This book reflects the author's experience in teaching a mathematics content course for pre-service elementary teachers. The book addresses a number of recommendations of the Conference Board of the Mathematical Sciences for the preparation of teachers demonstrating how abstract mathematical concepts can be motivated by concrete activities. Such an approach, when enhanced by the use of technology, makes it easier for the teachers to grasp the meaning of generalization, formal proof, and the creation of an increasing number of concepts on higher levels of abstraction. A strong experiential component of the book made possible by the use of manipulative materials and digital technology such as spreadsheets, The Geometer's Sketchpad, Graphing Calculator 3.5 produced by Pacific Tech, and Kid Pix Studio Deluxe makes it possible to balance informal and formal approaches to mathematics, allowing the teachers to learn how the two approaches complement each other. Classroom observations of the t