Intellectual Development and Mathematics Learning 9789811987564, 9789811987571
139 109 2MB
English Pages 277 Year 2023
Table of contents :
Foreword
Preface
Contents
About the Author
Part I The Mystery of Intelligence
1 The Nature of Intelligence
Intellectual Activity is a Mental Activity
Definitions, Compositions, and Levels of Intelligence
The Definition of Intelligence and Ability
The Composition of Intelligence
Levels of Intelligence
Relationships Between Knowledge, Skills, and Intelligence
The Main Views of Intelligence in the International Psychological Community
Factor Theory and Structure Theory
Piaget’s Theory of Intelligence
The View of Cognitive Psychology of Intelligence
Gardner’s Theory of Multiple Intelligences
Sternberg’s Theory of Successful Intelligence
Goleman and Mayer’s Theory of Emotional Intelligence
References
2 The Laws of Intellectual Development and Mathematics Learning
Nature and Nurture in Intellectual Development
Three Opposing Viewpoints
Heredity and even Physiological Maturity Are the Biological Prerequisites for Intellectual Development
The Role of Environment and Education
The Internal and External Causes in Intellectual Development
The Internal Causes in Intellectual Development
The Role of Human Agency and Intelligence
Education and Intellectual Development
Children’s and Adolescents’ Parameters Regarding Thinking and Intellectual Development
The Role and Function of Education in Intellectual Development
Heuristic Teaching in Mathematics
The Relationship Between Age Characteristics and Individual Differences
The Phase of Intellectual Development in Psychological Development
The Representativeness of Age Characteristics of Intellectual and even Psychological Development
The “Critical Age” in Intellectual and even Psychological Development
The Maturation Period of Elementary and Secondary School Students in Intellectual and even Psychological Development
The Stability and Variability of Age Characteristics of Intellectual and even Psychological Development
References
3 Intelligence and Creativity
Part II Mathematics: The Gymnastics of Human Thinking
Characteristics of Creative Talents and Growth Environment
Creative Thinking (Creative Intellectual Factors)
Creative Personality (Creative Non-intellectual Factors)
Creative or Innovative Environment
Implementation of Creative Education and the Training Model of “T”-Type Talents
Creative Education Comprises Three Groups in Schools that Produce Five Components of Effectiveness
Everyone Has Creativity
Integrating Eastern and Western Education Models and Cultivating the “T”-Type Talents
Approaches to Developing Students’ Creativity Through Creative Learning
Characteristics of Creative Learning
Behavioral Characteristics of Creative Students
Seven Approaches to Developing Students’ Creativity in Creative Learning
Approaches to Developing Students’ Creativity in Mathematics Teaching
Examples of Mathematicians from Ancient and Modern Times and Creativity Development
Development and Training of Mathematics Creativity
Mathematics Learning Motivation and Creativity Development
Mathematical Knowledge Teaching and Creativity Development
Mathematics Practice and Creativity Development
References
4 The Complete Structure of Mathematical Thinking
The Triangular Pyramid Structure of Thinking
Purpose of Thinking
Process of Thinking
Material of Thinking
Quality of Thinking
Monitoring of Thinking
Non-cognitive Factors of Thinking
Accomplishment of Mathematical Entirety
Unity
Connection
Comparison
Symmetries
Conservation
Communication
Students’ Mathematical Abilities Are the Structural Integrity of Thinking
The Special Abilities of Subjects Reflect This Disciplinary Competence Most Directly
All Disciplinary Competences Are Based on Generalization Ability
The Structure of Disciplinary Competence Should Involve Thinking Qualities
Student’s Disciplinary Competence Should Reflect Their Characteristics
Mathematics Teaching Should Start from the Integrity of Thinking
Study the Textbook Carefully; Understand the Systematization and Science of the Textbook
Teach Students Systematic and Scientific Knowledge of Mathematics
Effectively Strengthen the Teaching of Basic Mathematical Concepts
Form an Integrated Mathematical Knowledge System Through Review
Improve Mathematical Comprehension Ability and Promote the Development of the Structural Integrity of Students’ Thinking
References
5 The Development of Student’s Thinking Ability in Arithmetic
Mathematics Learning and the Development of Students’ Generalization Ability
Clarify the Dominant Idea of Abstract Generalization, Guiding Students to Discover from Conjecture, Conjecture from Discovery
Provide Rich and Appropriate Materials for Student’s Abstract Generalization and Make Abstract Generation Concrete
Actively Promote the Process of Assimilation and Adaptation by Variation, Reflection, and Systematization
Mathematics Learning and the Development of Student’s Spatial Imagination Ability
Mathematics Learning and the Development of Student’s Proposition Ability
Mathematics Learning and the Development of Students’ Logical Reasoning Ability
Indirect and Direct Reasoning
Synthesis and Analysis
Inductive and Deductive Reasoning
Analogical and Comparative Reasoning
References
