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 book is the result of lesson studies over the past 50 years. It describes three perspectives of mathematical thinking: Mathematical Attitude (Minds set), Mathematical Methods in General and Mathematical Ideas with Content and explains how to develop them in the classroom with illuminating examples.

Description-Table Of Contents

ch. 1. Mathematical thinking as the aim of education. 1.1. Developing children who learn mathematics for themselves. 1.2. Mathematical thinking as an ability to think and to make decisions. 1.3. The hierarchy of ability and thinking -- ch. 2. The importance of cultivating mathematical thinking. 2.1. The importance of teaching mathematical thinking. 2.2. Example: how many squares are there? -- ch. 3. The mindset and mathematical thinking. 3.1. Mathematical thinking. 3.2. Structure of mathematical thinking -- ch. 4. Mathematical methods. 4.1. Inductive thinking. 4.2. Analogical thinking. 4.3. Deductive thinking. 4.4. Integrative thinking. 4.5. Developmental thinking. 4.6. Abstract thinking (abstraction). 4.7. Thinking that simplifies (simplifying). 4.8. Thinking that generalizes (generalization). 4.9. Thinking that specializes (specialization). 4.10. Thinking that symbolizes (symbolization). 4.11. Thinking that represents by numbers, quantities, and figures (quantification and schematization) -- ch. 5. Mathematical ideas. 5.1. Idea of sets. 5.2. Idea of units. 5.3. Idea of representation. 5.4. Idea of operation. 5.5. Idea of algorithms. 5.6. Idea of approximations. 5.7. Idea of fundamental properties. 5.8. Functional thinking. 5.9. Idea of expressions -- ch. 6. Mathematical attitude. 6.1. Objectifying. 6.2. Resonableness. 6.3. Clarity. 6.4. Sophistication -- ch. 7. Questioning to enhance mathematical thinking.