Poetic structures emerge in spoken language when speakers repeat grammatical phrases that were spoken before. They create the potential to amend or comment on previous speech, and to convey meaning through the structure of discourse. This paper considers the ways in which poetic structure analysis contributes to two perspectives on emergent mathematical reasoning: Toulmin's model of argumentation and Martin, Towers, & Pirie's theory of collaborative coactions in multi-speaker discourse. Poetic structures appear in varied argument types and at varied educational levels. They appear to facilitate speakers' expression of warrants, backings, qualifications, and coactions.