This article draws on a multi-phase study of collaboration in tertiary education programmes. This commenced with a survey of 111 students in Engineering and Creative Arts, contrasting their experiences of the teaching of collaboration in different faculties. This led to an iterative action research cycle, in which the conceptual boundaries that surrounded teachers' approaches to teaching collaboration were explored through qualitative interviews with teachers and observations of teaching practices. Within this article we discuss five specific threshold concepts that subsequently informed the design of the SALAM professional development programme for tertiary educators: enhancing explicit metacognition, scaffolding socialization, animating symmetry, animating pluralism, and embedding values. By bringing greater clarity to the graduate attribute of 'collaborative dexterity', we argue how these five threshold concepts present pedagogic responsibilities to teachers in Higher Education who are seeking to constructively align the teaching of collaborative dexterity with assessment procedures, teaching activities and course content.