Drawing on large-scale survey data and interviews with students during their first year at university, and case studies in their institutions, we explore the problems faced by students taking mathematically demanding courses, e.g. physics and engineering. These students are often taught mathematics as a service subject by lecturers of mathematics. Analysis of students' perceptions of transition suggests that "the lecture" in Higher Education continues to pose problems. Thematic analysis of interview data shows that these problems relate to the way lectures involve "time pressure" and "lack of dialogue/interaction" which are practices that we associate with transmissionist pedagogy generally and can also create negative dispositions. A case study of one mathematics course for engineering that we argue made a difference is presented, and conclusions drawn for developing practice which are especially pertinent with the introduction of the Teaching Excellence Framework to monitor and assess teaching in universities.