Foreword |
|
xix | |
|
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) |
|
|
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) |
|
|
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) |
|
|
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) |
|
|
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) |
|
|
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) |
|
|
48 | (4) |
|
Properties And Utilities For Strategic Competence |
|
|
52 | (7) |
|
|
52 | (1) |
|
Decomposing Numbers Flexibly |
|
|
53 | (2) |
|
|
55 | (1) |
|
|
56 | (1) |
|
|
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) |
|
|
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) |
|
|
78 | (1) |
|
|
78 | (1) |
|
|
79 | (1) |
|
|
80 | (4) |
|
|
80 | (1) |
|
|
81 | (2) |
|
|
83 | (1) |
|
3 Use Partials (Addition, Subtraction, Multiplication, And Division) |
|
|
84 | (5) |
|
|
84 | (4) |
|
|
88 | (1) |
|
|
89 | (1) |
|
4 Break Apart to Multiply (Multiplication) |
|
|
89 | (4) |
|
|
89 | (2) |
|
|
91 | (2) |
|
|
93 | (1) |
|
5 Halve And Double (Multiplication) |
|
|
93 | (3) |
|
|
93 | (1) |
|
|
94 | (1) |
|
|
95 | (1) |
|
6 Compensation (Addition, Subtraction, And Multiplication) |
|
|
96 | (5) |
|
|
96 | (2) |
|
|
98 | (3) |
|
7 Use An Inverse Relationship (Subtraction And Division) |
|
|
101 | (1) |
|
|
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) |
|
|
108 | (4) |
|
Learning Progression For Automaticity With Basic Facts |
|
|
108 | (1) |
|
|
109 | (2) |
|
Tips For Developing Procedural Automaticities |
|
|
111 | (1) |
|
Procedural Automaticities |
|
|
112 | (15) |
|
Breaking Apart All Numbers Through 10 |
|
|
113 | (2) |
|
|
115 | (2) |
|
|
117 | (1) |
|
|
118 | (2) |
|
|
120 | (1) |
|
|
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) |
|
|
139 | (5) |
|
|
144 | (3) |
|
|
147 | (3) |
|
|
150 | (2) |
|
|
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) |
|
|
154 | (10) |
|
Planning Forand Assessing Strategies And Automaticities |
|
|
155 | (4) |
|
Assessing Fluency Components And Actions |
|
|
159 | (4) |
|
|
163 | (1) |
|
Assessment Options Beyond Quizzes And Tests |
|
|
164 | (10) |
|
|
165 | (2) |
|
|
167 | (2) |
|
|
169 | (3) |
|
|
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) |
|
|
187 | (1) |
|
|
188 | (1) |
|
|
189 | (1) |
|
|
190 | (1) |
|
Figuring Out Fluency: Engaging Families |
|
|
190 | (2) |
|
9 Fluency Is The Focus: Planning, Agreement, And Action |
|
|
192 | (18) |
|
|
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 | |