Coaching has become an increasingly utilized professional development strategy to improve mathematics instruction at the elementary level. However, little research has been conducted on the nature of mathematics coaching and its effects. This study has examined factors that affected elementary teachers who participated in a specific coaching model which focused on the teachers' mathematics subject matter knowledge, pedagogical content knowledge, and self-efficacy. To answer the research questions, qualitative research design was employed. All of the first grade teachers at an urban elementary school in a mid-sized, culturally and linguistically diverse city in the Northeast participated in the study with the researcher, who was embedded as the mathematics coach. Collected data include teacher background surveys, three sets of semi-structured interviews conducted by an independent researcher, audiotapes of coaching sessions, coaching logs, and teacher artifacts. The most prevalent theme of the study involved the full implementation of the Common Core standards and how the coaching model served as the primary professional development strategy. In the context of implementing the Common Core standards, participating teachers demonstrated increased subject matter knowledge, pedagogical content knowledge, and self-efficacy. The teachers and the coach found several aspects of coaching to be effective, including unpacking new standards, collaboratively planning Common Core-aligned modules of study, incorporating new instructional strategies and manipulatives, collecting, reporting, and analyzing multiple sources of student data, and developing interventions for struggling students. [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://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]