This study was an investigation of mathematics instruction and professional development at a rural elementary school. The Department of Education in a southern U.S. state implemented a new curriculum in 2007 that required major changes in mathematics instruction. The problems were that teachers engaged in different levels of training and many students experienced a decline in mathematics scores on the Criterion-Referenced Competency Test (CRCT). The historical learning theories of Piaget and Vygotsky framed the study. The guiding questions focused on how to improve mathematics instruction through professional development for teachers. Nine elementary school educators served as purposefully selected participants. The research design was a case study that included triangulation of data from teacher interviews, a research journal, and documents such as lesson plans. Open coding and selective analysis generated 9 themes and 9 subthemes to answer the guiding questions. Findings showed that participants believed content and pedagogy should be addressed through professional development led by teachers themselves. Additional findings were that teachers valued collaboration, literature and research, observation, vertical alignment, engagement, relevance, and support. Results were used to guide the design of a mathematics professional development program (MPDP), a collection of relevant tasks, literature, and online resources geared toward improving teachers' content and pedagogical knowledge. The MPDP is immediately applicable in an elementary school setting. The implications for positive social change include better mathematics instruction that will prepare U.S. students to compete in the modern economy and world of mathematical and scientific advances. [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.]