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.

在本文中，我调查了两阶段考试是否有助于大学数学学习，这是通过学生在随后的考试中的表现来衡量的。在两个阶段的考试中，学生分别完成考试，然后分成两个小组，以再次解决问题，并根据两个阶段的组合进行评分。先前在其他学科中进行的研究发现，它们对随后的表现产生的影响参差不齐，而对其在本科数学中的使用了解甚少。在这里，我报告了三项研究，这些研究调查了在不同的本科数学环境中使用两阶段考试的情况。前两项研究复制了先前研究的观察方法，并发现了小组合作产生积极影响的迹象。第三项研究是实验性的，发现在延迟的测试后，在以两阶段考试形式回答相关问题的学生和没有合作第二阶段的对照组之间，表现没有差异。研究结果表明，两阶段考试可能不会对数学的长期学习产生太大影响，但教师仍可能希望使用它们来强调协作式课堂教学法。