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The Psychology of Arithmetic

By Edward L. (Edward Lee) Thorndike
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Table of Contents
  • THE PSYCHOLOGY OF ARITHMETIC
    • PREFACE
    • CONTENTS
    • GENERAL INTRODUCTION
    • THE PSYCHOLOGY OF THE ELEMENTARY SCHOOL SUBJECTS
    • THE PSYCHOLOGY OF ARITHMETIC
  • THE PSYCHOLOGY OF ARITHMETIC
    • CHAPTER I
    • THE NATURE OF ARITHMETICAL ABILITIES
      • KNOWLEDGE OF THE MEANINGS OF NUMBERS
        • THE SERIES IDEA OVEREMPHASIZED
        • THE RATIO IDEA OVEREMPHASIZED
        • THE RELATIONAL IDEA OVEREMPHASIZED
        • ARITHMETICAL LANGUAGE
        • PROBLEM-SOLVING
        • Samples of Desirable Applications of Arithmetic in Problems where the Situation is Actually Present to Sense in Whole or in Part
        • Samples of Desirable Applications of Arithmetic where the Situation is Not Present to Sense
        • A
        • B
        • C
        • Samples of Undesirable Applications of Arithmetic[1]
        • ARITHMETICAL REASONING
        • SUMMARY
        • THE SOCIOLOGY OF ARITHMETIC
      • THE SERIES IDEA OVEREMPHASIZED
      • THE RATIO IDEA OVEREMPHASIZED
      • THE RELATIONAL IDEA OVEREMPHASIZED
      • ARITHMETICAL LANGUAGE
      • PROBLEM-SOLVING
      • Samples of Desirable Applications of Arithmetic in Problems where the Situation is Actually Present to Sense in Whole or in Part
      • Samples of Desirable Applications of Arithmetic where the Situation is Not Present to Sense
      • A
      • B
      • C
      • Samples of Undesirable Applications of Arithmetic[1]
      • ARITHMETICAL REASONING
      • SUMMARY
      • THE SOCIOLOGY OF ARITHMETIC
    • KNOWLEDGE OF THE MEANINGS OF NUMBERS
      • THE SERIES IDEA OVEREMPHASIZED
      • THE RATIO IDEA OVEREMPHASIZED
      • THE RELATIONAL IDEA OVEREMPHASIZED
      • ARITHMETICAL LANGUAGE
      • PROBLEM-SOLVING
      • Samples of Desirable Applications of Arithmetic in Problems where the Situation is Actually Present to Sense in Whole or in Part
      • Samples of Desirable Applications of Arithmetic where the Situation is Not Present to Sense
      • A
      • B
      • C
      • Samples of Undesirable Applications of Arithmetic[1]
      • ARITHMETICAL REASONING
      • SUMMARY
      • THE SOCIOLOGY OF ARITHMETIC
    • THE SERIES IDEA OVEREMPHASIZED
    • THE RATIO IDEA OVEREMPHASIZED
    • THE RELATIONAL IDEA OVEREMPHASIZED
    • ARITHMETICAL LANGUAGE
    • PROBLEM-SOLVING
    • Samples of Desirable Applications of Arithmetic in Problems where the Situation is Actually Present to Sense in Whole or in Part
    • Samples of Desirable Applications of Arithmetic where the Situation is Not Present to Sense
    • A
    • B
    • C
    • Samples of Undesirable Applications of Arithmetic[1]
