Prologue / 2

Ⅰ.
11 Real-Life Math Lessons for Solving Life's Problems
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Why Real-Life-Centered Math Classes? 13
2.
Dewey's Pragmatic Education and Problem-Based Learning (PBL) 15
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Special Education Teachers Share Their Stories About Real-Life Math Classes 17
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17 Math Education Essential for Students with Disabilities
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To teach the essential content in a limited time, 18
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Math Lessons Using Real-Life Materials 18
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Math Lessons Using Everyday Objects 19
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Provide opportunities to apply what you learn in class to your life 20
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Creating an environment where students can naturally be stimulated by mathematical elements 20
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Transferable and Generalizable Assessment 21
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22 Teaching Tips from Fellow Teachers for Real-Life Math Classes
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Designing Real-Life Math Lessons 23
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I'm curious, Professor 33

Ⅱ.
Math Lessons to Boost Motivation 43
1.
Why Math Classes Boost Motivation? 45
2.
Keller's Learning Motivation Model (ARCS Model) 47
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Special Education Teachers Share Their Stories on Math Classes That Boost Motivation 49
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49 Math Lessons That Take Student Needs into Consideration
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50 Math Lessons That Explore Student Interests Through Various Trials
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50 Math Lessons That Use Students' Favorite Materials
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51 Math Lessons Using Familiar Materials
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52 Fun and Enjoyable Math Lessons for Students
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53 Topic-Based Math Lessons for Students to Access
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54 Teaching Tips from Fellow Teachers to Boost Motivation in Math Classes
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55 Math Lesson Designs to Boost Motivation
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I'm curious, Professor 67

Ⅲ.
71 Level-Based Math Lessons for All Students
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Why Leveled Math Classes? 73
2.
Bruner's Structure of Knowledge 75
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Special Education Teachers Talk About Level-Based Math Classes 77
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77 Math Lessons Offering Basic Content Appropriate to Students with Disabilities
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77 Math classes with content and activities tailored to each student's level
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78 Math Classes with Level-Based Materials that Offer Different Representations
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79 Math Lessons That Attempt to Engage Students with Severe Disabilities
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Preferred method for level-based instruction: One-on-One Math Lessons 80
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Level-based assessment for planning the next lesson 81
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82 Teaching Tips from Fellow Teachers for Level-Based Math Classes
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Designing Math Lessons by Level 83
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I'm curious, Professor 90

Ⅳ.
Activity-Based Math Lessons to Build Student Capabilities 93
1.
Why Activity-Based Math Classes Develop Student Capabilities? 95
2.
Effective Study Methods, Learning Pyramid 97
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Special Education Teachers Talk About Activity-Based Math Lessons 99
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99 hands-on, participatory math classes
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100 Math Lessons That Give Students First Chance by Waiting
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Math Classes 101: Giving Students Choices
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Math Lessons 102: Encouraging Participation Through Concrete Manipulations
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Creating a well-equipped teaching environment 103
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A permissive atmosphere that boosts students' confidence 104
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106 Teaching Tips from Fellow Teachers for Activity-Based Math Classes
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Activity-Based Math Lesson Design 108
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I'm curious, Professor 118

V.
Interactive Math Lesson 121
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Why interactive math classes? 123
2.
Piaget and Vygotsky's Theories 125
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Special Education Teachers Share Their Stories About Interactive Math Classes 127
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Math classes where feedback occurs through active interaction between teachers and students 127
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Peer Professor 128 Teaching and Learning with Friends
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Math Class 128: Students Evaluate and Praise Each Other
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Math Lessons 130: Math Goals Infused with Exciting Play
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132 Teaching Tips from Fellow Teachers for Creating Interactive Math Classes
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Designing Interactive Math Lessons 133
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I'm curious, Professor 147

Ⅵ.
Math Classes That Give Students Success Experiences 153
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Why Math Classes Provide Students with Successful Experiences? 155
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157 Praises That Increase a Student's Chances of Success
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Special Education Teachers Share Their Stories About Math Classes That Give Students Successful Experiences 159
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Math Lesson 159: Thoroughly Prepared and Designed for Class
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160 Math classes that achieve goals through various teaching strategies
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163 Repetitive Math Lessons Using Various Methods
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Creating a quiet and conducive learning environment 165
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Checking students' condition and mindset for attending class 166
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167 Tips from Fellow Teachers for Creating Successful Math Classes
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How to Intervene in Challenging Behaviors of Students with Disabilities in Classrooms? 169
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I'm curious, Professor 173

Ⅶ.
Curriculum-Based Math Lessons 177
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Why Curriculum-Based Math Classes? 179
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Restructuring the Curriculum Based on Classroom Situations and Contexts 183
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Special Education Teachers' Stories on Curriculum-Based Math Instruction 186
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Curriculum-Based Math Lessons 186
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Math Class with Mathematical Hierarchy 188
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Math Classes Reconstructing the Curriculum 189
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Math Class 190, covering all areas of mathematics
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192 Teaching Tips from Fellow Teachers for Curriculum-Based Math Classes
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Instructional Methods for the Regularity Area According to the Hierarchy of the Curriculum 193
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Curriculum-Based Mathematics Lesson Design 196
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I'm curious, Professor 205

Ⅷ.
Math class 213 using process-centered assessment
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Why do math classes use process-based assessments? 215
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Backward Design Emphasizing 'Evaluation' 217
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Special Education Teachers' Stories About Math Classes Using Process-Based Assessment 219
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Backward design to plan evaluation in advance 219
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Immediate evaluation of class content 220
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Observations and Records 221
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Portfolio Evaluation 222
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223 Teaching Tips from Fellow Teachers for Math Classes Using Process-Based Assessment
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I'm curious, Professor 224

Ⅸ.
Collaborative Math Class 227
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Why Collaborative Math Classes? 229
2.
Collaborative 'Professional Learning Community' among Teachers 231
3.
Special Education Teachers Share Their Collaborative Math Lessons 233
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Math Class 233: Connecting and Collaborating with Home
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Math Class 235 with Support Staff
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Math Lessons Collaborating with Inclusive Classroom Teachers 237
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238 Teaching Tips from Fellow Teachers for Collaborative Math Classes
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I'm curious, Professor 239

Appendix I.
A Look at a Good Class 243
Appendix II.
Reviewing the Revised Basic Curriculum Mathematics Content System and Achievement Standards 251
References / 274
Epilogue / 278