Many schools employ coaches to support mathematics instruction and student learning. This research study investigated the roles of coaches from five school districts in Virginia. Participants included 125 elementary mathematics coaches and 59 principals. Results from cross-sectional surveys revealed that most coaches did not have a degree in mathematics education or hold a mathematics specialist endorsement. Principals did not value the mathematics specialist endorsement as a selection criterion as much as they valued other criteria. Coaches were serving in multiple roles, predominantly acting as classroom supporters, resource providers, instructional specialists, and data coaches. They were also acting as pull-out teachers, providing remediation to students. Coaches' work with teachers was largely determined by teachers' comfort level and willingness to be coached. Principals thought classroom supporter, catalyst for change, instructional specialist, data coach, and school leader were the most important roles. Statistically significant differences showed that principals and coaches disagreed about the importance of three coaching roles (catalyst for change, school leader, and resource provider). Many principals were not aware that they did not share common understandings with their coaches about the coaches' roles and responsibilities, their vision of mathematics instruction, and their mutual communication. [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.]