6 Differences and Development of Students’ Intellectual Qualities in Arithmetic
Profundity of Students’ Thinking and Its Cultivation
Cultivation of Profundity in Elementary School Students’ Mathematical Thinking
Cultivation of Profundity in Secondary School Students’ Mathematical Thinking
Flexibility of Students’ Thinking and Its Cultivation
Creativity of Students’ Thinking and Its Cultivation
Criticality of Students’ Thinking and Its Cultivation
Agility of Students’ Thinking and Its Cultivation
Importance of Studying Students’ Thinking Qualities
References
Part III Development of Mathematical Abilities in Children and Adolescents
7 Preschool Children’s Arithmetic Thinking Ability and Early Education of Mathematics
The Characteristics of Thinking and the Developmental Profile of Arithmetic Thinking Abilities
Preschool Children’s Acquisition of Preliminary Concepts
Development of Preschool Children's Number Concepts
Development of Preschool Children’s Arithmetic Abilities
Development of Preschool Children’s Ability to Recognize Shapes
The Development of Level of Thinking Activity in Acquisition of Number Concepts
Related International Academic Communities and Domestic Perspectives
My Research
Recent Research on the Development of Mathematical Abilities in Children Aged 0–6 Years
Development of Quantitative Representations
Understanding and Applying Number Labels
Fraction and Proportional Cognition
Early Teaching of Mathematics
From Early Education to Early Mathematics Teaching
Stages of Early Education and National Perspectives on Early Childhood Education
Some Suggestions for Early Mathematics Education
References
8 Mathematics Learning and Intellectual Development of Elementary School Students
Development of Mathematical Intelligence in Elementary School Students
Development of Elementary School Students’ Number Generalization Ability
The Development of Elementary School Students’ Proposition Ability and Arithmetic Rules
The Development of Elementary School Students’ Reasoning Ability
Basing Elementary School Mathematics Teaching on Age Characteristics of Arithmetic Thinking Ability
Recent Studies on the Development of Elementary School Students’ Mathematical Ability
Further Development of Elementary School Students’ Quantitative Representational Ability
Elementary School Students’ Computational Strategies and Their Relationship with the Development of Basic Cognitive Functions
Development of Fraction Concepts in Elementary School Students
The Characteristics and Development of Elementary School Students’ Level of Representation in Word Problems
Elementary School Students’ Emotional Experience of Mathematics and Mathematics Achievement
Analysis of the Characteristics of Elementary School Students with Mathematics Learning Difficulties
Improving Elementary School Students’ Abilities to Solve Word Problems
One-Step Word Problems: The Basis for Solving Compound Word Problems
Two-Step Word Problems: The Key to Solving Compound Word Problems
Mastering the Various Types of Structures of Word Problems for Composite Operations
Research on the Regularity of Mathematical Word Problems
Strategies for Valuing Mental Representations of Mathematical Word Problems
From “Wormy Formula” to Thinking Training Questions
“Wormy Formula” Thinking Training Questions
Thinking Training Questions and Mathematical Olympics Training
Key Points that Elementary School Mathematics Teaching Should Pay Attention to
Explain the Concepts, Laws, Formulas, and Methods of Problem Solving
Highlighting the Key Points, Solving the Difficulties, and Explaining the Doubts
Strengthen the Practice
Connection with Reality
References
9 Mathematics Learning and Intellectual Development of Secondary School Students
Development of Mathematical Intelligence in Secondary School Students
Characteristics of Secondary School Students’ Thinking Development
Contradictory Manifestations of the Quality of Secondary School Students’ Thinking
Characteristics of the Development of Secondary School Students’ Arithmetic Thinking
Recent Studies on the Development of Secondary School Students’ Mathematical Abilities
Analogical Transfer in Secondary School Mathematics Learning
Cognitive Factors Affecting Secondary School Mathematics Performance
Secondary School Students’ Mathematics Anxiety
Research on Secondary School Student’s Mathematics Core Literacy
Emphasis on the Development of Mathematical Ability Before Intellectual Maturity
Emphasis on the Premature Intellectual Development of Students in Secondary School Mathematics Teaching
Cultivating Secondary School Students’ Self-Study Ability
Modern Mathematics Helps the Development of Abstract Thinking
The Mathematical Olympiad and Intellectual Development of Secondary School Students
Mathematical Olympiad Training Effectively Expands Secondary School Students’ Mathematical Horizons and Enriches and Improves Their Mathematical Knowledge Structure
Compared with Secondary School Mathematics Textbooks, the Mathematical Thoughts and Methods Applied in the Mathematical Olympiad are More Skillful and Flexible and Often Require Specialized Training
Mathematical Olympiad Training is a Cognitive Activity that Simultaneously, Challenges the Intellect and Stimulates Curiosity
References
