| CHAPTER | | PAGE |
| Introduction: The Psychology of the Elementary School Subjects | xi |
|
| I. | The Nature of Arithmetical Abilities | 1 |
| Knowledge of the Meanings of Numbers |
| Arithmetical Language |
| Problem Solving |
| Arithmetical Reasoning |
| Summary |
| The Sociology of Arithmetic |
|
| II. | The Measurement of Arithmetical Abilities | 27 |
| A Sample Measurement of an Arithmetical Ability |
| Ability to Add Integers |
| Measurements of Ability in Computation |
| Measurements of Ability in Applied Arithmetic: the Solution of Problems |
|
| III. | The Constitution of Arithmetical Abilities | 51 |
| The Elementary Functions of Arithmetical Learning |
| Knowledge of the Meaning of a Fraction |
| Learning the Processes of Computation |
|
| IV. | The Constitution of Arithmetical Abilities (continued) | 70 |
| The Selection of the Bonds to Be Formed |
| The Importance of Habit Formation |
| Desirable Bonds Now Often Neglected |
| Wasteful and Harmful Bonds |
| Guiding Principles |
|
| V. | The Psychology of Drill in Arithmetic: The Strength of Bonds | 102 |
| 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 |
|
| VI. | The Psychology of Drill in Arithmetic: The Amount of Practice and the Organization of Abilities | 122 |
| The Amount of Practice |
| Under-learning and Over-learning |
| The Organization of Abilities |
|
| VII. | The Sequence of Topics: The Order of Formation of Bonds | 141 |
| Conventional versus Effective Orders |
| Decreasing Interference and Increasing Facilitation |
| Interest |
| General Principles |
|
| VIII. | The Distribution of Practice | 156 |
| The Problem |
| Sample Distributions |
| Possible Improvements |
|
| IX. | The Psychology of Thinking: Abstract Ideas and General Notions in Arithmetic | 169 |
| Responses to Elements and Classes |
| Facilitating the Analysis of Elements |
| Systematic and Opportunistic Stimuli to Analysis |
| Adaptations to Elementary-school Pupils |
|
| X. | The Psychology of Thinking: Reasoning in Arithmetic | 185 |
|
