JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . Many consider proof to be central to the discipline of mathematics and the practice of mathematicians. In fact, Ross (1998) contended that "the essence of mathematics lies in proofs" (p. 254). Yet, surprisingly, the role of proof in secondary school mathematics has traditionally been peripheral at best, usually limited to the domain of Euclidean geometry. According to Wu (1996), however, the scarcity of proof outside of geometry is a misrepresentation of the nature of proof in mathematics. He argued that this absence is a glaring defect in the present-day mathematics education in high school, namely, the fact that outside geometry there are essentially no proofs. Even as anomalies in education go, this is certainly more anomalous than others inasmuch as it presents a totally falsified picture of mathematics itself (p. 228). National Council of Teachers of Mathematics Similarly, Schoenfeld (1994) maintained that "proof is not a thing separable from mathematics, as it appears to be in our curricula; it is an essential component of doing, communicating, and recording mathematics. And I believe it can be embedded in our curricula, at all levels" (p. THEORETICAL PERSPECTIVES Authors have suggested various roles that proof plays in mathematics: to verify that a statement is true, to explain why a statement is true, to communicate math-1 My use of the term conceptions includes both subject matter knowledge and beliefs. Although separating teachers' knowledge and beliefs serves as a useful heuristic for thinking about and studying factors influencing their instructional practices, the separation is less distinct in reality than it is in theor
