| Foreword |
|
9 | (2) |
| Acknowledgements |
|
11 | (2) |
| Preface: Good Teaching Is Good Teaching |
|
13 | (4) |
|
Chapter 1 Comprehension Strategies for Mathematics |
|
|
17 | (28) |
|
Concerns about Mathematical Achievement in the United States |
|
|
17 | (1) |
|
Global Achievement Gap in Mathematics |
|
|
18 | (2) |
|
Instructional Strategies for Student Achievement |
|
|
20 | (1) |
|
Reading and Mathematics Connections |
|
|
21 | (1) |
|
Reading and Mathematics Comprehension |
|
|
22 | (6) |
|
|
|
23 | (1) |
|
Knowledge About Structure |
|
|
24 | (1) |
|
|
|
25 | (1) |
|
Knowledge About the Social/Situational Context |
|
|
26 | (2) |
|
Teaching for Comprehension |
|
|
28 | (1) |
|
The Seven Comprehension Strategies |
|
|
29 | (2) |
|
|
|
31 | (4) |
|
|
|
32 | (1) |
|
|
|
32 | (1) |
|
|
|
32 | (1) |
|
Modeling How to Perform the Strategy |
|
|
33 | (1) |
|
Guiding Students as They Practice |
|
|
34 | (1) |
|
Giving Students Independent Practice |
|
|
34 | (1) |
|
Using Comprehension Strategies |
|
|
35 | (3) |
|
|
|
35 | (1) |
|
|
|
36 | (1) |
|
|
|
37 | (1) |
|
Comprehension Strategies for Conceptual Understanding |
|
|
38 | (1) |
|
Teaching Comprehension Strategies for Mathematics |
|
|
39 | (3) |
|
|
|
39 | (1) |
|
|
|
39 | (1) |
|
|
|
40 | (1) |
|
|
|
41 | (1) |
|
|
|
42 | (1) |
|
|
|
43 | (2) |
|
Chapter 2 Recognizing and Understanding Mathematical Vocabulary |
|
|
45 | (40) |
|
|
|
45 | (2) |
|
The Importance of Vocabulary Instruction |
|
|
47 | (2) |
|
Direct Vocabulary Instruction |
|
|
49 | (6) |
|
Choosing Mathematics Terms to Teach |
|
|
55 | (4) |
|
Engaging Students in Learning Mathematical Vocabulary |
|
|
59 | (21) |
|
Encouraging Parental Involvement |
|
|
60 | (1) |
|
|
|
60 | (3) |
|
Mathematical Writing to Reinforce Vocabulary Knowledge |
|
|
63 | (4) |
|
|
|
67 | (2) |
|
|
|
69 | (7) |
|
Games and Other Learning Activities |
|
|
76 | (4) |
|
Literature Links to Mathematical Vocabulary Acquisition |
|
|
80 | (1) |
|
|
|
81 | (2) |
|
|
|
83 | (2) |
|
Chapter 3 Making Mathematical Connections |
|
|
85 | (30) |
|
Making Connections to Enhance Learning |
|
|
86 | (1) |
|
|
|
87 | (5) |
|
Kinds of Mathematical Connections |
|
|
92 | (3) |
|
|
|
92 | (1) |
|
|
|
93 | (1) |
|
Math-to-World Connections |
|
|
93 | (2) |
|
Teaching Students to Make Mathematical Connections |
|
|
95 | (13) |
|
Modeling and Think-Alouds |
|
|
95 | (2) |
|
|
|
97 | (1) |
|
One-Minute Schema Determiner |
|
|
98 | (1) |
|
|
|
99 | (4) |
|
Mathematical Current Events |
|
|
103 | (1) |
|
Sharing Class Connections with Anchor Charts |
|
|
104 | (1) |
|
In the Context of Problem Solving |
|
|
105 | (3) |
|
Using Children's Literature |
|
|
108 | (2) |
|
Distinguishing Meaningful Connections from Distracting Connections |
|
|
110 | (3) |
|
|
|
113 | (1) |
|
|
|
114 | (1) |
|
Chapter 4 Increasing Comprehension by Asking Questions |
|
|
115 | (32) |
|
