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Why is 2 times 3 equal to 3 times 2? One may think this is an axiom, but it has a proof, and a beautiful one at that. Elementary mathematics is as deep and as beautiful as higher mathematics. It includes some of the most important mathematical discoveries ever, for example the concept of the number, and the place-value method of representing numbers. About the Author. Acknowledgments. Introduction. What’s in the Book. Thinking Mathematics. Didactics. Kindergarten. More Teaching Principles. Operations in Search of Meaning. There Shalt Be Order: The Decimal System. The Checkered Notebook: Calculation. More Teaching Principles. Fractions. Decimal Fractions. Educational Revolutions. Proportion. Geometry. Congruence and Similarity. The Ruler and the Compass. Length, Area, and Volume. The Magic Circle. Index