How Humans Learn to Think Mathematically : Exploring the Three Worlds of Mathematics (Paperback)

Part I. Prelude: 1. About this book; Part II. School Mathematics and its Consequences: 2. The foundations of mathematical thinking; 3. Compression, connection and blending of mathematical ideas; 4. Set-befores, met-befores and long-term learning; 5. Mathematics and the emotions; 6. The three worlds of mathematics; 7. Journeys through embodiment and symbolism; 8. Problem-solving and proof; Part III. Interlude: 9. The historical evolution of mathematics; Part IV. University Mathematics and Beyond: 10. The transition to formal knowledge; 11. Blending knowledge structures in calculus; 12. Expert thinking and structure theorems; 13. Contemplating the infinitely large and the infinitely small; 14. Expanding frontiers through mathematical research; 15. Reflections; Appendix: where the ideas came from.