This dissertation examines the development of combinatorial reasoning in high school students through an in-depth analysis of a problem-solving session involving the Pizza Problem. The study, part of the long-term Rutgers-Kenilworth longitudinal research project, focuses on four 11th-grade students as they explore and connect concepts related to combinatorics, Pascal's Triangle, and isomorphic relationships between and among different problem contexts. Using a qualitative approach that combines Powell et al.'s (2003) seven nonlinear phases and a grounded theory approach, the research analyzes video data and student work to trace the evolution of students' mathematical reasoning. The study employs VMCAnalytics to create detailed video narratives that capture key moments in the students' problem-solving process. Key findings reveal the non-linear nature of students' learning, the importance of multiple representations in developing structural understanding, and the critical role of collaborative discourse in mathematical sense-making. The research highlights how students progressively recognize and leverage isomorphic relationships between a series of counting problems: the Pizza Problem, the Towers Problem, and Pascal's Triangle, demonstrating a sophisticated level of mathematical thinking. This study contributes to our understanding of how students develop advanced mathematical concepts, particularly in combinatorics. It offers insights into effective teaching strategies that foster deep, flexible, and transferable mathematical understanding, with implications for curriculum design, instructional practices, and assessment in mathematics education. [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.]