What are the effective approaches of teaching and learning mathematics? How do teachers build on knowledge of students' thinking? What knowledge is needed for teachers to teach effectively? Shuhua An answers these questions by examining the differences between the pedagogical content knowledge of elementary and middle school mathematics teachers in the U.S. and China and investigates how these differences are revealed in their beliefs, planning, teaching methods, and knowledge of students' thinking. She reveals the current dilemmas in mathematics education in the U.S and China, traces the...