To stay up with society and technology, pedagogical changes are needed. Even a well-designed curriculum depends on teachers, who implement it. Knowledge drives this field's educators' actions. This dissertation examined how the Southwest New Mexico Elementary Mathematics Specialists (EMS) program affects elementary mathematics teachers' PCK. Social constructivism and cognitive learning theories (Hmelo et al., 1998; Vygotsky, 1926) supported this study. This dissertation uses triangulation, which combines several data collection and analysis methodologies, to understand the multiple perspectives on how the EMS MAE program affects EMTs' PCK in Southwest New Mexico school districts. EMS Survey, FAT, Interview I, Review of three EMS Math Syllabi, Interview II, and Member Check are the procedures used. EMS MAE cohorts 1 and 2 offered participants. Descriptive statistics and narrative analysis helped me understand the data. The study found that students in elementary school usually know how to count and use the base 10 number system. However, they struggle to understand the relationship between their early number cognition and fractions and with geometric representations of numbers, fractions, and operations. Understanding the necessary background material helps students learn mathematics and build on their mathematical knowledge. Their thinking influences their numerical skills, but even bright students can struggle with new math concepts, but their flexibility may allow them to handle and pick up the concepts more quickly than others; graduates of the EMS master's degree are more empathic toward their students, have a new perspective on how to teach numbers, and have improved their math teaching and learning skills and knowledge of research-based pedagogical practices. Thus, after completing the EMS program, EMS teachers should work with primary math teachers in selected schools in their districts to improve leadership abilities. Participants will be able to share the program's benefits with educators who couldn't participate, achieving the program's leadership goals. This may also encourage EMTs to participate in the program, which will have multiplicative and long-term consequences, and the EMS program should include interactive sessions where alumni can communicate to current students about their experiences. This will prepare students for field challenges and allow them to propose solutions alongside peers and teachers. [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.]