While previous mathematics education research has shown that norms can change in mathematics classrooms, little research has closely documented the struggles, concessions, and compromises involved in the negotiation process. Negotiating norms is a complex process entailing deliberate teacher moves intended to promote norms, often met with misunderstandings or resistance from students. This thesis documented the negotiation process that occurred when a teacher attempted to require conceptual explanations from students who had not previously been accustomed to doing so. I recorded six days of instruction in a 9th grade algebra unit, transcribed the class discussions, and inferred norms "at play" for each line of speech in the transcripts. Inspection of these norms revealed a hierarchy of norms, with groups of smaller micro norms constituting larger macro norms. The data showed that meeting a macro norm was done by meeting a sufficient number of its micro norms. In addition to describing a hierarchy of norms, I identified 7 norm negotiation moves (NNMs) used by the teacher, one of which was also used by students. I looked beyond individual lines of speech to analyze whole discussions to see how the teacher used NNMs to accomplish goals concerning norms. My analysis revealed that the teacher used a combination of multiple NNMs to achieve the purposes of introducing, refining, and reinforcing norms. These results offer researchers a new theoretical framework for the structure of norms and can give teachers additional insights into the process of norm negotiation, better preparing them to successfully negotiate norms as they create effective and supportive learning environments.