    • ARITHMETICAL REASONING
    • SUMMARY
    • THE SOCIOLOGY OF ARITHMETIC
    • CHAPTER II
    • THE MEASUREMENT OF ARITHMETICAL ABILITIES
      • A SAMPLE MEASUREMENT OF AN ARITHMETICAL ABILITY: THE ABILITY TO ADD INTEGERS
        • MEASUREMENTS OF ABILITIES IN COMPUTATION
        • MEASUREMENTS OF ABILITY IN APPLIED ARITHMETIC: THE SOLUTION OF PROBLEMS
        • TEST 1
      • MEASUREMENTS OF ABILITIES IN COMPUTATION
      • MEASUREMENTS OF ABILITY IN APPLIED ARITHMETIC: THE SOLUTION OF PROBLEMS
      • TEST 1
    • A SAMPLE MEASUREMENT OF AN ARITHMETICAL ABILITY: THE ABILITY TO ADD INTEGERS
      • MEASUREMENTS OF ABILITIES IN COMPUTATION
      • MEASUREMENTS OF ABILITY IN APPLIED ARITHMETIC: THE SOLUTION OF PROBLEMS
      • TEST 1
    • MEASUREMENTS OF ABILITIES IN COMPUTATION
    • MEASUREMENTS OF ABILITY IN APPLIED ARITHMETIC: THE SOLUTION OF PROBLEMS
    • TEST 1
    • CHAPTER III
      • THE CONSTITUTION OF ARITHMETICAL ABILITIES
        • THE ELEMENTARY FUNCTIONS OF ARITHMETICAL LEARNING
        • KNOWLEDGE OF THE MEANING OF A FRACTION
        • KNOWLEDGE OF THE SUBTRACTION AND DIVISION TABLES
        • LEARNING THE PROCESSES OF COMPUTATION
      • THE ELEMENTARY FUNCTIONS OF ARITHMETICAL LEARNING
      • KNOWLEDGE OF THE MEANING OF A FRACTION
      • KNOWLEDGE OF THE SUBTRACTION AND DIVISION TABLES
      • LEARNING THE PROCESSES OF COMPUTATION
    • THE CONSTITUTION OF ARITHMETICAL ABILITIES
      • THE ELEMENTARY FUNCTIONS OF ARITHMETICAL LEARNING
      • KNOWLEDGE OF THE MEANING OF A FRACTION
      • KNOWLEDGE OF THE SUBTRACTION AND DIVISION TABLES
      • LEARNING THE PROCESSES OF COMPUTATION
    • THE ELEMENTARY FUNCTIONS OF ARITHMETICAL LEARNING
    • KNOWLEDGE OF THE MEANING OF A FRACTION
    • KNOWLEDGE OF THE SUBTRACTION AND DIVISION TABLES
    • LEARNING THE PROCESSES OF COMPUTATION
    • CHAPTER IV
      • THE CONSTITUTION OF ARITHMETICAL ABILITIES (CONTINUED): THE SELECTION OF THE BONDS TO BE FORMED
        • THE IMPORTANCE OF HABIT-FORMATION
        • DESIRABLE BONDS NOW OFTEN NEGLECTED
        • WASTEFUL AND HARMFUL BONDS
        • GUIDING PRINCIPLES
      • THE IMPORTANCE OF HABIT-FORMATION
      • DESIRABLE BONDS NOW OFTEN NEGLECTED
      • WASTEFUL AND HARMFUL BONDS
      • GUIDING PRINCIPLES
    • THE CONSTITUTION OF ARITHMETICAL ABILITIES (CONTINUED): THE SELECTION OF THE BONDS TO BE FORMED
      • THE IMPORTANCE OF HABIT-FORMATION
      • DESIRABLE BONDS NOW OFTEN NEGLECTED
      • WASTEFUL AND HARMFUL BONDS
      • GUIDING PRINCIPLES
    • THE IMPORTANCE OF HABIT-FORMATION
    • DESIRABLE BONDS NOW OFTEN NEGLECTED
    • WASTEFUL AND HARMFUL BONDS
    • GUIDING PRINCIPLES
    • CHAPTER V
      • THE PSYCHOLOGY OF DRILL IN ARITHMETIC: THE STRENGTH OF BONDS
        • THE NEED OF STRONGER ELEMENTARY BONDS
        • EARLY MASTERY
