A poetic structure occurs when a speaker's comment repeats some of the syntax and words of a previous comment. During a collaborative algebra task, a student explained a property five times over a few minutes, in slightly different ways. He consistently used poetic structures that were marked elaborately through discursive modes such as pause, intonation and gestures, in ways that foreshadowed conclusions, shifted attention from known to less-known concepts and emphasized the logical structure of arguments. This suggests that multimodal poetic structures are experiential linguistic resources for expressing and animating mathematical insights.