Using a round-robin data set assembled from over 60 teams of more than 500 scientists and engineers across a variety of science and engineering disciplines, as well as longitudinal research productivity data, this study examines differences in how men and women in science and engineering teams evaluate their colleagues' expertise and how that affects team performance. Because these teams are assembled to enhance innovations, they are most productive if they fully utilize the expertise of all team members. Applying a social relations modeling approach, two studies conducted in multidisciplinary research centers in a large public U.S. university test whether a team's gender composition predicts how well women's expertise is used within the team, based on peer evaluations of male and female team members with varying education levels. A third study returns to the same two research centers to examine whether the larger context in which the team operates affects the use of expertise and the team's productivity. An important finding is that the gender and educational attributes of the person being evaluated are less critical to the recognition of expertise than the attributes of the person conducting the evaluation and the relationship between these two team members. In addition, context matters: gender-integrated teams with a higher proportion of highly educated women are more productive in disciplines with a greater female faculty representation.