        • THE STRENGTH OF BONDS FOR TEMPORARY SERVICE
        • THE STRENGTH OF BONDS WITH TECHNICAL FACTS AND TERMS
        • THE STRENGTH OF BONDS CONCERNING THE REASONS FOR ARITHMETICAL PROCESSES
        • PROPÆDEUTIC BONDS
      • THE NEED OF STRONGER ELEMENTARY BONDS
      • EARLY MASTERY
      • THE STRENGTH OF BONDS FOR TEMPORARY SERVICE
      • THE STRENGTH OF BONDS WITH TECHNICAL FACTS AND TERMS
      • THE STRENGTH OF BONDS CONCERNING THE REASONS FOR ARITHMETICAL PROCESSES
      • PROPÆDEUTIC BONDS
    • THE PSYCHOLOGY OF DRILL IN ARITHMETIC: THE STRENGTH OF BONDS
      • THE NEED OF STRONGER ELEMENTARY BONDS
      • EARLY MASTERY
      • THE STRENGTH OF BONDS FOR TEMPORARY SERVICE
      • THE STRENGTH OF BONDS WITH TECHNICAL FACTS AND TERMS
      • THE STRENGTH OF BONDS CONCERNING THE REASONS FOR ARITHMETICAL PROCESSES
      • PROPÆDEUTIC BONDS
    • THE NEED OF STRONGER ELEMENTARY BONDS
    • EARLY MASTERY
    • THE STRENGTH OF BONDS FOR TEMPORARY SERVICE
    • THE STRENGTH OF BONDS WITH TECHNICAL FACTS AND TERMS
    • THE STRENGTH OF BONDS CONCERNING THE REASONS FOR ARITHMETICAL PROCESSES
    • PROPÆDEUTIC BONDS
    • CHAPTER VI
      • THE PSYCHOLOGY OF DRILL IN ARITHMETIC: THE AMOUNT OF PRACTICE AND THE ORGANIZATION OF ABILITIES
        • THE AMOUNT OF PRACTICE
        • UNDERLEARNING AND OVERLEARNING
        • THE ORGANIZATION OF ABILITIES
      • THE AMOUNT OF PRACTICE
      • UNDERLEARNING AND OVERLEARNING
      • THE ORGANIZATION OF ABILITIES
    • THE PSYCHOLOGY OF DRILL IN ARITHMETIC: THE AMOUNT OF PRACTICE AND THE ORGANIZATION OF ABILITIES
      • THE AMOUNT OF PRACTICE
      • UNDERLEARNING AND OVERLEARNING
      • THE ORGANIZATION OF ABILITIES
    • THE AMOUNT OF PRACTICE
    • UNDERLEARNING AND OVERLEARNING
    • THE ORGANIZATION OF ABILITIES
    • CHAPTER VII
      • THE SEQUENCE OF TOPICS: THE ORDER OF FORMATION OF BONDS
        • DECREASING INTERFERENCE AND INCREASING FACILITATION
        • INTEREST
        • GENERAL PRINCIPLES
      • DECREASING INTERFERENCE AND INCREASING FACILITATION
      • INTEREST
      • GENERAL PRINCIPLES
    • THE SEQUENCE OF TOPICS: THE ORDER OF FORMATION OF BONDS
      • DECREASING INTERFERENCE AND INCREASING FACILITATION
      • INTEREST
      • GENERAL PRINCIPLES
    • DECREASING INTERFERENCE AND INCREASING FACILITATION
    • INTEREST
    • GENERAL PRINCIPLES
    • CHAPTER VIII
    • THE DISTRIBUTION OF PRACTICE
      • THE PROBLEM
      • SAMPLE DISTRIBUTIONS
        • POSSIBLE IMPROVEMENTS
      • POSSIBLE IMPROVEMENTS
    • THE PROBLEM
    • SAMPLE DISTRIBUTIONS
      • POSSIBLE IMPROVEMENTS
    • POSSIBLE IMPROVEMENTS
    • CHAPTER IX
      • THE PSYCHOLOGY OF THINKING: ABSTRACT IDEAS AND GENERAL NOTIONS IN ARITHMETIC[11]
        • RESPONSES TO ELEMENTS AND CLASSES
        • FACILITATING THE ANALYSIS OF ELEMENTS
