This book features a comparative study of American and Chinese mathematics teachers. How teachers understand the content of mathematics and their practice of mathematics teaching is examined. The differences between Chinese and U.S. teachers' knowledge of mathematics for teaching are documented, and how Chinese teachers' understanding of mathematics and its teaching contributes to their students' success is discussed. This book include approaches to teaching subtraction with regrouping, addressing students' mistakes in multidigit number multiplication, generating representations for division by fractions, and exploring new knowledge by examining the relationship between perimeter and area. Teachers' subject matter knowledge and how the profound understanding of fundamental mathematics is attained are discussed. This book is relevant to the preservice preparation of teachers as well as to understanding of teachers' work and their career-long professional development. (KHR)