Improving mathematics instruction is an essential issue many school leaders are encountering as they feel increased pressure to ensure high-quality learning for all students. Key responsibilities of school leaders in leading mathematics improvement include observing instruction and providing teachers with feedback. If school leaders fulfill these responsibilities effectively and help teachers become better practitioners in the classroom, they can have a substantial impact on raising student achievement. As a result of minimal research and contradictory recommendations guiding school leaders towards mathematics leadership, many school leaders are not effectively fostering growth in mathematics instruction. The purpose of this study was to provide clarity to school leaders by pinpointing what elementary school leaders need to know in order to effectively observe mathematics instruction and provide teachers with feedback. More specifically, the study examined the necessity of a school leader's mathematics content knowledge, student pedagogical knowledge, and knowledge of how teachers learn to teach mathematics. The study was conducted using a three-round Delphi method completed by an expert panel composed of 15 stakeholders with diverse perspectives in the area of mathematics leadership. The study yielded guidelines regarding what school leaders need to know in order to effectively observe elementary mathematics instruction and provide informed feedback to teachers. The experts unanimously concluded that school leaders must understand elementary mathematics as a process of reasoning rather than merely rules, facts, and procedures. One-hundred percent of the panel also strongly agreed that mathematics instruction must occur in student-centered classrooms where teachers act as a facilitator of learning and use effective questioning to engage students in developing mathematical understandings and connections. The study concluded with 11 additional critical findings. [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.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]