In this paper, I investigate whether two-stage exams aid learning in undergraduate mathematics, as measured by students' performance on subsequent exams. In a two-stage exam, students complete the exam individually then form into groups to solve it again, with grades based on a combination of the two stages. Previous research in other disciplines has found mixed results about their effect on subsequent performance, and little is known about their use in undergraduate mathematics. Here, I report on three studies which investigate the use of two-stage exams in different undergraduate mathematics contexts. The first two studies replicate observational methods from previous research, and find indications of a positive impact from group collaboration. The third study is experimental and finds that, in a delayed post-test, there is no difference in performance between students who answered related questions in a two-stage exam format and a control group which had no collaborative second stage. The findings suggest that two-stage exams may have little impact on longer-term learning of mathematics, but instructors may still wish to use them to emphasise a collaborative classroom pedagogy.