The Quality of Questioning in Classrooms |
|
|
115 | (2) |
|
The Relationship Between Questions and Learning |
|
|
117 | (2) |
|
Strategic Questioning to Critically Evaluate Mathematical Information |
|
|
119 | (1) |
|
What Students Need to Know about Asking Questions for Mathematical Comprehension |
|
|
120 | (6) |
|
|
|
126 | (3) |
|
Question Answer Relationships |
|
|
126 | (2) |
|
|
|
128 | (1) |
|
|
|
129 | (1) |
|
Teaching Students to Ask Meaningful Questions |
|
|
129 | (13) |
|
Modeling and Think-Alouds in Strategy Sessions |
|
|
130 | (5) |
|
Generating Questions with Thinking Stems |
|
|
135 | (1) |
|
|
|
135 | (1) |
|
|
|
136 | (1) |
|
|
|
137 | (1) |
|
Math Stretches to Promote Questions |
|
|
138 | (3) |
|
In the Context of Problem Solving |
|
|
141 | (1) |
|
Using Children's Literature |
|
|
142 | (2) |
|
|
|
144 | (1) |
|
|
|
145 | (2) |
|
Chapter 5 The Importance of Visualizing Mathematical Ideas |
|
|
147 | (24) |
|
Visualization and Cognition |
|
|
148 | (1) |
|
What Students Need to Know about Visualization for Mathematical Comprehension |
|
|
149 | (3) |
|
Visualizing Multiple Representations of Mathematical Ideas |
|
|
152 | (1) |
|
Building the Ability to Visualize from Words |
|
|
153 | (3) |
|
Teaching Students the Strategy of Visualization for Mathematical Comprehension |
|
|
156 | (10) |
|
Modeling and Think-Alouds |
|
|
156 | (5) |
|
"Picture Walks" to Build Capacity to Visualize |
|
|
161 | (1) |
|
Visualize, Draw, and Share |
|
|
162 | (1) |
|
Multiple Representations Graphic Organizers |
|
|
163 | (2) |
|
Math Stretches to Encourage Visualization |
|
|
165 | (1) |
|
Using Children's Literature |
|
|
166 | (2) |
|
|
|
168 | (1) |
|
|
|
169 | (2) |
|
Chapter 6 Making Inferences and Predictions |
|
|
171 | (28) |
|
The Relationship between Inferences and Predictions |
|
|
172 | (1) |
|
What Students Need to Know about Inferring and Predicting |
|
|
173 | (4) |
|
Building Student Ability to Infer and Predict |
|
|
177 | (2) |
|
Inferring Requires Time for Reflection |
|
|
179 | (1) |
|
One-on-One Conferences to Promote Effective Inferences and Predictions |
|
|
180 | (2) |
|
Teaching Students to Infer and Predict to Enhance Mathematical Understanding |
|
|
182 | (12) |
|
Modeling and Think-Alouds |
|
|
182 | (4) |
|
|
|
186 | (1) |
|
|
|
187 | (1) |
|
Math Stretches to Encourage Students to Infer and Predict |
|
|
188 | (3) |
|
In the Context of Problem Solving |
|
|
191 | (3) |
|
Using Children's Literature |
|
|
194 | (2) |
|
|
|
196 | (1) |
|
|
|
197 | (2) |
|
Chapter 7 Determining Importance |
|
|
199 | (28) |
|
The Levels of Determining Importance |
|
|
200 | (1) |
|
Critically Examining Mathematical Information |
|
|
201 | (1) |
|
What Students Need to Know about Determining Importance |
|
|
202 | (4) |
|
Teasing the Important Ideas from Mathematical Text |
|
|
206 | (4) |
|
|
|
207 | (1) |
|
|
|
208 | (1) |
|
