This article is an analysis of a high school geometry teacher's gesture and embodied social action in the context of classroom instruction, and its role in the communication of an implicit theory of the ontological status of mathematical knowledge. In particular, I argue that the teacher's bodily performance in the classroom setting communicates the Platonic position of abstract‐realism—that mathematical entities are ontologically real abstractions—which is associated with the high epistemological authority and social efficacy of mathematics. Thus, in addition to the teacher's use of language to reference mathematical knowledge, I document her patterns of embodied social action, which communicate an additional and ideologically specific theory about the ontological status of the items thus referenced. I propose the concept of a metaphor of participation—an iconic projection based on the pattern of bodily participation in the speech event—as a tool to theorize the bodily communication of ideologies.