This book reflects the author's experience in teaching a mathematics content course for pre-service elementaryteachers. The book addresses a number of recommendations of the Conference Board of the Mathematical Sciencesfor the preparation of teachers demonstrating how abstract mathematical concepts can be motivated byconcrete activities. Such an approach, when enhanced by the use of technology, makes it easier for the teachersto grasp the meaning of generalization, formal proof, and the creation of an increasing number of concepts onhigher levels of abstraction. A strong experiential component of the book made possible by the use of manipulativematerials 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 formalapproaches to mathematics, allowing the teachers to learn how the two approaches complement each other.Classroom observations of the teachers' learning mathematics as a combination of theory and experiment confirmthat this approach elevates one's mathematical understanding to a higher ground. The book not only showsthe importance of mathematics content knowledge for teachers but better still, how this knowledge can be graduallydeveloped in the context of exploring grade-appropriate activities and tasks and using computational andmanipulative environments to support these explorations.Most of the chapters are motivated by a problem/activity typically found in the elementary mathematics curricula and/or standards (either National orNew York State - the context in which the author prepares teachers). By exploring such problems in depth, the teachers can learn fundamental mathematicalconcepts and ideas hidden within a seemingly mundane problem/activity. The need to have experience in going beyond traditional expectationsfor learning is due to the constructivist orientation of contemporary mathematics pedagogy that encourages students to ask questions aboutmathematics they study. Each chapter includes an activity set that can be used for the development of the variety of assignments for the teachers.The material included in the book is original in terms of the approach used to teach mathematics to the teachers and it is based on a number of journalarticles published by the author in the United States and elsewhere. Mathematics educators who are interested in integrating hands-on activities anddigital technology into the teaching of mathematics will find this book useful. Mathematicians who teach mathematics to the teachers as part of theirteaching load will be interested in the material included in the book as it connects childhood mathematics content and mathematics for the teachers.
