Improving the engagement of students in their own learning and in wider teaching and learning issues is a now an important driver in most institutions of higher education. The Higher Education Academy has identified student engagement as a priority area for development. What student engagement means in practice for the MSOR community is not clear. The purpose of this paper is to report on a workshop to which undergraduate mathematics students from several Midlands universities were invited. In the workshop students were asked to reflect upon and discuss their own engagement as individual learners and as part of a wider mathematics community. The extent to which students want to be engaged as partners in their learning was explored, together with their views as to what would be the characteristics of a department with high levels of student engagement. This paper reports upon the findings from the workshop.