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In this paper, we report on the outcomes of a survey of students across 12 higher education institutions in Ireland and the UK. Participants were asked to give their views on what tutors should do and not do when they are providing Mathematics Learning Support to students. We present the categories that emerged from an analysis of student responses, including tutor behaviour, teaching methods, content knowledge and management items. We discuss the implications that these responses have for tutor selection and training, how they relate to mathematical pedagogy and we consider the high expectations that students appear to have for tutors, who are providing this supplemental support. [ABSTRACT FROM AUTHOR]