In 2015 an urban school district reported that 84.6% of third graders did not demonstrate proficiency on the Math Standardized Test, which challenges students to solve problems and justify solutions. Since 2006 there has been a negative trend of proficiency levels on the New York State (NYS) Math Exam in third grade. I propose that students may be more academically successful if these skills needed for the NYS math exam begin in kindergarten and the teachers had high self-efficacy when teaching lessons that focus on justifying solutions. The purpose of this study was to explore kindergarten teachers' level of self-efficacy in their instruction in mathematics that challenges students to justify solutions. Further, kindergarten teachers' instructional strategies related to problem solving and justifying solutions were explored. The analysis of the data revealed a connection between self-efficacy and instructional strategies. The results of this study may be valuable for scholars and practitioners with interests in the instruction of mathematical principles in the early childhood educational environment.