This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what problems and questions help elicit them. Special features of the book help teachers develop their own understanding of mathematics along with their students. Teacher Commentaries captures the voices of a number of teachers providing realistic portrayals of what happens in class. The Challenge offers a variety of problems and activities for teachers to increase their own knowledge of mathematics and help their students develop algebraic thinking. The accompanying CD provides rich illustrations of ideas in the book clearly linked to the text. (KHR)