This paper describes an intervention for improving the quality of peer assessment conferences in calculus. Although a body of work highlights the learning benefits of peer assessment, few papers have described the nature of student conversations during peer conferences/assessment in detail. This paper provides deeper insight into what those conversations actually look like, and shows the impact of systematic training on conferences. The study took place over two consecutive semesters of introductory college calculus, and analyses show that students had considerably improved conversations after training. The improved conversations consisted of much more on-topic talk and productive feedback; after training, students provided more feedback related to processes (communication and underlying reasoning) than products (correctness or incorrectness).