Description: Introduction: The Roots of My Theory. Preliminary Questions. How Do We Meet a Structure? How Do We Recognize a Structure? Rigid and Feeble Structures. What Is a Structure? Properties of a Structure. The Media in Which Structure Acts. Levels of Thinking. The Consequences and a More Exact Analysis of the Theory of Levels of Thinking. A Psychological Approach to Levels of Thinking. Intuition. Reality, Individual, and Language. Structures at Different Levels. Consequences of the Languages at Different Levels. The Development of Number. Levels of Structure in Argument. The Intuitive Foundations of Mathematics. Direct Reactions to Visual Structures. Direct Interactions between Reality and Common Human Knowledge. Switching Over from One Structure to Another. The Relations among the Media of Structure. Is it Possible to Test Insight? A Phenomenal Introduction to Geometry. The Significance of Intention in the Learning Process. The Problem of Motivation in Education. System Separation and Transfer. The Relation between Theory and Problems in Arithmetic and Algebra. Proportion and Fraction. Objectivity. A Step in the Direction of Philosophy. References. Index.

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