
Checks For Reasonableness
9(6)
Fluency For Each And Every Student
15(5)
Mathematics Identity And Agency Through Fluency
16(2)
Productive Beliefs About Access And Equity For Fluency
18(1)
Effective Teaching Practices For Fluency Instruction
19(1)
Figuring Out Fluency: Setting Clear Goals
20(3)
2 Fluency Fallacies And Related Truths
23(24)
Language Fallacies
23(5)
Fluency Fallacy #1: Fluency Is About Basic Facts
24(1)
Fluency Fallacy #2: Mastery, Fluency, And Automaticityare The Same Thing
25(1)
Fluency Fallacy #3: Representations Are Strategies
26(2)
Standard Algorithms
28(3)
Fluency Fallacy #4: Strategies And Algorithms Are The Same Thing
28(1)
Fluency Fallacy #5: Once Learned, The Standard Algorithm Isthe Best Choice
29(2)
Access And Equity
31(4)
Fluency Fallacy #6: Standard Algorithms Are Standard Everywhere
31(2)
Fluency Fallacy #7: Some Students Are Better Off With Knowing Just One Way
33(2)
Teaching And Assessing
35(7)
Fluency Fallacy #8: Procedural Fluency Practice Is A Low-Level Cognitive Experience
36(2)
Fluency Fallacy #9: First Learn Concepts, Then Learn Procedures
38(2)
Fluency Fallacy #10: There Is A Set List Of Strategies For Any Given Topic
40(1)
Fluency Fallacy #11: Skills Tests Assess Fluency
41(1)
Fluency Fallacy #12: Conceptual Understanding Is More Important Than Learning Skills
42(1)
Figuring Out Fluency: Replacing Fallacies With Truths
42(5)
3 Good (And Necessary) Beginnings For Fluency
47(29)
Conceptual Understanding
48(4)
Properties And Utilities For Strategic Competence
52(7)
Distance From A10
52(1)
Decomposing Numbers Flexibly
53(2)
Part-Part-Whole
55(1)
Skipcounting
56(1)
Distributive Property
57(2)
Good Beginnings: Basic Fact Fluency
59(8)
#1A Strategy-Based Approach Leads To "Better'-Learned Facts
59(5)
#2 Facts Strategies Are Needed Beyond Basic Facts
64(2)
#3 Learning Basic Fact Strategies Develops Mathematical Agency
66(1)
Computational Estimation
67(7)
Computational Estimation Strategies
68(4)
Tips For Advancing Computational Estimation
72(1)
The Effect Of Operating On Numbers
73(1)
Figuring Out Fluency: Good Beginnings
74(2)
4 Seven Significant Strategies For Developing Fluency
76(31)
Developing Strategic Competence
77(1)
1 Count On/Count Back (Addition And Subtraction)
78(2)
What It Is
78(1)
Visuals to support
78(1)
Situations That Connect
79(1)
2 Make Tens (Addition)
80(4)
What It Is
80(1)
Visuals to support
81(2)
Situations That Connect
83(1)
3 Use Partials (Addition, Subtraction, Multiplication, And Division)
84(5)
What It Is
84(4)
Visuals to support
88(1)
Situations That Connect
89(1)
4 Break Apart to Multiply (Multiplication)
89(4)
What It Is
89(2)
Visuals to support
91(2)
Situations That Connect
93(1)
5 Halve And Double (Multiplication)
93(3)
What It Is
93(1)
Visuals to support
94(1)
Situations That Connect
95(1)
6 Compensation (Addition, Subtraction, And Multiplication)
96(5)
What It Is
96(2)
Visuals to support
98(3)
7 Use An Inverse Relationship (Subtraction And Division)
101(1)
What It Is
101(1)
Visuals To Support And Situations That Connect
101(1)
Explicit Strategy Instruction
102(2)
Figuring Out Fluency: Seven Significant Reasoning Strategies
104(3)
5 Automaticity Beyond The Basic Facts
107(23)
Automaticity
108(4)
Learning Progression For Automaticity With Basic Facts
108(1)
Automaticity And Fluency
109(2)
Tips For Developing Procedural Automaticities
111(1)
Procedural Automaticities
112(15)
Breaking Apart All Numbers Through 10
113(2)
Base 10 Combinations
115(2)
Using 25S
117(1)
Using 15S And 30S
118(2)
Doubling
120(1)
Halving
121(4)
Fraction Equivalents Within Fraction Families
125(1)
Conversions Between Common Decimals And Fractions
126(1)
Figuring Out Fluency: Procedural Automaticities
127(3)
6 Fluency Practice Is Not A Worksheet
130(24)
Characteristics Of Quality Fluency Practice
131(8)
Quality Practice Is Focused
131(2)
Quality Practice Is Varied
133(1)
Quality Practice Is Processed
134(2)
Quality Practice Is Connected
136(1)
Frequently Asked Questions About Fluency Practice
137(2)
Types Of Fluency Practice
139(13)
Fluency Routines
139(5)
Worked Examples
144(3)
Games
147(3)
Centers
150(2)
Independent Practice
152(1)
Figuring Out Fluency: Quality Practice
152(2)
7 Obeyond Accuracy: What We Need To Assess And The Tools To Do It
154(22)
Assessing Fluency
154(10)
Planning Forand Assessing Strategies And Automaticities
155(4)
Assessing Fluency Components And Actions
159(4)
Grading Fluency
163(1)
Assessment Options Beyond Quizzes And Tests
164(10)
Observations
165(2)
Student Interviews
167(2)
Journal Prompts
169(3)
Self-Assessments
172(2)
Figuring out fluency: Assessing Fluency
174(2)
8 Engaging Families In Fluency
176(16)
Frequently Asked Questions About Fluency Instruction
177(7)
Faq #1 Why Does Fluency Matter For My Child?
