A local urban school district recently reported that 86% of third graders did not demonstrate proficiency on the Math Standardized Test, which challenges students to solve problems and justify solutions. It is beneficial if these skills are developed prior to third grade. Students may be more academically successful if kindergarten teachers have moderate to high self-efficacy when teaching lessons that focus on justifying solutions. Bandura's self-efficacy theory was incorporated into this study as the conceptual framework lens. Research questions were designed to investigate kindergarten teachers' instruction in mathematics that focused on justifying solutions, their self-efficacy in challenging students to justify solutions, and the identification of professional development. Voluntary participants for this study were selected from the 11 elementary schools in the district. Within the 11 elementary schools, there were 33 lead teachers who were invited to participate in the study and 7 agreed to participate in interviews and observations. The data were analyzed using both situation and strategy coding. The analysis of the data revealed a connection between professional development, self-efficacy, and instructional strategies. A relationship was identified between professional development and the teachers' ability to challenge students to problem solve and justify solutions. These findings may be valuable for early childhood stakeholders within the education field. Professional development tends to improve the self-efficacy of teachers and the instructional strategies they incorporate. [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.]