A new team learning assessment process was designed and tested in a first-year university physics laboratory class. The assessment process was designed to provide a strong incentive for students to cooperate and feel responsible for each other's learning and fostering a sense of collaboration rather than competition. Specifically, the new assessment process involves randomly dividing students into teams of four to work on a physics experiment and, at the end of the laboratory session, randomly selecting only one team member to carry out a post-laboratory session performance task. The results indicate that learning outcomes were not compromised in the new assessment process and that peer instruction was employed to a greater extent compared to our standard process. Student responses from a post-assessment survey revealed that 76% of students considered our new assessment process to be fair, whereas 57% of students felt our standard process was fair. The new assessment process used in this study led to a 75% reduction in grading duties--an advantage for large class management.