This study aims to broaden the current understanding of undergraduate university mathematics teaching by conducting a multimodal analysis of video-recorded segments of classroom teaching by an experienced professor and a less experienced Teaching Assistant (TA). The study focuses on the participants" use of discursive strategies and multimodal features including gestures, gaze, and facial expressions, as they are used to elicit responses from students and promote participation in the classroom. The analysis is conducted through the qualitative multimodal thematic coding of video-recorded segments, and audio transcripts, and with the quantitization of the participants" strategies used to elicit student responses. Findings show that despite variance in the teaching location, educational backgrounds, and levels of experience of the participants, the discursive and multimodal strategies that they used during teaching are remarkably similar; in other words, the participants use the same genre of teaching undergraduate mathematics. Findings also reveal subtle differences between the teaching practices of the experienced professor and less experienced TA. Conclusions present undergraduate mathematics teaching as a complex, multimodal, and wholly interactive genre of teaching.