Elementary school mathematics teaching begins with the teacher's understanding of the mathematical content to be taught. The teacher knows how to "do" the mathematics, i. e., understands the concepts and truths concerning that mathematics. The teacher then decides how to present the mathematics. Based on the students' background in mathematics, the teacher selects the explanations and instructional strategies that will help the students build on their current background and develop a thorough understanding. After selecting the strategies, the teacher designs and implements a series of activities aimed at facilitating all students' learning of the mathematics. These activities may include direct instruction, group work, guided discovery, or any other of the many pedagogical tools available. The teacher then assesses the students' level of understanding, diagnosing areas of misunderstanding, and designs additional activities to alleviate those misunderstandings. Based on this description of elementary school mathematics teaching, an elementary school teacher certainly needs a strong conceptual understanding of mathematical content and an equally thorough understanding of pedagogical skills and practices. However, the lack of any research conclusively connecting either of these two sets of knowledge with student success in learning mathematics seems to indicate that something is missing. The National Council for Accreditation of Teacher Education (NCATE) recently recognized pedagogical content knowledge as a distinct and important aspect of a teacher's knowledge base. In the 2002 edition of its "Professional Standards for the Accreditation of Schools, Colleges and Departments of Education," NCATE discusses three types of Candidate Knowledge, Skills and Dispositions (Standard 1). They are: (1) Content Knowledge for Teacher Candidates; (2) Pedagogical Content Knowledge for Teacher Candidates; and (3) Professional and Pedagogical Knowledge and Skills for Teacher Candidates. NCATE will begin evaluating teacher preparation programs on the strength of their candidates' pedagogical content knowledge, in addition to their content knowledge and pedagogical skills, in 2002. This article explores pedagogical content knowledge in the context of elementary school mathematics, and its relationship to students' learning of mathematics.