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Table of Contents
Intro
Textbook for Normal Colleges and Universities
Contents
1 Introduction
1.1 Scientific Mathematics and Mathematics as an Educational Science
1.1.1 Scientific Mathematics
1.1.2 Mathematics as an Educational Science
1.2 Emergence and Development of Mathematics Education
1.3 Nature, Task, and Significance of Mathematics Pedagogy
1.3.1 Nature of Mathematics Pedagogy
1.3.2 Task of Mathematics Pedagogy
1.3.3 Significance of Mathematics Pedagogy
2 Secondary School Mathematics Logic
2.1 Secondary School Mathematics Concepts
2.1.1 Meaning of Concept
2.1.2 Structure of Concept
2.1.3 Relationship Between Concepts
2.1.4 Definition of Concept
2.1.5 Series of Concept
2.1.6 Classification of Concepts
2.2 Secondary School Mathematics Propositions
2.2.1 Judgement
2.2.2 Proposition
2.2.3 Generation of Reverse Proposition
2.2.4 Identity Principle of Propositions
2.3 Basic Laws of Formal Logic
2.3.1 Law of Identity
2.3.2 Law of Contradiction
2.3.3 Law of Excluded Middle
2.3.4 Law of Sufficient Reason
2.4 Secondary School Mathematics Inference
2.4.1 Inductive Inference
2.4.2 Analogical Inference
2.4.3 Deductive Inference
2.5 Secondary School Mathematics Proof
2.5.1 Analysis Method and Synthesis Method
2.5.2 Direct and Indirect Proof
2.6 Teaching of Secondary School Mathematics Concepts and Propositions
2.6.1 Teaching of Mathematical Concepts
2.6.2 Teaching of Mathematical Propositions
3 Secondary School Mathematics Thinking
3.1 Meaning of Mathematical Thinking
3.2 Methods of Secondary School Mathematics Thinking
3.2.1 Observation and Experimentation
3.2.2 Analysis and Synthesis
3.2.3 Comparison and Classification
3.2.4 Abstraction and Generalization
3.2.5 Concretization, Specialization, and Systematization
3.2.6 Analogy, Induction, and Deduction
3.2.7 Imagination and Intuition
3.3 Quality of Secondary School Mathematics Thinking
3.3.1 Broadness of Thinking
3.3.2 Profoundness of Thinking
3.3.3 Criticalness of Thinking
3.3.4 Flexibility of Thinking
3.3.5 Sense of Organization of Thinking
3.3.6 Creativity of Thinking
3.4 Cultivation of Mathematical Thinking Ability in Secondary Schools
3.4.1 Divergent Thinking and Its Basic Approach to Development
3.4.2 Reverse Thinking and Its Basic Approach to Development
3.4.3 Creative Thinking and Its Basic Approach to Development
4 Secondary School Mathematics Methods
4.1 Meaning of Mathematical Methods
4.1.1 Meaning of Mathematical Methods
4.1.2 Approaches to Studying Mathematical Methods
4.1.3 Significance of Studying Mathematical Methods
4.2 Reduction Method
4.2.1 Overview of Reduction Method
4.2.2 Direction of Reduction
4.2.3 Methods of Reduction
4.2.4 Understanding Reduction Dialectically
4.3 Discovery Methods
4.3.1 Analogy Method
4.3.2 Induction Method
4.3.3 Association Method
4.3.4 Intuitive Method
Textbook for Normal Colleges and Universities
Contents
1 Introduction
1.1 Scientific Mathematics and Mathematics as an Educational Science
1.1.1 Scientific Mathematics
1.1.2 Mathematics as an Educational Science
1.2 Emergence and Development of Mathematics Education
1.3 Nature, Task, and Significance of Mathematics Pedagogy
1.3.1 Nature of Mathematics Pedagogy
1.3.2 Task of Mathematics Pedagogy
1.3.3 Significance of Mathematics Pedagogy
2 Secondary School Mathematics Logic
2.1 Secondary School Mathematics Concepts
2.1.1 Meaning of Concept
2.1.2 Structure of Concept
2.1.3 Relationship Between Concepts
2.1.4 Definition of Concept
2.1.5 Series of Concept
2.1.6 Classification of Concepts
2.2 Secondary School Mathematics Propositions
2.2.1 Judgement
2.2.2 Proposition
2.2.3 Generation of Reverse Proposition
2.2.4 Identity Principle of Propositions
2.3 Basic Laws of Formal Logic
2.3.1 Law of Identity
2.3.2 Law of Contradiction
2.3.3 Law of Excluded Middle
2.3.4 Law of Sufficient Reason
2.4 Secondary School Mathematics Inference
2.4.1 Inductive Inference
2.4.2 Analogical Inference
2.4.3 Deductive Inference
2.5 Secondary School Mathematics Proof
2.5.1 Analysis Method and Synthesis Method
2.5.2 Direct and Indirect Proof
2.6 Teaching of Secondary School Mathematics Concepts and Propositions
2.6.1 Teaching of Mathematical Concepts
2.6.2 Teaching of Mathematical Propositions
3 Secondary School Mathematics Thinking
3.1 Meaning of Mathematical Thinking
3.2 Methods of Secondary School Mathematics Thinking
3.2.1 Observation and Experimentation
3.2.2 Analysis and Synthesis
3.2.3 Comparison and Classification
3.2.4 Abstraction and Generalization
3.2.5 Concretization, Specialization, and Systematization
3.2.6 Analogy, Induction, and Deduction
3.2.7 Imagination and Intuition
3.3 Quality of Secondary School Mathematics Thinking
3.3.1 Broadness of Thinking
3.3.2 Profoundness of Thinking
3.3.3 Criticalness of Thinking
3.3.4 Flexibility of Thinking
3.3.5 Sense of Organization of Thinking
3.3.6 Creativity of Thinking
3.4 Cultivation of Mathematical Thinking Ability in Secondary Schools
3.4.1 Divergent Thinking and Its Basic Approach to Development
3.4.2 Reverse Thinking and Its Basic Approach to Development
3.4.3 Creative Thinking and Its Basic Approach to Development
4 Secondary School Mathematics Methods
4.1 Meaning of Mathematical Methods
4.1.1 Meaning of Mathematical Methods
4.1.2 Approaches to Studying Mathematical Methods
4.1.3 Significance of Studying Mathematical Methods
4.2 Reduction Method
4.2.1 Overview of Reduction Method
4.2.2 Direction of Reduction
4.2.3 Methods of Reduction
4.2.4 Understanding Reduction Dialectically
4.3 Discovery Methods
4.3.1 Analogy Method
4.3.2 Induction Method
4.3.3 Association Method
4.3.4 Intuitive Method