Foreword |
|
ix | |
|
Preface |
|
xi | |
Acknowledgments |
|
xiii | |
About the Authors |
|
xv | |
|
Mathematics Assessment Probes |
|
|
1 | (21) |
|
What Types of Understandings and Misunderstandings Does a Mathematics Assessment Probe Uncover? |
|
|
2 | (5) |
|
How Were the Mathematics Assessment Probes Developed? |
|
|
7 | (3) |
|
What Is the Structure of a Mathematics Assessment Probe? |
|
|
10 | (5) |
|
What Additional Information Is Provided With Each Mathematics Assessment Probe? |
|
|
15 | (5) |
|
What Mathematics Assessment Probes Are Included in the Book? |
|
|
20 | (2) |
|
Instructional Implications |
|
|
22 | (10) |
|
Differentiating Instruction |
|
|
23 | (1) |
|
|
24 | (1) |
|
Analyzing Trends in Student Thinking |
|
|
24 | (1) |
|
Giving Student Interviews |
|
|
25 | (1) |
|
Promoting Student-to-Student Dialogue |
|
|
26 | (1) |
|
|
26 | (2) |
|
Allowing for Individual Think Time |
|
|
28 | (1) |
|
Improving Students' Processing Skills |
|
|
29 | (1) |
|
Assessing Effectiveness of Instructional Activities |
|
|
29 | (1) |
|
Moving Beyond the Individual Classroom |
|
|
30 | (1) |
|
|
31 | (1) |
|
Number and Operations Assessment Probes |
|
|
32 | (74) |
|
What Is the Value of the Digit? |
|
|
33 | (5) |
|
Teachers' Notes: What Is the Value of the Digit? |
|
|
34 | (3) |
|
Student Responses to ``What Is the Value of the Digit?'' Probe |
|
|
37 | (1) |
|
Variation: What Is the Value of the Digit? Card Sort |
|
|
38 | (1) |
|
What Is the Meaning of 2/3? |
|
|
39 | (5) |
|
Teachers' Notes: What Is the Meaning of 2/3? |
|
|
40 | (3) |
|
Student Responses to ``What Is the Meaning of 2/3?'' |
|
|
43 | (1) |
|
Variation: What Is the Meaning of 2/3? Card Sort |
|
|
44 | (1) |
|
|
45 | (5) |
|
Teachers' Notes: Is It Equivalent? |
|
|
46 | (3) |
|
Student Responses to ``Is It Equivalent?'' |
|
|
49 | (1) |
|
Variation: Is It Equivalent? Card Sort |
|
|
50 | (1) |
|
|
51 | (5) |
|
Teachers' Notes: What's Your Estimate? |
|
|
52 | (3) |
|
Student Responses to ``What's Your Estimate?'' |
|
|
55 | (1) |
|
|
56 | (5) |
|
Teachers' Notes: Is It an Estimate? |
|
|
57 | (2) |
|
Student Responses to ``Is It an Estimate?'' |
|
|
59 | (2) |
|
|
61 | (4) |
|
Teachers' Notes: Is It Simplified? |
|
|
62 | (2) |
|
Student Responses to ``Is It Simplified?'' |
|
|
64 | (1) |
|
Is It Simplified? Algebraic Variation |
|
|
65 | (1) |
|
|
66 | (5) |
|
Teachers' Notes: Where Is One Million? |
|
|
67 | (2) |
|
Student Responses to ``Where Is One Million?'' |
|
|
69 | (2) |
|
|
71 | (4) |
|
Teachers' Notes: How Low Can You Go? |
|
|
72 | (2) |
|
Student Responses to ``How Low Can You Go?'' |
|
|
74 | (1) |
|
Variation: How Low Can You Go? |
|
|
75 | (1) |
|
What's Your Addition Strategy? |
|
|
76 | (6) |
|
Teachers' Notes: What's Your Addition Strategy? |
|
|
77 | (4) |
|
Student Responses to ``What's Your Addition Strategy?'' |
|
|
81 | (1) |
|
Variation: What's Your Addition Strategy? Decimals |
|
|
82 | (1) |
|
Variation: What's Your Addition Strategy? Fractions |
|
|
83 | (1) |
|
What's Your Subtraction Strategy? |
|
|
84 | (6) |
|
Teachers' Notes: What's Your Subtraction Strategy? |
|
|
85 | (4) |
|
Student Responses to ``What's Your Subtraction Strategy?'' |
|
|
89 | (1) |
|
Variation: What's Your Subtraction Strategy? Decimals |
|
|
90 | (1) |
|
Variation: What's Your Subtraction Strategy? Fractions |
|
|
91 | (1) |
|
What's Your Multiplication Strategy? |
|
|
92 | (6) |
|
Teachers' Notes: What's Your Multiplication Strategy? |
|
|
93 | (3) |
|