Read a Little, Think a Little |
|
|
209 | (1) |
|
Teaching Students to Determine Mathematical Importance |
|
|
210 | (11) |
|
Modeling and Think-Alouds |
|
|
210 | (4) |
|
|
|
214 | (1) |
|
|
|
215 | (1) |
|
|
|
215 | (2) |
|
Math Stretches to Support Determining Importance |
|
|
217 | (2) |
|
In the Context of Problem Solving |
|
|
219 | (2) |
|
Using Children's Literature |
|
|
221 | (3) |
|
|
|
224 | (1) |
|
|
|
225 | (2) |
|
Chapter 8 Synthesizing Information |
|
|
227 | (22) |
|
Strands of Mathematical Proficiency |
|
|
228 | (1) |
|
Synthesizing and Mathematizing |
|
|
229 | (1) |
|
What Students Need to Know about Synthesizing |
|
|
230 | (2) |
|
Teaching Students to Synthesize for Making Mathematical Meaning |
|
|
232 | (10) |
|
Modeling and Think-Alouds |
|
|
233 | (2) |
|
Creating Concrete Experiences |
|
|
235 | (2) |
|
|
|
237 | (2) |
|
Math Stretches to Explore Synthesizing |
|
|
239 | (1) |
|
In the Context of Problem Solving |
|
|
240 | (2) |
|
Using Children's Literature |
|
|
242 | (4) |
|
|
|
246 | (1) |
|
|
|
247 | (2) |
|
Chapter 9 Monitoring Mathematical Comprehension |
|
|
249 | (26) |
|
|
|
250 | (1) |
|
Monitoring Understanding for Mathematics Learners |
|
|
251 | (4) |
|
|
|
252 | (2) |
|
|
|
254 | (1) |
|
What Students Need to Know about Monitoring and Repairing Mathematical Comprehension |
|
|
255 | (5) |
|
|
|
257 | (3) |
|
Teaching Students to Monitor Mathematical Understanding |
|
|
260 | (8) |
|
Modeling and Think-Alouds |
|
|
261 | (2) |
|
|
|
263 | (1) |
|
Ticket Out the Door Comprehension Check |
|
|
264 | (1) |
|
Comprehension Constructor |
|
|
264 | (2) |
|
Using Math Stretches for Monitoring Comprehension |
|
|
266 | (1) |
|
In the Context of Problem Solving |
|
|
267 | (1) |
|
Using Children's Literature |
|
|
268 | (5) |
|
|
|
273 | (1) |
|
|
|
274 | (1) |
|
Chapter 10 In the Guided Math Classroom |
|
|
275 | (16) |
|
The Foundational Principles of a Guided Math Classroom |
|
|
276 | (3) |
|
The Components of a Guided Math Classroom |
|
|
279 | (7) |
|
A Classroom Environment of Numeracy |
|
|
281 | (1) |
|
Math Stretches and Calendar Board Activities |
|
|
282 | (1) |
|
|
|
283 | (1) |
|
Guided Math Instruction with Small Groups of Students |
|
|
284 | (1) |
|
|
|
284 | (1) |
|
|
|
285 | (1) |
|
An Ongoing System of Assessment |
|
|
285 | (1) |
|
Teaching Students to Become Mathematicians |
|
|
286 | (3) |
|
|
|
289 | (1) |
|
|
|
290 | (1) |
|
|
|
291 | (7) |
|
Appendix A Frayer Diagram |
|
|
291 | (1) |
|
Appendix B Math Connections |
|
|
292 | (1) |
|
Appendix C Question Journal |
|
|
293 | (1) |
|
Appendix D Multiple Representations Graphic Organizer |
|
|
294 | (1) |
|
Appendix E Inference and Evidence Chart |
|
|
295 | (1) |
|
Appendix F Comprehension Checklist |
|
|
296 | (1) |
|
Appendix G Comprehension Constructor |
|
|
297 | (1) |
| References Cited |
|
298 | (6) |
| Children's Literature |
|
304 | |
