As more women enter engineering, the climate of engineering teams must be improved to ensure that women feel included and inspired to design innovative solutions. Prior research suggests that women in STEM often report lower levels of self-efficacy, which could limit their engagement in collaborative design tasks. Unfortunately, little research has explored how designers' gender and self-efficacy play a role in collaborative ideation and we aim to explore this research gap. We conducted an observational study with nominal -- that is, non-interacting -- and balanced four-member design teams, involving a collaborative ideation task. From the results, we see that the mean frequency of new ideas proposed by men was greater than those proposed by women. This result suggests that men may emphasize creating new ideas rather than acknowledging others' ideas. Furthermore, we see that men with higher self-efficacy provided more compliments and criticisms, and these relationships were relatively weaker or the opposite for women. These results suggest that participants with different gender identities may make different design moves in collaboration ideation, and these differences are further influenced by their self-efficacy. These results call for further exploration into the role of self-efficacy in creating inclusive collaborative design environments, especially for designers belonging to historically underrepresented identities.