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,…

Originating from interviews with mathematics colleagues, written accounts of mathematicians engaging with mathematics, and Wes's reflections on his own mathematical work, we describe a process that we call mathematical foresight: the imagining of a resolution to a mathematical situation and a path to that resolution. In a sense, mathematical…