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

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

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

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

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Overview

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.


Product Details

ISBN-13: 9781071818428
Publisher: SAGE Publications
Publication date: 04/06/2021
Series: Corwin Mathematics Series
Pages: 264
Sales rank: 33,039
Product dimensions: 7.00(w) x 9.90(h) x 0.50(d)

About the Author

John J. San Giovanni is a mathematics coordinator in Howard County, Maryland. There, he leads mathematics curriculum development, digital learning, assessment, and professional development. John is an adjunct professor and coordinator of the Elementary Mathematics Instructional Leadership graduate program at Mc Daniel College. In addition to this Figuring Out Fluency series, some of his many Corwin books include Daily Routines to Jump-Start Problem Solving, Grades K-8, 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 currently on the board of directors for the National Council of Supervisors of Mathematics (NCSM).

Table of Contents

Foreword Christina Tondevold xix

Preface xxi

Acknowledgments xxvi

About the Authors xxviii

1 What does Fluency Really mean, and Why Does it Matter? 1

What is Fluency in Mathematics? 1

Fluency Actions 4

Checks for Reasonableness 9

Fluency for each and Every Student 15

Mathematics Identity and Agency through Fluency 16

Productive beliefs about Access and Equity for Fluency 18

Effective Teaching Practices for Fluency Instruction 19

Figuring Out Fluency: Setting Clear Goals 20

2 Fluency Fallacies and Related Truths 23

Language Fallacies 23

Fluency Fallacy #1: Fluency is about Basic Facts 24

Fluency Fallacy #2: Mastery, Fluency, and Automaticity are the Same Thing 25

Fluency Fallacy #3: Representations are Strategies 26

Standard Algorithms 28

Fluency Fallacy #4: Strategies and Algorithms are the Same Thing 28

Fluency Fallacy #5: Once Learned, the Standard Algorithm is the Best Choice 29

Access and Equity 31

Fluency Fallacy #6: Standard Algorithms are Standard Everywhere 31

Fluency Fallacy #7: Some Students are Setter Off with Knowing Just One Way 33

Teaching and Assessing 35

Fluency Fallacy #8: Procedural Fluency Practice is a Low-Level Cognitive Experience 36

Fluency Fallacy #9: First Learn Concepts, Then Learn Procedures 38

Fluency Fallacy #10: There is a Set List of Strategies for any Given Topic 40

Fluency Fallacy #11: Skills Tests Assess Fluency 41

Fluency Fallacy #12: Conceptual Understanding is More Important than Learning Skills 42

Figuring Out Fluency: Replacing Fallacies with Truths 42

3 Good (And Necessary) Beginnings for Fluency 47

Conceptual Understanding 48

Properties and Utilities for Strategic Competence 52

Distance from a 10 52

Decomposing Numbers Flexibly 53

Part-Part-Whole 55

Skip Counting 56

Distributive Property 57

Good Beginnings: Basic Fact Fluency 59

#1 A Strategy-Based Approach Leads to "Better"-Learned Facts 59

#2 Facts Strategies are Needed Beyond Basic Facts 64

#3 Learning Basic Fact Strategies Develops Mathematical Agency 66

Computational Estimation 67

Computational Estimation Strategies 68

Tips for Advancing Computational Estimation 72

The Effect of Operating on Numbers 73

Figuring Out Fluency: Good Beginnings 74

4 Seven Significant Strategies for Developing Fluency 76

Developing Strategic Competence 77

1 Count On/Count Back (Addition and Subtraction) 78

What it is 78

Visuals to Support 78

Situations that Connect 79

2 Make Tens (Addition) 80

What it is 80

Visuals to Support 81

Situations that Connect 83

3 Use Partials (Addition, Subtraction, Multiplication, and Division) 84

What it is 84

Visuals to Support 88

Situations that Connect 89

4 Break Apart to Multiply (Multiplication) 89

What it is 89

Visuals to Support 91

Situations that Connect 93

5 Halve and Double (Multiplication) 93

What it is 93

Visuals to Support 94

Situations that Connect 95

6 Compensation (Addition, Subtraction, and Multiplication) 96

What it is 96

Visuals to Support 98

7 Use an Inverse Relationship (Subtraction and Division) 101

What it is 101

Visuals to Support and Situations that Connect 101

Explicit Strategy Instruction 102

Figuring Out Fluency: Seven Significant Reasoning Strategies 104

5 Automaticity Beyond the Basic Facts 107

Automaticity 108

Learning Progression for Automaticity with Basic Facts 108

Automaticity and Fluency 109

Tips for Developing Procedural Automaticities 111

Procedural Automaticities 112

Breaking Apart all Numbers Through 10 113

Base 10 Combinations 115

Using 25s 117

Using 15s and 30s 118

Doubling 120

Halving 121

Fraction Equivalents within Fraction Families 125

Conversions Between Common Decimals and Fractions 126

Figuring Out Fluency: Procedural Automaticities 127

6 Fluency Practice is Not a Worksheet 130

Characteristics of Quality Fluency Practice 131

Quality Practice is Focused 131

Quality Practice is Varied 133

Quality Practice is Processed 134

Quality Practice is Connected 136

Frequently Asked Questions about Fluency Practice 137

Types of Fluency Practice 139

Fluency Routines 139

Worked Examples 144

Games 147

Centers 150

Independent Practice 152

Figuring Out Fluency: Quality Practice 152

7 Beyond Accuracy: What We Need to Assess and the Tools to do it 154

Assessing Fluency 154

Planning for and Assessing Strategies and Automaticities 155

Assessing Fluency Components and Actions 159

Grading Fluency 163

Assessment Options Beyond Quizzes and Tests 164

Observations 165

Student Interviews 167

Journal Prompts 169

Self-Assessments 172

Figuring Out Fluency: Assessing Fluency 174

8 Engaging Families in Fluency 176

Frequently asked Questions about Fluency Instruction 177

FAQ #1: Why Does Fluency Matter for My Child? 178

FAQ #2: When Will they Ever Need all of these Strategies? 178

FAQ #3: How Will this Help My Child Do Well on the Tests they Have to Take? 178

FAQ #4: Why is this Math so Different from What I Learned? 179

FAQ #5: Why are Basic Facts and the Procedures We Learned Not Taught any Longer? 179

FAQ #6: Why Doesn't Speed Matter Anymore? 180

FAQ #7: Math Is Right or Wrong. So Why Doesn't the Right Answer Count Anymore? 180

FAQ #8: Why Do They Have to Solve a Problem in So Many Different Ways? 180

FAQ #9: Don't All of these Strategies Just Confuse Children? 183

FAQ #10: Why Don't Children Practice Basic Facts and Algorithms a Lot (Like We Did)? 183

Tips for Responding to FAQs 183

Taking Action to Inform And Engage Families 184

Back-to-School and Orientation Events 184

Newsletters, Classroom Updates, and Websites 186

Fluency Brochures 187

Family Fluency Events 188

Video Shorts 189

Classroom Visits 190

Figuring Out Fluency: Engaging Families 190

9 Fluency is the Focus: Planning, Agreement, and Action 192

Planning for Fluency 192

Unit Planning for Fluency 194

Daily Planning for Fluency 196

Collaborative Agreements: Adapting, Adopting, and Eliminating 199

Figuring Out Fluency: Taking Action 209

Appendix A Activity List 210

Appendix B Strategy and Automaticity Reference Page 213

References 214

Index 222

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