This study addresses first graders' conceptual knowledge exhibited in addition strategies in relation to instructional practices and teachers' beliefs in a suburban Alabama school. To address the purpose of the study, the central question was "What is the nature of the relationship between curricular practices and beliefs and students' advanced strategy use for addition in first grade?" The study employs a case study design to obtain a deeper and more comprehensive view of students' conceptual understanding exhibited in advanced addition strategies in the context of the first-grade classroom. Student addition strategies were compared to instructional practices and teachers' beliefs to examine how practices and beliefs related to student strategy use. [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.]