Conceptualizing and Measuring Mathematical Sophistication Jennifer E. Szydlik, Eric Kuennen, Jason Belnap and Amy Parrott University of Wisconsin Oshkosh Carol E. Seaman University of North Carolina at Greensboro Abstract In this paper, we elaborate a framework to define, and a paper-and-pencil instrument to measure, the mathematical sophistication of prospective elementary teachers. We call an individual mathematically sophisticated if her values and practices reflect those of the mathematical community on nine interwoven categories involving patterns, conjectures, structure, definitions, examples and models, relationships, arguments, language, and notation. We argue that mathematical sophistication provides access not only to mathematical understandings but to mathematical knowledge for teaching. We describe the development of a Mathematical Sophistication Instrument and report the results of our study of its reliability, validity, and capacity to measure changes. We hope that the instrument provides educators a tool for assessing programs designed to nurture mathematical practices. Key Words: mathematical sophistication, habits of mind, standards for mathematical practice, teacher education, teacher knowledge, instrument development This work was supported in part by a University of Wisconsin Oshkosh Faculty Development grant