This study set out to examine how interactions between a mathematics instructional coach and a teacher influence teacher pedagogical content knowledge, instructional practices, and a classroom culture of mathematical inquiry (CCMI). The research literature on mathematics instructional coaching was limited, but showed promise in supporting teachers' learning regarding reform-based mathematics teaching and learning. Learning through teaching has been well documented in the literature; however, teaching experience is not sufficient in teacher learning. An instructional coach's role is to support teacher learning through job-embedded professional development. The study examined (a) the nature of coach-teacher interactions on the development of teacher's pedagogical content, effective mathematics teaching practices, and the development of a CCMI; (b) the conditions that made such interactions productive; and (c) the manifestations of change in teacher practices regarding teacher pedagogical content knowledge, effective mathematics teaching practices and CCMI. The study was a qualitative, single-case study. This was a naturalistic study in which the data were collected in the natural setting: the classroom. The researcher was the instructional coach in the study. One first-grade teacher participated in the study as well as twelve of her students. The site of the investigation was a kindergarten through grade five school with approximately 480 students, of which 85% received free or reduced lunch. The data examined in this study included the components of a coaching cycle, pre- and post-conferences, classroom coaching sessions and coach/researcher reflections. In addition, the researcher conducted interviews and observations at the beginning and end of the coaching cycle and three months after the coaching cycle ended. The interviews and conferences were audiotaped, and the classroom coaching sessions and observations were videotaped. The interview, conference, and observation data were analyzed using the constant comparative method. These data were used to determine the conceptual categories used to analyze the data, while the literature was used to define these categories. The classroom coaching sessions were viewed repeatedly to identify significant episodes based on the conceptual framework used in this study. Using all sources of data, a narrative timeline was written and used to analyze the data for ways in which teaching practices evolved over time. This study found that PCK, teaching practices, and CCMI were primary themes in the coach-teacher interactions. The coach's role during mathematics lessons was limited due to the teacher's comfort level. This required use of spontaneous instead of planned coaching moves. The conditions that contributed to implementation of teacher's practices included (a) zone of proximal development; (b) visualization of practices; (c) ease of implementation; (d) teacher's beliefs; (e) messages from the broader community; and (f) the coach's understanding of PCK, teaching practices, and CCMI. Success of implementation of strategies depended on the coach's ability to help the teacher visualize practices and to trim and decompress teaching practices. Finally, a model for coach growth-of-knowledge is proposed based on the model by Perks and Prestage (2008) for teacher and mathematics teacher educator (MTE) growth-of-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.]