This book is dedicated to all the teachers who are willing to ask WHY and use the manipulatives to help students find out. This book is a celebration of over 55 years of classroom teaching, and weaving together of "old" and "new" interpretations of a style of teaching based on ASKING and DISCOVERING by doing. It began for me in 1955 when I was asked to train elementary teachers to teach the new math meaningfully. This experience led me to create a model for an ideal elementary math program. I was able to implement this model at the Nueva Center for Learning and to add a young teachernamed Peggy McLean. For years Peggy worked with me learning and modifying activities to meet all the levens of thinking in the classroom. She encouraged me to write this book. Our close friend, Margaret Smart, has listened to us, edited and illustrated the ideas we wish to share with the world. My sister, Martha Kyzer, designed the cover to illustrate the weaving of mathematics. Mary Laycock