| Preface to the Series | p. v |
| Preface to the Book | p. vii |
| Acknowledgements | p. xi |
| Introductory Chapter: Problem Solving Approach to Develop Mathematical Thinking | p. 1 |
| Mathematical Thinking: Theory of Teaching Mathematics to Develop Children Who Learn Mathematics for Themselves | p. 29 |
| Mathematical Thinking as the Aim of Education | p. 31 |
| Developing Children Who Learn Mathematics for Themselves | p. 31 |
| Mathematical Thinking as an Ability to Think and to Make Decisions | p. 32 |
| The Hierarchy of Ability and Thinking | p. 35 |
| The Importance of Cultivating Mathematical Thinking | p. 37 |
| The Importance of Teaching Mathematical Thinking | p. 37 |
| Example: How Many Squares Are There? | p. 39 |
| The Mindset and Mathematical Thinking | p. 47 |
| Mathematical Thinking | p. 47 |
| Structure of Mathematical Thinking | p. 49 |
| Mathematical Methods | p. 53 |
| Inductive Thinking | p. 53 |
| Analogical Thinking | p. 56 |
| Deductive Thinking | p. 59 |
| Integrative Thinking | p. 62 |
| Developmental Thinking | p. 66 |
| Abstract Thinking (Abstraction) | p. 70 |
| Thinking That Simplifies (Simplifying) | p. 74 |
| Thinking That Generalizes (Generalization) | p. 76 |
| Thinking That Specializes (Specialization) | p. 78 |
| Thinking That Symbolizes (Symbolization) | p. 81 |
| Thinking That Represents by Numbers, Quantities, and Figures (Quantification and Schematization) | p. 83 |
| Mathematical Ideas | p. 87 |
| Idea of Sets | p. 87 |
| Idea of Units | p. 89 |
| Idea of Representation | p. 91 |
| Idea of Operation | p. 95 |
| Idea of Algorithms | p. 98 |
| Idea of Approximations | p. 100 |
| Idea of Fundamental Properties | p. 102 |
| Functional Thinking | p. 104 |
| Idea of Expressions | p. 108 |
| Mathematical Attitude | p. 111 |
| Objectifying | p. 111 |
| Reasonableness | p. 113 |
| Clarity | p. 115 |
| Sophistication | p. 117 |
| Questioning to Enhance Mathematical Thinking | p. 121 |
| Appendix for the List of Questions for Mathematical Thinking | p. 127 |
| Developing Mathematical Thinking with Number Tables: How to Teach Mathematical Thinking from the Viewpoint of Assessment | p. 129 |
| Sugoroku: Go Forward Ten Spaces If You Win, or One If You Lose | p. 137 |
| Type of Mathematical Thinking to Be Cultivated | p. 137 |
| Grade Taught | p. 137 |
| Preparation | p. 137 |
| Overview of the Lesson Process | p. 137 |
| Worksheet | p. 138 |
| Let's play this game! | p. 139 |
| Lesson Process | p. 140 |
| Summarization on the Blackboard | p. 148 |
| Evaluation | p. 148 |
| Arrangements of Numbers on the Number Table | p. 149 |
| Type of Mathematical Thinking to Be Cultivated | p. 149 |
| Grade Taught | p. 149 |
| Preparation | p. 149 |
| Overview of the Lesson Process | p. 149 |
| Worksheet | p. 150 |
| Lesson Process | p. 151 |
| Summarization on the Blackboard | p. 156 |
| Evaluation | p. 156 |
| Extension of Number Arrangements | p. 159 |
| Type of Mathematical Thinking to Be Cultivated | p. 159 |
| Grade Taught | p. 159 |
| Preparation | p. 159 |
| Overview of the Lesson Process | p. 159 |
| Worksheet | p. 160 |
| Lesson Process | p. 163 |
| Summarization on the Blackboard | p. 171 |
| Evaluation | p. 171 |
| Number Arrangements: Sums of Two Numbers | p. 173 |
| Type of Mathematical Thanking to Be Cultivated | p. 173 |
| Grade Taught | p. 173 |