178(1)
Faq #2 When Will They Ever Need All Of These Strategies?
178(1)
Faq #3 How Will This Help My Child Do Well On The Tests They Have To Take?
178(1)
Faq #4 Whyis This Math So Different From What I Learned?
179(1)
Faq #5 Why Are Basic Facts And The Procedures We Learned Not Taught Any Longer?
179(1)
Faq #6 Why Doesn't Speed Matter Anymore?
180(1)
Faq #7 Math Is Right Or Wrong. So Why Doesn't The Right Answer Count Anymore?
180(1)
Faq #8 Why Do They Have To Solve A Problem In So Many Different Ways?
180(3)
Faq #9 Don't All Of These Strategies Justconfuse Children?
183(1)
Faq #10 Why Don't Children Practice Basic Facts And Algorithms A Lot (Like We Did)?
183(1)
Tips For Responding To Faqs
183(1)
Taking Action To Inform And Engage Families
184(6)
Back-To-School And Orientation Events
184(2)
Newsletters, Classroom Updates, And Websites
186(1)
Fluency Brochures
187(1)
Family Fluency Events
188(1)
Video Shorts
189(1)
Classroom Visits
190(1)
Figuring Out Fluency: Engaging Families
190(2)
9 Fluency Is The Focus: Planning, Agreement, And Action
192(18)
Planning For Fluency
192(7)
Unit planning For Fluency
194(2)
Daily Planning For Fluency
196(3)
Collaborative Agreements: Adapting, Adopting, And Eliminating
199(10)
Figuring Out fluency: Taking Action
209(1)
Appendix A Activity List 210(3)
Appendix B Strategy And Automaticity Reference Page 213(1)
References 214(8)
Index 222
Jennifer M. Bay-Williams is a professor of mathematics education at the University of Louisville, where she teaches preservice teachers, emerging elementary mathematics specialists, and doctoral students in mathematics education. She has authored over 40 books and 100 journal articles/book chapters, many of which focus on procedural fluency and developing mathematical proficiency. Beyond the Figuring out Fluency series, these include Math Fact Fluency, and Everything you Need for Mathematics Coaching and Elementary: Teaching Developmentally and Middle School Mathematics. Jennifers national leadership includes NCTM Board of Directors, the TODOS: Mathematics for All Board of Directors, and as president and secretary of the Association of Mathematics Teacher Educators (AMTE). John J. SanGiovanni is a mathematics coordinator in Howard County, Maryland. There, he leads mathematics curriculum development, digital learning, assessment, and professional development. John is passionate about growing new mathematics leaders in the district and through McDaniel College. In addition to the Figuring Out Fluency series, some of his many Corwin books include Daily Routines to Jump-Start Problem Solving, Grades K8; Answers to Your Biggest Questions About Teaching Elementary Math; the Daily Routines to Jump-Start Math series; and Productive Math Struggle: A 6-Point Action Plan for Fostering Perseverance. John is a national mathematics curriculum and professional learning consultant who also speaks frequently at national conferences and institutes. He is active in state and national professional organizations, recently serving on the board of directors for the National Council of Teachers of Mathematics (NCTM) and on the board of directors for NCSM.