        • SYSTEMATIC AND OPPORTUNISTIC STIMULI TO ANALYSIS
        • ADAPTATIONS TO ELEMENTARY SCHOOL PUPILS
      • RESPONSES TO ELEMENTS AND CLASSES
      • FACILITATING THE ANALYSIS OF ELEMENTS
      • SYSTEMATIC AND OPPORTUNISTIC STIMULI TO ANALYSIS
      • ADAPTATIONS TO ELEMENTARY SCHOOL PUPILS
    • THE PSYCHOLOGY OF THINKING: ABSTRACT IDEAS AND GENERAL NOTIONS IN ARITHMETIC[11]
      • RESPONSES TO ELEMENTS AND CLASSES
      • FACILITATING THE ANALYSIS OF ELEMENTS
      • SYSTEMATIC AND OPPORTUNISTIC STIMULI TO ANALYSIS
      • ADAPTATIONS TO ELEMENTARY SCHOOL PUPILS
    • RESPONSES TO ELEMENTS AND CLASSES
    • FACILITATING THE ANALYSIS OF ELEMENTS
    • SYSTEMATIC AND OPPORTUNISTIC STIMULI TO ANALYSIS
    • ADAPTATIONS TO ELEMENTARY SCHOOL PUPILS
    • CHAPTER X
      • THE PSYCHOLOGY OF THINKING: REASONING IN ARITHMETIC
        • THE ESSENTIALS OF ARITHMETICAL REASONING
        • REASONING AS THE COÖPERATION OF ORGANIZED HABITS
      • THE ESSENTIALS OF ARITHMETICAL REASONING
      • REASONING AS THE COÖPERATION OF ORGANIZED HABITS
    • THE PSYCHOLOGY OF THINKING: REASONING IN ARITHMETIC
      • THE ESSENTIALS OF ARITHMETICAL REASONING
      • REASONING AS THE COÖPERATION OF ORGANIZED HABITS
    • THE ESSENTIALS OF ARITHMETICAL REASONING
    • REASONING AS THE COÖPERATION OF ORGANIZED HABITS
    • CHAPTER XI
      • ORIGINAL TENDENCIES AND ACQUISITIONS BEFORE SCHOOL
        • THE UTILIZATION OF INSTINCTIVE INTERESTS
        • THE ORDER OF DEVELOPMENT OF ORIGINAL TENDENCIES
        • INVENTORIES OF ARITHMETICAL KNOWLEDGE AND SKILL
        • THE PERCEPTION OF NUMBER AND QUANTITY
        • THE EARLY AWARENESS OF NUMBER
      • THE UTILIZATION OF INSTINCTIVE INTERESTS
      • THE ORDER OF DEVELOPMENT OF ORIGINAL TENDENCIES
      • INVENTORIES OF ARITHMETICAL KNOWLEDGE AND SKILL
      • THE PERCEPTION OF NUMBER AND QUANTITY
      • THE EARLY AWARENESS OF NUMBER
    • ORIGINAL TENDENCIES AND ACQUISITIONS BEFORE SCHOOL
      • THE UTILIZATION OF INSTINCTIVE INTERESTS
      • THE ORDER OF DEVELOPMENT OF ORIGINAL TENDENCIES
      • INVENTORIES OF ARITHMETICAL KNOWLEDGE AND SKILL
      • THE PERCEPTION OF NUMBER AND QUANTITY
      • THE EARLY AWARENESS OF NUMBER
    • THE UTILIZATION OF INSTINCTIVE INTERESTS
    • THE ORDER OF DEVELOPMENT OF ORIGINAL TENDENCIES
    • INVENTORIES OF ARITHMETICAL KNOWLEDGE AND SKILL
    • THE PERCEPTION OF NUMBER AND QUANTITY
    • THE EARLY AWARENESS OF NUMBER
    • CHAPTER XII
      • INTEREST IN ARITHMETIC
        • CENSUSES OF PUPILS' INTERESTS
        • RELIEVING EYESTRAIN
        • SIGNIFICANCE FOR RELATED ACTIVITIES
        • INTRINSIC INTEREST IN ARITHMETICAL LEARNING
      • CENSUSES OF PUPILS' INTERESTS
      • RELIEVING EYESTRAIN
      • SIGNIFICANCE FOR RELATED ACTIVITIES
      • INTRINSIC INTEREST IN ARITHMETICAL LEARNING
