Abstract
Mathematics teacher educators (MTEs) charged with the content preparation of prospective elementary teachers (PTs) receive widespread recommendations on a variety of issues, including which mathematical topics to include in their courses, the types of pedagogical strategies to use when working with PTs, and how to foster the development of particular mathematical practices. The nature of the mathematical tasks that MTEs can use to best support and extend PTs ' content knowledge is another area that deserves attention. This article considers uncertainty as a task feature and explains how it can be incorporated into mathematical tasks in order to support PTs ' specialized content knowledge. Using Zaslavsky 's (2005) three types of uncertainty - competing claims, unknown path or questionable conclusion, and non-readily verifiable outcomes - we provide three classroom examples of ways in which MTEs incorporated uncertainty into their mathematical tasks. Each example provides detail about the task design, background research on PTs' knowledge of the underlying mathematical content, the type of uncertainty the task generated for PTs, and the ways in which that uncertainty may have contributed to PTs ' understandings of the content. Each example concludes with recommendations for MTEs on specific ways to incorporate that particular type of uncertainty into their own teaching.