Several prior studies in introductory physics have found a gender gap, i.e., a difference between male and female students' performance on conceptual assessments such as the Force Concept Inventory (FCI) and the Conceptual Survey of Electricity and Magnetism (CSEM) with male students performing better than female students. Moreover, prior studies in the context of mathematics have also found that activation of a negative stereotype about a group or stereotype threat, e.g., asking test takers to indicate their ethnicity before taking a test, can lead to deteriorated performance of the stereotyped group. Here, we describe two studies in which we investigated the impact of interventions on the gender gap on the FCI and CSEM in large (more than 100 students) introductory physics courses at a large research university. In the first study, we investigated whether asking introductory physics students to indicate their gender immediately before taking the CSEM increased the gender gap compared to students who were not asked for this information. We found no difference in performance between male and female students in the two conditions. In the second study, we investigated the prevalence of the belief that men generally perform better in physics than women and the extent to which this belief is correlated with the performance of both female and male students on the FCI and the CSEM in algebra-based and calculus-based physics courses. We found that at the end of the year-long calculus-based introductory physics sequence, in which female students are significantly underrepresented, agreeing with a gender stereotype was correlated negatively with the performance of female students on the conceptual physics surveys. The fact that female students who agreed with the gender stereotype performed worse than female students who disagreed with it at the end of the calculus-based physics course may be partly due to an increased stereotype threat that female students experience.