Mathematical poetic structures: The sound shape of collaboration.

• Poetic structures are conversational repetitions of syntax and words. • Recency and comment length help identify mathematical poetic structures. • Multimodal poetic structures facilitate many collaborative mathematical insights. • Poetic analysis bridges discourse analysis with mathematical reasoning. This paper outlines a new method of mathematical discourse analysis focused on identifying poetic structures in students' mathematical conversations. Following the linguistic anthropology tradition inspired by Roman Jakobson, poetic structures refer to any conversational repetition of sounds, words or syntax; this repetition draws attention to the form of the message. In mathematical conversations, poetic structures can express patterns, rhythms, similarities or dissimilarities associated with a task. Methodological dilemmas associated with identifying and representing poetic structures and pragmatic responses are highlighted. An analysis of a nine minute algebraic problem-solving conversation revealed eight types of mathematical poetic structures that collectively assisted all of the students' vital mathematical insights. The paper aims to demonstrate that poetic analysis of mathematical conversations can bridge the illusory distinction between mathematical discourse and mathematical reasoning. [ABSTRACT FROM AUTHOR]