Student Responses to ``What's Your Multiplication Strategy?'' |
|
|
96 | (2) |
|
Variation: What's Your Multiplication Strategy? Decimals |
|
|
98 | (1) |
|
What's Your Division Strategy? |
|
|
99 | (6) |
|
Teachers' Notes: What's Your Division Strategy? |
|
|
100 | (3) |
|
Student Responses to ``What's Your Division Strategy?'' |
|
|
103 | (2) |
|
Variation: What's Your Division Strategy? Decimals |
|
|
105 | (1) |
|
Geometry, Measurement, and Data Assessment Probes |
|
|
106 | (51) |
|
|
107 | (4) |
|
Teachers' Notes: What's the Measure? |
|
|
108 | (2) |
|
Student Responses to ``What's the Measure?'' |
|
|
110 | (1) |
|
Variation: What's the Measure? |
|
|
111 | (1) |
|
Are Area and Perimeter Related? |
|
|
112 | (5) |
|
Teachers' Notes: Are Area and Perimeter Related? |
|
|
113 | (2) |
|
Student Responses to ``Are Area and Perimeter Related?'' |
|
|
115 | (2) |
|
|
117 | (5) |
|
Teachers' Notes: What's the Area? |
|
|
118 | (2) |
|
Student Responses to ``What's the Area?'' |
|
|
120 | (2) |
|
|
122 | (4) |
|
Teachers' Notes: What's the Capacity? |
|
|
123 | (2) |
|
Student Responses to ``What's the Capacity?'' |
|
|
125 | (1) |
|
|
126 | (5) |
|
Teachers' Notes: Is It Transformed? |
|
|
127 | (3) |
|
Student Responses to ``Is It Transformed?'' |
|
|
130 | (1) |
|
|
131 | (5) |
|
Teachers' Notes: Are They Similar? |
|
|
132 | (2) |
|
Student Responses to ``Are They Similar?'' |
|
|
134 | (2) |
|
|
136 | (8) |
|
Teachers' Notes: What Do You Mean? |
|
|
137 | (5) |
|
Student Responses to ``What Do You Mean?'' |
|
|
142 | (2) |
|
Variation: What Do You Mean? |
|
|
144 | (1) |
|
|
145 | (6) |
|
Teachers' Notes: Name of the Graph? |
|
|
146 | (3) |
|
Student Responses to ``Name of the Graph?'' |
|
|
149 | (2) |
|
|
151 | (6) |
|
Teachers' Notes: Graph Construction |
|
|
152 | (3) |
|
Student Responses to ``Graph Construction'' |
|
|
155 | (2) |
|
Algebra Assessment Probes |
|
|
157 | (63) |
|
Expressions: Equal or Not Equal? |
|
|
158 | (7) |
|
Teachers' Notes: Expressions: Equal or Not Equal? |
|
|
159 | (4) |
|
Student Responses to ``Expressions: Equal or Not Equal?'' |
|
|
163 | (2) |
|
|
165 | (5) |
|
Teachers' Notes: Is It the Same as a + b? |
|
|
166 | (2) |
|
Student Responses to ``Is It the Same as a + b?'' |
|
|
168 | (2) |
|
|
170 | (5) |
|
Teachers' Notes: M & N's? |
|
|
171 | (2) |
|
Student Responses to ``M & N's?'' |
|
|
173 | (2) |
|
|
175 | (5) |
|
Teachers' Notes: What's the Substitute? |
|
|
176 | (3) |
|
Student Responses to ``What's the Substitute?'' |
|
|
179 | (1) |
|
|
180 | (7) |
|
Teachers' Notes: Is It True? |
|
|
181 | (4) |
|
Student Responses to ``Is It True?'' |
|
|
185 | (2) |
|
|
187 | (7) |
|
Teachers' Notes: Solving Equations |
|
|
188 | (4) |
|
Student Responses to ``Solving Equations'' |
|
|
192 | (2) |
|
Correct Representation of the Inequality? |
|
|
194 | (6) |
|
Teachers' Notes: Correct Representation of the Inequality? |
|
|
195 | (4) |
|
Student Responses to ``Correct Representation of the Inequality?'' |
|
|
199 | (1) |
|
|
200 | (7) |
|
Teachers' Notes: Is It a Variable? |
|
|
201 | (4) |
|
Student Responses to ``Is It a Variable?'' |
|
|
205 | (2) |
|
|
207 | (6) |
|
Teachers' Notes: Binomial Expansion |
|
|
208 | (3) |
|
Student Responses to ``Binomial Expansion'' |
|
|
211 | (2) |
|
|
213 | (7) |
|
Teachers' Notes: Is It Quadratic? |
|
|
214 | (4) |
|
Student Responses to ``Is It Quadratic?'' |
|
|
218 | (2) |
Resource A: Note Template |
|
220 | (2) |
References |
|
222 | (3) |
Index |
|
225 | |