Teaching Mathematics Today (Practical Strategies for Successful Classrooms)

Cover
......Page 1
Title: Teaching Mathematics Today
......Page 3
Copyright
......Page 4
Table of Contents......Page 5
Overview of Research......Page 9
Common Approaches in Mathematics Instruction......Page 10
A Balanced Approach in Mathematics Instruction......Page 12
Standards-Based Instruction......Page 14
Integrated Curriculum......Page 15
Student Engagement......Page 17
Cooperative Learning......Page 18
Guided Practice......Page 19
Manipulatives, Games, and Calculators......Page 20
Vocabulary Development......Page 21
Intervention......Page 22
The National Council of Teachers of Mathematics Standards/Focal Points......Page 23
How to Use This Book......Page 25
Post-Reading Reflection......Page 26
Team Building......Page 27
Team Building in Mathematics Instruction......Page 28
Cross-Curricular Team Building......Page 29
Vertical Team Building......Page 30
The Need for Mathematics Standards......Page 31
Dissecting the Mathematics Standards......Page 32
Choosing Resources to Teach Mathematical Concepts......Page 34
Guidelines for Planning the Mathematics Curriculum Timeline......Page 35
Directions for the Mathematics Curriculum Timeline......Page 36
Guidelines for Accelerating and Decelerating the Introduction of New Concepts......Page 38
Accelerating the Introduction of New Concepts......Page 39
Decelerating the Introduction of New Concepts......Page 41
Post-Reading Reflection......Page 43
Involving Parents and Students to Improve Program Efficacy......Page 45
Parent Involvement......Page 46
Student Involvement......Page 47
Parent Letter......Page 48
Student Letter......Page 49
Social Contract......Page 50
Teacher/Parent Contact Log......Page 51
The Affective Filter......Page 52
Questioning......Page 53
“Everyone Involved” Questioning Strategy......Page 57
The “Leveled" Questioning Strategy......Page 58
Pacing a Mathematics Lesson......Page 59
The Physical Environment......Page 61
Interactive Learning Activities......Page 63
Mathematics Classroom Procedures......Page 64
Maximizing Instructional Minutes......Page 65
Be Prepared......Page 66
Utilizing Additional Instructional Time......Page 67
Managing Classroom Time with Efficient Transitions......Page 69
Post-Reading Reflection......Page 71
The Importance of Differentiated Instruction......Page 73
Differentiated Learning......Page 74
Differentiation by Specific Need......Page 75
Differentiation Strategies......Page 78
Paired Learning/Working with Partners......Page 80
Cooperative Learning......Page 81
Choosing a Grouping Strategy......Page 83
Group Activities......Page 84
Post-Reading Reflection......Page 86
Specialized Mathematical Vocabulary for All Learners......Page 87
Vocabulary Development for English Language Learners......Page 88
Types of Language Proficiency......Page 89
Levels of Language Acquisition
......Page 90
Vocabulary-Development Activities......Page 92
Activity 1: Chart and Match
......Page 93
Activity 2: Vocabulary Bingo
......Page 95
Activity 3: Which Statement Is Inaccurate?
......Page 96
Activity 4: Sharing Markers
......Page 97
Activity 5: Sentence Frames for Vocabulary
......Page 99
Post-Reading Reflection......Page 101
Management of Mathematics Manipulatives......Page 103
Types of Mathematics Manipulatives and How They Are Used......Page 106
Preventing Manipulative Dependency......Page 109
Post-Reading Reflection......Page 111
Building on Understanding......Page 113
Teaching More Than One Way......Page 115
Taking Notes......Page 117
Creative Ways to Practice......Page 118
Whiteboard Cooperative Group Activity......Page 119
Graphic Organizer Review Activity......Page 120
Working as a Team Cooperative Activity......Page 121
Post-Reading Reflection......Page 122
Why Teach Problem Solving?......Page 123
Steps for the Problem-Solving Process......Page 124
Step Two: Planning and Communicating a Solution
......Page 125
Step Three: Reflecting and Generalizing
......Page 126
Strategy One—Drawing a Diagram......Page 127
Strategy Two—Drawing a Table......Page 130
Strategy Three—Acting it Out or Using Concrete Materials......Page 132
Strategy Four—Guessing and Checking......Page 133
Strategy Five—Creating an Organized List......Page 135
Strategy Six—Looking for a Pattern......Page 136
Strategy Seven—Creating a Tree Diagram......Page 137
Strategy Eight—Working Backwards......Page 138
Strategy Nine—Using Simpler Numbers......Page 139
Strategy Ten—Open-Ended Problem Solving......Page 140
Strategy Eleven—Analyzing and Investigating......Page 141
Strategy Twelve—Using Logical Reasoning......Page 142
How to Create Word Problems......Page 143
Post-Reading Reflection......Page 145
Integrating Mathematics and Literacy......Page 147
Reading in a Mathematics Class......Page 148
How to Integrate Fiction and Nonfiction......Page 149
Writing......Page 150
Integrating Mathematics and Science......Page 151
Word Problems......Page 153
Connecting to Historical Data......Page 154
Mathematics in the Real World......Page 155
Differentiation within Technology-Embedded Mathematics......Page 157
Using Spreadsheets in a Mathematics Classroom......Page 158
Money......Page 159
What Are Applets?......Page 160
Classroom Use......Page 161
Classroom Management of Calculator Use......Page 166
Teaching Graphing Calculator Skills......Page 167
The “I Do, We Do, You Do” Approach......Page 168
Post-Reading Reflection......Page 169
Aligning Assessment with Instruction......Page 171
When to Assess......Page 172
Recording Methods......Page 173
Check for Understanding......Page 174
Tests and Quizzes......Page 175
The Effectiveness of Using Rubrics......Page 176
Creating a Mathematics Rubric......Page 177
A General Overview of Rubric Guidelines......Page 178
Two-Point Rubric......Page 179
Four-Point Rubric......Page 180
General Rubric......Page 181
Data-Driven Instruction......Page 182
Assessment Item Analysis......Page 183
Assessment Item Analysis by Standard......Page 185
Strategies for Identifying Student Misconceptions......Page 187
Addressing Student Misconceptions......Page 189
Communicating with the Community......Page 190
Post-Reading Reflection......Page 191
Developing an Intervention Curriculum......Page 193
Before-/After-School Program......Page 194
Keys to Remember When Using an Intervention Program......Page 195
What Should Mathematics Instruction Look Like?......Page 196
Key Strategies for Implementing a Successful Mathematics Program......Page 198
Post-Reading Reflection......Page 199
References Cited......Page 200