We contribute a preiously unidentified way representational gestures are used to organise participation and the co-construction of knowledge in whole-class interactions in Science, Technology, Engineering, and Mathematics (STEM) classrooms. Drawing on ethnomethodology and conversation analysis (EMCA), we characterise students' "gestured candidate responses" and how teachers respond to them. To answer teachers' questions, students sometimes use representational gestures to provide silent, 'off-the-record' tentative responses that we call "gestured candidate responses" (GCRs). Teachers can respond to GCRs by "ratifying" or "declining" students' responses. Teachers' responses to GCRs include (1) ratifying the GCR by "nominating" students to share the response, (2) ratifying the GCR by "repeating" the gestured response for the class, (3) declining the GCR by "not publicly pursuing" the contribution, or (4) declining the GCR by "publicly rejecting" the contribution. Our analysis contributes to a better understanding of how students use gesture and how teachers attend and respond to students' gestures in STEM classroom discourse.