This study investigates students' development of metamathematical understanding of axioms. Based on four semesters of experiments teaching neutral, axiomatic geometry, often through guided reinvention, I identify five categories of student interpretations of their axiomatizing activity. Similar to previously observed patterns in student interpretations of definitions and proofs, the most problematic student interpretations of axioms resulted from focusing exclusively on the referents of mathematical theory, which precluded generalization through abstraction. As a result of engaging in axiomatizing, study participants constructed several quite sophisticated views of axiomatizing compatible with various aspects of modern mathematical practice--what I call stipulated and formal interpretations.