Previously we showed how we measured pedagogy and revealed its association with learning outcomes of sixth-form college mathematics students. In this project we followed a similar approach to the study of university transition. We particularly sought to identify the students' perceptions of the transitional experience, and measure the association with learning outcomes. We drew on longitudinal surveys of students entering different programmes in five universities. Following them into their first year or so, allowed us to track their "disposition to complete the course" and their "disposition to study more mathematics", inter alia. We developed and validated two "fit-for-purpose" measures of students' perception of their transition, one we call "perception of the transitional gap/jump" and one we call "degree of positive feeling about the transition". We report some statistically and educationally significant associations between these and the students' developing dispositions, and discuss the prospects for this approach to studying transition. (Contains 13 notes, 9 tables, and 9 figures.)