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Mathematical Thinking : How to Develop It in the Classroom.
Developing mathematical thinking is one of major aims of mathematics education. In mathematics education research, there are a number of researches which describe what it is and how we can observe in experimental research. However, teachers have difficulties developing it in the classrooms. This boo...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific,
2012.
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| Colección: | Monographs on lesson study for teaching mathematics and sciences.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface to the Series; Preface to the Book; Acknowledgements; Contents; Introductory Chapter: Problem Solving Approach to Develop Mathematical Thinking; 1.1 The Teaching Approach as the Result of Lesson Study; 1.1.1 Learning mathematics by/for themselves; 1.1.2 The difference between tasks and problems (problematic); 1.1.3 Teachers' questioning, and changing and adding representations; 1.1.4 Extending the ideas which we have already learned; 1.2 Setting the Activities for Explaining, Listening, Reflecting, and Appreciating in Class; 1.2.1 Structure of Problem Solving Approaches.
- 1.2.2 Diversity of solutions and the objective of the class1.2.3 Comparison based on the problematic; 1.2.4 Using the blackboard for illustrating children's thinking process; 1.3 The Roles of the Curriculum and Textbooks; 1.4 Perspectives for Developing Mathematical Thinking; 1.4.1 Mathematical thinking: a major research topic of lesson study; 1.4.2 Mathematical thinking: a bird's-eye view; References; Part I Mathematical Thinking: Theory of Teaching Mathematics to Develop Children Who Learn Mathematics for Themselves; Chapter 1 Mathematical Thinking as the Aim of Education.
- 1.1 Developing Children Who Learn Mathematics for Themselves1.2 Mathematical Thinking as an Ability to Think and to Make Decisions; 1.3 The Hierarchy of Ability and Thinking; Chapter 2 The Importance of Cultivating Mathematical Thinking; 2.1 The Importance of Teaching Mathematical Thinking; 2.1.1 The driving forces in pursuing knowledge and skills; 2.1.2 Achieving independent thinking and the ability to learn independently; 2.2 Example: How Many Squares Are There?; 2.2.1 The usual lesson process; 2.2.2 Problems with this method; 2.2.3 The preferred method.
- 2.2.4 Mathematical thinking is the key ability hereChapter 3 The Mindset and Mathematical Thinking; 3.1 Mathematical Thinking; 3.1.1 Focus on the mindset: attitude and disposition; 3.1.2 Three variables for thinking mathematically; 3.1.3 Importance of Denotative understanding of mathematical thinking; 3.1.4 Mathematical thinking is the driving force behind knowledge and skills; 3.2 Structure of Mathematical Thinking; Chapter 4 Mathematical Methods; 4.1 Inductive Thinking; Meaning; Examples; Important aspects about teaching inductive thinking; 4.2 Analogical Thinking; Meaning; Examples.
- Important aspects about teaching analogical thinking4.3 Deductive Thinking; Meaning; Examples; Important aspect about teaching deductive thinking; 4.4 Integrative Thinking; Meaning; Type I integration (high-level integration); Type II integration (comprehensive integration); Type III integration (extensional thinking); Example for type I; Example 2 for type II; Example 3 for type III; Important aspects about teaching integrative thinking; 4.5 Developmental Thinking; Meaning; Examples; Important aspects about teaching developmental thinking; 4.6 Abstract Thinking (Abstraction); Meaning.