This dissertation study describes the nature of the mathematical knowledge required to teach a unit on exponents at the secondary school level, and further explores the adequacy of extant theoretical models for characterizing that knowledge. Researchers agree that teacher content knowledge contributes to teaching quality, which in turn contributes to student learning. Prior foundational research focused on the mathematical knowledge needed for teaching at the elementary level but not at the secondary level. Case study methodology was used with a constant comparative analytic process, modeled on similar successful methodologies used in investigating mathematical knowledge for elementary school teaching. The site was purposefully selected to maximize the opportunity to observe the use of mathematical knowledge in teaching. Data collected during the unit of instruction included lesson plans, video-recordings of all class sessions, and audio-recordings of daily follow-up interviews with the teacher. Results include a detailed description of the mathematical knowledge demanded in teaching a unit in secondary mathematics. The knowledge described in the results included substantial knowledge about the domain of mathematics and how it is practiced by mathematicians, especially in relation to definitions, definition extension, and proof. It also demanded that this knowledge be connected to specific content, exponents, in a way that allowed the teacher to see exponents as a case of a larger set of mathematical practices. This type of knowledge is not well described by existing frameworks for teacher knowledge, and the study's implications explore why and how existing theory might be adjusted to better account for such knowledge. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]