    • INTEREST IN ARITHMETIC
      • CENSUSES OF PUPILS' INTERESTS
      • RELIEVING EYESTRAIN
      • SIGNIFICANCE FOR RELATED ACTIVITIES
      • INTRINSIC INTEREST IN ARITHMETICAL LEARNING
    • CENSUSES OF PUPILS' INTERESTS
    • RELIEVING EYESTRAIN
    • SIGNIFICANCE FOR RELATED ACTIVITIES
    • INTRINSIC INTEREST IN ARITHMETICAL LEARNING
    • CHAPTER XIII
      • THE CONDITIONS OF LEARNING
        • EXTERNAL CONDITIONS
        • CONCERNING THE RATING OF COURSES OF STUDY
        • THE HYGIENE OF THE EYES IN ARITHMETIC
        • THE USE OF CONCRETE OBJECTS IN ARITHMETIC
        • ORAL, MENTAL, AND WRITTEN ARITHMETIC
      • EXTERNAL CONDITIONS
      • CONCERNING THE RATING OF COURSES OF STUDY
      • THE HYGIENE OF THE EYES IN ARITHMETIC
      • THE USE OF CONCRETE OBJECTS IN ARITHMETIC
      • ORAL, MENTAL, AND WRITTEN ARITHMETIC
    • THE CONDITIONS OF LEARNING
      • EXTERNAL CONDITIONS
      • CONCERNING THE RATING OF COURSES OF STUDY
      • THE HYGIENE OF THE EYES IN ARITHMETIC
      • THE USE OF CONCRETE OBJECTS IN ARITHMETIC
      • ORAL, MENTAL, AND WRITTEN ARITHMETIC
    • EXTERNAL CONDITIONS
    • CONCERNING THE RATING OF COURSES OF STUDY
    • THE HYGIENE OF THE EYES IN ARITHMETIC
    • THE USE OF CONCRETE OBJECTS IN ARITHMETIC
    • ORAL, MENTAL, AND WRITTEN ARITHMETIC
    • CHAPTER XIV
      • THE CONDITIONS OF LEARNING: THE PROBLEM ATTITUDE
        • ILLUSTRATIVE CASES
        • GENERAL PRINCIPLES
        • DIFFICULTY AND SUCCESS AS STIMULI
        • FALSE INFERENCES
      • ILLUSTRATIVE CASES
      • GENERAL PRINCIPLES
      • DIFFICULTY AND SUCCESS AS STIMULI
      • FALSE INFERENCES
    • THE CONDITIONS OF LEARNING: THE PROBLEM ATTITUDE
      • ILLUSTRATIVE CASES
      • GENERAL PRINCIPLES
      • DIFFICULTY AND SUCCESS AS STIMULI
      • FALSE INFERENCES
    • ILLUSTRATIVE CASES
    • GENERAL PRINCIPLES
    • DIFFICULTY AND SUCCESS AS STIMULI
    • FALSE INFERENCES
    • CHAPTER XV
      • INDIVIDUAL DIFFERENCES
        • NATURE AND AMOUNT
        • DIFFERENCES WITHIN ONE CLASS
        • THE CAUSES OF INDIVIDUAL DIFFERENCES
        • THE INTERRELATIONS OF INDIVIDUAL DIFFERENCES
      • NATURE AND AMOUNT
      • DIFFERENCES WITHIN ONE CLASS
      • THE CAUSES OF INDIVIDUAL DIFFERENCES
      • THE INTERRELATIONS OF INDIVIDUAL DIFFERENCES
      • FOOTNOTES
    • INDIVIDUAL DIFFERENCES
      • NATURE AND AMOUNT
      • DIFFERENCES WITHIN ONE CLASS
      • THE CAUSES OF INDIVIDUAL DIFFERENCES
      • THE INTERRELATIONS OF INDIVIDUAL DIFFERENCES
    • NATURE AND AMOUNT
    • DIFFERENCES WITHIN ONE CLASS
    • THE CAUSES OF INDIVIDUAL DIFFERENCES
    • THE INTERRELATIONS OF INDIVIDUAL DIFFERENCES
    • FOOTNOTES
    • BIBLIOGRAPHY OF REFERENCES MADE IN THE TEXT
    • INDEX
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