Speakers in conversation typically repeat and modify earlier comments. In mathematics conversations, these repetitions, or poetic structures, can facilitate the collaborative discovery of mathematical relationships. A close analysis of 90 turns of an algebraic problem-solving conversation reveals eight types of poetic structures. This report summarizes the general results of the analysis and highlights the role of a particular type of poetic structure, the reversal. In a reversal poetic structure, two elements switch places syntactically, for example, subject and predicate or adjective and noun switch roles. Students working with no teacher intervention used the reversal poetic structure as they rearranged variables and coefficients in their verbal method, and as they transitioned from a spoken method to written mathematical notation. This analysis highlights the ways in which speaking supports mathematical thinking. [For the complete proceedings, see ED583608.]