| Preparation | p. 173 |
| Overview of the Lesson Process | p. 173 |
| Worksheet | p. 174 |
| Lesson Process | p. 176 |
| Summarization on the Blackboard | p. 183 |
| Evaluation | p. 183 |
| When You Draw a Square on a Number Table, What Are the Sum of the Numbers at the Vertices, the Sum of the Numbers Along the Perimeter, and the Grand Total of All the Numbers? | p. 185 |
| Type of Mathematical Thinking to Be Cultivated | p. 185 |
| Grade Taught | p. 185 |
| Preparation | p. 185 |
| Overview of the Lesson Process | p. 185 |
| Worksheet | p. 186 |
| Lesson Process | p. 189 |
| Summarization on the Blackboard | p. 199 |
| Evaluation | p. 200 |
| Further Development | p. 200 |
| Where Do Two Numbers Add up to 99? | p. 203 |
| Types of Mathematical Thinking to Be Cultivated | p. 203 |
| Grade Taught | p. 203 |
| Preparation | p. 203 |
| Overview of the Lesson Process | p. 203 |
| Worksheet | p. 204 |
| Lesson Process | p. 206 |
| Summarization on the Blackboard | p. 215 |
| Evaluation | p. 215 |
| Further Development | p. 216 |
| The Arrangement of Multiples | p. 217 |
| Type of Mathematical Thinking to Be Cultivated | p. 217 |
| Grade Taught | p. 217 |
| Preparation | p. 217 |
| Overview of the Lesson Process | p. 217 |
| Worksheet | p. 218 |
| Lesson Process | p. 219 |
| Summarization on the Blackboard | p. 230 |
| Evaluation | p. 230 |
| How to Find Common Multiples | p. 231 |
| Type of Mathematical Thinking to Be Cultivated | p. 231 |
| Grade Taught | p. 231 |
| Preparation | p. 231 |
| Overview of the Lesson Process | p. 231 |
| Worksheet | p. 232 |
| Lesson Process | p. 233 |
| Summarization on the Blackboard | p. 242 |
| Evaluation | p. 242 |
| Further Development | p. 242 |
| The Arrangement of Numbers on an Extended Calendar | p. 245 |
| Introduction | p. 245 |
| Type of Mathematical Thinking to Be Cultivated | p. 245 |
| Grade Taught | p. 245 |
| Preparation | p. 245 |
| Overview of the Lesson Process | p. 246 |
| Worksheet | p. 246 |
| Lesson Process | p. 248 |
| Summarization on the Blackboard | p. 253 |
| Evaluation | p. 253 |
| Development of the Arrangement of Numbers in the Extended Calendar | p. 255 |
| Introduction | p. 255 |
| Type of Mathematical Thinking to be Cultivated | p. 255 |
| Grade Taught | p. 255 |
| Preparation | p. 255 |
| Overview of the Lesson Process | p. 256 |
| Worksheet | p. 256 |
| Lesson Process | p. 259 |
| Summarization on the Blackboard | p. 267 |
| Evaluation | p. 267 |
| Sums of Two Numbers in an Odd Number Table | p. 269 |
| Introduction | p. 269 |
| Type of Mathematical Thinking to Be Cultivated | p. 269 |
| Grade Taught | p. 269 |
| Preparation | p. 270 |
| Overview of the Lesson Process | p. 270 |
| Worksheet | p. 270 |
| Lesson Process | p. 272 |
| Summarization on the Blackboard | p. 281 |
| Evaluation | p. 281 |
| When You Draw a Square on an Odd Number Table, What Are the Sum of the Numbers at the Vertices and the Grand Total of All the Numbers? | p. 283 |
| Introduction | p. 283 |
| Type of Mathematical Thinking to Be Cultivated | p. 283 |
| Grade Taught | p. 283 |
| Preparation | p. 283 |
| Overview of the Lesson Process | p. 284 |
| Worksheet | p. 284 |
| Lesson Process | p. 286 |
| Summarization on the Blackboard | p. 296 |
| Evaluation | p. 296 |
| Further Development | p. 296 |
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