In the field of physics education research, numerous studies have been dedicated to investigating the relationship between gender identity and physics learning. However, these studies have predominantly employed binary gender measurement methods, which may limit the range of research questions that can be explored and impede the discovery of crucial insights. In this study, we adapted gradational measures from prior research to investigate students' self-identified femininity, masculinity, and androgyny, as well as their reflected appraisal of femininity, masculinity, and androgyny (i.e., perceptions of how others perceive them) in both algebra-based and calculus-based introductory physics courses. The use of gradational measures revealed significant variation in students' self-identified femininity, masculinity, and androgyny within the binary categories of women and men, providing new insights into gender dynamics in physics. We found that self-identified women in the calculus-based courses, where they are underrepresented, tend to perceive themselves as more masculine and less feminine than how they believe others perceive them. Similarly, students of color are also more likely than White students to perceive themselves as more masculine than they believe others perceive them. Using structural equation modeling, we found that students' gender stigma consciousness plays an important role in mediating the effects of identifying as women and students of color on the observed discrepancies. Additionally, we found that women also exhibit a tendency to perceive themselves as more androgynous than they believe others perceive them in both algebra-based and calculus-based physics courses, and this phenomenon is also related to gender stigma consciousness. Moreover, our analyses revealed that students in the calculus-based courses tend to have a higher level of gender stigma consciousness even after controlling for gender and race. Our findings underscore the potential of gradational gender measurements in deepening our understanding of genderrelated issues in physics education, shedding light on the complex interplay between students' gender identity, perceptions from others, and their educational experiences in the field.
