This study analyzed and categorized the conceptions of mathematics of three high school mathematics teachers. The complex ways in which mathematics teachers conceptualize their content area has been unintentionally oversimplified in the existing literature. This study presents a new framework for classifying the conceptions of mathematics for high school teachers. The framework includes three domains: the teacher\u27s perspective on the nature of mathematics, the teacher\u27s orientation toward mathematical knowledge, and the teacher\u27s theory of teaching and learning. Two findings emerged from the case studies. First, the configuration of the domains of the teacher\u27s conception of mathematics was as important to the teacher\u27s overall conception as the teacher\u27s views within each domain. Second, the inclusion of two domains in the framework dedicated to mathematics allowed for the examination of similarities and differences between the teacher\u27s beliefs, views, values, meanings, rules, and preferences about mathematics at a large scale and a small scale. The findings suggests that the potential for a teacher to change his or her practice relies greatly on whether or not the teacher experiences dissonance between his or her conception of mathematics and his or her instructional practice
